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QUESTION: 1

The velocity of water in a river is 18 km/hr near the surface. If the river is 5 m deep, find the shearing stress between the horizontal layers of water. The co-efficient of viscosity of water = 10^{–2 }poise.

Solution:

F = – nA dv/dx

now stress = F/A = 10^{–3}

QUESTION: 2

Four bulbs B_{1}, B_{2}, B_{3} and B_{4} of 100 W each are connected to 220 V main as shown in the figure. The reading in an ideal ammeter will be

Solution:

Resistance of any bull

Net resistance of the cks

v = i R_{eq}

220 × i × 121

i = 1.81 Amp. (total current supplied by the battery)

Current in each branch in i = 1.81/4amp. = 0.45 amp.

Reading of ammeter = 3 × 0.45 = 1.3575 amp.

QUESTION: 3

In a Young's double slit experiment, the distance between the two identical slits is 6.1 times larger than the slit width. Then the number of intensity maxima observed within the central maximum of the single slit diffraction pattern is

Solution:

d = 6.1 a

width of central maxima

QUESTION: 4

A body is in simple harmonic motion with time period half second (T = 0.5 s) and amplitude one cm (A = 1 cm). Find the average velocity in the interval in which it moves from equilibrium position to half of its amplitude.

Solution:

QUESTION: 5

A bullet looses of its velocity passing through one plank. The number of such planks that are required to stop the bullet can be :

Solution:

O = V^{2} – 2 ans

QUESTION: 6

Long range radio transmission is possible when the radiowaves are reflected from the ionosphere.For this to happen the frequency of the radiowaves must be in the range :

Solution:

QUESTION: 7

A ray of light is incident from a denser to a rarer medium. The critical angle for total internal reflection is θ_{iC} and the Brewster's angle of incidence is θ_{iB}, such that sinθ_{iC}/sinθ_{iB} = η = 1.28. The relative refractive index of the two media is :

Solution:

QUESTION: 8

If denote microwaves, X rays, infrared, gamma rays, ultra-violet, radio waves and visible parts of the electromagnetic spectrum by M, X, I, G, U, R and V, the following is the arrangement in ascending order of wavelength :

Solution:

The desending order of energy for following waves

E_{y} > E_{x} > E_{uv} > E_{vissible} > V_{iR }> V_{MW}

QUESTION: 9

A piece of wood from a recently cut tree shows 20 decays per minute. A wooden piece of same size placed in a museum (obtained from a tree cut many years back) shows 2 decays per minute. If half life of C^{14} is 5730 years, then age of the wooden piece placed in the museum is approximately :

Solution:

QUESTION: 10

A square frame of side 10 cm and a long straight wire carrying current 1 A are in the plane of the paper. Starting from close to the wire, the frame moves towards the right with a constant speed of 10 ms^{–1} (see figure). The e.m.f induced at the time the left arm of the frame is at x = 10 cm from the wire is :

Solution:

QUESTION: 11

Given : A and B are input terminals.

Logic 1 = > 5 V

Logic 0 = < 1 V

Which logic gate operation, the following circuit does ?

Solution:

QUESTION: 12

The gravitational field in a region is given by . The change in the gravitational potential energy of a particle of mass 2 kg when it is taken from the origin to a point (7m, –3 m) is :

Solution:

Energy = 1 × 2 = 2J

QUESTION: 13

Match **List-I** (Event) with **List-II** (Order of the time interval for happening of the event) and select the correct option from the options given below the lists.

Solution:

QUESTION: 14

Match **List-I** (Experiment performed ) with **List-II **(Phenomena discovered/ associated) and select the correct option from the options given below the lists :

Solution:

(a) Davisson - germar give experimental verification for wave nature of electron.

(b) Millikna's formed experiment about change of an electron

(c) Rutherford performed gold foil experiment and found the exisitance of nucleus.

(d) Franck - Hertz gives information about quantisation of energy level.

