Only One Option Correct Type Each question has four choices (A), (B), (C) and (D) out of which ONLY ONE is correct.
A metallic rod of length L is rotated with an angular speed of ω normal to a uniform magnetic field B about an axis passing through one end of rod as shown in figure. The induced emf will be :
.
Question No. 2
Only One Option Correct Type Each question has four choices (A), (B), (C) and (D) out of which ONLY ONE is correct.
The logic gate equivalent to the given circuit diagram is :
Question No. 3
Only One Option Correct Type Each question has four choices (A), (B), (C) and (D) out of which ONLY ONE is correct.
The frequency (ν) of an oscillating liquid drop may depend upon radius (r) of the drop, density (ρ) of liquid and the surface tension (s) of the liquid as: ν=raρbsc. The values of a,b and c respectively are
Question No. 4
Only One Option Correct Type Each question has four choices (A), (B), (C) and (D) out of which ONLY ONE is correct.
Given below are two statements:
Statement I: Acceleration due to earth's gravity decreases as you go 'up' or 'down' from earth's surface.
Statement II: Acceleration due to earth's gravity is same at a height 'h' and depth 'd' from earth's surface, if h=d.
In the light of above statements, choose the most appropriate answer form the options given below
Question No. 5
Only One Option Correct Type Each question has four choices (A), (B), (C) and (D) out of which ONLY ONE is correct.
The electric field and magnetic field components of an electromagnetic wave going through vacuum is described by
Ex=E0sin(kz−ωt)
By=B0sin(kz−ωt)
Then the correct relation between E0 and B0 is given by
Question No. 6
Only One Option Correct Type Each question has four choices (A), (B), (C) and (D) out of which ONLY ONE is correct.
The velocity-time graph of a body moving in a straight line is shown in figure.
The ratio of displacement and distance travelled by the body in time 0 to 10s is
Question No. 7
Only One Option Correct Type Each question has four choices (A), (B), (C) and (D) out of which ONLY ONE is correct.
A tuning fork vibrates with frequency 256Hz and gives one best per second with the third normal mode of vibration of an open pipe. What is the length of the pipe? (Speed of sound of air is 340ms−1 )
Question No. 8
Only One Option Correct Type Each question has four choices (A), (B), (C) and (D) out of which ONLY ONE is correct.
Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R
Assertion A: A pendulum clock when taken to Mount Everest becomes fast.
Reason R: The value of g (acceleration due to gravity) is less at Mount Everest than its value on the surface of earth.
In the light of the above statements, choose the most appropriate answer from the options given below
Question No. 9
Only One Option Correct Type Each question has four choices (A), (B), (C) and (D) out of which ONLY ONE is correct.
If the distance of the earth from Sun is 1.5×106km, then the distance of an imaginary planet from Sun, if its period of revolution is 2.83 years is:
Question No. 10
Only One Option Correct Type Each question has four choices (A), (B), (C) and (D) out of which ONLY ONE is correct.
An α particle, a proton and an electron have the same kinetic energy. Which one of the following is correct in case of their de-Broglie wavelength:
Question No. 11
Only One Option Correct Type Each question has four choices (A), (B), (C) and (D) out of which ONLY ONE is correct.
The electric potential at the centre of two concentric half rings of radii R1 and R2, having same linear charge density λ is
.
Question No. 12
Only One Option Correct Type Each question has four choices (A), (B), (C) and (D) out of which ONLY ONE is correct.
If two vectors P⃗ =iˆ+2mjˆ+mkˆ and Q⃗ =4iˆ−2jˆ+mkˆ are perpendicular to each other. Then, the value of m will be
Question No. 13
Only One Option Correct Type Each question has four choices (A), (B), (C) and (D) out of which ONLY ONE is correct.
A long solenoid is formed by winding 70 turns cm−1 . If 2.0A current flows, then the magnetic field produced inside the solenoid is ______________.
(µ0=4π×10–7TmA–1)
Question No. 14
Only One Option Correct Type Each question has four choices (A), (B), (C) and (D) out of which ONLY ONE is correct.
When a beam of white light is allowed to pass through convex lens parallel to principal axis, the different colours of light converge at different point on the principle axis after refraction. This is called :
Question No. 15
Only One Option Correct Type Each question has four choices (A), (B), (C) and (D) out of which ONLY ONE is correct.
