Q1
MATHS
Unit 2: Complex Numbers and Quadratic Equations
If $f(x)=\dfrac{\tan 1^\circ+\log_e(123)}{x\log_e(1234)-\tan 1^\circ}$, $x>0$, then the least value of $f(f(x))+f\!\left(f\!\left(\dfrac{4}{x}\right)\right)$ is
- B. 2
- C. 4
- D. 8
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Q9
MATHS
Unit 8: Integral Calculus
Let $f$ be a differentiable function such that $x^2 f(x)-x=4\int_0^x t f(t)\,dt$, $f(1)=\frac{2}{3}$. Then $18f(3)$ is equal to
- A. 150
- B. 160
- C. 180
- D. 210
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Q10
MATHS
Unit 9: Differential Equations
The slope of tangent at any point $(x,y)$ on a curve $y=y(x)$ is $\dfrac{x^2+y^2}{2xy}$, $x>0$. If $y(2)=0$, then a value of $y(8)$ is
- A. $4\sqrt{3}$
- B. $-4\sqrt{2}$
- C. $2\sqrt{3}$
- D. $-2\sqrt{3}$
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Q11
MATHS
Unit 10: Co-ordinate Geometry
Let the ellipse $E: x^2+9y^2=9$ intersect the positive $x$- and $y$-axes at the points $A$ and $B$ respectively. Let the major axis of $E$ be a diameter of the circle $C$. Let the line passing through $A$ and $B$ meet the circle $C$ at the point $P$. If the area of the triangle with vertices $A, P$ and the origin $O$ is $\frac{m}{n}$, where $m$ and $n$ are coprime, then $m-n$ is equal to
- A. 15
- B. 16
- C. 17
- D. 18
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Q12
MATHS
Unit 11: Three Dimensional Geometry
A line segment $AB$ of length $\lambda$ moves such that the points $A$ and $B$ remain on the periphery of a circle of radius $\lambda$. Then the locus of the point, that divides the line segment $AB$ in the ratio $2:3$, is a circle of radius
- A. $\frac{\sqrt{19}}{7}\lambda$
- B. $\frac{\sqrt{19}}{5}\lambda$
- C. $\frac{2}{3}\lambda$
- D. $\frac{3}{5}\lambda$
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Q13
MATHS
Unit 12: Vector Algebra
Let two vertices of a triangle $ABC$ be $(2,4,6)$ and $(0,-2,-5)$, and its centroid be $(2,1,-1)$. If the image of the third vertex in the plane $x+2y+4z=11$ is $(\alpha,\beta,\gamma)$, then $\alpha\beta+\beta\gamma+\gamma\alpha$ is equal to
- A. 70
- B. 72
- C. 74
- D. 76
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Q14
MATHS
Unit 11: Three Dimensional Geometry
Let $P$ be the point of intersection of the line $\dfrac{x+3}{3}=\dfrac{y+2}{1}=\dfrac{1-z}{2}$ and the plane $x+y+z=2$. If the distance of the point $P$ from the plane $3x-4y+12z=32$ is $q$, then $q$ and $2q$ are the roots of the equation
- A. $x^2+18x+72=0$
- B. $x^2-18x-72=0$
- C. $x^2+18x-72=0$
- D. $x^2-18x+72=0$
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Q15
MATHS
Unit 11: Three Dimensional Geometry
The shortest distance between the lines $\dfrac{x+2}{1}=\dfrac{y}{-2}=\dfrac{z-5}{2}$ and $\dfrac{x-4}{1}=\dfrac{y-1}{2}=\dfrac{z+3}{0}$ is
- A. 6
- B. 7
- C. 8
- D. 9
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Q16
MATHS
Unit 12: Vector Algebra
Let $O$ be the origin and the position vector of the point $P$ be $-\hat{i}-2\hat{j}+3\hat{k}$. If the position vectors of the points $A$, $B$ and $C$ are $-2\hat{i}+\hat{j}-3\hat{k}$, $2\hat{i}+4\hat{j}-2\hat{k}$ and $-4\hat{i}+2\hat{j}-\hat{k}$ respectively, then the projection of the vector $\overrightarrow{OP}$ on a vector perpendicular to the vectors $\overrightarrow{AB}$ and $\overrightarrow{AC}$ is
- A. $\frac{7}{3}$
- B. $\frac{8}{3}$
- C. 3
- D. $\frac{10}{3}$
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Q17
MATHS
Unit 12: Vector Algebra
An arc $PQ$ of a circle subtends a right angle at its centre $O$. The midpoint of the arc $PQ$ is $R$. If $\overrightarrow{OP}=\vec{u}$, $\overrightarrow{OR}=\vec{v}$ and $\overrightarrow{OQ}=\alpha\vec{u}+\beta\vec{v}$, then $\alpha,\beta^2$ are the roots of the equation
