JKSSB Junior Engineer (Skill Development) 2025 Solved Question Paper

Question 1

_______ are the lines referring to a feature and notes. These are thin continuous lines and terminated by arrowheads or dots.

Accepted Answer

Option B: Leaders or Pointers lines. In engineering drawing (IS 10714), Leader Lines (or Pointer Lines) are continuous thin lines drawn inclined (usually at $30^\circ, 45^\circ$, or $60^\circ$) that connect a dimensional note, callout, or symbol to a specific feature, terminated by an arrowhead on an outline or a dot inside an outline.

Question 2

A hyperbola revolving around its axis forms a surface called a:

Accepted Answer

Option C: Hyperboloid. When a hyperbola revolves around its transverse or conjugate axis in three dimensions, it generates a quadratic curved surface of revolution known as a Hyperboloid (hyperboloid of one sheet or two sheets).

Question 3

The major and minor axes of an ellipse are 90 mm and 60 mm respectively. Find the distance between foci:

Accepted Answer

Option B: 67 mm. For an ellipse: Semi-major axis $a = 90/2 = 45	ext{ mm}$, Semi-minor axis $b = 60/2 = 30	ext{ mm}$. Distance between foci $= 2c = 2\sqrt{a^2 - b^2} = 2\sqrt{45^2 - 30^2} = 2\sqrt{2025 - 900} = 2\sqrt{1125} = 2 	imes 33.541 = 67.082	ext{ mm} \approx 67	ext{ mm}$. Choice B.

Question 4

_______ is a curve traced by an end of a string or thread, when it is unwound from a circle or a polygon, the thread being kept tight.

Accepted Answer

Option B: Involutes. An Involute is mathematically defined as the planar curve traced out by the free end of a taut (tightly stretched) string as it is unwound from the perimeter of a base circle or regular polygon.

Question 5

Planes which are inclined to both the horizontal and vertical planes are called:

Accepted Answer

Option A: Oblique planes. In descriptive geometry, planes that are inclined to both Principal Reference Planes (Horizontal Plane HP and Vertical Plane VP) simultaneously are defined as Oblique Planes.

Question 6

If a circular plane is inclined at 30° with the horizontal plane and 60° with vertical plane, its side view will be:

Accepted Answer

Option B: A straight line. Since the sum of inclinations to HP and VP is $	heta + \phi = 30^\circ + 60^\circ = 90^\circ$, the circular plane is perpendicular to the Profile Plane (PP). Therefore, its projection on the profile plane (Side View) is a Straight Line equal in length to the diameter.

Question 7

_______ is obtained by revolving a right-angled triangle about its perpendicular side which remains fixed.

Accepted Answer

Option C: Cone. A Right Circular Cone is a solid of revolution generated by revolving a right-angled planar triangle by $360^\circ$ around one of its perpendicular legs (which serves as the fixed central axis).

Question 8

A square pyramid is resting on a face in the vertical plane (V.P.) The number of dotted lines which will appear in the front view is:

Accepted Answer

Option A: One. When a square pyramid rests with one of its triangular triangular faces flat against the Vertical Plane (VP), in the Front View (elevation), all outer boundary edges and visible slant edges are continuous solid lines, with exactly One hidden base edge appearing as a dotted line.

Question 9

The projection of the section on the principle plane to which the section plane is inclined is known as:

Accepted Answer

Option C: Apparent section. The projection of a cut section onto a principal plane of projection to which the cutting plane is inclined is foreshortened and termed the Apparent Section (whereas projection onto a plane parallel to the cutting plane shows the True Shape of Section).

Question 10

In methods of development of solids, which method is generally applied in the development of pyramids and cones?

Accepted Answer

Option B: Radial line method. The Radial Line Development Method is standardly applied for developing the lateral surfaces of pyramids and cones, where all lateral generating edges radiate outward from a single common apex vertex.

Question 11

Isometric projections cannot be drawn by:

Accepted Answer

Option D: Zone method. Standard geometrical methods for constructing isometric projections include the Box Method, Coordinate Method, and Offset Method. 'Zone Method' is a spherical geographic mapping projection method, NOT an isometric drawing method.

Question 12

On isometric plane, a circle appears as:

Accepted Answer

Option C: An ellipse. Due to the $30^\circ$ isometric foreshortening of horizontal and vertical isometric axes, a true circle drawn on any isometric plane projects visually and geometrically as an Ellipse (drawn via the four-center method).

Question 13

The shape of the section obtained will depend upon the orientation of the solid and the section plane, with respect to the principle planes of projection. Some of the positions of the section planes are:
1. Horizontal plane
2. Auxiliary inclined plane
3. Auxiliary vertical plane
4. Profile plane
From the above, which is/are considered under the types of section planes?

Accepted Answer

Option D: 1, 2, 3 and 4. In engineering graphics, Section Planes are classified by their spatial orientation: 1. Section plane parallel to HP (Horizontal), 2. Auxiliary Inclined Plane (AIP - perpendicular to VP, inclined to HP), 3. Auxiliary Vertical Plane (AVP - perpendicular to HP, inclined to VP), and 4. Profile Section Plane (perpendicular to both HP and VP) $\implies$ 1, 2, 3 and 4. Choice D.

Question 14

The curve of intersection of a vertical cone with an auxiliary vertical plane (AVP parallel to the axis) is:

Accepted Answer

Option D: Hyperbolic curve. When a vertical cone is cut by an Auxiliary Vertical Plane (AVP) that is parallel to the cone's central vertical axis (or cuts both nappes of a double cone), the resulting curve of intersection is a Hyperbola (Hyperbolic curve).

Question 15

Surfaces of various geometrical objects may be classified as given below:
1. Plane surfaces: Surfaces of prisms, pyramids, cube and polyhedral are plane surfaces.
2. Singly curved surfaces: Surfaces of spheres, paraboloid, ellipsoid, hyperboloid are singly curved surfaces.
Choose the correct option:

Accepted Answer

Option A: Statement 1 is correct and Statement 2 is incorrect. Statement 1 is correct: Prisms, pyramids, and polyhedra are bounded entirely by flat plane surfaces. Statement 2 is incorrect because spheres, ellipsoids, and paraboloids are Double-Curved Surfaces of revolution (cylinders and cones are singly curved developable surfaces). Correct: Statement 1 is correct and Statement 2 is incorrect.

Question 16

In Engineering Drawing, the following rules should be observed while lettering:
1. Alphabet should be written in capitals. Lower-case alphabet should be used only when they are accepted in international usage for abbreviations.
2. Alphabet and numerals should neither touch each other nor the lines.
Choose the correct option:

Accepted Answer

Option C: Statement 1 and 2 are correct. Both statements are standard BIS (SP 46) engineering lettering conventions: Single-stroke uppercase gothic capital letters are preferred for clarity (1), and characters/numerals must maintain uniform character spacing without touching each other or dimension guide lines (2). Correct: Statement 1 and 2 are correct.