QUESTION: 15

A heavy box is to be dragged along a rough horizontal floor. To do so, person A pushes it at an angle 30° from the horizontal and requires a minimum force F_{A}, while person B pulls the box at an angle 60° from the horizontal and needs minimum force F_{B}. If the coefficient of friction between the box and the floor is , the ratio is :

Solution:

QUESTION: 16

A gas is compressed from a volume of 2 m^{3} to a volume of 1m^{3} at a constant pressure of 100 N/m^{2}. Then it is heated at constant volume by supplying 150 J of energy. As a result, the internal energy of the gas :

Solution:

Case1 Fcos30 = (mg + F_{A}sin 30)µ

Case2 FB cos 60 = (mg – f sin 60) µ

Dividing (1) by (2) we get

QUESTION: 17

A particle is released on a vertical smooth semicircular track from point X so that OX makes angle θ from the vertical (see figure). The normal reaction of the track on the particle vanishes at point Y where OY makes angle φ with the horizontal. Then :

Solution:

QUESTION: 18

In the diagram shown, the difference in the two tubes of the manometer is 5 cm, the cross-section of the tube at A and B is 6 mm^{2} and 10 mm^{2} respectively. The rate at which water flows through the tube is (g = 10 ms^{–2})

Solution:

QUESTION: 19

Consider a cylinder of mass M resting on a rough horizontal rug that is pulled out from under it with acceleration 'a' perpendicular to the axis of the cylinder. What is F_{friction} at point P ? It is assumed that the cylinder does not slip.

Solution:

Ma = f

QUESTION: 20

A large number of liquid drops each of radius r coalesce to from a single drop of radius R. The energy released in the process is converted into kinetic energy of the big drop so formed. The speed of the big drop is (given surface tension of liquid T, density r)

Solution:

QUESTION: 21

The gap between the plates of a parallel plate capacitor of area A and distance between plates d, is filled with a dielectric whose permittivity varies linearly from at one plate toat the other. The capacitance of capacitor is :

Solution:

QUESTION: 22

A gas molecule of mass M at the surface of the Earth has kinetic energy equivalent to 0°C. If it were to go up straight without colliding with any other molecules, how high it would rise? Assume that the height attained is much less than radius of the earth, (kB is Boltzmann constant)

Solution:

QUESTION: 23

The electric field in a region of space is given by, The flux of this field through a circular surface of radius 0.02 m parallel to the Y-Z plane is nearly

Solution:

QUESTION: 24

A ball of mass 160 g is thrown up at an angle of 60° to the horizontal at a speed of 10 ms^{–1}. The angular momentum of the ball at the highest point of the trajectory with respect to the point from which the ball is thrown is nearly (g = 10 ms^{–2})

Solution:

QUESTION: 25

In an experiment for determining the gravitational acceleration g of a place with the help of a simple pendulum, the measured time period square is plotted against the string length of the pendulum in the figure.

Q. What is the value of g at the place?

Solution:

g = π^{2} = 9.87

QUESTION: 26

An example of a perfect diamagnet is a superconductor. This implies that when a superconductor is put in a magnetic field of intensity B, the magnetic field Bs inside the superconductor will be such that :

Solution:

QUESTION: 27

The total length of a sonometer wire between fixed ends is 110 cm. Two bridges are placed to divide the length of wire in ratio 6 : 3 : 2. The tension in the wire is 400 N and the mass per unit length is 0.01 kg/m. What is the minimum common frequency with which three parts can vibrate?

Solution:

QUESTION: 28

A black coloured solid sphere of radius R and mass M is inside a cavity with vacuum inside. The walls of the cavity are maintained at temperature T_{0}. The initial temperature of the sphere is 3T_{0}. If the specific heat of the material of the sphere varies as αT^{3} per unit mass with the temperature T of the sphere, where α is a constant, then the time taken for the sphere to cool down to temperature 2T_{0} will be (σ is Stefan Boltzmann constant)

Solution:

QUESTION: 29

Figure shows a circular area of radius R where a uniform magnetic field is going into the plane of paper and increasing in magnitude at a constant rate. In that case, which of the following graphs, drawn schematically, correctly shows the variation of the induced electric field E(r)?