- A. $3x^2-2x-1=0$
- B. $3x^2+2x-1=0$
- C. $x^2-x-2=0$
- D. $x^2+x-2=0$
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Q18
MATHS
Unit 4: Permutations and Combinations
Let $N$ denote the sum of the numbers obtained when two dice are rolled. If the probability that $2^N < N!$ is $\frac{m}{n}$, where $m$ and $n$ are coprime, then $4m-3n$ is equal to
- A. 12
- B. 10
- C. 8
- D. 6
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Q19
MATHS
Unit 14: Trigonometry
$96\cos \frac{\pi}{33}\cos \frac{2\pi}{33}\cos \frac{4\pi}{33}\cos \frac{8\pi}{33}\cos \frac{16\pi}{33}$ is equal to
- A. 1
- B. 2
- C. 3
- D. 4
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Q20
CHEMISTRY
Unit 14: Some Basic Principles of Organic Chemistry
The negation of the statement $(p\vee q)\wedge(q\vee(\sim r))$ is
- A. $(p\vee r)\wedge(\sim q)$
- B. $((\sim p)\vee r)\wedge(\sim q)$
- C. $((\sim p)\vee(\sim q))\vee(\sim r)$
- D. $((\sim p)\vee(\sim q))\wedge(\sim r)$
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Q31
PHYSICS
Unit 8: Thermodynamics
A particle executes S.H.M. of amplitude $A$ along $x$-axis. At $t=0$, the position of the particle is $x=\frac{A}{2}$ and it moves along positive $x$-axis. The displacement of particle in time $t$ is $x= A\sin(\omega t+\delta)$, then the value $\delta$ will be
- A. $\frac{\pi}{2}$
- B. $\frac{\pi}{3}$
- C. $\frac{\pi}{4}$
- D. $\frac{\pi}{6}$
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Q32
PHYSICS
Unit 9: Kinetic Theory of Gases
Match List I with List II :
List I
(A) 3 Translational degrees of freedom
(B) 3 Translational, 2 rotational degrees of freedoms
(C) 3 Translational, 2 rotational and 1 vibrational degrees of freedom
(D) 3 Translational, 3 rotational and more than one vibrational degrees of freedom
List II
(I) Monoatomic gases
(II) Polyatomic gases
(III) Rigid diatomic gases
(IV) Nonrigid diatomic gases
Choose the correct answer from the options given below :
- A. (A)-(I), (B)-(IV), (C)-(III), (D)-(II)
- B. (A)-(I), (B)-(III), (C)-(IV), (D)-(II)
- C. (A)-(IV), (B)-(III), (C)-(II), (D)-(I)
- D. (A)-(IV), (B)-(II), (C)-(I), (D)-(III)
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Q33
PHYSICS
Unit 8: Thermodynamics
Consider two containers A and B containing monoatomic gases at the same Pressure $(P)$, Volume $(V)$ and Temperature $(T)$. The gas in A is compressed isothermally to $\frac{1}{8}$ of its original volume while the gas in B is compressed adiabatically to $\frac{1}{8}$ of its original volume. The ratio of final pressure of gas in B that of gas in A is
- A. $\frac{3}{8^2}$
- B. 4
- C. 8
- D. $\frac{1}{8}$
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Q34
PHYSICS
Unit 6: Gravitation
Two satellites of masses $m$ and $3m$ revolve around the earth in circular orbits of radii $r$ and $3r$ respectively. The ratio of orbital speeds of the satellites respectively is
- A. 1 : 1
- B. $\sqrt{3} : 1$
- C. 9 : 1
- D. 3 : 1
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Q35
PHYSICS
Unit 1: Units and Measurements
A physical quantity $P$ is given as
$$P = \frac{a^2 b^3}{c\sqrt{d}}$$
The percentage error in the measurement of $a$, $b$, $c$ and $d$ are $1\%$, $2\%$, $3\%$ and $4\%$ respectively. The percentage error in the measurement of quantity $P$ will be
- A. 12%
- B. 14%
- C. 16%
- D. 13%
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Q36
PHYSICS
Unit 7: Properties of Solids and Liquids
Given below are two statements :
Statement I : Pressure in a reservoir of water is same at all points at the same level of water.