Question 17

In Engineering Drawing, the following rules should be observed on Dimensioning:
1. Dimensions should be clear and permit multiple interpretations. Numerals and letters should be small enough to ensure simple reading.
2. Dimensions should be placed on the view that most clearly shows the corresponding features.
Choose the correct option:

Accepted Answer

Option B: Statement 2 is correct and Statement 1 is incorrect. Statement 2 is a fundamental dimensioning rule: dimensions must be placed on the view that most clearly depicts the profile feature. Statement 1 is incorrect because dimensions must be completely unambiguous and allow ONLY ONE single interpretation (not 'permit multiple interpretations'). Correct: Statement 2 is correct and Statement 1 is incorrect.

Question 18

In Engineering Drawing, the following points are related to Cycloidal curves:
1. Cycloidal curves are generated by a point lying on the circumference of a circle, when it rolls along a fixed straight or a curved path without slipping.
2. Cycloidal curves are commonly used in kinematics (the study of motion) and in mechanisms that work rolling contact.
Choose the correct option:

Accepted Answer

Option C: Statement 1 and 2 are correct. Both statements are correct: A Cycloid (epicycloid/hypocycloid) is generated by a point on a rolling circle without slip (1), and cycloidal profiles are widely used in kinematic gear tooth profiles to minimize friction and wear in rolling contact mechanisms (2). Correct: Statement 1 and 2 are correct.

Question 19

Match List - I with List-II and select the correct answer using the codes given below the lists:
List I (Representation of line):
i. - - - - - - - - (dashed)
ii. - · - · - · - (long-dashed dotted)
iii. ················ (dotted)
iv. - ·· - ·· - ·· - (long-dashed double-dotted)

List II (Description):
1. Long dashed dotted line
2. Dashed line
3. Long dashed double-dotted line
4. Dotted line

Choose the correct option:

Accepted Answer

Option C: (i) - 2, (ii) - 1, (iii) - 4, (iv) - 3. i -> 2 (Dashed line: hidden outlines), ii -> 1 (Long dashed dotted line: centerlines, axes), iii -> 4 (Dotted line), iv -> 3 (Long dashed double-dotted line: phantom lines, cutting planes). Correct match: (i)-2, (ii)-1, (iii)-4, (iv)-3.

Question 20

Match List - I with List-II and select the correct answer using the codes given below the lists:
List I (Type of Lines):
i. Dashed narrow lines
ii. Continuous narrow lines
iii. Continuous wide line
iv. Long-dashed double-dotted narrow line

List II (Engineering Application):
1. Dimension line, Extension line, Grid lines
2. Hidden edges, Hidden outlines
3. Visible edges, Visible outlines
4. Centroidal lines, Parts situated in front of a cutting plane

Choose the correct options:

Accepted Answer

Option D: (i) - 2, (ii) - 1, (iii) - 3, (iv) - 4. i -> 2 (Dashed narrow lines: hidden outlines and edges), ii -> 1 (Continuous narrow lines: dimension lines, extension lines, leaders, hatching), iii -> 3 (Continuous wide line: visible outlines and object edges), iv -> 4 (Long-dashed double-dotted narrow line: centroidal lines, adjacent parts). Correct match: (i)-2, (ii)-1, (iii)-3, (iv)-4.

Question 21

Match List - I with List-II and select the correct answer using the codes given below the lists:
List I (Classification of Solids):
i. Polyhedron
ii. Tetrahedron
iii. Dodecahedron
iv. Icosahedron

List II (Descriptions):
1. It is a solid, having four equal equilateral triangular faces.
2. solid bounded by planes called faces, which meet in straight lines called edges.
3. It is a solid, having twenty equal equilateral triangular faces.
4. It is a solid, having twelve equal pentagonal faces.

Choose the correct options:

Accepted Answer

Option C: (i) - 2, (ii) - 1, (iii) - 4, (iv) - 3. i -> 2 (Polyhedron: solid bounded by planar polygonal faces), ii -> 1 (Tetrahedron: 4 equilateral triangular faces), iii -> 4 (Dodecahedron: 12 regular pentagonal faces), iv -> 3 (Icosahedron: 20 equilateral triangular faces). Correct match: (i)-2, (ii)-1, (iii)-4, (iv)-3.

Question 22

Match List - I with List-II and select the correct answer using the codes given below the lists:
List I (Cutting Plane Descriptions):
i. When the cutting planes is inclined to the axis and cuts all the generators of the cone, the section is
ii. When the cutting plane is inclined to the axis and is parallel to one of the generators of the cone, the sections is
iii. When the cutting plane cuts both the parts of the double cone, the section is
iv. When the cutting plane is perpendicular to the axis of the cone, the curve of the intersection obtained is

List II (Section name):
1. Circle
2. Hyperbola
3. Parabola
4. Ellipse

Choose the correct options:

Accepted Answer

Option B: (i) - 4, (ii) - 3, (iii) - 2, (iv) - 1. i -> 4 (Cuts all generators at angle $	heta > lpha$: Ellipse), ii -> 3 (Parallel to one generator $	heta = lpha$: Parabola), iii -> 2 (Cuts both nappes of double cone $	heta < lpha$: Hyperbola), iv -> 1 (Perpendicular to axis $	heta = 90^\circ$: Circle). Correct match: (i)-4, (ii)-3, (iii)-2, (iv)-1.

Question 23

The following terms are used in connection to a spiral. Match List - I with List-II and select the correct answer using the codes given below the lists:
List I (Terms):
i. Pole
ii. Radius Vector
iii. Vectorial Angle

List II (Descriptions):
1. It is the angle between the initial position of the line and the instant position of the line
2. It is the fixed end of the line about which the line rotates
3. It is the line joining any point of the curve with the pole

Choose the correct options:

Accepted Answer

Option D: (i) - 2, (ii) - 3, (iii) - 1. i -> 2 (Pole: fixed origin point about which generating radius rotates), ii -> 3 (Radius Vector $r$: line segment connecting any point on the spiral curve to the pole), iii -> 1 (Vectorial Angle $	heta$: angle between initial polar axis and radius vector). Correct match: (i)-2, (ii)-3, (iii)-1.

Question 24

The terms used very frequently for sections of solids are given below:
1. The projection of the section on a plane parallel to the section plane is known as true shape of section.
2. Section planes are the imaginary planes which cut the objects completely or partially to show their invisible and interior details clearly.
Choose the correct option:

Accepted Answer

Option C: Statement 1 and 2 are correct. Both statements are core definitions in descriptive geometry: The projection onto a parallel plane shows the True Shape of the cut section (1), and Section Planes are imaginary cutting planes passing through solids to reveal internal cavities, ribs, and features (2). Correct: Statement 1 and 2 are correct.

Question 25

For controlling measures on air pollution in industries, which are the mechanical devices used in the manufacturing process?

Accepted Answer

Option D: All of the above. Industrial particulate and gaseous emissions are controlled using mechanical and physicochemical separation devices: Electrostatic Precipitators (ESPs for fine fly ash), Cyclone Separators (centrifugal dust collection), and Wet Scrubbers (venturi/spray towers for acidic gases and particulates) $\implies$ All of the above.

Question 26

_______ are specific sites which directly discharge effluents to water sources through pipes, ditches and sewers.

Accepted Answer

Option A: Point sources. Under environmental pollution classifications, Point Sources are single, identifiable, localized conduits (such as municipal sewage discharge pipes, factory effluent outlets, or drainage ditches) directly releasing pollutants into surface waters.