Solution:

B = B_{0}t

r > R

QUESTION: 30

The diameter of the objective lens of microscope makes an angle β at the focus of the microscope. Further, the medium between the object and the lens is an oil of refractive index n. Then the resolving power of the microscope.

Solution:

QUESTION: 31

For an ideal solution of two components A and B, which of the following is true?

Solution:

QUESTION: 32

Choose the correct statement with respect to the vapour pressure of a liquid among the following-:

Solution:

The reason behind helical structure of DNA is Hydrogen bonding.

QUESTION: 33

Which of these statements is not true?

Solution:

QUESTION: 34

Nickel(Z = 28) combines with a uninegative monodentate ligand to form a dia magnetic complex [NiL_{4}]^{2–}. The hybridisation involved and the number of unpaired electrons present in the complex are respectively :

Solution:

QUESTION: 35

Zirconium phosphate [Zr_{3}(PO_{4})_{4}] dissociates into three zirconium cations of charge +4 and four phosphate anions of charge –3. If molar solubility of zirconium phosphate is denoted by S and its solubility product by K_{sp} then which of the following relationship between S and K_{sp} is correct ?

Solution:

QUESTION: 36

For the reaction 3A + 2B → C + D the differential rate law can be written as

Solution:

QUESTION: 37

Which one of the following molecules is paramagnetic?

Solution:

QUESTION: 38

Ionization energy of gaseous Na atoms is 495.5 kjmol^{–1}. The lowest possible frequency of light that ionizes a sodium atom is (h = 6.626 × 10^{–34} Js, N_{A }= 6.022 × 10^{23} mol^{–1})

Solution:

v = 1.24 × 10^{15} sec^{–1}

QUESTION: 39

The major product formed when 1,1,1 - trichloro - propane is treated with aqueous potassium hydroxide is :

Solution:

QUESTION: 40

The final product formed when Methyl amine is treated with NaNO_{2} and HCI is :

Solution:

CH_{3}–NH_{2} + HNO_{2} → CH_{3}–OH

it is third order reaction.

QUESTION: 41

Which one of the following has largest ionic radius ?

Solution:

QUESTION: 42

Which one of the following is an example of thermosetting polymers?

Solution:

Bakelite becomes find on heating and the process is irreversible

QUESTION: 43

Consider the reaction

Q. Which of the following statements is correct?

Solution:

QUESTION: 44

The correct IUPAC name of the following compound is:

Solution:

QUESTION: 45

Which one of the following ores is known as Malachite

Solution:

QUESTION: 46

For the decomposition of the compound, represented as

the K_{P }= 2.9 × l0^{–5} atm^{3}.

If the reaction is started with 1 mol of the compound, the total pressure at equilibrium would be :

Solution:

QUESTION: 47

The reason for double helical structure of DNA is the operation of :

Solution:

QUESTION: 48

Amongst LiCl , RbCl , BeCl_{2} and MgCl_{2} the compounds with the greatest and the least ionic character, respectively are:

Solution:

QUESTION: 49

Which one of the following compounds will not be soluble in sodium bicarbonate?

Solution:

Bicarbonates are weak bases can 't react with wenler acid

QUESTION: 50

Among the following organic acids, the acid present in rancid butter is:

Solution:

QUESTION: 51

The total number of octahedral void(s) per atom present in a cubic close packed structure is :-

Solution:

CCP no. of octrahedral void =

per atom octrahedral void is 1.

QUESTION: 52

The observed osmotic pressure for a 0.10 M solution of Fe(NH_{4})_{2}(SO_{4})_{2} at 25°C is 10.8 atm.

The expected and experimental (observed) values of Van't Hoff factor (i) will be respectively : (R= 0.082 L atm k^{–} mol^{–1})

Solution:

π = CRTi

i = 4.42 (observed)

QUESTION: 53

Sulphur dioxide and oxygen were allowed to diffuse through a porous partition. 20 dm^{3} of SO_{2} diffuses through the porous partition in 60 seconds. The volume of O_{2} in dm^{3} which diffuses under the similar condition in 30 seconds will be (atomic mass of sulphur = 32u)

Solution:

QUESTION: 54

An octahedral complex with molecular composition M.5NH_{3}.Cl.SO_{4} has two isomers, A and B. The solution of A gives a white precipitate with AgNO_{3} solution and the solution of B gives white precipitate with BaCl_{2} solution.

