The incident ray, reflected ray and the outward drawn normal are denoted by the unitvectors $\vec{a}, \vec{b}$ and $\vec{c}$
respectively. Then choose the correct relation for these vectors.
Two stream of photons, possessing energies equal to twice and ten times the work function of metal are
incident on the metal surface successively. The value of ratio of maximum velocities of the photoelectrons
emitted in the two respective cases is $x: 3$ The value of $x$ is
✓ Accepted Answer:1
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Q3nat
A particle executes S.H.M. with amplitude $A$ and time period $T$ . The displacement of the particle when its
speed is half of maximum speed is $\frac{\sqrt{x}A}{2}.$ The value of $x$ is
✓ Accepted Answer:3
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Q4mcq
The length of metallic wire is $l_{1}$ when tension in it is $T_{1}$ . It is $l_{2}$ when the tension is $T_{2}$ . The original length of
the wire will be :
Given below are two statements : one is labeled as Assertion $A$ and the other is labeled as Reason $R$ .
Assertion $A$ : For a simple microscope, the angular size of the object equals the angular size of the image.
Reason $R$ : Magnification is achieved as the small object can be kept much closer to the eye than $25\, cm$ and
hence it subtends a large angle. In the light of the above statements, choose the most appropriate answer from
the options given below:
a.
$A$ is false but $R$ is true
b.
Both $A$ and $R$ are true but $R$ is NOT the correct
explanation of $A$
c.
$A$ is true but $R$ is false
d.
Both $A$ and $R$ are true and $R$ is the correct
explanation of $A$
Correct Answer
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Q6mcq
A cord is wound round the circumference of wheel of radius $r$ , The axis of the wheel is horizontal and the
moment of inertia about it is $I$ . A weight $mg$ is attached to the cord at the end. The weight falls from rest. After
falling through a distance $h,$ the square of angular velocity of wheel will be
a.
$\frac{2mgh}{I+mr^{2}}$
Correct Answer
b.
$\frac{2mgh}{I+2mr^{2}}$
c.
$2gh$
d.
$\frac{2gh}{I+mr^{2}}$
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Q7nat
If the highest frequency modulating a carrier is $5\, kHz$ , then the number of $AM$ broadcast stations
accommodated in a $90\, kHz$ bandwidth are
✓ Accepted Answer:9
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Q8nat
A point source of light $S$ , placed at a distance $60\, cm$ infront of the centre of a plane mirror of width $50\, cm$ ,
hangs vertically on a wall. A man walks infront of the mirror along a line parallel to the mirror at a distance
$1. 2\,m$ from it (see in the figure). The distance between the extreme points where he can see the image of the
light source in the mirror is__ $cm$
✓ Accepted Answer:150
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Q9nat
In the reported figure of earth, the value of acceleration due to gravity is same at point $A$ and $C$ but it is
smaller than that of its value at point $B$ (surface of the earth). The value of $OA:AB$ will be $x: 5$ . The value
of $x$ is
✓ Accepted Answer:4
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Q10mcq
Find the peak current and resonant frequency of the following circuit (as shown in figure).
a.
$2\,A$ and $50\, Hz$
b.
$0. 2\,A$ and $100\, Hz$
c.
$2\,A$ and $100\, Hz$
d.
$0. 2\,A$ and $50\, Hz$
Correct Answer
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A radioactive sample is undergoing $\alpha$ decay, At any time $t_{1},$ its activity is $A$ and another time $t_{2},$ the activity is
$\frac{A}{5}$ . What is the average life time for the sample ?
a.
$\frac{ln 5}{t_{2}-t_{1}}$
b.
$\frac{ln(t_{2}+t_{1})}{2}$
c.
$\frac{t_{2}-t_{1}}{ln 5}$
d.
$\frac{t_{1}-t_{2}}{ln 5}$
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An aeroplane, with its wings spread $10\,m,$ is flying at a speed of $180\, km \,h^{-1}$ in a horizontal direction. The
total intensity of earth's field at that part is $2. 5 \times 10^{-4}\, Wb \,m^{-2}$ and the angle of dip is $60^{\circ}.$ The emf induced
between the tips of the plane wings will be
a.
$108. 25\, mV$
b.
$54. 125\, mV$
c.
$88. 37\, mV$
d.