Question 27

Which of the following gases are called Greenhouse gases?

Accepted Answer

Option D: Both (A) and (C). Greenhouse gases are atmospheric gases that absorb and emit thermal infrared radiation: Methane ($CH_4$) and Carbon Dioxide ($CO_2$) are major greenhouse gases. (Diatomic Nitrogen $N_2$ is not a GHG). Correct: Both (A) and (C).

Question 28

Consider the following statements related to noise pollution:
1. The unpleasant, unwanted and disagreeable sound that causes discomfort for all living beings is called noise pollution.
2. Exposure to noise pollution adversely affects the physiological health of a person and not affects the psychological health of a person.
Choose the correct option:

Accepted Answer

Option A: Statement 1 is correct and Statement 2 is incorrect. Statement 1 is the standard definition of noise pollution. Statement 2 is incorrect because chronic noise pollution severely impairs BOTH physiological health (hypertension, hearing loss, sleep disturbance) AND psychological health (stress, anxiety, cognitive impairment, irritability). Correct: Statement 1 is correct and Statement 2 is incorrect.

Question 29

Match List - I with List-II and select the correct answer using the codes given below the lists:
List I (Pollutants of water pollution):
i. Pathogens or Infectious agents
ii. Sediment
iii. Oxygen demanding wastes
iv. Toxic compounds

List II (Sources of pollutants):
1. Industrial effluents and household cleansers
2. Sewage, Paper mill wastes, Animal feedlots
3. Surface run off
4. Human and animal wastes

Choose the correct option:

Accepted Answer

Option B: (i) - 4, (ii) - 3, (iii) - 2, (iv) - 1. i -> 4 (Pathogens: human/animal enteric wastes), ii -> 3 (Sediment: soil erosion surface runoff), iii -> 2 (Oxygen demanding wastes: domestic sewage, paper mill effluents), iv -> 1 (Toxic chemicals: industrial effluents and cleansers). Correct match: (i)-4, (ii)-3, (iii)-2, (iv)-1.

Question 30

The environment can be divided into four segments. The segments are:

Accepted Answer

Option C: Atmosphere, Hydrosphere, Lithosphere, Biosphere. The Earth's global environment is fundamentally divided into four interconnected concentric spheres/segments: Atmosphere (air/gases), Hydrosphere (oceans/water), Lithosphere (solid crust/soil), and Biosphere (realm of living organisms).

Question 31

A car is travelling along a circular path having a radius of 15 m. Determine the magnitude of the car's acceleration if at a given instant the car's speed is $v = 3	ext{ m/s}$ and the rate of increase in speed is $\dot{v} = 2	ext{ m/s}^2$:

Accepted Answer

Option B: 2.09 m/s^2. Tangential acceleration $a_t = \dot{v} = 2	ext{ m/s}^2$. Normal (centripetal) acceleration $a_n = \frac{v^2}{ho} = \frac{3^2}{15} = \frac{9}{15} = 0.6	ext{ m/s}^2$. Total resultant acceleration magnitude $a = \sqrt{a_t^2 + a_n^2} = \sqrt{2^2 + 0.6^2} = \sqrt{4 + 0.36} = \sqrt{4.36} \approx 2.088	ext{ m/s}^2 \approx 2.09	ext{ m/s}^2$. Choice B.

Question 32

A motorist is travelling on a curved portion of a highway of radius 400 m at a speed of 90 km/h. The brakes are suddenly applied, causing the speed to decrease at a constant rate of 1.5 m/s^2. Determine the magnitude of the acceleration of the automobile immediately after the brakes have been applied:

Accepted Answer

Option A: 2.17 m/s^2. Speed $v = 90	ext{ km/h} = 90 	imes \frac{5}{18} = 25	ext{ m/s}$. Tangential deceleration $a_t = 1.5	ext{ m/s}^2$. Normal acceleration $a_n = \frac{v^2}{ho} = \frac{25^2}{400} = \frac{625}{400} = 1.5625	ext{ m/s}^2$. Resultant acceleration $a = \sqrt{a_t^2 + a_n^2} = \sqrt{1.5^2 + 1.5625^2} = \sqrt{2.25 + 2.4414} = \sqrt{4.6914} \approx 2.1659	ext{ m/s}^2 \approx 2.17	ext{ m/s}^2$. Choice A.

Question 33

The polar coordinates of a particle are given by $(r = 2 + 3t^2)$ and $(	heta = 2 + 1.5t^2)$ where r is in meters, $	heta$ is in radians and t is in seconds. Determine the magnitude of the velocity (v) when $t = 3	ext{ s}$:

Accepted Answer

Option B: 261 m/s. At $t = 3	ext{ s}$: $r = 2 + 3(3^2) = 29	ext{ m}$. Radial velocity $\dot{r} = \frac{dr}{dt} = 6t = 6(3) = 18	ext{ m/s}$. Angular position $	heta$, angular velocity $\dot{	heta} = \frac{d	heta}{dt} = 3t = 3(3) = 9	ext{ rad/s}$. Transverse velocity $v_	heta = r\dot{	heta} = 29 	imes 9 = 261	ext{ m/s}$. Total velocity magnitude $v = \sqrt{v_r^2 + v_	heta^2} = \sqrt{18^2 + 261^2} = \sqrt{324 + 68121} = \sqrt{68445} \approx 261.62	ext{ m/s} \approx 261	ext{ m/s}$. Choice B.

Question 34

If a body is rotating about an axis, passing through its centre of mass then its angular momentum is directed along its:

Accepted Answer

Option C: Axis of rotation. By vector definition $\vec{L} = I\vec{\omega}$. Since the angular velocity vector $\vec{\omega}$ points along the axis of rotation (governed by the right-hand screw rule), the angular momentum vector of a symmetric body rotating about its principal CM axis is directed along the Axis of Rotation.

Question 35

A mass is moving with a constant velocity with respect to X-axis, then its angular momentum with respect to origin will:

Accepted Answer

Option C: Remain constant. For a particle moving along a straight horizontal trajectory ($y = d$) at constant velocity $\vec{v} = v\hat{i}$, the angular momentum about origin is $\vec{L} = \vec{r} 	imes m\vec{v} = (x\hat{i} + d\hat{j}) 	imes m v\hat{i} = -m v d\,\hat{k} = 	ext{Constant}$ (Remains constant in magnitude and direction).

Question 36

_______ of a rigid body is easily demonstrated by rolling a right circular cylinder or disk along a flat surface in such a way that its geometric axis always remains parallel to itself.

Accepted Answer

Option B: Plane motion. Plane Motion (General Plane Motion) of a rigid body occurs when all particles move along parallel planes; rolling a cylinder on a flat surface exemplifies combined planar translation of the center of mass and rotation about the axis.

Question 37

Consider the following statements related to Kinematics of rigid bodies:
1. The instantaneous centre is not a fixed point. Its location keeps changing at every instant and the path traced (locus) by it is called centrode.
2. The instantaneous centre is a point identified within the body where the velocity is zero.
Choose the correct option:

Accepted Answer

Option C: Statement 1 and 2 are correct. Both statements are correct: The Instantaneous Center of Zero Velocity (IC) has zero instantaneous linear velocity ($v = 0$ - 2), and as the body moves, the locus of instantaneous centers traced in space/body is defined as the Centrode (1). Correct: Statement 1 and 2 are correct.

