A bus moving along a straight highway with speed of $72\,km/h$ is brought to halt within $4s$ after applying the
brakes. The distance travelled by the bus during this time (Assume the retardation is uniform) is _____m.
✓ Accepted Answer:40
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Q2mcq
A cyclist starts from the point $P$ of a circular ground of radius $2\,km$ and travels along its circumference to the
point $S$ . The displacement of a cyclist is:
a.
$\sqrt{8}\,km$
Correct Answer
b.
$8\,km$
c.
$6\,km$
d.
$4\,km$
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Q3mcq
A $90\,kg$ body placed at $2R$ distance from surface of earth experiences gravitational pull of :
$\,(\,R = \,Radius of earth,\,g = 10\,m\,s^{-2}\,)\,$
a.
$100\,N$
Correct Answer
b.
$300\,N$
c.
$225\,N$
d.
$120\,N$
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Q4nat
The displacement of a particle executing SHM is given by $x= 10 sin(wt+ \frac{\pi}{3})m$ . The time period of motion
is $3.14\,s$ . The velocity of the particle at $t= 0$ is ______ $m/s$ .
✓ Accepted Answer:10
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Q5nat
A light ray is incident on a glass slab of thickness $4\sqrt{3}\,cm$ and refractive index $\sqrt{2}$ . The angle of incidence is
equal to the critical angle for the glass slab with air. The lateral displacement of ray after passing through glass
slab is _____ $cm$ . $($ Given $sin 15^{\circ } = 0.25)$
✓ Accepted Answer:2
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Q6mcq
Given below are two statements : Statement I : The contact angle between a solid and a liquid is a property of
the material of the solid and liquid as well. Statement II : The rise of a liquid in a capillary tube does not depend
on the inner radius of the tube. In the light of the above statements, choose the correct answer from the options
given below:
a.
Statement I is true but Statement II is false.
Correct Answer
b.
Statement I is false but Statement II is true.
c.
Both Statement I and Statement II are false.
d.
Both Statement I and Statement II are true.
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Q7mcq
Given below are two statements: one is labelled as Assertion $A$ and the other is labelled as Reason R.
Assertion A: Number of photons increases with increase in frequency of light. Reason R: Maximum kinetic
energy of emitted electrons increases with the frequency of incident radiation. In the light of the above
statements, choose the most appropriate answer from the options given below:
a.
Both $A$ and $R$ are correct and $R$ is the correct
explanation of $A$ .
b.
Both $A$ and $R$ are correct and $R$ is NOT the
correct explanation of $A$ .
c.
$A$ is not correct but $R$ is correct.
Correct Answer
d.
$A$ is correct but $R$ is not correct.
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Q8mcq
The width of one of the two slits in a Young's double slit experiment is 4 times that of the other slit. The ratio
of the maximum of the minimum intensity in the interference pattern is:
a.
$1 : 1$
b.
$4 : 1$
c.
$9 : 1$
Correct Answer
d.
$16 : 1$
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Q9mcq
A charge $q$ is placed at the center of one of the surface of a cube. The flux linked with the cube is:
a.
$\frac{q}{2\epsilon _{0}}$
Correct Answer
b.
$\frac{q}{8\epsilon _{0}}$
c.
Zero
d.
$\frac{q}{4\epsilon _{0}}$
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Q10mcq
According to Bohr's theory, the moment of momentum of an electron revolving in $4^{th\,}$ orbit of hydrogen atom
is:
a.
$\frac{h}{\pi}$
b.
$\frac{h}{2\pi}$
c.
$8\frac{h}{\pi}$
d.
$2\frac{h}{\pi}$
Correct Answer
No explanation saved for this question yet.
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In simple harmonic motion, the total mechanical energy of given system is $E$ . If mass of oscillating particle $P$
is doubled then the new energy of the system for same amplitude is:
a.
$E$
b.
$E/\sqrt{2}$
c.
$2E$
d.
$E\sqrt{2}$
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The magnetic moment of a bar magnet is $0.5Am^{2}$ . It is suspended in a uniform magnetic field of $8 \times 10^{-2}\,T$ .
The work done in rotating it from its most stable to most unstable position is:
a.
$8 \times 10^{-2}\,J$
b.
$4 \times 10^{-2}\,J$
c.
Zero
d.