$62. 50\, mV$
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Two masses $A$ and $B$ , each of mass $M$ are fixed together by a massless spring, A force acts on the mass $B$ as
shown in figure. If the mass $A$ starts moving away from mass $B$ with acceleration $a$ , then the acceleration of
mass $B$ will be :
a.
$\frac{MF}{F+Ma}$
b.
$\frac{F+Ma}{M}$
c.
$\frac{Ma-F}{M}$
d.
$\frac{F-Ma}{M}$
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The trajectory of a projectile in a vertical plane is $y=\alpha x- \beta x^{2},$ where $\alpha$ and $\beta$ are constants and $x\,&\,y$ are
respectively the horizontal and vertical distances of the projectile from the point of projection. The angle of
projection $\theta$ and the maximum height attained $H$ are respectively given by
A tuning fork $A$ of unknown frequency produces $5\, beats \,s^{-1}$ with a fork of known frequency $340\, Hz$ . When
fork $A$ is filed, the beat frequency decreases to $2\, beats \,s^{-1}$ . What is the frequency of fork $A$ ?
a.
$335\, Hz$
b.
$338\, Hz$
c.
$345\, Hz$
d.
$342\, Hz$
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The volume $V$ of a given mass of monoatomic gas changes with temperature $T$ according to the relation
$V =KT \frac{2}{3}$ . The workdone when temperature changes by $90\,K$ will be $xR$ . The value of $x$ is
[ $R$ universal gas constant ]
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A wire of $1\,\Omega$ has a length of $1\,m$ . It is stretched till its length increases by $25%$ . The percentage change in
resistance to the nearest integer is :
a.
$12. 5%$
b.
$76%$
c.
$25%$
d.
$56%$
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A scooter accelerates from rest for time $t_{1}$ at constant rate $a_{1}$ and then retards at constant rate $a_{2}$ for time $t_{2}$ and
comes to rest. The correct value of $\frac{t_{1}}{t_{2}}$ will be :
a.
$\frac{a}{a_{1}}^{2}$
b.
$\frac{a}{a_{2}}^{1}$
c.
$\frac{a_{1}+a_{2}}{a_{1}}$
d.
$\frac{a_{1}+a_{2}}{a_{2}}$
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Given below are two statements
Statement $I$ : An electric dipole is placed at the centre of a hollow sphere. The flux of electric field through the
sphere is zero, but the electric field is not zero anywhere in the sphere.
Statement $II$ : If $R$ is the radius of a solid metallic sphere and $Q$ be the total charge on it. The electric field at
any point on the spherical surface of radius $r(<R)$ is zero but the electric flux passing through this closed
spherical surface of radius $r$ is not
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.
Statement $I$ is false but Statement $II$ is true
c.
Statement $I$ is true but Statement $II$ is false
d.
Both Statement $I$ and Statement $II$ are false
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Time period of a simple pendulum is $T$ . The time taken to complete $\frac{5}{8}$ oscillations starting from mean position
is $\frac{\alpha}{12}T$ . The value of $\alpha$ is $______$ .
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An inclined plane making an angle of $30^{\circ}$ with the horizontal is placed in a uniform horizontal electric field
$200\frac{N}{C}$ as shown in the figure. A body of mass $1\, kg$ and charge $5\, mC$ is allowed to slide down from rest at a
height of $1\,m$ . If the coefficient of friction is $0. 2,$ find the time taken by the body to reach the bottom.
$[g= 9. 8\,m\,s^{-2}; \, sin 30^{\circ}= \frac{1}{2} ; \, cos 30^{\circ}= \frac{\sqrt{3}}{2}]$
a.
$0. 92\,s$
b.
$1. 3\,s$
c.
$0. 46\,s$
d.
$2. 3\,s$
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Given below are two statements:
Statement $I$ : A second's pendulum has a time period of $1$ second.
Statement $II$ : It takes precisely one second to move between the two extreme positions. In the light of the
above statements,
choose the correct answer from the options given below
a.
Statement $I$ is false but Statement $II$ is true
b.
Both Statement $I$ and Statement $II$ are true
c.
Both Statement $I$ and Statement $II$ are False
d.
Statement $I$ is true but Statement $II$ is false
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$1$ mole of rigid diatomic gas performs a work of $\frac{Q}{5}$ when heat $Q$ is supplied to it. The molar heat capacity of
the gas during this transformation is $\frac{xR}{8}.$ The value of $x$ is
[ $R$ universal gas constant]
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$27$ similar drops of mercury are maintained at $10\,V$ each. All these spherical drops combine into a single big
drop. The potential energy of the bigger drop is ___________ times that of a smaller drop.