In an Isothermal change, the change in pressure and volume of a gas can be represented for three different temperature; T3>T2>T1 as:
Question No. 16
Only One Option Correct Type Each question has four choices (A), (B), (C) and (D) out of which ONLY ONE is correct.
Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R
Assertion (A) : Steel is used in the construction of buildings and bridges. Reason (R) : Steel is more elastic and its elastic limit is high.
In the light of above statements, choose the most appropriate answer from the options given below
Question No. 17
Only One Option Correct Type Each question has four choices (A), (B), (C) and (D) out of which ONLY ONE is correct.
A photon is emitted in transition from n=4ton=1 level in hydrogen atom. The corresponding wavelength for this transition is (given, h=4×10−15eVs)
Question No. 18
Only One Option Correct Type Each question has four choices (A), (B), (C) and (D) out of which ONLY ONE is correct.
A cell of emf 90V is connected across series combination of two resistors each of 100Ω resistance. A voltmeter of resistance 400Ω is used to measure the potential difference across each resistor. The reading of the voltmeter will be:
Question No. 19
Only One Option Correct Type Each question has four choices (A), (B), (C) and (D) out of which ONLY ONE is correct.
Let γ1 be the ratio of molar specific heat at constant pressure and molar specific heat at constant volume of a monoatomic gas and γ2 be the similar ratio of diatomic gas. Considering the diatomic gas molecule as a rigid rotator, the ratio γ1γ2 is:
Question No. 20
Only One Option Correct Type Each question has four choices (A), (B), (C) and (D) out of which ONLY ONE is correct.
A body of mass 200g is tied to a spring of spring constant 12.5Nm−1, while the other end of spring is fixed at point O. If the body moves about O in a circular path on a smooth horizontal surface with constant angular speed 5rads−1, then the ratio of extension in the spring to its natural length will be :
Physics Numerical (Maximum Marks: 20)
Question No. 1
Numerical Type The answer has to be filled into the input box provided below.
The energy released per fission of nucleus of X240 is 200MeV. The energy released if all the atoms in 120g of pure X240 undergo fission is _____×1025MeV.
(Given NA=6×1023)
Question No. 2
Numerical Type The answer has to be filled into the input box provided below.
A body of mass 1kg begins to move under the action of a time dependent force F⃗ =(tiˆ+3t2jˆ)N, where iˆ and jˆ are the unit vectors along x and y axis. The power developed by above force, at the time t=2s, will be _______W.
Question No. 3
Numerical Type The answer has to be filled into the input box provided below.
A parallel plate capacitor with air between the plate has a capacitance of 15pF. The separation between the plate becomes twice and the space between them is filled with a medium of dielectric constant 3.5. Then the capacitance becomes x4pF. The value of x is____.
Question No. 4
Numerical Type The answer has to be filled into the input box provided below.
Three identical resistors with resistance R=12Ω and two identical inductors with sell inductance L=5mH are connected to an ideal battery with emf of 12V as shown in figure. The current through the battery long after the switch has been closed will be________A.
Question No. 5
Numerical Type The answer has to be filled into the input box provided below.
A single turn current loop in the shape of a right angle triangle with sides 5cm,12cm,13cm is carrying a current of 2A. The loop is in a uniform magnetic field of magnitude 0.75T whose direction is parallel to the current in the 13cm side of the loop. The magnitude of the magnetic force on the 5cm side will be x130N. The value of x is _______.
Question No. 6
Numerical Type The answer has to be filled into the input box provided below.
A spherical ball of radius 1mm and density 10.5gcc−1 is dropped in glycerine of coefficient of viscosity 9.8 poise and density 1.5gcc−1. Viscous force on the ball when it attains constant velocity is 3696×10−xN. The value of x is
(Given, g=9.8ms−2andπ=227)
Question No. 7
Numerical Type The answer has to be filled into the input box provided below.
A convex lens of refractive index 1.5 and focal length 18cm in air is immersed in water. The change in focal length of the lens will be_____cm.
(Given refractive index of water=43)
Question No. 8
Numerical Type The answer has to be filled into the input box provided below.