$16 \times 10^{-2}\,J$
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A parallel plate capacitor of capacitance $12.5pF$ is charged by a battery connected between its plates to
potential difference of $12.0\,V$ . The battery is now disconnected and a dielectric slab $(\epsilon _{r} = 6)$ is inserted
between the plates. The change in its potential energy after inserting the dielectric slab is _____ $10^{-12}\,J$ .
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Applying the principle of homogeneity of dimensions, determine which one is correct, where $T$ is time period,
$G$ is gravitational constant, $M$ is mass, $r$ is radius of orbit.
a.
$T^{2} = \frac{4\pi ^{2}r^{2}}{GM}$
b.
$T^{2} = \frac{4\pi ^{2}r}{GM^{2}}$
c.
$T^{2} = \frac{4\pi ^{2}r^{3}}{GM}$
d.
$T^{2} = 4\pi ^{2}r^{3}$
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A body of $m\,kg$ slides from rest along the curve of vertical circle from point $A$ to $B$ in friction less path. The
velocity of the body at $B$ is:
$\,(given,\,R= 14\,m,g= 10\,m/s^{2}\,and\, = 1.4\,)\,\sqrt{2}$
a.
$16.7\,m/s$
b.
$19.8\,m/s$
c.
$10.6\,m/s$
d.
$21.9\,m/s$
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Arrange the following in the ascending order of wavelength: A. Gamma rays $(\lambda _{1})$ B. $x$ - rays $(\lambda _{2})$ C. Infrared
waves $(\lambda _{3})$ D. Microwaves $(\lambda _{4})$ Choose the most appropriate answer from the options given below
Two wires $A$ and $B$ are made up of the same material and have the same mass. Wire $A$ has radius of $2.0\,mm$
and wire $B$ has radius of $4.0\,mm$ . The resistance of wire $B$ is $2\Omega$ . The resistance of wire $A$ is _____ $\Omega$ .
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Mercury is filled in a tube of radius $2\,cm$ up to a height of $30\,cm$ . The force exerted by mercury on the bottom
of the tube is _____ N. (Given, atmospheric pressure $= 10^{5}Nm^{-2}$ , density of mercury $= 1.36 \times 10^{4}\,kg\,m^{-}$
$^{3}, \,g = 10\,m\,s^{-2},\pi = \frac{22}{7})$
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The disintegration energy $Q$ for the nuclear fission of $^{235}U ^{140}Ce +^{94}Zr +n$ is ______ $MeV$ . Given
atomic masses of $^{235}U : 235.0439u;^{140}Ce : 139.9054u$ , $^{94}Z\vec{r}: 93.9063u;n: 1.0086u,\,$ Value of
$c^{2} = 931MeV/u$
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A $2\,kg$ brick begins to slide over a surface which is inclined at an angle of $45^{\circ }$ with respect to horizontal axis.
The co-efficient of static friction between their surfaces is:
a.
$1.7$
b.
$\frac{1}{\sqrt{3}}$
c.
$0.5$
d.
$1$
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A rod of length $60\,cm$ rotates with a uniform angular velocity $20rads^{-1}$ about its perpendicular bisector, in a
uniform magnetic filed $0.5T$ . The direction of magnetic field is parallel to the axis of rotation. The potential
difference between the two ends of the rod is _____V.
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In a system two particles of masses $m_{1} = 3\,kg$ and $m_{2} = 2\,kg$ are placed at certain distance from each other.
The particle of mass $m_{1}$ is moved towards the center of mass of the system through a distance $2\,cm$ . In order
to keep the center of mass of the system at the original position, the particle of mass $m_{2}$ should move towards
the center of mass by the distance _____ $cm$ .
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Two parallel long current carrying wire separated by a distance $2r$ are shown in the figure. The ratio of
magnetic field at $A$ to the magnetic field produced at $C$ is $\frac{x}{7}$ . The value of $x$ is _____
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A sample of gas at temperature $T$ is adiabatically expanded to double its volume. Adiabatic constant for the gas
is $\gamma = 3/2$ . The work done by the gas in the process is: $(\mu = 1\,mole)$
a.
$RT[1 -2\sqrt{2}]$
b.
$RT[\sqrt{2}-2]$
c.
$RT[2 - \sqrt{2}]$
d.