Statement II : The pressure applied to enclosed water is transmitted in all directions equally.
In the light of the above statements, choose the correct answer from the options given below :
- A. Both Statement I and Statement II are true
- B. Both Statement I and Statement II are false
- C. Statement I is true but Statement II is false
- D. Statement I is false but Statement II is true
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Q37
PHYSICS
Unit 6: Gravitation
Assuming the earth to be a sphere of uniform mass density, the weight of a body at a depth $d = \frac{R}{2}$ from the surface of earth, if its weight on the surface of earth is $200\ \text{N}$, will be :
(Given $R$ = radius of earth)
- A. 300 N
- B. 500 N
- C. 400 N
- D. 100 N
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Q38
PHYSICS
Unit 2: Kinematics
The position-time graphs for two students A and B returning from the school to their homes are shown in figure.
(A) A lives closer to the school
(B) B lives closer to the school
(C) A takes lesser time to reach home
(D) A travels faster than B
(E) B travels faster than A
Choose the correct answer from the options given below:
- A. (A), (C) and (D) only
- B. (A) and (E) only
- C. (B) and (E) only
- D. (A), (C) and (E) only
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Q39
PHYSICS
Unit 2: Kinematics
The range of the projectile projected at an angle of $15^\circ$ with horizontal is $50\ \text{m}$. If the projectile is projected with same velocity at an angle of $45^\circ$ with horizontal, then its range will be
- A. 50 m
- B. $50\sqrt{2}$ m
- C. 100 m
- D. $100\sqrt{2}$ m
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Q40
PHYSICS
Unit 3: Laws of Motion
A particle of mass $m$ moving with velocity $v$ collides with a stationary particle of mass $2m$. After collision, they stick together and continue to move together with velocity
- A. $v$
- B. $\frac{v}{2}$
- C. $\frac{v}{3}$
- D. $\frac{v}{4}$
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Q41
PHYSICS
Unit 12: Current Electricity
The equivalent capacitance of the combination shown is
- A. $\frac{C}{2}$
- B. $\frac{5}{3}C$
- C. $2C$
- D. $4C$
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Q42
PHYSICS
Unit 10: Oscillations and Waves
A carrier wave of amplitude $15\ \text{V}$ is modulated by a sinusoidal base band signal of amplitude $3\ \text{V}$. The ratio of maximum amplitude to minimum amplitude in an amplitude modulated wave is
- A. 2
- B. 5
- C. 1
- D. $\frac{3}{2}$
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Q43
PHYSICS
Unit 19: Electronic Devices
A zener diode of power rating $1.6\ \text{W}$ is to be used as voltage regulator. If the zener diode has a breakdown of $8\ \text{V}$ and it has to regulate voltage fluctuating between $3\ \text{V}$ and $10\ \text{V}$. The value of resistance $R_s$ for safe operation of diode will be
- A. $10\ \Omega$
- B. $12\ \Omega$
- C. $13\ \Omega$
- D. $13.3\ \Omega$
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Q44
PHYSICS
Unit 18: Atoms and Nuclei
The angular momentum for the electron in Bohr's orbit is $L$. If the electron is assumed to revolve in second orbit of hydrogen atom, then the change in angular momentum will be
- A. $2L$
- B. $L$
- C. $\dfrac{L}{2}$
- D. zero
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Q45
PHYSICS
Unit 10: Oscillations and Waves
Given below are two statements :
Statement I : Maximum power is dissipated in a circuit containing an inductor, a capacitor and a resistor connected in series with an AC source, when resonance occurs
Statement II : Maximum power is dissipated in a circuit containing pure resistor due to zero phase difference between current and voltage.