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A ball weighing $10\,g$ is moving with a velocity of $90\,m\,s^{-1}.$ If the uncertainty in its velocity is $5%$ , then the
uncertainty in its position is _ $\times 10^{-33}\,m.$ (Rounded off to the nearest integer)
[Given: $h = 6. 63 \times 10^{-34}\, Js$ ]
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The average $S -F$ bond energy in $kJ \, mol^{-1}$ of $SF_{6}$ is _. (Rounded off to the nearest integer)
[Given : The values of standard enthalpy of formation of $SF_{6}(g), \,S(g)$ and $F(g)$ are $-1100, \,275$ and
$80\, kJ \, mol^{-1}$ respectively.]
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The $NaNO_{3}$ weighed out to make $50\, mL$ of an aqueous solution containing $70. 0\, mg \, Na^{+}$ per $mL$ is_ $g$ .
(Rounded off to the nearest integer) [Given : Atomic weight in $gmol^{-1} -Na \, : \,23; \,N\, : \,14; \,O\, : \,16$ ]
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$Emf$ of the following cell at $298\,K$ in $V$ is $x \times 10^{-2}$
$Zn Zn^{2+}(0. 1M) Ag^{+}(0. 01M) Ag$
The value of $x$ is ________________ (Rounded off to the nearest integer)
$[Given : \,E^{\theta }_{Zn^{2+}/ Zn} = -0. 76\,V; \,E^{\theta }_{Ag^{+}/ Ag} = +0. 80\,V; \,\,\frac{2.303 RT}{F} = 0. 059]$
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When $12. 2\,g$ of benzoic acid is dissolved in $100\,g$ of water, the freezing point of solution was found to be
$-0. 93\,^{\circ}C(K_{f}(H_{2}O) = 1. 86\,K\, kg \, mol^{-1})$ . The number $(n)$ of benzoic acid molecules associated (assuming
$100%$ association) is _.
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Match List- $I$ with List- $II$ .
List- $I$ List- $II$
(a) Sucrose (i) $\beta$ $-D-$ Galactose and $\beta$ $-D-$ Glucose
(b) Lactose (ii) $\alpha$ $-D-$ Glucose and $\beta$ $-D-$ Fructose
(c) Maltose (iii) $\alpha$ $-D-$ Glucose and $\alpha$ $-D-$ Glucose
Choose the correct answer from the options given below:
Given below are two statements: one is labelled as Assertion $A$ and the other is labelled as Reason $R$ .
Assertion $A :$ In $TlI_{3},$ isomorphous to $CsI_{3}$ , the metal is present in $+1$ oxidation state.
Reason $R : Tl$ metal has fourteen $f$ electrons in its electronic configuration.
In the light of the above statements, choose the most appropriate answer from the options given below:
a.
$A$ is correct but $R$ is not correct
b.
Both $A$ and $R$ are correct and $R$ is the correct
explanation of $A$
c.
$A$ is not correct but $R$ is correct
d.
Both $A$ and $R$ are correct but $R$ is $NOT$ the
correct explanation of $A$
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If the activation energy of a reaction is $80. 9\, kJ \, mol^{-1}$ , the fraction of molecules at $700\,K$ , having enough
energy to react to form products is $e^{-x}$ . The value of $x$ is (Rounded off to the nearest integer) [Use
$R = 8. 31\,J\,K^{-1}\, mol^{-1}$ ]
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Let $a$ be an integer such that all the real roots of the polynomial $2x^{5} + 5x^{4} + 10x^{3} + 10x^{2} + 10x+ 10$ lie in
the interval $(a,a+ 1)$ . Then, $|a|$ is equal to ______.
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Let $A_{1}$ be the area of the region bounded by the curves $y= sinx,y= cosx$ and $y$ -axis in the first quadrant.
Also, let $A_{2}$ be the area of the region bounded by the curves $y= sinx,y= cosx$ , $x$ -axis and $x= \frac{\pi}{2}$ in the first
quadrant. Then,
a.
$2A_{1} =A_{2}$ and $A_{1}+A_{2} = 1 + \sqrt{2}$
b.