The type of isomerism exhibited by the complex is :

Solution:

QUESTION: 55

In a set of reactions p - nitrotoluene yielded a product E

The product E would be :-

Solution:

QUESTION: 56

How many electrons are involved in the following redox reaction ?

Solution:

QUESTION: 57

Amongst the following, identify the species with an atom in +6 oxidation state :

Solution:

*Multiple options can be correct

QUESTION: 58

Example of a three-dimensional silicate is :

Solution:

QUESTION: 59

Williamson synthesis of ether is an example of

Solution:

Nucleophilic substitution

QUESTION: 60

Which one of the following substituents at para-position is most effective in stabilizing the phenoxide ion?

Solution:

is an electron withdrawing group which stabilises the anion.

QUESTION: 61

Let, M and σ^{2} be respectively the mean, mode and variance of n observations x_{1}, x_{2}, ...., x_{n} and di = - xi - a, i = 1, 2, ..., n, where a is any number.

Statement I : Variance of d_{1}, d_{2}, ..., d_{n} is σ^{2}.

Statement II : Mean and mode of d_{1}, d_{2}, ..., d_{n} are –– a and – M –a, respectively

Solution:

Mean & mode depends upon change in origin and scale so mean & mode of –x; – a is –x – a and – M – a

but variance never depends upon change in origin & it is always positive so veriance if – x – a is same i.e. σ^{2}

QUESTION: 62

Let function F be defined as then the value of the integral , where a > 0, is:-

Solution:

t + a = p , dt = dp

QUESTION: 63

If the function is continuous at x = π, then k equals:-

Solution:

x = π - h

QUESTION: 64

For all complex numbers z of the form 1 + iα ,α ∈ R, If z^{2} = x + iy, then:-

Solution:

QUESTION: 65

If the volume of a spherical ball is increasing at the rate of 4π cc/sec, then the rate of increase of its radius (in cm/sec), when the volume is 288π cc, is :-

Solution:

v = 288π

2 × 2 × 2 × 2 × 2 × 3 × 3 =

r = 6

QUESTION: 66

The equation where x is real, has:-

Solution:

No solution [∵ both values are not satisfied]

QUESTION: 67

The tangent at an extremity (in the first quadrant) of latus rectum of the hyperbola , meets x -axis and y-axis at A and B respectively. Then (OA)^{2} – (OB)^{2} , where O is the origin, equals:-

Solution:

Eq of tangent

3x – 2y = 4

OA^{2} – OB^{2} = 16/20 = -4 =

QUESTION: 68

A chord is drawn through the focus of the parabola y^{2} = 6x such that its distance from the vertex of this parabola is then its slope can be :-

Solution:

Eq of chord

y – 0 = m (x – 3/2)

QUESTION: 69

Let f : R → R be defined by f(x) = then f is:-

Solution:

QUESTION: 70

The circumcentre of a triangle lies at the origin and its centroid is the mid point of the line segment joining the points (a^{2} + 1, a^{2} + 1) and (2a, –2a), a ≠ 0. Then for any a, the orthocentre of this triangle lies on the line :

Solution:

QUESTION: 71

Let f(n) = , where [n] denotes the greatest integer less than or equal to n. Then is equal to :-

Solution:

= 11 (5 × 28 – 23) + 112

= 11 × 117 + 112

= 1287 + 112

= 1399

QUESTION: 72

If and then the magnitude of the projection of on :-

Solution:

QUESTION: 73

The equation of the circle described on the chord 3x + y + 5 = 0 of the circle x^{2} + y^{2} = 16 as diameter is:-

Solution:

QUESTION: 74

The principal value of tan^{–1 }is:-

Solution:

tan^{–1}[cot (11π - π/4)]

= tan^{-1} [-cot π/4]

= -tan^{-1} (cot π/4)

= - tan^{-1} (1)

= – π/4

QUESTION: 75

Let A and E be any two events with positive probabilities :

Statement - 1 : P(E/A) ≥ P(A/E)P(E)

Statement - 2 : P(A/E) ≥ P(A∩E).