If a copper wire is stretched to increase its length by 20%. The percentage increase in resistance of the wire is _____%.
Question No. 9
Numerical Type The answer has to be filled into the input box provided below.
A mass m attached to free end of a spring executes SHM with a period of 1s. If the mass is increased by 3kg the period of oscillation increases by one second, the value of mass m is ________ kg.
Question No. 10
Numerical Type The answer has to be filled into the input box provided below.
A uniform solid cylinder with radius R and length L has moment of inertia I1, about the axis of cylinder. A concentric solid cylinder of radius R′=R2 and length L′=L2 is carved out of the original cylinder. If I2 is the moment of inertia of the carved out portion of the cylinder then I1I2= __________.
(Both I1 and I2 are about the axis of the cylinder)
Chemistry Single Correct (Maximum Marks: 80)
Question No. 1
Only One Option Correct Type Each question has four choices (A), (B), (C) and (D) out of which ONLY ONE is correct.
Given below are two statements :
Statement I :
under Clemmensen reduction conditions will give
Statement II :
under Wolff-Kishner reduction condition will give
In the light of the above statements, choose the correct answer from the options given below :
Question No. 2
Only One Option Correct Type Each question has four choices (A), (B), (C) and (D) out of which ONLY ONE is correct.
Which one amongst the following are good oxidising agents?
(a) Sm2+
(b) Ce2+
(c) Ce4+
(d) Tb4+
Choose the most appropriate answer from the options given below :
Question No. 3
Only One Option Correct Type Each question has four choices (A), (B), (C) and (D) out of which ONLY ONE is correct.
Given below are two statements, one is labelled as
Assertion A and the other is labelled as Reason R.
Assertion A : Benzene is more stable than hypothetical cyclohexatriene.
Reason R : The delocalized π electron cloud is attracted more strongly by nuclei of carbon atoms.
In the light of the above statements, choose the correct answer from the options given below:
Question No. 4
Only One Option Correct Type Each question has four choices (A), (B), (C) and (D) out of which ONLY ONE is correct.
Which of the following cannot be explained by crystal field theory?
Question No. 5
Only One Option Correct Type Each question has four choices (A), (B), (C) and (D) out of which ONLY ONE is correct.
Find out the major products from the following reactions.
Question No. 6
Only One Option Correct Type Each question has four choices (A), (B), (C) and (D) out of which ONLY ONE is correct.
lodoform can be prepared from all except :
Question No. 7
Only One Option Correct Type Each question has four choices (A), (B), (C) and (D) out of which ONLY ONE is correct.
The catenation tendency of C,Si and Ge is in the order Ge<Si<C. The bond energies (in kJmol−1 ) of C−C,Si−Si and Ge−Ge bonds are respectively ;
Question No. 8
Only One Option Correct Type Each question has four choices (A), (B), (C) and (D) out of which ONLY ONE is correct.
What is the number of unpaired electron(s) in the highest occupied molecular orbital of the following species : N2,N+2,O2,O+2 ?
Question No. 9
Only One Option Correct Type Each question has four choices (A), (B), (C) and (D) out of which ONLY ONE is correct.
Given below are two statements :
Statement I : Pure Aniline and other arylamines are usually colourless.
Statement II : Arylamines get coloured on storage due to atmospheric reduction.
In the light of the above statements, choose the most appropriate answer from the options given below :
Question No. 10
Only One Option Correct Type Each question has four choices (A), (B), (C) and (D) out of which ONLY ONE is correct.
Choose the correct colour of the product for the following reaction.
Question No. 11
Only One Option Correct Type Each question has four choices (A), (B), (C) and (D) out of which ONLY ONE is correct.
Which will undergo deprotonation most readily in basic medium?
Question No. 12
Only One Option Correct Type Each question has four choices (A), (B), (C) and (D) out of which ONLY ONE is correct.
K2Cr2O7 paper acidified with dilute H2SO4 turns green when exposed to
Question No. 13
Only One Option Correct Type Each question has four choices (A), (B), (C) and (D) out of which ONLY ONE is correct.
The hybridization and magnetic behaviour of cobalt ion in [Co(NH3)6]3+ complex, respectively is
Question No. 14
Only One Option Correct Type Each question has four choices (A), (B), (C) and (D) out of which ONLY ONE is correct.