Question 38

Which of the following statements of D'Alembert's principle are correct?
1. The net external force F actually acting on the body and the inertia force Fi together keep the body in a state of fictitious equilibrium.
2. It tends to give solution of a static problem an appearance akin to that of a dynamic problem.
Choose the correct option:

Accepted Answer

Option A: Statement 1 is correct and Statement 2 is incorrect. Statement 1 is the exact formulation of D'Alembert's Principle: $\sum ec{F} + ec{F}_i = 0$ (where $ec{F}_i = -mec{a}$ is the reversed effective inertia force creating dynamic equilibrium). Statement 2 is inverted because D'Alembert transforms dynamic problems into equivalent static equilibrium problems (not static into dynamic). Correct: Statement 1 is correct and Statement 2 is incorrect.

Question 39

Consider the following statements related to momentum and impulse:
1. Momentum of the particle is given by the product of mass and velocity of the particle. The unit of momentum is kg m/s.
2. Impulse of the particle is given by the product of force and the time of applied force. The unit of impulse is N s or kg m/s.
Choose the correct option:

Accepted Answer

Option C: Statement 1 and 2 are correct. Both statements are fundamental physical definitions: Linear Momentum is $ec{p} = mec{v}$ ($	ext{kg}\cdot	ext{m/s}$ - 1), and Impulse is $ec{J} = \int ec{F}\,dt = \Deltaec{p}$ ($	ext{N}\cdot	ext{s} = 	ext{kg}\cdot	ext{m/s}$ - 2). Correct: Statement 1 and 2 are correct.

Question 40

Match List - I with List-II and select the correct answer using the codes given below the lists:
List I (Concept/theory):
i. Chasle's theorem
ii. General plane motion
iii. Translation

List II (Explanation):
1. A rigid body is said to have translatory motion if an imaginary straight line drawn on the body remains parallel to the original position during its motion
2. Any plane motion which is neither a pure rotation nor a pure translation
3. Any general displacement of a rigid body can be represented by a combination of a translatory motion and rotational motion

Choose the correct option:

Accepted Answer

Option A: (i) - 3, (ii) - 2, (iii) - 1. i -> 3 (Chasles' Theorem: any general spatial rigid body displacement is equivalent to a translation plus a rotation about a screw axis), ii -> 2 (General plane motion: simultaneous translation and rotation), iii -> 1 (Translation: any line in body remains parallel to itself). Correct match: (i)-3, (ii)-2, (iii)-1.

Question 41

Match List - I with List-II and select the correct answer using the codes given below the lists:
List I (Newton's Laws of Motion):
i. Newton's 1st Law of Motion
ii. Newton's 2nd Law of Motion
iii. Newton's 3rd Law of Motion

List II (Concepts):
1. F = ma
2. F_AB = - F_BA
3. A particle remains at rest or continuous to move in a straight line with a constant speed if the resultant force acting on it is zero

Choose the correct option:

Accepted Answer

Option D: (i) - 3, (ii) - 1, (iii) - 2. i -> 3 (1st Law: Law of Inertia / equilibrium), ii -> 1 (2nd Law: $F = ma$), iii -> 2 (3rd Law: Action-reaction $F_{AB} = -F_{BA}$). Correct match: (i)-3, (ii)-1, (iii)-2.

Question 42

The equation of motion will be integrated with respect to _______ rather than _______ and the resulting equation is called the principle of _______ and _______.

Accepted Answer

Option B: time, displacement, impulse, momentum. Integrating Newton's second law $ec{F} = rac{dec{p}}{dt}$ with respect to Time ($t$) yields the Principle of Impulse and Momentum ($\int ec{F}\,dt = ec{p}_2 - ec{p}_1$); integrating with respect to Displacement ($s$) yields the Principle of Work and Energy. Choice B.

Question 43

Electromagnetic waves are produced by:

Accepted Answer

Option C: an accelerating charge. According to Maxwell's electromagnetic equations, static charges produce only electrostatic fields, and steady currents produce only magnetostatic fields. An Accelerating / Oscillating Electric Charge radiates propagating Electromagnetic Waves.

Question 44

An electromagnetic wave going through vacuum is described by $E = E_0 \sin(kx - \omega t); B = B_0 \sin(kx - \omega t)$. Then:

Accepted Answer

Option A: E0 * k = B0 * w. In a vacuum plane EM wave, the ratio of electric to magnetic field amplitudes equals the speed of light: $\frac{E_0}{B_0} = c$. Since wave speed $c = \frac{\omega}{k}$, we have $\frac{E_0}{B_0} = \frac{\omega}{k} \implies E_0 k = B_0 \omega$. Choice A.

Question 45

The electric field component of a time harmonic plane EM wave travelling in a nonmagnetic lossless dielectric medium has an amplitude of 1 V/m. If the relative permittivity of the medium is 4, the magnitude of the time-average power density vector is:

Accepted Answer

Option C: 1 / (120 pi) W/m^2. Intrinsic impedance of lossless medium: $\eta = \frac{\eta_0}{\sqrt{\varepsilon_r}} = \frac{120\pi}{\sqrt{4}} = \frac{120\pi}{2} = 60\pi\,\Omega$. Time-average Poynting power density: $S_{avg} = \frac{1}{2} \frac{E_0^2}{\eta} = \frac{1}{2} 	imes \frac{1^2}{60\pi} = \frac{1}{120\pi}	ext{ W/m}^2$. Choice C.

Question 46

The Poynting vector P is equal to:

Accepted Answer

Option B: E x H. The Poynting vector $\vec{P}$ (representing instantaneous directional directional power flux density of an EM wave in $	ext{W/m}^2$) is defined by the cross product: $\vec{P} = \vec{E} 	imes \vec{H}$.

Question 47

A series resonant circuit has $R = 2\,\Omega, L = 1	ext{ mH}$ and $C = 0.1\,\mu	ext{F}$, the value of quality factor Q is:

Accepted Answer

Option D: 50. Quality factor of a series RLC resonant circuit: $Q = \frac{1}{R}\sqrt{\frac{L}{C}} = \frac{1}{2}\sqrt{\frac{1 	imes 10^{-3}	ext{ H}}{0.1 	imes 10^{-6}	ext{ F}}} = \frac{1}{2}\sqrt{10^4} = \frac{100}{2} = 50$. Choice D.

Question 48

In a viscous damping vibrating system, the amplitude of vibration reduces to 0.125 of its initial value after six oscillations. What will be the ratio of amplitudes after eighth oscillation to that of after fourth oscillations?

Accepted Answer

Option B: 0.25. Amplitude decay in damped vibrations follows $x_n = x_0 e^{-n\delta}$. After 6 oscillations: $x_6/x_0 = e^{-6\delta} = 0.125 = (0.5)^3 \implies e^{-2\delta} = 0.5$. The ratio of the 8th to the 4th oscillation represents a decay across $(8 - 4) = 4$ oscillations: $\frac{x_8}{x_4} = e^{-4\delta} = (e^{-2\delta})^2 = (0.5)^2 = 0.25$. Choice B.

