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QUESTION: 1

A damped harmonic oscillator has a frequency of 5 oscillations per second. The amplitude drops to half its value for every 10 oscillations. The time it will take to dropto 1/1000 of the original amplitude is close to:

Solution:

QUESTION: 2

A cell of internal resistance r drives current through an external resistance R. Thepower delivered by the cell to the external resistance will be maximum when:

Solution:

Power maximum when R=r.

QUESTION: 3

A uniform rectangular thin sheet ABCD of mass M has length a and breadth b, as shown in the figure. If the shaded portion HBGO is cut–off, the coordinates of the centre of mass of the remaining portion will be

Solution:

QUESTION: 4

In a line of sight radio communication, a distance of about 50 km is kept betweenthe transmitting and receiving antennas. If the height of the receiving antenna is 70m, then the minimum height of the transmitting antenna should be:(Radius of the Earth = 6.4*10^{6} m)

Solution:

QUESTION: 5

In a simple pendulum experiment for determination of acceleration due to gravity(g), time taken for 20 oscillations is measured by using a watch of 1 second leastcount. The mean value of time taken comes out to be 30 s. The length of pendulum ismeasured by using a meter scale of least count 1 mm and the value obtained is55.0 cm. The percentage error in the determination of g is close to:

Solution:

QUESTION: 6

A parallel plate capacitor has 1μF capacitance. One of its two plates is given +2μCcharge and the other plate, +4μC charge. The potential difference developed acrossthe capacitor is:

Solution:

QUESTION: 7

Two magnetic dipoles X and Y are placed at a separation d, with their axes perpendicular to each ot.her. The dipole moment 0f Y is twice that of X. A particle of charge q is passing through their mid–point P, at angle θ = 45° with the

horizontal line, as shown in figure. What would be the magnitude of force on the particleat that instant ? (d is much larger than the dimensions of the dipole)

Solution:

QUESTION: 8

A solid sphere and solid cylinder of identical radii approach an incline with the same linear velocity (see figure). Both roll without slipping all throughout. The two climb maximum heights h_{sph} and h_{cyl} on the incline. The ratio

is given by:

Solution:

QUESTION: 9

A nucleus A, with a finite de–broglie wavelength λ_{A}, undergoes spontaneous fission into two nuclei B and C of equal mass. B flies in the same direction as that of A, while C flies in the opposite direction with a velocity equal to half of that of B. The de–Broglie wavelengths λ_{B} and λ_{C} of B and C are respectively :

Solution:

QUESTION: 10

The temperature, at which the root mean square velocity of hydrogen molecules equals their escape velocity from the earth, is closest to:

[Boltzmann Constant kB =1.38 X 10–23 J/K Avogadro Number NA = 6.02 X 1026 /kg Radius of Earth : 6.4 X 106 m

Gravitational acceleration on Earth = 10 ms–2]

Solution:

(But according to given data in the question no answer, avogadro number is given wrong )

QUESTION: 11

A circuit connected to an ac source of emf e=e_{0} sin(100t) with t in seconds, gives aphase difference of π/4 between the emf e and current i. Which of the followingcircuits will exhibit this?

Solution:

QUESTION: 12

Young’s moduli of two wires A and B are in the ratio 7:4. Wire A is 2m long and hasradius R. Wire B is 1.5 m long and has radius 2 mm. If the two wires stretch by thesame length for a given load, then the value of R is close to :

Solution:

QUESTION: 13

A body of mass m1 moving with an unknown velocity of , undergoes a collinearcollision with a body of mass m2 moving with a velocity . After collision, m1 andm2 move with velocities of and , respectively. If m_{2}=0.5 m_{1} and v_{3} =0.5 v_{1} ,then v_{1} is:

Solution:

QUESTION: 14

A particle starts from origin O from rest and moves with a uniform acceleration along the positive x– axis. Identify the figure that incorrectly represent the motion qualitatively. (a = acceleration, = velocity, x = displacement, t = time)

Solution:

QUESTION: 15

A positive point charge is released from rest at a distance ro from a positive line charge with uniform density. The speed of the point charge, as a function of instantaneous distance r from line charge, is proportional to:

Solution:

QUESTION: 16

The electric field in a region is given by , where E is in NC^{–1} and x is in metres. The values of constants are A=20 SI unit and B=10 SI unit. If the potential at x=1 isV_{1} and that at x= –5 is V_{2}, then V_{1} –V_{2}is:

Solution:

QUESTION: 17

The ratio of mass densities of nuclei of^{ 40}Ca and ^{16}O is close to:

Solution:

Radius of the nucleus is given by R= R_{O}A^{1/3} So, Density constant

QUESTION: 18

Solution:

QUESTION: 19

Two very long, straight, and insulated wires are kept at 90° angle from each other in xy–plane as shown in the figure.