Which of the following forms stable +4 oxidation state?
Question No. 15
Only One Option Correct Type Each question has four choices (A), (B), (C) and (D) out of which ONLY ONE is correct.
Glycosidic linkage is actually an :
Question No. 16
Only One Option Correct Type Each question has four choices (A), (B), (C) and (D) out of which ONLY ONE is correct.
The ratio of masses of oxygen and nitrogen in a particular gaseous mixture is 1 : 4. The ratio of number of their molecules is:
Question No. 17
Only One Option Correct Type Each question has four choices (A), (B), (C) and (D) out of which ONLY ONE is correct.
A student has studied the decomposition of a gas AB3 at 25°C. He obtained the following data
p(mmHg)
50
100
200
400
Relative t12(s)
4
2
1
0.5
The order of the reaction is
Question No. 18
Only One Option Correct Type Each question has four choices (A), (B), (C) and (D) out of which ONLY ONE is correct.
Which one of the following molecules is expected to exhibit paramagnetic behaviour?
Question No. 19
Only One Option Correct Type Each question has four choices (A), (B), (C) and (D) out of which ONLY ONE is correct.
Choose the correct representation of conductometric titration of benzoic acid vs sodium hydroxide.
Question No. 20
Only One Option Correct Type Each question has four choices (A), (B), (C) and (D) out of which ONLY ONE is correct.
Given : XNa2HAsO3+YNaBrO3+ZHCl→NaBr+H3AsO4+NaCl The values of X,Y and Z in the above redox reaction are respectively :
Chemistry Numerical (Maximum Marks: 20)
Question No. 1
Numerical Type The answer has to be filled into the input box provided below.
One mole of an ideal monoatomic gas is subjected to changes as shown in the graph. The magnitude of the work done (by the system or on the system) is _______ J (nearest integer)
Given : log 2 = 0.3, ln 10 = 2.3
Question No. 2
Numerical Type The answer has to be filled into the input box provided below.
Maximum number of isomeric monochloro derivatives which can be obtained from 2,2,5,5- tetramethylhexane by chlorination is _________
Question No. 3
Numerical Type The answer has to be filled into the input box provided below.
The rate constant of a zero order reaction is 2.0×10−2molL−1s−1. If the concentration of the reactant after 25 seconds is 0.5M. What is the initial concentration?
Question No. 4
Numerical Type The answer has to be filled into the input box provided below.
Following figure shows spectrum of an ideal black body at four different temperatures. The number of correct statement/s from the following is _______.
A. T4 > T3 > T2 > T1 B. The black body consists of particles performing simple harmonic motion. C. The peak of the spectrum shifts to shorter wavelength as temperature increases. D. not equal to constant E. The given spectrum could be explained using quantisation of energy
Question No. 5
Numerical Type The answer has to be filled into the input box provided below.
Sum of π-bonds present in peroxodisulphuric acid and pyrosulphuric acid is
Question No. 6
Numerical Type The answer has to be filled into the input box provided below.
The Total pressure observed by mixing two liquid AandB is 350mmHg when their mole fractions are 0.7and0.3 respectively. The Total pressure becomes410mmHg if the mole fractions are changed to0.2and0.8 respectively for AandB. The vapour pressure of pure A is ______ mmHg. (Nearest integer) Consider the liquids and solutions behave ideally
Question No. 7
Numerical Type The answer has to be filled into the input box provided below.
The number of units, which are used to express concentration of solutions from the following is _________.
Numerical Type The answer has to be filled into the input box provided below.
Total number of tripeptides possible by mixing of valine and proline is ________ .
Question No. 9
Numerical Type The answer has to be filled into the input box provided below.
A current of 10.0A flows for 2.00h through an electrolytic cell containing a molten salt of metal X. This results in the decomposition of 0.250mol of metal X at the cathode. The oxidation state of X in the molten salt is:
(F=96,500C)
Question No. 10
Numerical Type The answer has to be filled into the input box provided below.