$A_{1} :A_{2} = 1 : \sqrt{2}$ and $A_{1}+A_{2} = 1$
c.
$A_{1} :A_{2} = 1 : 2$ and $A_{1}+A_{2} = 1$
d.
$A_{1} =A_{2}$ and $A_{1}+A_{2} = \sqrt{2}$
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Let $f(x)$ be a differentiable function at $x=a$ with $f'(a) = 2$ and $f(a) = 4$ . Then $_{x}lim_{\rightarrow \rightarrow a} \frac{xf(a)-af(x)}{x-a}$ equals:
a.
$a+ 4$
b.
$2a-4$
c.
$4 -2a$
d.
$2a+ 4$
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Let $L$ be a line obtained from the intersection of two planes $x+ 2y+z= 6$ and $y+ 2z= 4$ . If point
$P(\alpha ,\beta ,\gamma )$ is the foot of perpendicular from $(3, 2, 1)$ on $L$ , then the value of $21(\alpha +\beta +\gamma )$ equals:
a.
$102$
b.
$142$
c.
$68$
d.
$136$
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$1 0 0 1 0 0$
$[ ] [ ]$
If the matrix $A= 0 2 0$ satisfies the equation $A^{20} +\alpha A^{19} +\beta A= 0 4 0$ for some real numbers
$[3 0 -1] [0 0 1]$
$\alpha$ and $\beta$ , then $\beta - \alpha$ is equal to ______.
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$\{2 sin(-\frac{\pi x}{2}), \, if \,x< -1$
Let $f :R\rightarrow \rightarrowR$ be defined as $f(x) = ax^{2} +x+b , \, if \, -1 \leq x\leq 1$
$\{$
$sin(\pi x), \, if \,x> 1$
If $f(x)$ is continuous on $R$ , then $a+b$ equals :
a.
$1$
b.
$3$
c.
$-3$
d.
$-1$
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Let $\alpha$ and $\beta$ be two real numbers such that $\alpha +\beta = 1$ and $\alpha \beta = -1$ . Let $p_{n} = (\alpha )^{n} + (\beta )^{n}$ , $p_{n-1} = 11$ and
$p_{n+1} = 29$ for some integer $n⩾ 1$ . Then, the value of $p^{2}_{n}$ is______.
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Let slope of the tangent line to a curve at any point $P(x,y)$ be given by $\frac{xy^{2}+y}{x}$ . If the curve intersects the line
$x+ 2y= 4$ at $x= -2$ , then the value of $y$ , for which the point $(3,y)$ lies on the curve, is :
a.
$-\frac{4}{3}$
b.
$\frac{18}{35}$
c.
$-\frac{18}{19}$
d.
$- \frac{18}{11}$
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If the mirror image of the point $(1, 3, 5)$ with respect to the plane $4x-5y+ 2z= 8$ is $(\alpha ,\beta ,\gamma )$ , then
$5(\alpha +\beta +\gamma )$ equals :
a.
$43$
b.
$47$
c.
$41$
d.
$39$
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Let $L$ be a common tangent line to the curves $4x^{2} + 9y^{2} = 36$ and $(2x)^{2} + (2y)^{2} = 31$ . Then the square of the
slope of the line $L$ is ______.
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Let $A= {1, 2, 3, … , 10}$ and $f :A\rightarrow \rightarrow A$ be defined as
$k+ 1 if \,k\,is odd$
$f(k) ={$
$k if \,k\,is even$
Then the number of possible functions $g:A\rightarrow \rightarrow A$ such that $gof =f$ is:
a.
$^{10}C_{5}$
b.
$5^{5}$
c.
$5!$
d.
$10^{5}$
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If $0 <a,b< 1$ , and $tan^{-1} a+ tan^{-1} b= \frac{\pi}{4}$ , then the value of $(a+b) - ( \frac{a^{2}+b^{2}}{2} )+( \frac{a^{3}+b^{3}}{3})- (\frac{a^{4}+b^{4}}{4})+ …$
is :
a.
$log_{e}(\frac{e}{2})$
b.
$e$
c.
$e^{2} -1$
d.
$log_{e}2$
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A natural number has prime factorization given by $n= 2^{x}3^{y}5^{z}$ , where $y$ and $z$ are such that $y+z= 5$ and
$y^{-1} +z^{-1} = \frac{5}{6} ,y>z$ . Then the number of odd divisors of $n$ , including $1$ , is:
a.