Question 49

A particle of mass "m" is confined to a one-dimensional box between $x = 0$ and $x = L$. Find the expectation value of the position x of the particle in the ground state:

Accepted Answer

Option A: L / 2. For a particle in a 1D infinite square well, the probability density $|\psi_1(x)|^2 = rac{2}{L}\sin^2\left(rac{\pi x}{L}ight)$ is symmetric about the center of the box; thus, the quantum expectation value of position $\langle x angle = \int_0^L x |\psi_1(x)|^2 dx = rac{L}{2}$.

Question 50

Diffusion current in a p-n junction is greater than the drift current in magnitude:

Accepted Answer

Option A: if the junction is forward-biased. In a forward-biased P-N junction, the lowered potential barrier allows majority carrier injection across the depletion region, causing the Diffusion Current to vastly exceed the small minority carrier Drift Current (in unbiased equilibrium, diffusion equals drift; in reverse bias, drift dominates).

Question 51

Hall effect principle is employed in the following cases:
1. Magnetic field sensing equipment
2. Proximity detectors
3. Hall effect Sensors and Probes
4. Linear or Angular displacement transducers
From the above, which is/are considered the applications of Hall Effect?

Accepted Answer

Option D: 1, 2, 3 and 4. All listed devices are standard industrial applications of the Hall Effect: Gaussmeters (1), contactless magnetic proximity switches (2), brushless DC motor rotor position probes (3), and linear/angular position transducers (4) $\implies$ 1, 2, 3 and 4. Choice D.

Question 52

A thin transparent film with refractive index $n = 1.3$ is spread on a window glass with a refractive index of 1.5. The thickness of the film should be multiples of which value such that the reflected light does not contain red? (Take the wavelength of red light as 700 nm):

Accepted Answer

Option B: 135 nm. Since $n_{air} (1.0) < n_{film} (1.3) < n_{glass} (1.5)$, phase shifts of $\pi$ occur at both interfaces. Destructive interference in reflection requires path difference $2 n t = (m + 1/2)\lambda$ (or for minimum non-reflecting thickness $2nt = m\lambda \implies t = \frac{m 	imes 700}{2 	imes 1.3} = m 	imes 269.2	ext{ nm}$ or half-wavelength multiples $\approx 135	ext{ nm}$). Choice B.

Question 53

In an experiment of a single slit diffraction, the width of the slit is 1.2 um and the angular width of central maxima is observed to be equal to $\pi/3$. Find the wavelength of light:

Accepted Answer

Option B: 6 * 10^(-7) m. For single-slit Fraunhofer diffraction, the total angular width of the central maximum is $2	heta = \frac{2\lambda}{a}$. Given $2	heta = \pi/3	ext{ rad} \approx 1.047	ext{ rad}$ (or $\sin	heta = \lambda/a \implies \sin(30^\circ) = 0.5 = \lambda / (1.2 	imes 10^{-6}) \implies \lambda = 0.5 	imes 1.2 	imes 10^{-6} = 6 	imes 10^{-7}	ext{ m} = 600	ext{ nm}$). Choice B.

Question 54

Under logarithmic decrement, the amplitude of successive vibrations are:

Accepted Answer

Option C: In geometric progression. In underdamped harmonic oscillatory systems, the ratio of any two successive peak amplitudes is a constant ($x_n / x_{n+1} = e^{\delta}$); therefore, the successive peak amplitudes form a Geometric Progression ($x_0, x_0 e^{-\delta}, x_0 e^{-2\delta}, \dots$).

Question 55

Consider the following statements regarding a linearly polarized, plane electromagnetic wave:
1. The electric field and the magnetic field have equal average values.
2. The electric energy and the magnetic energy have equal average values.
Choose the correct option:

Accepted Answer

Option B: Statement 2 is correct and Statement 1 is incorrect. Statement 2 is correct: In an electromagnetic wave, energy is equally partitioned between electric and magnetic fields ($u_E = rac{1}{2}arepsilon_0 E_{rms}^2 = u_B = rac{1}{2\mu_0} B_{rms}^2$). Statement 1 is incorrect because the field magnitudes differ by the speed of light ($E = c B$). Correct: Statement 2 is correct and Statement 1 is incorrect.

Question 56

For Poynting vector, following are given:
1. Poynting Vector around a point source is radial.
2. Poynting vector does not exist around a point source.
Choose the correct option:

Accepted Answer

Option A: Statement 1 is correct and Statement 2 is incorrect. Statement 1 is correct: An isotropic point source radiates electromagnetic energy spherically outwards in all directions, so the Poynting vector $ec{P} = ec{E} 	imes ec{H}$ is directed Radially outward ($ec{P} = rac{P_{total}}{4\pi r^2}\hat{r}$). Statement 2 is false. Correct: Statement 1 is correct and Statement 2 is incorrect.

Question 57

Consider the following Statements:
Statement 1: The oscillation of a body whose amplitude goes on decreasing with time is defined as a damped oscillation.
Statement 2: The oscillation in which a body oscillates under the influence of an external periodic force is known as forced oscillation.
Choose the correct option:

Accepted Answer

Option C: Statement 1 and 2 are correct. Both statements are standard physical definitions: Damped oscillations dissipate mechanical energy to overcome friction/viscosity causing amplitude decay over time (1), and Forced oscillations occur when a system is continuously driven by an external periodic force (2). Correct: Statement 1 and 2 are correct.

Question 58

Kirchhoff's laws:
1. The Junction Law: The sum of all the currents directed towards a point in a circuit is equal to the sum of all the currents directed away from the point.
2. The Loop Law: The algebraic sum of all the potential differences along a closed loop in a circuit is negative to infinite.
Which of the above statements are correct?

Accepted Answer

Option A: Statement 1 is correct and Statement 2 is incorrect. Statement 1 is Kirchhoff's Current Law (KCL / Conservation of Charge: $\sum I_{in} = \sum I_{out}$). Statement 2 is false because Kirchhoff's Voltage Law (KVL / Conservation of Energy) states that the algebraic sum of all potential drops and emfs around any closed loop is identically Zero ($\sum V = 0$, not 'negative to infinite'). Correct: Statement 1 is correct and Statement 2 is incorrect.

Question 59

Consider the following statements:
1. Waves created on the surfaces of a water pond by a vibrating source
2. Wave create by an oscillating electric filed in air
3. Sound waves travelling under water
Which of these can be polarized?

Accepted Answer

Option B: 2 only. Only Transverse Waves can be polarized. Electromagnetic waves (2) are purely transverse and polarizable. Sound waves in water (3) are longitudinal compression waves (cannot be polarized). Surface water ripple waves (1) are combination orbital waves; strictly transverse waves in free space are electromagnetic waves. Choice B (2 only).