In the light of the above statements, choose the correct answer from the options given below :
- A. Both Statement I and Statement II are true
- B. Both Statement I and Statement II are false
- C. Statement I is true but Statement II is false
- D. Statement I is false but Statement II is true
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Q46
PHYSICS
Unit 17: Dual Nature of Matter and Radiation
The de Broglie wavelength of a molecule in a gas at room temperature $(300\ \text{K})$ is $\lambda_1$. If the temperature of the gas is increased to $600\ \text{K}$, then the de Broglie wavelength of the same gas molecule becomes
- A. $\dfrac{1}{2}\lambda_1$
- B. $2\lambda_1$
- C. $\dfrac{1}{\sqrt{2}}\lambda_1$
- D. $\sqrt{2}\lambda_1$
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Q47
PHYSICS
Unit 16: Optics
An object is placed at a distance of $12\ \text{cm}$ in front of a plane mirror. The virtual and erect image is formed by the mirror. Now the mirror is moved by $4\ \text{cm}$ towards the stationary object. The distance by which the position of image would be shifted, will be
- A. $2\ \text{cm}$ towards mirror
- B. $4\ \text{cm}$ towards mirror
- C. $8\ \text{cm}$ towards mirror
- D. $8\ \text{cm}$ away from mirror
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Q48
PHYSICS
Unit 15: Electromagnetic Waves
The energy of an electromagnetic wave contained in a small volume oscillates with
- A. zero frequency
- B. the frequency of the wave
- C. double the frequency of the wave
- D. half the frequency of the wave
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Q49
PHYSICS
Unit 12: Current Electricity
Given below are two statements :
Statement I : If the number of turns in the coil of a moving coil galvanometer is doubled then the current sensitivity becomes double.
Statement II : Increasing current sensitivity of a moving coil galvanometer by only increasing the number of turns in the coil will also increase its voltage sensitivity in the same ratio
In the light of the above statements, choose the correct answer from the options given below :
- A. Both Statement I and Statement II are true
- B. Both Statement I and Statement II are false
- C. Statement I is true but Statement II is false
- D. Statement I is false but Statement II is true
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Q50
PHYSICS
Unit 12: Current Electricity
The equivalent resistance of the circuit shown below between points $a$ and $b$ is :
- A. $16\ \Omega$
- B. $20\ \Omega$
- C. $24\ \Omega$
- D. $3.2\ \Omega$
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Q61
CHEMISTRY
Unit 1: Some Basic Concepts in Chemistry
The number of molecules and moles in 2.8375 litres of $\mathrm{O_2}$ at STP are respectively
- A. $1.505 \times 10^{23}$ and $0.250\ \mathrm{mol}$
- B. $7.527 \times 10^{23}$ and $0.125\ \mathrm{mol}$
- C. $7.527 \times 10^{22}$ and $0.125\ \mathrm{mol}$
- D. $7.527 \times 10^{22}$ and $0.250\ \mathrm{mol}$
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Q62
CHEMISTRY
Unit 4: Chemical Thermodynamics
Given
(A) $2\mathrm{CO}(g)+\mathrm{O_2}(g) \rightarrow 2\mathrm{CO_2}(g)$, $\Delta H_1^{\circ}=-x\ \mathrm{kJ\ mol^{-1}}$
(B) $\mathrm{C(graphite)}+\mathrm{O_2}(g) \rightarrow \mathrm{CO_2}(g)$, $\Delta H_2^{\circ}=-y\ \mathrm{kJ\ mol^{-1}}$
The $\Delta H^{\circ}$ for the reaction
$\mathrm{C(graphite)}+\frac{1}{2}\mathrm{O_2}(g) \rightarrow \mathrm{CO}(g)$ is
- A. $\frac{x+2y}{2}$
- B. $2y-x$
- C. $\frac{2x-y}{2}$
- D. $\frac{x-2y}{2}$
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Q63
CHEMISTRY
Unit 4: Chemical Thermodynamics
The enthalpy change for the adsorption process and micelle formation respectively are
- A. $\Delta H_{\text{ads}}<0$ and $\Delta H_{\text{mic}}<0$
- B. $\Delta H_{\text{ads}}>0$ and $\Delta H_{\text{mic}}>0$
- C. $\Delta H_{\text{ads}}>0$ and $\Delta H_{\text{mic}}<0$
- D. $\Delta H_{\text{ads}}<0$ and $\Delta H_{\text{mic}}>0$
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Q64
CHEMISTRY
Unit 12: Coordination Compounds
Which of the following is used as a stabilizer during the concentration of sulphide ores?