If the pKa of lactic acid is 5, then the pH of 0.005M calcium lactate solution at 25°C is __________ ×10–1 (Nearest integer)
Mathematics Single Correct (Maximum Marks: 80)
Question No. 1
Only One Option Correct Type Each question has four choices (A), (B), (C) and (D) out of which ONLY ONE is correct.
Let y=y(x) be the solution of the differential equation (x2–3y2)dx+3xydy=0,y(1)=1. Then 6y2(e) is equal to
Question No. 2
Only One Option Correct Type Each question has four choices (A), (B), (C) and (D) out of which ONLY ONE is correct.
The value of (1+sin2π9+icos2π91+sin2π9−icos2π9)3 is
Question No. 3
Only One Option Correct Type Each question has four choices (A), (B), (C) and (D) out of which ONLY ONE is correct.
The set of values of a for which limx→a([x−5]−[2x+2])=0, where, [ζ] denotes the greatest integer less than or equal to ζ is equal to
Question No. 4
Only One Option Correct Type Each question has four choices (A), (B), (C) and (D) out of which ONLY ONE is correct.
If f(x)=22x22x+2, x∈R, then f(12023)+f(22023)+f(32023).........f(20222023) is equal to
Question No. 5
Only One Option Correct Type Each question has four choices (A), (B), (C) and (D) out of which ONLY ONE is correct.
Let α⃗ =4iˆ+3jˆ+5kˆ and β⃗ =iˆ+2jˆ−4kˆ. Let β⃗ 1 be parallel to α⃗ and β⃗ 2 be perpendicular to α⃗ . If β⃗ =β⃗ 1+β⃗ 2, then the value of 5β⃗ 2⋅(iˆ+jˆ+kˆ) is
Question No. 6
Only One Option Correct Type Each question has four choices (A), (B), (C) and (D) out of which ONLY ONE is correct.
The number of real solutions of the equation 3(x2+1x2)−2(x+1x)+5=0, is
Question No. 7
Only One Option Correct Type Each question has four choices (A), (B), (C) and (D) out of which ONLY ONE is correct.
ABC is a triangle in a plane with vertices A(2,3,5),B(−1,3,2) and C(λ,5,μ) . If the median through A is equally inclined to the coordinate axes, then the value of (λ3+μ3+5) is
Question No. 8
Only One Option Correct Type Each question has four choices (A), (B), (C) and (D) out of which ONLY ONE is correct.
Let f(x) be a function such that f(x+y)=f(x)⋅f(y) for all x,y∈N, If f(1)=3 and ∑nk=1f(k)=3279, then the value of n is
Question No. 9
Only One Option Correct Type Each question has four choices (A), (B), (C) and (D) out of which ONLY ONE is correct.
The number of square matrices of order 5 with entries from the set {0,1}, such that the sum of all the elements in each row is 1 and the sum of all the elements in each column is also 1, is
Question No. 10
Only One Option Correct Type Each question has four choices (A), (B), (C) and (D) out of which ONLY ONE is correct.
If (27)999 is divided by 7, then the remainder is
Question No. 11
Only One Option Correct Type Each question has four choices (A), (B), (C) and (D) out of which ONLY ONE is correct.
If f(x)=x3−x2f′(1)+xf′′(2)−f'''(3), x∈R, then
Question No. 12
Only One Option Correct Type Each question has four choices (A), (B), (C) and (D) out of which ONLY ONE is correct.
The number of integers, greater than 7000 that can be formed, using the digits 3,5,6,7,8 without repetition is
Question No. 13
Only One Option Correct Type Each question has four choices (A), (B), (C) and (D) out of which ONLY ONE is correct.
The locus of the middle points of the chords of the circle C1:(x−4)2+(y−5)2=4 which subtend an angle θi at the centre of the circle Ci, is a circle of radius ri. If θ1=π3, θ3=2π3 and r12=r22+r32, then θ2 is equal to
Question No. 14
Only One Option Correct Type Each question has four choices (A), (B), (C) and (D) out of which ONLY ONE is correct.
Let A be a 3×3 matrix such that |adj(adj(adj.A))|=124. Then ∣∣A−1adjA∣∣ is equal to
Question No. 15
Only One Option Correct Type Each question has four choices (A), (B), (C) and (D) out of which ONLY ONE is correct.