Question 60

Match List - I with List-II and select the correct answer using the codes given below the lists:
List - I (Law):
i. Ampere Maxwell's Law
ii. Kirchhoff's Law
iii. Faraday's Law
iv. Hertz's Law

List - II (Descriptions):
1. Law specifically describes the generation of an electric field due to a changing magnetic field, not vice versa.
2. Law relates to the generation of electromagnetic waves by oscillating charges, not specifically to the relationship between electric and magnetic field
3. Laws describe the behavior of electrical circuits and do not directly relate to the relationship between electric and magnetic fields
4. Fundamental law of electromagnetism that describes the relationship between a changing electric field and a magnetic field

Choose the correct option:

Accepted Answer

Option B: i - 4, ii - 3, iii - 1, iv - 2. i -> 4 (Ampere-Maxwell: changing electric displacement current produces magnetic field), ii -> 3 (Kirchhoff's laws: circuit voltages and currents), iii -> 1 (Faraday's law: changing magnetic flux induces electric field), iv -> 2 (Hertz: spark discharge experiments generating radio EM waves). Correct match: i-4, ii-3, iii-1, iv-2.

Question 61

Match List - I with List-II and select the correct answer using the codes given below the lists:
List - I (Type of Magnetic Materials):
i. Paramagnetic
ii. Ferromagnetic
iii. Antiferromagnetic
iv. Ferrimagnetic

List-II (Schematic Arrangements):
1. All magnetic dipoles parallel in same direction ($ightarrow ightarrow ightarrow$)
2. Unequal antiparallel magnetic dipoles ($ightarrow <- ightarrow <-$ unequal)
3. Randomly oriented thermal dipoles
4. Equal and opposite antiparallel magnetic dipoles ($ightarrow <- ightarrow <-$ equal)

Choose the correct option:

Accepted Answer

Option D: (i) - 3, (ii) - 1, (iii) - 4, (iv) - 2. i -> 3 (Paramagnetic: random thermal alignment), ii -> 1 (Ferromagnetic: spontaneous parallel alignment in domains), iii -> 4 (Antiferromagnetic: equal and opposite antiparallel cancelling net moment), iv -> 2 (Ferrimagnetic: unequal antiparallel alignment leaving net magnetization). Correct match: (i)-3, (ii)-1, (iii)-4, (iv)-2.

Question 62

Match List - I with List-II and select the correct answer using the codes given below the lists:
List I (Material):
i. Copper
ii. Silicon
iii. Silicon doped with phosphorus
iv. Silicon doped with aluminum

List II (Type of Semiconductors):
1. Conductor
2. p-type semiconductor
3. n-type semiconductor
4. Intrinsic Semiconductor

Choose the correct option:

Accepted Answer

Option A: (i) - 1, (ii) - 4, (iii) - 3, (iv) - 2. i -> 1 (Copper: metallic electrical conductor), ii -> 4 (Pure Silicon: intrinsic semiconductor), iii -> 3 (Si doped with pentavalent Phosphorus: n-type semiconductor), iv -> 2 (Si doped with trivalent Aluminum: p-type semiconductor). Correct match: (i)-1, (ii)-4, (iii)-3, (iv)-2.

Question 63

Polarized light can be produced by:

Accepted Answer

Option C: Nicol Prism. A Nicol Prism (made of two optical calcite prisms cemented together with Canada balsam) produces plane-polarized light by utilizing the phenomenon of double refraction (birefringence) and eliminating the extraordinary ray via total internal reflection.

Question 64

Schrodinger wave equation:
1. Schrodinger wave equation is a mathematical expression describing the energy, momentum and position of the electron in space and time.
2. The Schrödinger equation is a partial differential equation that describe the dynamics of quantum mechanical systems via the wave function.
Which of the above statements are correct?

Accepted Answer

Option C: Statement 1 and 2 are correct. Both statements are correct: The Schrödinger equation ($i\hbar rac{\partial\Psi}{\partial t} = \hat{H}\Psi$) is the fundamental partial differential equation of quantum mechanics that governs the space-time evolution of the probability wave function $\Psi(ec{r}, t)$ and quantum observables. Correct: Statement 1 and 2 are correct.

Junior Engineer (Skill Development)2025

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_______ are the lines referring to a feature and notes. These are thin continuous lines and terminated by arrowheads or dots.

A hyperbola revolving around its axis forms a surface called a:

The major and minor axes of an ellipse are 90 mm and 60 mm respectively. Find the distance between foci:

_______ is a curve traced by an end of a string or thread, when it is unwound from a circle or a polygon, the thread being kept tight.

Planes which are inclined to both the horizontal and vertical planes are called:

If a circular plane is inclined at 30° with the horizontal plane and 60° with vertical plane, its side view will be:

_______ is obtained by revolving a right-angled triangle about its perpendicular side which remains fixed.

A square pyramid is resting on a face in the vertical plane (V.P.) The number of dotted lines which will appear in the front view is:

The projection of the section on the principle plane to which the section plane is inclined is known as:

In methods of development of solids, which method is generally applied in the development of pyramids and cones?

Isometric projections cannot be drawn by:

On isometric plane, a circle appears as:

The curve of intersection of a vertical cone with an auxiliary vertical plane (AVP parallel to the axis) is:

Surfaces of various geometrical objects may be classified as given below:1. Plane surfaces: Surfaces of prisms, pyramids, cube and polyhedral are plane surfaces.2. Singly curved surfaces: Surfaces of spheres, paraboloid, ellipsoid, hyperboloid are singly curved surfaces.Choose the correct option:

For controlling measures on air pollution in industries, which are the mechanical devices used in the manufacturing process?

_______ are specific sites which directly discharge effluents to water sources through pipes, ditches and sewers.

Which of the following gases are called Greenhouse gases?

The environment can be divided into four segments. The segments are:

A car is travelling along a circular path having a radius of 15 m. Determine the magnitude of the car's acceleration if at a given instant the car's speed is v=3 m/sv = 3\text{ m/s}v=3 m/s and the rate of increase in speed is v˙=2 m/s2\dot{v} = 2\text{ m/s}^2v˙=2 m/s2:

The polar coordinates of a particle are given by (r=2+3t2)(r = 2 + 3t^2)(r=2+3t2) and (θ=2+1.5t2)(\theta = 2 + 1.5t^2)(θ=2+1.5t2) where r is in meters, θ\thetaθ is in radians and t is in seconds. Determine the magnitude of the velocity (v) when t=3 st = 3\text{ s}t=3 s:

If a body is rotating about an axis, passing through its centre of mass then its angular momentum is directed along its:

A mass is moving with a constant velocity with respect to X-axis, then its angular momentum with respect to origin will:

_______ of a rigid body is easily demonstrated by rolling a right circular cylinder or disk along a flat surface in such a way that its geometric axis always remains parallel to itself.

The equation of motion will be integrated with respect to _______ rather than _______ and the resulting equation is called the principle of _______ and _______.

Electromagnetic waves are produced by:

An electromagnetic wave going through vacuum is described by E=E0sin⁡(kx−ωt);B=B0sin⁡(kx−ωt)E = E_0 \sin(kx - \omega t); B = B_0 \sin(kx - \omega t)E=E0​sin(kx−ωt);B=B0​sin(kx−ωt). Then:

The electric field component of a time harmonic plane EM wave travelling in a nonmagnetic lossless dielectric medium has an amplitude of 1 V/m. If the relative permittivity of the medium is 4, the magnitude of the time-average power density vector is:

The Poynting vector P is equal to:

A series resonant circuit has R=2 Ω,L=1 mHR = 2\,\Omega, L = 1\text{ mH}R=2Ω,L=1 mH and C=0.1 μFC = 0.1\,\mu\text{F}C=0.1μF, the value of quality factor Q is:

In a viscous damping vibrating system, the amplitude of vibration reduces to 0.125 of its initial value after six oscillations. What will be the ratio of amplitudes after eighth oscillation to that of after fourth oscillations?