These wires carry currents of equal magnitude I, whose directions are shown in the figure. The net magnetic field at point P will be:

Solution:

QUESTION: 20

A common emitter amplifier circuit, built using an npn transistor, is shown in the figure. Its dc current gain is 250, R_{C =}1KΩ and VCC = 10V. What is the minimum base current for V_{CE} to reach saturation?

Solution:

QUESTION: 21

If Surface tension (S), Moment of Inertia (I) and Planck's constant (h), were to betaken as the fundamental units, the dimensional formula for Linear momentumwould be:

Solution:

QUESTION: 22

An electric dipole is formed by two equal and opposite charges q with separation d.The charges have same mass m. It is kept in a uniform electric field E. If it is slightly rotated from its equilibrium orientation, then its angular frequency ω is:

Solution:

QUESTION: 23

A rocket has to be launched from earth in such a way that it never returns. If E is the minimum energy delivered by the rocket launcher, what should be the mjnimum energy that the launcher should have if the same rocket is to be launched from the surface of the moon ? Assume that the density of the earth and the moon are equal and that the earth's volume is 64 times the volume of the moon.

Solution:

QUESTION: 24

A convex lens (of focal length 20 cm) and a concave mirror, having their principalaxes along the same lines, are kept 80 cm apart from each other. The concavemirror is to the right of the convex lens. When an object is kept at a distance of 30cm to the left of the convex lens, its image remains at the same position even if theconcave mirror is removed. The maximum distance of the object for which thisconcave mirror, by itself would produce a virtual image would be

Solution:

Focal length of concave mirror is 10cm

QUESTION: 25

In the circuit shown, a four–wire potentiometer is made of a 400 cm long wire,which extends between A and B. The resistance per unit length of the potentiometer wire is r= 0.01 Ω/cm If an ideal voltmeter is connected as shown with jockey J at 50 cm from end A, the expected reading of the voltmeter will be:

Solution:

Total resistance of potentiometer wire is 4Ω

Total potential drop across wire is 4/6*3V =2V

For 50cm voltmeter reading

QUESTION: 26

A rectangular solid box of length 0.3 m is held horizontally, with one of its sides on the edge of a platform of height 5 m. When released, it slips off the table in a very short time τ =0.01 s, remaining essentially horizontal. The angle by which it would rotate when it hits the ground will be (in radians) close to

Solution:

QUESTION: 27

Calculate the limit of resolution of a telescope objective having a diameter of 200cm,if it has to detect Light of wavelmgth 500 nm coming from a star.

Solution:

QUESTION: 28

In the figure shown, what is the current (in Ampere) drawn from the battery? You are given:

Solution:

Reff = 160/3

QUESTION: 29

The magnetic field of an electromagnetic wave is given by:

The associated electric field will be:

Solution:

QUESTION: 30

The given diagram shows four processes i.e., isochoric, isobaric, isothermal and adiabatic. The correct assignment of the processes, in the same order is given by:

Solution:

PV^{n} = constant

If n = 0, isobaric

n = 1 isothermal

n= adiabatic

n = ∞ isochoric

QUESTION: 31

The maximum prescribed concentration of copper in drinkmg water is:

Solution:

QUESTION: 32

The major product obtained in the following reaction is

Solution:

QUESTION: 33

Fructose and glucose can be distinguished by :

Solution:

Barfoed's test: Positive for Fructose and glucose.

Seliwanoff’s test: Positive for Fructose and negative for glucose.

Benedict’s test: Positive for Fructose and glucose.

Fehling’s test: Positive for Fructose and glucose.