- A. Xanthates
- B. Pine oils
- C. Cresols
- D. Fatty acids
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Q65
CHEMISTRY
Unit 4: Chemical Thermodynamics
Given below are two reactions, involved in the commercial production of dihydrogen ($\mathrm{H_2}$). The two reactions are carried out at temperature $T_1$ and $T_2$, respectively
$\mathrm{C(s)}+\mathrm{H_2O(g)} \xrightarrow{T_1} \mathrm{CO(g)}+\mathrm{H_2(g)}$
$\mathrm{CO(g)}+\mathrm{H_2O(g)} \xrightarrow{T_2} \mathrm{CO_2(g)}+\mathrm{H_2(g)}$
The temperatures $T_1$ and $T_2$ are correctly related as
- A. $T_1>T_2$
- B. $T_1<T_2$
- C. $T_1=T_2$
- D. $T_1=100\ \mathrm{K},\ T_2=1270\ \mathrm{K}$
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Q66
CHEMISTRY
Unit 10: p-Block Elements
Lime reacts exothermically with water to give 'A' which has low solubility in water. Aqueous solution of 'A' is often used for the test of $\mathrm{CO_2}$, a test in which insoluble B is formed. If B is further reacted with $\mathrm{CO_2}$ then soluble compound is formed. 'A' is
- A. Quick lime
- B. Lime water
- C. Slaked lime
- D. White lime
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Q67
CHEMISTRY
Unit 10: p-Block Elements
The compound which does not exist is
- A. $\mathrm{PbEt_4}$
- B. $\mathrm{(NH_4)_2BeF_4}$
- C. $\mathrm{NaO_2}$
- D. $\mathrm{BeH_2}$
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Q68
CHEMISTRY
Unit 11: d- and f-Block Elements
Which of the following statements are correct?
(A) The $\mathrm{M^{3+}/M^{2+}}$ reduction potential for iron is greater than manganese.
(B) The higher oxidation states of first row d-block elements get stabilized by oxide ion.
(C) Aqueous solution of $\mathrm{Cr^{2+}}$ can liberate hydrogen from dilute acid.
(D) Magnetic moment of $\mathrm{V^{2+}}$ is observed between 4.4 - 5.2 BM.
Choose the correct answer from the options given below:
- A. (A), (B) only
- B. (B), (C) only
- C. (C), (D) only
- D. (A), (B), (D) only
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Q69
CHEMISTRY
Unit 12: Coordination Compounds
The octahedral diamagnetic low spin complex among the following is
- A. $[CoF_6]^{3-}$
- B. $[NiCl_4]^{2-}$
- C. $[Co(NH_3)_6]^{3+}$
- D. $[CoCl_6]^{3-}$
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Q70
CHEMISTRY
Unit 20: Principles Related to Practical Chemistry
Match List I with List II
List I
Industry
(A) Steel plants
(B) Thermal power plants
(C) Fertilizer industries
(D) Paper mills
List II
Waste Generated
(I) Gypsum
(II) Fly ash
(III) Slag
(IV) Bio-degradable wastes
Choose the correct answer from the options given below:
- A. (A)-(III), (B)-(II), (C)-(I), (D)-(IV)
- B. (A)-(III), (B)-(IV), (C)-(I), (D)-(II)
- C. (A)-(II), (B)-(III), (C)-(IV), (D)-(I)
- D. (A)-(IV), (B)-(I), (C)-(II), (D)-(III)
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Q71
CHEMISTRY
Unit 14: Some Basic Principles of Organic Chemistry
Using column chromatography, mixture of two compounds ‘A’ and ‘B’ was separated. ‘A’ eluted first, this indicates ‘B’ has
- A. high $R_f$, weaker adsorption
- B. high $R_f$, stronger adsorption
- C. low $R_f$, weaker adsorption
- D. low $R_f$, stronger adsorption
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Q72
CHEMISTRY
Unit 14: Some Basic Principles of Organic Chemistry
The pair from the following pairs having both compounds with net non-zero dipole moment is
- A. cis-butene, trans-butene
- B. $CH_2Cl_2$, $CHCl_3$
- C. 1,4-Dichlorobenzene, 1,3-Dichlorobenzene
- D. Benzene, anisidine
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Q73
CHEMISTRY
Unit 16: Organic Compounds Containing Halogens