If a,b,c are sides of a scalene triangle, then the value of ∣∣∣∣abcbcacab∣∣∣∣ is :
Question No. 16
Only One Option Correct Type Each question has four choices (A), (B), (C) and (D) out of which ONLY ONE is correct.
The coefficient of x10 in the expansion of (1+x)2(1+x2)3(1+x3)4 is equal to
Question No. 17
Only One Option Correct Type Each question has four choices (A), (B), (C) and (D) out of which ONLY ONE is correct.
A hyperbola whose transverse axis is along the major axis of the conic x23+y24=4 and has vertices at the foci of the conic. If the eccentricity of the hyperbola is 32, then which of the following points does not lie on the hyperbola ?
Question No. 18
Only One Option Correct Type Each question has four choices (A), (B), (C) and (D) out of which ONLY ONE is correct.
A variable circle passes through the fixed point A(p,q) and touches x-axis. The locus of the other end of the diameter through A is
Question No. 19
Only One Option Correct Type Each question has four choices (A), (B), (C) and (D) out of which ONLY ONE is correct.
Let the six numbers a1,a2,...,a6 be in A.P. and a1+a3=10.If the mean of these six numbers is 192 and their variance is σ2, then 8σ2 is equal to
Question No. 20
Only One Option Correct Type Each question has four choices (A), (B), (C) and (D) out of which ONLY ONE is correct.
∫33√432√4489−4x2√dx is equal to
Mathematics Numerical (Maximum Marks: 20)
Question No. 1
Numerical Type The answer has to be filled into the input box provided below.
Let x,y,z be positive real numbers such that x+y+z=12 and x3y4z5=(0.1)(600)3. Then x3+y3+z3 is equal to
Question No. 2
Numerical Type The answer has to be filled into the input box provided below.
Let he sum of the coefficient of first three terms in the expansion of (x−3x2)n;x=0,n∈N be 376. Then, the coefficient of x4 is equal to:
Question No. 3
Numerical Type The answer has to be filled into the input box provided below.
If the shortest distance between the lines x+6√2=y−6√3=z−6√4 and x−λ3=y−26√4=z+26√5 is 6, then square of sum of all possible values(s) of λ is
Question No. 4
Numerical Type The answer has to be filled into the input box provided below.
If the area of the region bounded by the curves y2−2y=−x and x+y=0 is A, then 8A=
Question No. 5
Numerical Type The answer has to be filled into the input box provided below.
Let fk(x)=1k(sinkx+coskx) where x∈R and k≥1. Then f4(x)−f6(x) equals M, find 1M.
Question No. 6
Numerical Type The answer has to be filled into the input box provided below.
The urns A,B and C contains 4 red, 6 black; 5 red, 5 black and λ red, 4 black balls respectively. One of the urns is selected at random and a ball is drawn. If the ball drawn is red and the probability that it is drawn from urn C is 0.4, then the square of length of the side of largest equilateral triangle, inscribed in the parabola y2=λx with one vertex at vertex of parabola is
Question No. 7
Numerical Type The answer has to be filled into the input box provided below.
Let a⃗ =iˆ+2jˆ+λkˆ, b⃗ =3iˆ−5jˆ−λkˆ, a⃗ ⋅c⃗ =7, 2(b⃗ ⋅c⃗ )+43=0, a⃗ ×c⃗ =b⃗ ×c⃗ , then a⃗ ⋅b⃗ is equal to
Question No. 8
Numerical Type The answer has to be filled into the input box provided below.
The equations of the sides AB,BC&CA of a triangle ABC are 2x+y=0, x+py=21a(a≠0) and x−y=3 respectively. Let P(2,a) be the centroid of the triangle ABC, then (BC)2 is equal to
Question No. 9
Numerical Type The answer has to be filled into the input box provided below.
The minimum number of elements that must be added to relation R={(a,b),(b,c),(b,d)} on the set {a,b,c,d}, so that it is an equivalence relation is
Question No. 10
Numerical Type The answer has to be filled into the input box provided below.
Let f be a differentiable function defined on [0,π2] such that f(x)>0 and f(x)+∫x0f(t)1−(loge(f(t)))2−−−−−−−−−−−−−√dt=e∀x∈[0,π2], then {6loge(f(π6))}2 is equal to
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