Solution:

L.H.S.

R.H.S.

So,

St. - I is true

St. - 2

So

st - 2 is true

QUESTION: 76

If a line L is perpendicular to the line 5x – y = 1, and the area of the triangle formed by the line L and the coordinate axes is 5, then the distance of line L from the line x + 5y = 0 is :-

Solution:

Equation = of line L is x + 5y + c = 0

⇒ c = ± 5√2

∴ Eq of line L is

x + 5y ± 5√2 = 0

Its distance from x + 5y = 0 is

QUESTION: 77

Let A and B be any two 3 × 3 matrices. If A is symmetric and B is skewsymmetric, then the matrix AB – BA is :

Solution:

So AB – BA is symmetric

QUESTION: 78

If the angle between the line 2(x + 1) = y = z + 4 and the plane is π/6, then the value of λ is:-

Solution:

QUESTION: 79

If and y (0) = 1, then y(π) is equal to :-

Solution:

QUESTION: 80

Two women and some men participated in a chess tournament in which every participant played two games with each of the other participants. If the number of games that the men played between themselves exceeds the number of games that the men played with the women by 66, then the number of men who participated in the tournament lies in the interval :

Solution:

Let n men participated

n^{2} – 5n – 66 = 0

n = 11, (not possible)

which lies in [10, 12]

QUESTION: 81

The number of terms in an A.P. is even; the sum of the odd terms in it is 24 and that the even terms is 30. If the last term exceeds the first term by , then the number of terms in the A.P. is :

Solution:

Let no. of terms = 2n

sum of even terms

....... (i)

sum of odd terms

........ (ii)

....... (iii)

eq. (i)....eq. (ii)

........(iv)

........... (v)

n = 4 so no. of terms = 8

QUESTION: 82

If Δ_{r} = then the value of :-

Solution:

=

R_{1} and R_{3 }are identical so

is independent of a, and n

QUESTION: 83

If non-zero real numbers b and c are such that min f(x) > max g(x), where

f (x) = x^{2} + 2bx + 2c^{2} and

g(x) = – x^{2} – 2cx + b^{2} (x ∈ R) ; then lies in the interval:-

Solution:

QUESTION: 84

Equation of the line of the shortest distance between the lines and is:

Solution:

QUESTION: 85

The coefficient of x 10^{12} in the expansion of (where n ≤ 22 is any positive integer), is:-

Solution:

let x^{1012} occurs in general terms

0 ≤ r_{1}, r_{2} r_{3} ≤ 10

when

r_{1} + r_{2} + r_{3} = 10

nr_{2} + 253r_{3} = 1012

only one case possible

r_{1} = 6, r_{2} = 0, r_{3} = 4

so coeff = = ^{10}C_{4}

QUESTION: 86

The contrapositive of the statement "if I am not feeling well, then I will go to the doctor" is :

Solution:

Let p: I m not feeling well

q: I will go to doctor

Given statement :- p → q

its contrapositive ~ q → ~ p

∵ If I will not go to the doctor then i am feeling well.

QUESTION: 87

The function f(x) = |sin 4x| + |cos 2x|, is a periodic function with period :-

Solution:

f(x) = |sin 4x| + |cos 2x|

Period = π/2

QUESTION: 88

Let f : R → R be a function such that for all x ∈ R. Then, at x = 0 , f is:

Solution:

≤ 0

= 0

Conti at x = 0

L.H.D. = R.H.D.

QUESTION: 89

The area of the region above the x-axis bounded by the curve y = tan x, 0 ≤ x ≤ and the tangent to the curve at x = is :-

Solution:

tangent at point

y – 1 = 2 (x – π/4) on x-axis

Area =

QUESTION: 90

If m is a non - zero number and = f (x) + c, then f(x) is:-

Solution:

put

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