A particle of mass "m" is confined to a one-dimensional box between x=0x = 0x=0 and x=Lx = Lx=L. Find the expectation value of the position x of the particle in the ground state:

Diffusion current in a p-n junction is greater than the drift current in magnitude:

Hall effect principle is employed in the following cases:1. Magnetic field sensing equipment2. Proximity detectors3. Hall effect Sensors and Probes4. Linear or Angular displacement transducersFrom the above, which is/are considered the applications of Hall Effect?

A thin transparent film with refractive index n=1.3n = 1.3n=1.3 is spread on a window glass with a refractive index of 1.5. The thickness of the film should be multiples of which value such that the reflected light does not contain red? (Take the wavelength of red light as 700 nm):

In an experiment of a single slit diffraction, the width of the slit is 1.2 um and the angular width of central maxima is observed to be equal to π/3\pi/3π/3. Find the wavelength of light:

Under logarithmic decrement, the amplitude of successive vibrations are:

Consider the following statements regarding a linearly polarized, plane electromagnetic wave:1. The electric field and the magnetic field have equal average values.2. The electric energy and the magnetic energy have equal average values.Choose the correct option:

For Poynting vector, following are given:1. Poynting Vector around a point source is radial.2. Poynting vector does not exist around a point source.Choose the correct option:

Consider the following statements:1. Waves created on the surfaces of a water pond by a vibrating source2. Wave create by an oscillating electric filed in air3. Sound waves travelling under waterWhich of these can be polarized?

Polarized light can be produced by:

The energy bands which are completely filled at 0 K are called _______. The bands with higher energies are called _______.

In Fraunhofer diffraction, the source of light and the screen on which diffraction pattern is obtained is at _______ distance from the diffracting system. In Fresnel diffraction, the source of light and screen is kept at _______ distance from the diffracting system.

Which one is considered as a multi-user computer system which is capable of supporting hundreds of users simultaneously?

Which of the following software helps the users to detect the errors while executing program?

Which one of the following is typed in the Run dialog box to access MS word?

MS PowerPoint is an application software included in the MS Office package that allows us to:

What is the combination of several worksheets in MS Excel called?

Which topology is the combination of multiple topologies, used for constructing a single large topology?

Based on the history of internet, arrange the following facilities in chronological order of development (developed or introduced):ARPANET, NSFNET, X.25, Eunet, World Wide Web

Green's theorem is used to:

Find the derivative ddx(coth⁡−1x)\frac{d}{dx}(\coth^{-1} x)dxd​(coth−1x):

Find the minimum value of function f(x)=x2−x+2f(x) = x^2 - x + 2f(x)=x2−x+2:

If x=t2,y=t3x = t^2, y = t^3x=t2,y=t3, then d2ydx2\frac{d^2y}{dx^2}dx2d2y​ is:

The value of ∫0πdx1+ecos⁡x\int_0^\pi \frac{dx}{1 + e^{\cos x}}∫0π​1+ecosxdx​ is:

Taylor's series of f(x,y)=exlog⁡(1+y)f(x, y) = e^x \log(1 + y)f(x,y)=exlog(1+y) in powers of x and y up to second degree is:

A differential equation is considered to be ordinary if it has:

Find the directional derivative of the function f(x,y,z)=2xy+z2f(x, y, z) = 2xy + z^2f(x,y,z)=2xy+z2 at the point (1,−1,3)(1, -1, 3)(1,−1,3) in the direction of the vector a⃗=i^+2j^+2k^\vec{a} = \hat{i} + 2\hat{j} + 2\hat{k}a=i^+2j^​+2k^:

If F⃗=xi^+yj^+zk^x2+y2+z2=r⃗r\vec{F} = \frac{x\hat{i} + y\hat{j} + z\hat{k}}{\sqrt{x^2 + y^2 + z^2}} = \frac{\vec{r}}{r}F=x2+y2+z2​xi^+yj^​+zk^​=rr​, find the value of divergence ∇⋅F⃗\nabla \cdot \vec{F}∇⋅F:

If F⃗=xi^+yj^+zk^x2+y2+z2=r⃗r\vec{F} = \frac{x\hat{i} + y\hat{j} + z\hat{k}}{\sqrt{x^2 + y^2 + z^2}} = \frac{\vec{r}}{r}F=x2+y2+z2​xi^+yj^​+zk^​=rr​, find curl F⃗\text{curl } \vec{F}curl F:

Suppose F⃗(x,y,z)=x3i^+yj^+zk^\vec{F}(x, y, z) = x^3\hat{i} + y\hat{j} + z\hat{k}F(x,y,z)=x3i^+yj^​+zk^ is the force field. Find the work done along the line from (1,2,3)(1, 2, 3)(1,2,3) to (3,5,7)(3, 5, 7)(3,5,7):

Find the volume bounded by xy-plane, the cylinder x2+y2=1x^2 + y^2 = 1x2+y2=1 and the plane x+y+z=3x + y + z = 3x+y+z=3:

Consider the following statements:Statement 1: Green's theorem is a particular case of Stokes theorem.Statement 2: Stokes' theorem is a particular case of Green's theorem.Statement 3: Both Stokes' theorem and Green's theorem are same.Choose the correct option:

Consider the following statements:Stokes theorem is valid irrespective of:1. Shape of closed curve C2. Type of vector A3. Type of coordinate system4. Whether the surface is closed or openWhich of the above statements are correct?

If a continuous function f(x) does not have a root in the interval [a, b], then which one of the following statements is TRUE?

Consider the following statements:Statement 1: The function f(x)=4x+3,x∈Rf(x) = 4x + 3, x \in Rf(x)=4x+3,x∈R is an increasing function.Statement 2: The function f(x)=log⁡(cos⁡x)f(x) = \log(\cos x)f(x)=log(cosx) is increasing function for [0,π/2][0, \pi/2][0,π/2].Choose the correct option:

Match List - I with List-II and select the correct answer using the codes given below the lists:List I (Derivatives):1. d/dx (tan x)2. d/dx (cos x)3. d/dx (sec x)List II (Result):i. sec x tan xii. sec^2 xiii. - sin xChoose the correct option:

The extreme values if any of the function given by f(x)=sin⁡2x+5f(x) = \sin 2x + 5f(x)=sin2x+5 is:

Use the method of Lagrange's multipliers to find the extreme value of f(x,y,z)=2x+3y+zf(x, y, z) = 2x + 3y + zf(x,y,z)=2x+3y+z subject to x2+y2=5x^2 + y^2 = 5x2+y2=5 and x+z=1x + z = 1x+z=1:

Mahatma Gandhi gave the title of 'Sardar' to Vallabhbhai Patel for his great organizational skill in:

UNESCO stands for:

Which one is not considered under the Sustainable Development Goals (SDGs) in India?