$12$
b.
$6$
c.
$11$
d.
$6x$
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Let $F_{1}(A,B,C) = (A\wedge ~B) \vee [~C\wedge (A\vee B)] \vee ~A$ and $F_{2}(A,B) = (A\vee B) \vee (B\rightarrow ~\rightarrow A)$ be two logical
expressions. Then :
a.
$F_{1}$ is a tautology but $F_{2}$ is not a tautology
b.
$F_{1}$ is not a tautology but $F_{2}$ is a tautology
c.
Both $F_{1}$ and $F_{2}$ are not tautologies
d.
$F_{1}$ and $F_{2}$ both are tautologies
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If the locus of the mid-point of the line segment from the point $(3, 2)$ to a point on the circle, $x^{2} +y^{2} = 1$ is a
circle of radius $r$ , then $r$ is equal to
a.
$\frac{1}{4}$
b.
$1$
c.
$\frac{1}{3}$
d.
$\frac{1}{2}$
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Let $f(x) = sin^{-1} x$ and $g(x) = \frac{x^{2}-x-2}{2x^{2}-x-6}$ . If $g(2) =_{x}lim_{\rightarrow 2\rightarrow } g(x)$ , then the domain of the function $fog$ is
a.
$(-\infty , -1] \cup [2, \infty )$
b.
$(-\infty , -2]\cup [-\frac{3}{2}, \infty )$
c.
$(-\infty , -2]\cup [-\frac{4}{3} , \infty )$
d.
$(-\infty , -2] \cup [-1, \infty )$
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Let $A(1, 4)$ and $B(1, -5)$ be two points. Let $P$ be a point on the circle $((x-1))^{2} + (y-1)^{2} = 1$ , such that
$(PA)^{2} + (PB)^{2}$ have maximum value, then the points, $P, \,A$ and $B$ lie on
a.
a hyperbola
b.
a straight line
c.
an ellipse
d.
a parabola
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Consider the following system of equations:
$x+ 2y-3z=a$
$2x+ 6y-11z=b$
$x-2y+ 7z=c$
where $a,b$ and $c$ are real constants. Then the system of equations :
a.
has a unique solution when $5a= 2b+c$
b.
has no solution for all $a,b$ and $c$
c.
has infinite number of solutions when
$5a= 2b+c$
d.
has a unique solution for all $a,b$ and $c$
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Let $X_{1},X_{2}, … ,X_{18}$ be eighteen observations such that $\sum ^{18}_{i=1}(X_{i}- \alpha ) = 36$ and $\sum ^{18}_{i=1} (X_{i}- \beta )^{2} = 90$ ,
where $\alpha$ and $\beta$ are distinct real numbers. If the standard deviation of these observations is $1$ , then the value of
$|\alpha - \beta |$ is _______.
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$-^{Let}z^{be those complex numbers which satisfy}|z+ 5| \leq 4^{and}z(1 +i) +z(1 - i)^{⩾} -10,i^{=\sqrt{-1}. If the}$
maximum value of $|z+ 1|^{2}$ is $\alpha +\beta \sqrt{2}$ , then the value of $(\alpha +\beta )$ is
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$||$
$--$
If vectors $\vec{a}_{1} =xˆi -ˆj + ˆk$ and $\vec{a}_{2} = ˆi +yˆj +zˆk$ are collinear, then a possible unit vector parallel to the vector
$xˆi +yˆj +zˆk$ is:
a.
$\frac{1}{\sqrt{2}} (-ˆj +ˆk)$
b.
$\frac{1}{\sqrt{3}}(ˆi +ˆj - ˆk)$
c.
$\frac{1}{\sqrt{2}} (ˆi -ˆj)$
d.
$\frac{1}{\sqrt{3}}(ˆi -ˆj +ˆk)$
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Let the normals at all the points on a given curve pass through a fixed point $(a,b)$ . If the curve passes through
$(3, -3)$ and $(4, -2\sqrt{2})$ , given that $a-2\sqrt{2}\,b= 3$ , then $(a^{2} +b^{2} +ab)$ is equal to _____.
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If the arithmetic mean and the geometric mean of the $p^{th}$ and $q^{th}$ terms of the sequence $-16, 8, -4, 2, …$
satisfy the equation $4x^{2} -9x+ 5 = 0$ , then $p+q$ is equal to _______.
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