QUESTION: 34

The structure of Nylon–6 is:

Solution:

QUESTION: 35

The covalent alkaline earth metal halide (X = Cl, Br, I) is :

Solution:

Beryllium halides are covalent due to more polarizing power of small Be2+ ion with more charge density.

QUESTION: 36

0.27 g of a long chain fatty acid was dissolved in 100 cm3 of hexane. 10 mL of this solution was added dropwise to the surface of water in a round watch glass. Hexane evaporates and a monolayer is formed. The distance from edge to centre of the watch glass is 10 cm. What is the height of the monolayer ? [Density of fatty acid = 0.9 g cm-3 ; p = 3 ]

Solution:

QUESTION: 37

For the following reactions, equilibrium constans are given:

The equilibrium constant for the reaction,

Solution:

QUESTION: 38

The correct statement about ICl_{5}and ICl^{-}_{4} is:

Solution:

ICl_{5} have 4 B.P and 1 L.P. It is square pyramidal. ICl^{-}_{4}have 4 B.P. and 2 L.P. The two L.P occupy opposite corners of octahedral. So it square planar.

QUESTION: 39

The major product of the following reaction is:

Solution:

QUESTION: 40

The compound that inhibits the growth of tumors is:

Solution:

cis–platini is used as anti–tumer agent.

QUESTION: 41

For a reaction scheme , if the rate of formation of B is set to be zero then the concentration of B is given by:

Solution:

QUESTION: 42

Among the following molecules/ ions,

Which one is diamagnetic and has the shortest bond length?

Solution:

Bond order

is diamagnetic since all electrons are paired and have shortest bond length due to triple bond.

QUESTION: 43

The major product of the following reaction is:

Solution:

QUESTION: 44

Calculate the standard cell potential (in V) of the cell in which following reaction takes place:

Fe^{2+ }(aq) + Ag^{+} (aq) → Fe^{3+} (aq) + Ag (s)

Given that

Solution:

QUESTION: 45

The major product in the following reaction is:

Solution:

QUESTION: 46

The major product obtained in the following reaction is:

Solution:

Intramolecular aldol condensation

QUESTION: 47

Which one of the following alkenes when treated with HCl yields majority an anti Maxkovnikov product?

Solution:

QUESTION: 48

The calculated spin–only magnetic moments (BM) of the anionic and cationic species of [Fe(H_{2}O)_{6}]_{2} and [Fe(CN)_{6}], respectively, are :

Solution:

The compound containing [Fe(H_{2}O)_{6}]_{2} cation and [Fe(CN)_{6}] anion must be [Fe(H_{2}O)_{6}]_{2} [Fe(CN)_{6}]. It contains 2[Fe(H_{2}O)_{6}]^{2+} cation and [Fe(CN)_{6}]^{4–} anion in which Iron is present as Fe^{2+} ion. In [Fe(H_{2}O)_{6}]^{2+} since H_{2}O is weak ligand there will be 4 unpaired electrons with 4.9 BM while in [Fe(CN)_{6}]^{4–} all the electrons are paired as the CN^{–} is strong ligand with zero unpaired electrons and zero magnetic moment.

QUESTION: 49

The IUPAC symbol for the element with atomic number 119 would be:

Solution:

For 1 the abreviation is U (from unium) and for 9 is e (from enneium). So the IUPAC symbol is uue.

QUESTION: 50

The percentage composition of carbon by mole in methane is :

Solution:

% of C by mole = 1/5 x 100 = 20%

QUESTION: 51

The Mond process is used for the:

Solution:

Nickel is purified by Mond’s process using the formation of unstable volatile compound. Ni(CO)_{4}.

QUESTION: 52

The statement that is INCORRECT about the interstitial compounds is :

Solution:

They are relatively non reactive

QUESTION: 53

Polysubstitution is a major drawback in

Solution:

Polyalkylation – Products of Friedel–Crafts are even more reactive than starting material. Alkyl groups produced in Friedel–Crafts Alkylation are electron–donating substituents meaning that the products are more susceptible to electrophilic attack than reactant.

QUESTION: 54

For the solution of the gases w, x, y and z in water at 298 K, the Henrys law constants (K_{H}) are 0.5, 2, 35 and 40 kbar, respectively. The correct plot for the given data is :

Solution:

K_{H} for w, x, y, z are 0.5, 2, 35 & 40.