$RT[2\sqrt{2}-1]$
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Choose the Incorrect Statement about Dalton's Atomic Theory
a.
chemical reactions involve reorganization of
atoms
b.
Matter consists of indivisible atoms.
c.
Compounds are formed when atoms of different
elements combine in any ratio.
d.
Compounds are formed when atoms of different
elements combine in any ratio. All the atoms of a
given element have identical properties including
identical mass.
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Fuel cell, using hydrogen and oxygen as fuels, A. has been used in spaceship B. has as efficiency of $40%$ to
produce electricity C. uses aluminum as catalysts D. is eco-friendry E. is actually a type of Galvanic cell only
Choose the correct answer from the options given below:
a.
A, B, D, E only
b.
A, D, E only
c.
A, B, D only
d.
A, B, C only
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The adsorbent used in adsorption chromatography is/are - A. silica gel B. alumina C. quick lime D. magnesia
Choose the most appropriate answer from the options given below :
a.
A only
b.
B only
c.
C and D only
d.
A and B only
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The correct statement/s about Hydrogen bonding is/are A. Hydrogen bonding exists when $H$ is covalently
bonded to the highly electro negative atom. B. Intermolecular $H$ bonding is present in o-nitro phenol C.
Intramolecular $H$ bonding is present in HF. D. The magnitude of $H$ bonding depends on the physical state of
the compound. E. H-bonding has powerful effect on the structure and properties of compounds Choose the
correct answer from the options given below:
a.
A, B, D only
b.
A, D, E only
c.
A only
d.
A, B, C only
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A first row transition metal with highest enthalpy of atomisation, upon reaction with oxygen at high
temperature forms oxides of formula $M_{2}O_{n}$ (where $n = 3, 4$ , 5). The 'spin-only' magnetic moment value of the
amphoteric oxide from the above oxides is ______ $BM$ (near integer) (Given atomic number:
$Sc : 21, Ti : 22, \,V : 23, Cr : 24, Mn : 25, Fe : 26, Co : 27$ , $Ni : 28, Cu : 29, Zn : 30$ )
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Three moles of an ideal gas are compressed isothermally from $60\,L$ to $20\,L$ using constant pressure of $5\,atm$ .
Heat exchange $Q$ for the compression is - ______ Lit. atm.
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Number of compounds / species from the following with non-zero dipole moment is ______
$BeCl_{2}, BCl_{3}, NF_{3}, XeF_{4}, CCl_{4}, H_{2}O, H_{2}\,S, HBr, CO_{2}, H_{2}, HCl$
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The equilibrium constant for the reaction $SO_{3}(g)\rightleftharpoons SO_{2}(\,g) + \frac{1}{2}O_{2}(\,g)$ is $K_{c} = 4.9 \times 10^{-2}$ . The value of $K_{c}$
for the reaction given below is $2SO_{2}(\,g) + O_{2}(\,g)\rightleftharpoons 2SO_{3}(\,g)$ is :
a.
4.9
b.
49
c.
41.6
d.
416
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$2.7\,kg$ of each of water and acetic acid are mixed. The freezing point of the solution will be $-x^{\circ }C$ . Consider
the acetic acid does not dimerise in water, nor dissociates in water. $x=$ ______ (nearest integer) [Given: Molar
mass of water $= 18\,g\,mol^{-1}$ , acetic acid $= 60\,g\,mol^{-1} K_{f}H_{2}O : 1.86\,K\,kg\,mol^{-1} K_{f}$ acetic acid:
$3.90\,K\,kg\,mol^{-1}$ freezing point: $H_{2}O = 273\,K$ , acetic acid $= 290\,K$ ]
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Given below are two statements : Statement I : The correct order of first ionization enthalpy values of
$Li, Na, F$ and $Cl$ is $Na < Li < Cl < F$ . Statement II : The correct order of negative electron gain enthalpy
values of $Li$ , $Na, F$ and $Cl$ is $Na < Li < F < Cl$ In the light of the above statements, choose the correct
answer from the options given below :
a.
Statement I is true but Statement II is false
b.
Statement I is false but Statement II is true
c.
Both Statement I and Statement II are false
d.