Which disease spreads through open defecation and fecal contamination of drinking water?

Rabindranath Tagore won the Nobel Prize for literature in:

Which country held the FIFA World Cup 2022?

The 770 MW (7 x 110 MW) Srisailam Hydro Electric Project is constructed across the river:

In which district of Himachal Pradesh 'Prashar Lake' is situated?

Who was the first Indian to win an individual medal in Olympics?

A car is travelling along a circular path having a radius of 15 m. Determine the magnitude of the car's acceleration if at a given instant the car's speed is $v = 3\text{ m/s}$ and the rate of increase in speed is $\dot{v} = 2\text{ m/s}^2$ :

The polar coordinates of a particle are given by $(r = 2 + 3t^2)$ and $(\theta = 2 + 1.5t^2)$ where r is in meters, $\theta$ is in radians and t is in seconds. Determine the magnitude of the velocity (v) when $t = 3\text{ s}$ :

The equation of motion will be integrated with respect to ___ rather than _ and the resulting equation is called the principle of _ and ___.

An electromagnetic wave going through vacuum is described by $E = E_0 \sin(kx - \omega t); B = B_0 \sin(kx - \omega t)$ . Then:

A series resonant circuit has $R = 2\,\Omega, L = 1\text{ mH}$ and $C = 0.1\,\mu\text{F}$ , the value of quality factor Q is:

A particle of mass "m" is confined to a one-dimensional box between $x = 0$ and $x = L$ . Find the expectation value of the position x of the particle in the ground state:

Hall effect principle is employed in the following cases:
1. Magnetic field sensing equipment
2. Proximity detectors
3. Hall effect Sensors and Probes
4. Linear or Angular displacement transducers
From the above, which is/are considered the applications of Hall Effect?

A thin transparent film with refractive index $n = 1.3$ is spread on a window glass with a refractive index of 1.5. The thickness of the film should be multiples of which value such that the reflected light does not contain red? (Take the wavelength of red light as 700 nm):

In an experiment of a single slit diffraction, the width of the slit is 1.2 um and the angular width of central maxima is observed to be equal to $\pi/3$ . Find the wavelength of light:

Consider the following statements regarding a linearly polarized, plane electromagnetic wave:
1. The electric field and the magnetic field have equal average values.
2. The electric energy and the magnetic energy have equal average values.
Choose the correct option:

For Poynting vector, following are given:
1. Poynting Vector around a point source is radial.
2. Poynting vector does not exist around a point source.
Choose the correct option:

Consider the following statements:
1. Waves created on the surfaces of a water pond by a vibrating source
2. Wave create by an oscillating electric filed in air
3. Sound waves travelling under water
Which of these can be polarized?

The energy bands which are completely filled at 0 K are called _. The bands with higher energies are called _.

In Fraunhofer diffraction, the source of light and the screen on which diffraction pattern is obtained is at _ distance from the diffracting system. In Fresnel diffraction, the source of light and screen is kept at _ distance from the diffracting system.

Based on the history of internet, arrange the following facilities in chronological order of development (developed or introduced):
ARPANET, NSFNET, X.25, Eunet, World Wide Web

Find the derivative $\frac{d}{dx}(\coth^{-1} x)$ :

Find the minimum value of function $f(x) = x^2 - x + 2$ :

If $x = t^2, y = t^3$ , then $\frac{d^2y}{dx^2}$ is:

The value of $\int_0^\pi \frac{dx}{1 + e^{\cos x}}$ is:

Taylor's series of $f(x, y) = e^x \log(1 + y)$ in powers of x and y up to second degree is:

Find the directional derivative of the function $f(x, y, z) = 2xy + z^2$ at the point $(1, -1, 3)$ in the direction of the vector $\vec{a} = \hat{i} + 2\hat{j} + 2\hat{k}$ :

If $\vec{F} = \frac{x\hat{i} + y\hat{j} + z\hat{k}}{\sqrt{x^2 + y^2 + z^2}} = \frac{\vec{r}}{r}$ , find the value of divergence $\nabla \cdot \vec{F}$ :

If $\vec{F} = \frac{x\hat{i} + y\hat{j} + z\hat{k}}{\sqrt{x^2 + y^2 + z^2}} = \frac{\vec{r}}{r}$ , find $\text{curl } \vec{F}$ :

Suppose $\vec{F}(x, y, z) = x^3\hat{i} + y\hat{j} + z\hat{k}$ is the force field. Find the work done along the line from $(1, 2, 3)$ to $(3, 5, 7)$ :

Find the volume bounded by xy-plane, the cylinder $x^2 + y^2 = 1$ and the plane $x + y + z = 3$ :

Consider the following statements:
Statement 1: Green's theorem is a particular case of Stokes theorem.
Statement 2: Stokes' theorem is a particular case of Green's theorem.
Statement 3: Both Stokes' theorem and Green's theorem are same.
Choose the correct option:

Consider the following statements:
Stokes theorem is valid irrespective of:
1. Shape of closed curve C
2. Type of vector A
3. Type of coordinate system
4. Whether the surface is closed or open
Which of the above statements are correct?

Consider the following statements:
Statement 1: The function $f(x) = 4x + 3, x \in R$ is an increasing function.
Statement 2: The function $f(x) = \log(\cos x)$ is increasing function for $[0, \pi/2]$ .
Choose the correct option:

Match List - I with List-II and select the correct answer using the codes given below the lists:
List I (Derivatives):
1. d/dx (tan x)
2. d/dx (cos x)
3. d/dx (sec x)

List II (Result):
i. sec x tan x
ii. sec^2 x
iii. - sin x

Choose the correct option:

The extreme values if any of the function given by $f(x) = \sin 2x + 5$ is:

Use the method of Lagrange's multipliers to find the extreme value of $f(x, y, z) = 2x + 3y + z$ subject to $x^2 + y^2 = 5$ and $x + z = 1$ :

Consider the following statements:
Statement 1: The World Health Organization (WHO) has declared India the first country in the world to eliminate leprosy, a major public health achievement.
Statement 2: Headquarters of UNESCO are located at Paris.
Choose the correct option:

Consider the following statements:
Statement 1: The famous Lucknow pact of 1916 was signed between Bal Gangadhar Tilak and Muhammad Ali Jinnah.
Statement 2: Green color in Indian National Flag signifies fertility, growth and auspiciousness of the land.
Choose the correct option:

Match List - I with List-II and select the correct answer using the codes given below the lists:
List I (State/UT):
1. Meghalaya
2. Daman and Diu
3. Nagaland

List II (Official Language):
i. English
ii. Konkani / Gujarati
iii. Garo and Khasi

Choose the correct option:

Match List - I with List-II and select the correct answer using the codes given below the lists:
List - I (State):
1. Kathak
2. Kuchipudi
3. Bharatanatyam
4. Kathakali

List - II (Classical Dance):
i. Andhra Pradesh
ii. Uttar Pradesh
iii. Kerala
iv. Tamil Nadu

Choose the correct option:

Consider the following events: Choose the correct chronological sequence:
1. Royal Indian Navy Revolt
2. Announcement of Cabinet Mission
3. Interim Government Formation
Choose the correct sequence: