As shown in the figure, a plane mirror is fixed at a height of $50\, cm$ from the bottom of tank containing water
$(\mu = \frac{4}{3})$ . The height of water in the tank is $8\, cm$ . A small bulb is placed at the bottom of the water tank. The
distance of image of the bulb formed by mirror from the bottom of the tank is ______ $cm$ .
✓ Accepted Answer:4
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Q2mcq
The thermodynamic process, in which internal energy of the system remains constant is
a.
Isochoric
Correct Answer
b.
Adiabatic
c.
Isothermal
d.
Isobaric
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Q3mcq
A capacitor of capacitance $C$ is charged to a potential $V$ . The flux of the electric field through a closed surface
enclosing the positive plate of the capacitor is:
a.
$\frac{CV}{\epsilon _{0}}$
Correct Answer
b.
Zero
c.
$\frac{2 CV}{\epsilon _{0}}$
d.
$\frac{CV}{2\epsilon _{0}}$
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Q4mcq
A circular plate is rotating in horizontal plane, about an axis passing through its centre and perpendicular to the
plate, with an angular velocity $\omega$ . A person sits at the centre having two dumbbells in his hands. When he
stretched out his hands, the moment of inertia of the system becomes triple. If $E$ be the initial Kinetic energy of
the system, then final Kinetic energy will be $\frac{E}{x}$ . The value of $x$ is
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Q5mcq
Given below are two statements: one is labelled as
Assertion $A$ and the other is labelled as Reason $R$
Assertion $A$ :A bar magnet dropped through a metallic cylindrical pipe takes more time to come down
compared to a non-magnetic bar with same geometry and mass.
Reason $R$ :For the magnetic bar, Eddy currents are produced in the metallic pipe which oppose the motion of
the magnetic bar.
In the light of the above statements, choose the correct answer from the options given below
a.
$A$ is false but $R$ is true
b.
Both $A$ and R are true and $R$ is the correct
explanation of $A$
Correct Answer
c.
$A$ is true but $R$ is false
d.
Both $A$ and $R$ are true and $R$ is NOT the correct
explanation of $A$
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Q6mcq
A nucleus disintegrates into two nuclear parts, in such a way that ratio of their nuclear sizes is $1 : 2^{1/3}$ . Their
respective speed have a ratio of $n: 1$ . The value of $n$ is_________
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Q7nat
In satellite communication, the uplink frequency band used is:
✓ Accepted Answer:98
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Q8mcq
A space ship of mass $2 \times 10^{4}\, kg$ is launched into a circular orbit close to the earth surface. The additional
velocity to be imparted to the space ship in the orbit to overcome the gravitational pull will be (if $g= 10\,m\,s^{-2}$
and radius of earth $= 6400\, km$ ):
a.
$11. 2(\sqrt{2}-1)\, km \,s^{-1}$
b.
$8(\sqrt{2}-1)\, km \,s^{-1}$
c.
$7. 9(\sqrt{2}-1)\, km \,s^{-1}$
d.
$7. 4(\sqrt{2}-1)\, km \,s^{-1}$
Correct Answer
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Q9nat
An electron is allowed to move with constant velocity along the axis of current carrying straight solenoid.
(A) The electron will experience magnetic force along the axis of the solenoid.
(B) The electron will not experience magnetic force.
(C) The electron will continue to move along the axis of the solenoid.
(D) The electron will be accelerated along the axis of the solenoid.
(E) The electron will follow parabolic path-inside the solenoid.
Choose the correct answer from the option given below:
✓ Accepted Answer:300
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Q10mcq
The root mean square speed of molecules of nitrogen gas at $27^{\circ}C$ is approximately: (Given mass of a nitrogen
molecule $= 4. 6 \times 10^{-26}\, kg$ and take Boltzmann constant $k_{B} = 1. 4 \times 10^{-23}J\,K^{-1}$ )
a.
$27. 4\,m\,s^{-1}$
b.
$91\,m\,s^{-1}$
c.
$1260\,m\,s^{-1}$
Correct Answer
d.
$523\,m\,s^{-1}$
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A body of mass $500\,g$ moves along $x$ -axis such that it's velocity varies with displacement $x$ according to the
relation $v= 10\sqrt{x}\,m\,s^{-1}$ the force acting on the body is:
a.
$125\,N$
b.
$25\,N$
c.
$166\,N$
d.
$5\,N$
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The surface tension of soap solution is $3. 5 \times 10^{-2\,}N\,m^{-1}$ . The amount of work done required to increase the
radius of soap bubble from $10\, cm$ to $20\, cm$ is _____ $\times 10^{-4}\,J$ . (take $\pi = \frac{22}{7}$ )
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A projectile is projected at $30^{\circ}$ from horizontal with initial velocity $40\,m\,s^{-1}$ . The velocity of the projectile at
$t = 2\,s$ from the start will be:
a.
$40\,m\,s\sqrt{3}^{-1}$
b.
Zero
c.
$20\,m\,s^{-1}$
d.
$20\,m\,s\sqrt{3}^{-1}$
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A plane electromagnetic wave of frequency $20\, MHz$ propagates in free space along $x$ -direction. At a particular
space and time $\vec{E} = 6. 6jˆ\,\,V\,m^{-1}$ . What is $\vec{B}$ at this point?
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When vector $\vec{A}= 2ˆi+ 3ˆj+ 2ˆk$ is subtracted from vector $\vec{B}$ , it gives a vector equal to $2ˆj$ . Then the magnitude of
vector $\vec{B}$ will be:
a.
$\sqrt{5}$
b.
$3$
c.
$\sqrt{6}$
d.
$\sqrt{33}$
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A wire of density $8 \times 10^{3}\, kg \,m^{-3}$ is stretched between two clamps $0. 5\,m$ apart. The extension developed in
the wire is $3. 2 \times 10^{-4}\,m$ . If $Y = 8 \times 10^{10}\,N\,m^{-2}$ , the fundamental frequency of vibration in the wire will be
_____ $Hz$
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A car $P$ travelling at $20\,m\,s^{-1}$ sounds its horn at a frequency of $400\, Hz$ . Another car $Q$ is travelling behind the
first car in the same direction with a velocity $40\,m\,s^{-1}$ . The frequency heard by the passenger of the car $Q$ is
approximately [Take, velocity of sound $= 360\,m\,s^{-1}$ ]
a.
$421\, Hz$
b.
$471\, Hz$
c.
$485\, Hz$
d.
$514\, Hz$
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A metallic cube of side $15\, cm$ moving along $y$ -axis at a uniform velocity of $2\,m\,s^{-1}$ . In a region of uniform
magnetic field of magnitude $0. 5\,T$ directed along $z$ - axis. In equilibrium the potential difference between the
faces of higher and lower potential developed because of the motion through the field will be $mV$ .
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A block of mass $5\, kg$ starting from rest pulled up on a smooth incline plane making an angle of $30^{\circ}$ with
horizontal with an effective acceleration of $1\,m\,s^{-2}$ . The power delivered by the puling force at $t= 10\,s$ from
the start is _____ $W$ .
[Use $g= 10\,m\,s^{-2}$ ]
(Calculate the nearest integer value)
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A coil has an inductance of $2\,H$ and resistance of $4\,\Omega$ . A $10\,V$ is applied across the coil. The energy stored in
the magnetic field after the current has built up to its equilibrium value will be _____ $\times 10^{-2}\,J$
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Two identical cells each of emf $1. 5\,V$ are connected in series across a $10\,\Omega$ resistance. An ideal voltmeter
connected across $10\,\Omega$ resistance reads $1. 5\,V$ . The internal resistance of each cell is _____ $\Omega$ .
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The number of correct statements from the following is ...........
A. For $1s$ orbital, the probability density is maximum at the nucleus
B. For $2s$ orbital, the probability density first increases to maximum and then decreases sharply to zero.
C. Boundary surface diagrams of the orbitals encloses a region of $100%$ probability of finding the electron.
D. $p$ and $d$ -orbitals have $1$ and $2$ angular nodes respectively
E. probability density of $p$ -orbital is zero at the nucleus
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If $Ni^{2+}$ is replaced by $Pt^{2+}$ in the complex $[NiCl_{2}Br_{2}]^{2-}$ , which of the following properties are expected to
get changed?
A. Geometry
B. Geometrical isomerism
C. Optical isomerism
D. Magnetic properties
a.
A and D
b.
A, B and C
c.
B and C
d.
A, B and D
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The volume of hydrogen liberated at STP by treating $2. 4\,g$ of magnesium with excess of hydrochloric acid is
...... $\times 10^{-2}\,L$ . Given Molar volume of gas is $22. 4\,L$ at STP. Molar mass of magnesium is $24\,g\, mol^{-1}$
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Number of compounds from the following which will not produce orange red precipitate with Benedict
solution is........
Glucose, maltose, sucrose, ribose, $2$ -deoxyribose, amylose, lactose
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Match List I with List II
LIST-I LIST-II
Complex Colour
A. $Mg(NH_{4}) PO_{4}$ I. brown
B. $K_{3}[Co (NO_{2})_{6}]$ II. white
C. $MnO (OH)_{2}$ III. yellow
D. $Fe_{4}[Fe (CN)_{6}]_{3}$ IV. blue
Choose the correct answer from the options given below:
a.
A-III, B-IV, C-II, D-I
b.
A-II, B-III, C-I, D-IV
c.
A-II, B-IV, C-I, D-III
d.
A-II, B-III, C-IV, D-I
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The number of correct statements about modern adsorption theory of heterogeneous catalysis from the
following is ......
A. The catalyst is diffused over the surface of reactants.
B. Reactants are adsorbed on the surface of the catalyst.
C. Occurrence of chemical reaction on the catalyst's surface through formation of an intermediate.
D. It is a combination of intermediate compound formation theory and the old adsorption theory.
E. It explains the action of the catalyst as well as those of catalytic promoters and poisons.
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Given below are two statements:
Statement I: Ethane at $333$ to $343\,K$ and $6 -7$ atm pressure in the presence of $AlEt_{3}$ and $TiCl_{4}$ undergoes
addition polymerization to give LDP.
Statement II: Caprolactam at $533 -543\,K$ in $H_{2}O$ through step growth polymerizes to give $Nylon \,6$ .
In the light of the above statements, choose the correct answer from the options given below:
a.
Statement I is false butStatement II is true
b.
Statement I is true butStatement II is false
c.
Both Statement I andStatement II are true
d.
Both Statement I andStatement II are false
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The magnetic moment is measured in Bohr Magneton (BM). Spin only magnetic moment of $Fe$ in
$[Fe (H_{2}O)_{6}]^{3+}$ and $[Fe (CN)_{6}]^{3-}$ complexes respectively is:
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Given below are two statements, one is labelled as Assertion $A$ and the other is labelled as Reasom $R$ .
Assertion $A$ :A solution of the product obtained by heating a mole of glycine with a mole of chlorine in
presence of red phosphorous generates chiral carbon atom.
Reason $R$ :A molecule with $2$ chiral carbons is always optically active.
In the light of above statements, chose the correct answer from the options given below:
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The total number of intensive properties from the following is...........
Volume, Molar heat capacity, molarity, $E^{o}_{cell}$ ,Gibbs free energy change, Molar mass, Mole
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Given below are two statements, one is labelled as assertion $A$ and the other is labelled as Reason $R$ .
assertion $A$ : $[CoCl (NH_{3})_{5}]^{2+}$ absorbs at lower wavelength of light with respect to $[Co (NH_{3})_{5}(H_{2}O)]^{3+}$
Reason $R$ : It is because the wavelenght of light absorbed depends on the oxidation state of the metal ion.
In the light of the above statements,choose the correct answer from the options given below:
a.
$A$ is false but $R$ is true
b.
$A$ is true but $R$ is false
c.
Both $A$ and $R$ are true and $R$ is the correct
explaination of $A$
d.
Both $A$ and $R$ are true and $R$ is NOT the correct
explaination of $A$
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Given below are two statements, one is labelled as Assertion $A$ and the other is labelled as Reason $R$ .
Assertion $A$ : can be subjected to Wolff-Kishner reduction to give
Reason $R$ : Wolff-Kishner reduction is used to convert into
In the light of the above statements, choose the correct answer from the options given below:
a.
$A$ is true but $R$ is false
b.
$A$ is false but $R$ is true
c.
Both $A$ and $R$ are true and $R$ is the correct
explanation of $A$
d.
Both $A$ and $R$ are true and $R$ is NOT the correct
explanation of $A$
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Given below are two statements:
Statement I: In the metallurgy process,sulphide ore is converted to oxide before reduction.
Statement II: Oxide ores in general are easier to reduce.
In the light of the above statements, choose the most appropriate answer from the options given below:
a.
Statement Iis correct but Statement IIis
incorrect
b.
Both Statement Iand Statement IIare incorrect
c.
Statement Iis incorrect but Statement IIis
correct
d.
Both Statement Iand Statement IIare correct
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One mole of $P_{4}$ reacts with $8$ moles of $SOCl_{2}$ to give $4$ moles of $A$ , $x$ mole of $SO_{2}$ and $2$ moles of $B$ . $A, \,B$
and $x$ respectively are
a.
$POCl_{3}, \,S_{2}Cl_{2}$ and $2$
b.
$PCl_{3}, \,S_{2}Cl_{2}$ and $4$
c.
$PCl_{3}, \,S_{2}Cl_{2}$ and $2$
d.
$POCl_{3}, \,S_{2}Cl_{2}$ and $4$
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For a chemical reaction $A+B\rightarrow \rightarrow$ Product, the order is $1$ with respect to $A$ and $B$ .
Rate [A] [B]
$mol \,L^{-1}\,S^{-1} mol \,L^{-1} mol \,L^{-1}$
$0. 10 20 0. 5$
$0. 40 x 0. 5$
$0. 80 40 y$
What is the value of $x$ and $y$ ?
a.
$160$ and $4$
b.
$80$ and $4$
c.
$80$ and $2$
d.
$40$ and $4$
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$4. 5$ moles each of hydrogen and iodine is heated in a sealed ten litre vessel.At equilibrium, $3$ moles of $HI$ were
found. The equilibrium constant for $H_{2}(g) + I_{2}(g) \rightleftharpoons 2 HI_{(g)}$ is ........
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What weight of glucose must be dissolved in $100\,g$ of water to lower the vapour pressure by $0. 20\, mm \, Hg$ ?
(Assume dilute solution is being formed)
Given: Vapour pressure of pure water is $54. 2\, mm \, Hg$ at room temperature.Molar mass of glucose is
$180\,g\, mol^{-1}$
a.
$3. 59\,g$
b.
$3. 69\,g$
c.
$4. 69\,g$
d.
$2. 59\,g$
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The number of correct statements from the following is...........
A. $E_{cell}$ is an intensive parameter
B. A negative $E^{o}$ means that the redox couple is a stronger reducing agent than the $H^{+}/H_{2}$ couple.
C. The amount of electricity required for oxidation or reduction depends on the stoichiometry of the electrode
reaction.
D. The amount of chemical reaction which occurs at any electrode during electrolysis by a current is
proportional to the quantity of electricity passed through the electrolyte.
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Let the line $L:x= \frac{1-y}{-2} = \frac{z-3}{\lambda} ,\lambda \in R$ meet the plane $P : \,x+ 2\,y+ 3\,z= 4$ at the point $(\alpha ,\beta ,\gamma )$ . If the
angle between the line $L$ and the plane $P$ is $cos^{-1}(\sqrt{\frac{5}{14}})$ , then $\alpha + 2\beta + 6\gamma$ is equal to
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$x+ 1, \,\,\,\,\,\,x< 0 x+ 1, \,\,\,\,\,\,x< 0$
Let $f$ and $g$ be two functions defined by $f(x) ={$ and $g(x) ={$ .Then
$|x-1|, \,\,x\geq 0 1, \,\,\,\,\,\,\,\,\,\,\,\,x\geq 0$
$(gof)(x)$ is
a.
Continuous everywhere but not differentiable
exactly at one point
b.
Continuous everywhere but not differentiable at
$x= 1$
c.
Differentiable everywhere
d.
Not continuous at $x= 1$
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If the line $l_{1} : 3y-2x= 3$ is the angular bisector of the lines $l_{2} :x- y+ 1 = 0$ and $l_{3} :\alpha x+\beta y+ 17 = 0$ ,
then $\alpha ^{2} +\beta ^{2} - \alpha - \beta$ is equal to ............
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Let $A= {1, 3, 4, 6, 9}$ and $B= {2, 4, 5, 8, 10}$ . Let $R$ be a relation defined on $A\times B$ such that
$R= {(a_{1}, b_{1}), (a_{2},b_{2}) :a_{1} \leq b_{2}\,and\,b_{1} \leq a_{2}}$ . Then the number of elements in the set $R$ is
a.
$160$
b.
$52$
c.
$26$
d.
$180$
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Let $P$ be the plane passing through the points $(5, 3, 0), (13, 3, -2)$ and $(1, 6, 2)$ . For $\alpha \in N$ , if the distance of
the points $A(3, 4,\alpha )$ and $B(2,\alpha ,a)$ from the plane $P$ are $2$ and $3$ respectively, then the positive value of $a$ is
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$----$ For $a\in ^{C}$ , let $A= {z\in ^{C}:Re (a+z) >Im (a+z)}$ and $B= {z\in ^{C}:Re (a+z) <Im (a+z)}$ . Then
among the two statements:
$(S1)$ : If $Re (a), Im (a) > 0$ , then the set $A$ contains all the real numbers
$(S2)$ : If $Re (a), Im (a) < 0$ , then the set $B$ contains all the real numbers,
a.
Only $(S2)$ is true
b.
only $(S1)$ is true
c.
Both are true
d.
Both are false
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If the letters of the word MATHS are permuted and all possible words so formed are arranged as in a
dictionary with serial numbers, then the serial number of the word THAMS is
a.
$103$
b.
$102$
c.
$101$
d.
$104$
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Let $a,b,c$ and $d$ be positive real numbers such that $a+b+c+d= 11$ . If the maximum value of $a^{5}b^{3}c^{2}d$ is
$3750\beta$ , then the value of $\beta$ is
a.
$90$
b.
$110$
c.
$55$
d.
$108$
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Let the tangent to the parabola $y^{2} = 12x$ at the point $(3, \,\alpha )$ be perpendicular to the line $2x+ 2y= 3$ . Then the
square of distance of the point $(6, \, -4)$ from the normal to the hyperbola $\alpha ^{2}x^{2} -9y^{2} = 9\alpha ^{2}$ at its point
$(\alpha -1, \,\alpha + 2)$ is equal to .............
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$| |$
If $f :R\rightarrow \rightarrow R$ be a continuous function satisfying $\int _{0}\frac{$\pi$}{2} f(sin 2x) sin \,x dx+\alpha \int _{0}\frac{$\pi$}{4} f(cos 2x) cos \,x dx= 0$ , then
the value of $\alpha$ is
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The angle of elevation of the top $P$ of a tower from the feet of one person standing due south of the tower is
$45^{^{\circ}}$ and from the feet of another person standing due west of the tower is $30^{^{\circ}}$ . If the height of the tower is $5$
meters, then the distance (in meters) between the two persons is equal to
a.
$\frac{5}{2}\sqrt{5}$
b.
$10$
c.
$5$
d.
$5\sqrt{5}$
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Let $\vec{a}= ˆi+ 2ˆj+ 3ˆk$ and $\vec{b}= ˆi+ ˆj- ˆk$ . If $\vec{c}$ is a vector such that $\vec{a}\cdot \vec{c}= 11, \vec{b}\cdot (\vec{a}\times \vec{c})= 27$ and $\vec{b}\cdot \vec{c}=$
$-\sqrt{3} \vec{b}$ , then $\vec{a}\times \vec{c}^{2}$ is equal to
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If $A$ is the area in the first quadrant enclosed by the curve $C : 2x^{2} - y+ 1 = 0$ , the tangent to $C$ at the point
$(1, \,3)$ and the line $x+y= 1$ , then the value of $60A$ is................
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If the system of linear equations
$7x+ 11y+\alpha z= 13$
$5x+ 4y+ 7z=\beta$
$175x+ 194y+ 57z= 361$
has infinitely many solutions, then $\alpha +\beta + 2$ is equal to
a.
$4$
b.
$3$
c.
$5$
d.
$6$
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Let the line passing through the points $P(2, -1, 2)$ and $Q(5, 3, 4)$ meet the plane $x- y+z= 4$ at the point $R$ .
Then the distance of the point $R$ from the plane $x+ 2y+ 3z+ 2 = 0$ measured parallel to the line
$\frac{x-7}{2} = \frac{y+3}{2} = \frac{z-2}{1}$ is
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$2$
Let $y=y(x)$ be the solution of the differential equation $\frac{dy}{dx} + \frac{5}{x(x^{5}+1)} y= \frac{(x^{5}+1)}{x^{7}} , \,x> 0$ . If $y(1) = 2$ , then
$y(2)$ is equal to
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If the $1011^{th}$ term from the end in the binomial expansion of $(\frac{4x}{5} - \frac{5}{2x})^{2022}$ is $1024$ times $1011^{th}$ term from
the beginning, then $32|x|$ is equal to
a.
$15$
b.
$10$
c.
$12$
d.
$8$
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$| ||$
Let the probability of getting head for a biased coin be $\frac{1}{4}$ . It is tossed repeatedly until a head appears. Let $N$
be the number of tosses required. If the probability that the equation $64x^{2} + 5Nx+ 1 = 0$ has no real root is
$\frac{p}{q}$ , where $p$ and $q$ are co-prime, then $q- p$ is equal to..........
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For $k\in N$ , if the sum of the series $1 + \frac{4}{k} + \frac{8}{k^{2}} + \frac{13}{k^{3}} + \frac{19}{k^{4}}+. . . . . .$ is $10$ , then the value of $k$ is
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$e^{min{x^{2},x-[x]}}, x\in [0, 1)$
Let the function $f : [0, 2] \rightarrow \rightarrow R$ be defined as $f(x) ={$ , where $[t]$ denotes the greatest
$e^{[x-log_{e}x]}, x\in [1, 2]$
integer less than or equal to $t$ . Then the value of the integral $\int _{0}^{2} xf(x)dx$ is
a.
$1 + \frac{3e}{2}$
b.
$(e-1)(e^{2} + \frac{1}{2} )$
c.
$2e-1$
d.
$2e- \frac{1}{2}$
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Let $A= {1, 2, 3, 4, 5}$ and $B= {1, 2, 3, 4, 5, 6}$ . Then the number of functions $f :A\rightarrow \rightarrow B$ satisfying
$f(1) +f(2) =f(4) -1$ is equal to........
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