P = K_{H} X

P = K_{H} (1 - X_{water})

P = K_{H} - K_{H}X_{water }(y = c - mx)

K_{H} values increases in the order z > y > x > w.

QUESTION: 55

Consider the bcc unit cells of the solids 1 and 2 with the position of atoms as shown below. The radius of atom B is twice that of atom A. The unit cell edge length is 50% more in solid 2 than in 1. What is the approximate packing efficiency in solid 2?

Solution:

√3a = 2r + 4r = 6r

a = 2√3r

Packing fraction =

i.e. 90% is the packed in the solid B

QUESTION: 56

5 moles of an ideal gas at 100 K are allowed to undergo reversible compression till its temperature becomes 200 K. If C_{V} = 28 JK^{-}^{1} mol^{–1}, calcuIate Δ U and Δ PV for this process. ( R = 8.0 JK ^{-1} mol^{-1} )

Solution:

ΔU = 28x5x100 = 14kJ

Δ(pV) = p_{2}v_{2} - p_{1}v_{2} = nR (T_{2 }- T_{1})

= 5x8.314x100 ≈ 4KJ

QUESTION: 57

The ion that has sp^{3}d^{2} hybridization for the central atom, is:

Solution:

ICl_{4}^{-} have 4 B.P. and 2 L.P (steric number 6). So central atom is involved in sp^{3}d^{2} hybridization.

QUESTION: 58

If p is the momentum of the fastest electron ejected from a metal surface after the irradiation of light having wavelength λ , then for 1.5 p momentum of the photoelectron, the wavelength of the light should be: (Assume kinetic energy of ejected photoelectron to be very high in comparison to work function) :

Solution:

W_{0} is too small in comparision to K.E.

QUESTION: 59

Which of the following compounds will show the maximum ‘enol’ content ?

Solution:

CH_{3}COCH_{2}COOC_{2}H_{5} %enol = 0.00025

CH_{3}COCH_{2}CONH_{2} % enol = <7.5

CH_{3}COCH_{2}COCH_{3} %enol = 72

CH_{3}COCH_{3} %enol = 0.00025

QUESTION: 60

The strength of 11.2 volume solution of H_{2}O_{2} is:

[Given that molar mass of H=1 g mol^{–1} and O=16 g mol^{–1}]

Solution:

1M = 2N = 3.4% w/v = 11.2 vol.

QUESTION: 61

The tangent and the normal lines at the point ( √3,1) to the circle x^{2} + y^{2} = 4 and the x-axis form a triangle. The area of this triangle (in square units) is:

Solution:

QUESTION: 62

Let and ,for some real x.Then is possible if :

Solution:

QUESTION: 63

If three distinct numbers a, b, c are in G.P. and the equations ax^{2} + 2bx +c =0 and dx^{2} + 2ex + f = 0 have a common root, then which one of the following statements is correct ?

Solution:

QUESTION: 64

The sum is equal to

Solution:

QUESTION: 65

If the system of linear equations

x – 2y + kz =1

2x + y + z = 2

3x – y – kz =3

has a solution (x, y, z), z ≠ 0, then (x, y) lies on the straight line whose equation is:

Solution:

From the given eqs, (1) + (3) → 4x – 3y – 4 = 0

QUESTION: 66

The tangent to the parabola y^{2}=4x at the point where it intersects the circle x^{2 }+ y^{2} = 5 in the first quadrant, passes through the point :

Solution:

y^{2 }= 4x,x^{2 }+ y^{2} = 5 ⇒ x^{2} + 4x -5= 0

x =1 (x ≠-5) ⇒ y =2 Q (y>0)

Eq of tangent is 2y = 2(x+1) ⇒ x – y + 1 = 0

QUESTION: 67

If where C is a constant of integration, then the function f(x) is equal to :

Solution:

QUESTION: 68

Suppose that the points (h, k), (1, 2) and (–3, 4) lie on the line L_{1}. If a line L_{2} passing through the points (h, k) and (4, 3) is perpendicular to L_{1}, then k/h equals:

Solution:

eq of L_{1} is x + 2y = 5 ⇒

QUESTION: 69

Let the numbers 2, b, c be in an A.P. and If det(A) ∈ [2,16],then c lies in the interval:

Solution:

QUESTION: 70

The minimum number of times one has to toss a fair coin so that the probability of observing at least one head is at least 90% is:

Solution:

QUESTION: 71

Two vertical poles of heights, 20 m and 80 m stand apart on a horizontal plane. The height (in meters) of the point of intersection of the Lines joining the top of each pole to the foot of the other, from this horizontal plane is :

Solution:

QUESTION: 72

Let , where g is a non–zero even function. If f(x+5)=g(x), then equals:

Solution:

g(x) = f '(x) & g (- x) = g (x) = f (x + 5) = f (5 - x) and also f(x) is odd.

QUESTION: 73

Let be a diiferentiable function Satisfying f '(3) + f '(2) = 0 . Then is equal to

Solution:

QUESTION: 74

Let be deﬁned as

where [t] denotes the greatest integer less than or equal to t. Then, f is discontinuous at:

Solution:

QUESTION: 75

let and A(α) is area of the region S (α) . If for a λ, 0 < λ < 4, A(λ) : A(4) = 2 : 5 , then λ equals:

Solution:

QUESTION: 76

The number of integral values of m for which the equation (1 + m^{2}) x^{2} - 2 (1 + 3m) x + (1 + 8m) = 0 has no real root is:

Solution:

D < 0 ⇒ 8m^{3} -8m^{2} + 2m > 0 ⇒ 2m (2m-1)^{2} > 0 ⇒ m > 0

QUESTION: 77

If the eccmtricity of the standard hyperbola passing through the point (4, 6) is 2, then the equation of the tangent to the hyperbola at (4, 6) is :

Solution:

Eq. of hyperbola is it passes through (4,6) ⇒ a^{2}=4.

Eq. of tangent is 2x–y=2.

QUESTION: 78

If , then is equal to:

Solution:

QUESTION: 79

The height of a right circular cylinder of maximum volume inscribed in a sphere of radius 3 is :

Solution:

QUESTION: 80

The number of four–digit numbers strictly greater than 4321 that can be formed using the digits 0, 1, 2, 3, 4, 5 (repetition of digits is allowed) is :

Solution:

Total no. = 310.

QUESTION: 81

Let be written as f(x) =f_{1}(x) +f_{2}(x), where f_{1}(x) is an even function and f_{2}(x) is an odd function. Then f_{1}(x + y) +f_{1}(x – y) equals:

Solution:

QUESTION: 82

The vector equation of the plane through the line of intersection of the planes x+y+ z= 1 and 2x+3y+4z=5 which is perpendicular to the plane x – y+ z =0 is :

Solution:

Line of intersection of the planes x+y+z=1, 2x+3y+4z=5 is

Eq. of required plane is

QUESTION: 83

Which one of the following statements is not a tautology ?

Solution:

QUESTION: 84

Given that the slope of the tangent to a curve y = y ( x) at any point (x,y) is 2y/x^{2 }If the curve passes through the centre of the circle x^{2} + y^{2} – 2x – 2y = 0, then its equation is :

Solution:

QUESTION: 85

If a point R(4, y, z) lies on the line segment joining the points P (2,-3, 4) and Q(8, 0, 10), then the distance of R from the origin is:

Solution:

Here, P, Q, R are collinear ⇒

QUESTION: 86

In an ellipse, with centre at the origin, if the difference of the lengths of major axis and minor axis is 10 and one of the foci is at (0, 5 √3) , then the length of its latus rectum is:

Solution:

Here, given ellipse is vertical ellipse & b – a = 5, b^{2} – a^{2} = 75

QUESTION: 87

If the fourth term in the binomial expansion of is equal to 200,and x >1, then the value of x is:

Solution:

QUESTION: 88

If the lengths of the sides of a triangle are in A.P. and the greatest angle is double the smallest, then a ratio of lengths of the sides of this triangle is:

Solution:

QUESTION: 89

If f(1) = 1, f '(1) = 3, then the derivative of f(f(f ( x))) + (f ( x))^{2} of x=1 is

Solution:

QUESTION: 90

A student scores the following marks in ﬁve tests : 45, 54, 41, 57, 43. His score is not known for the sixth test. If the mean score is 48 in the six tests, then the standard deviation of the marks in six tests is :

Solution:

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