Identify the correct order of reactivity for the following pairs towards the respective mechanism
- A. $(B), (C) and (D) only$
- B. $(A), (B) and (D) only$
- C. $(A), (C) and (D) only$
- D. $(A), (B), (C) and (D)$
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Q74
CHEMISTRY
Unit 17: Organic Compounds Containing Oxygen
The major product 'P' formed in the given reaction is
- A. Compound with two $COOH$ groups and one side-chain $CH_2COOH$, plus reduced aromatic ring substituents
- B. A fused-ring dicarboxylic acid with two $COOH$ groups and one $CH_2COOH$ group
- C. Fused-ring compound containing $CH_2COOH$ and $COCH_3$ side chains
- D. A fused-ring tricarboxylic acid with three $COOH$ groups
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Q75
CHEMISTRY
Unit 16: Organic Compounds Containing Halogens
Suitable reaction condition for preparation of Methyl phenyl ether is
- A. $PhO^-Na^+$, $MeBr$
- B. $PhO^-Na^+$, $MeOH$
- C. $Ph-Br$, $MeO^-Na^+$
- D. Benzene, $MeBr$
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Q76
CHEMISTRY
Unit 18: Organic Compounds Containing Nitrogen
Isomeric amines with molecular formula $C_8H_{11}N$ give the following tests
Isomer (P) => Can be prepared by Gabriel phthalimide synthesis
Isomer (Q) => Reacts with Hinsberg's reagent to give solid insoluble in NaOH
Isomer (R) => Reacts with HONO followed by $\beta$-naphthol in NaOH to give red dye.
Isomers (P), (Q) and (R) respectively are
- A. Aniline derivative with one methyl and one ethyl substituent; phenethylamine; tertiary aromatic amine
- B. Phenethylamine; tertiary aromatic amine; primary aromatic amine with methyl substituent
- C. o-Ethylaniline; phenethylamine; N-ethylaniline
- D. Phenethylamine; N,N-dimethylaniline; o-ethylaniline
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Q77
CHEMISTRY
Unit 14: Some Basic Principles of Organic Chemistry
Match List I with List II
List I
Polymer
(A) Nylon-2-Nylon-6
(B) Buna-N
(C) Urea-formaldehyde resin
(D) Dacron
List II
Type / Class
(I) Thermosetting polymer
(II) Biodegradable polymer
(III) Synthetic rubber
(IV) Polyester
Choose the correct answer from the options given below:
- A. (A)-(II), (B)-(I), (C)-(IV), (D)-(III)
- B. (A)-(II), (B)-(III), (C)-(I), (D)-(IV)
- C. (A)-(IV), (B)-(I), (C)-(III), (D)-(II)
- D. (A)-(IV), (B)-(III), (C)-(I), (D)-(II)
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Q78
CHEMISTRY
Unit 3: Chemical Bonding and Molecular Structure
The one that does not stabilize $2^\circ$ and $3^\circ$ structures of proteins is
- A. H-bonding
- B. $-O-O-$ linkage
- C. $-S-S-$ linkage
- D. van der Waals forces
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Q79
CHEMISTRY
Unit 20: Principles Related to Practical Chemistry
Given below are two statements:
Statement I: Aqueous solution of $K_2Cr_2O_7$ is preferred as a primary standard in volumetric analysis over $Na_2Cr_2O_7$ aqueous solution.
Statement II: $K_2Cr_2O_7$ has a higher solubility in water than $Na_2Cr_2O_7$.
In the light of the above statements, choose the correct answer from the options given below:
- A. Both Statement I and Statement II are true
- B. Both Statement I and Statement II are false
- C. Statement I is true but Statement II is false
- D. Statement I is false but Statement II is true
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Q80
CHEMISTRY
Unit 11: d- and f-Block Elements
Prolonged heating is avoided during the preparation of ferrous ammonium sulphate to
- A. prevent hydrolysis
- B. prevent breaking
- C. prevent reduction
- D. prevent oxidation
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