Both Statement I and Statement II are true
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$List - I \frac{List - II}{\,Functional isomers\,}$
$\frac{\,A.\,}{\,B.\,} \alpha \,- Glucose and\,\alpha \,- Galactose\, \frac{\,I.\,}{\,II.\,}$
Match List I with List II $\alpha \,- Glucose and\,\beta \,- Glucose\, \frac{\,Homologous\,}{\,Anomers\,}$ Choose the
$\frac{\,C.\,}{\,D.\,} \alpha \,- Glucose and\,\alpha \,- Fructose\, \frac{\,III.\,}{\,IV.\,}$
$\alpha \,- Glucose and\,\alpha \,- Ribose\, \,Epimers\,$
correct answer from the options given below:
a.
A-IV, B-III, C-I, D-II
b.
A-III, B-IV, C-I, D-II
c.
A-IV, B-III, C-II, D-I
d.
A-III, B-IV, C-II, D-I
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The number of species from the following that have pyramidal geometry around the central atom is _______.
$S_{2}O^{2-}_{3} , SO^{2-}_{4} , SO^{2-}_{3} , S_{2}O^{2-}_{7}$
a.
4
b.
3
c.
2
d.
1
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For a strong electrolyte, a plot of molar conductivity against (concentration) $^{1/2}$ is a straight line, with a
negative slope, the correct unit for the slope is
a.
$Scm^{2}\,mol^{-3/2}\,L^{-1/2}$
b.
$Scm^{2}\,mol^{-3/2}\,L^{1/2}$
c.
$Scm^{2}\,mol^{-3/2}\,L$
d.
$Scm^{2}\,mol^{-1}\,L^{1/2}$
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Consider the following reaction, the rate expression of which is given below
$A + B \rightarrow C\rightarrow$
$\,rate\, = k[A]^{1/2}[\,B]^{1/2}$
The reaction is initiated by taking $1M$ concentration of $A$ and $B$ each. If the rate constant $(k)$ is $4.6 \times 10^{-2}\,s^{-1}$
, then the time taken for $A$ to become $0.1M$ is ______ sec. (nearest integer)
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Consider a hyperbola $H$ having centre at the origin and foci on the $x$ -axis. Let $C_{1}$ be the circle touching the
hyperbola $H$ and having the centre at the origin. Let $C_{2}$ be the circle touching the hyperbola $H$ at its vertex and
having the centre at one of its foci. If areas (in sq units) of $C_{1}$ and $C_{2}$ are $36\pi$ and $4\pi$ , respectively, then the
length (in units) of latus rectum of $H$ is
a.
$\frac{14}{3}$
b.
$\frac{28}{3}$
c.
$\frac{11}{3}$
d.
$\frac{10}{3}$
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Let $P$ be the point of intersection of the lines $\frac{x-2}{1} = \frac{y-4}{5} = \frac{z-2}{1}$ and $\frac{x-3}{2} = \frac{y-2}{3} = \frac{z-3}{2}$ . Then, the shortest
distance of P from the line $4x= 2y=z$ is
a.
$\frac{5\sqrt{14}}{7}$
b.
$\frac{3\sqrt{14}}{7}$
c.
$\frac{\sqrt{14}}{7}$
d.
$\frac{6\sqrt{14}}{7}$
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Let PQ be a chord of the parabola $y^{2} = 12x$ and the midpoint of PQ be at $(4, 1)$ . Then, which of the following
point lies on the line passing through the points $P$ and Q?
a.
$(3, -3)$
b.
$(2, -9)$
c.
$( \frac{3}{2}, -16)$
d.
$(\frac{1}{2}, -20)$
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If $\int cosec^{5} xdx=\alpha cotxcosecx(cossc^{2} x+ \frac{3}{2})+\beta log_{\epsilon } tan \frac{x}{2} +C$ where $\alpha ,\beta \in R$ and $C$ is the constant
of integration, then the value of $8(\alpha +\beta )$ equals _______
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There are 4 men and 5 women in Group A, and 5 men and 4 women in Group B. If 4 persons are selected from
each group, then the number of ways of selecting 4 men and 4 women is _____
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If the mean of the following probability distribution of a random variable $X$ :
$\frac{X}{P(X)}\frac{0}{a}\frac{2}{2a}\frac{4}{a+b}\frac{6}{2b}\frac{8}{3b}$ is $\frac{46}{9}$ , then the variance of the distribution is
a.
$\frac{173}{27}$
b.
$\frac{566}{81}$
c.
$\frac{151}{27}$
d.
$\frac{581}{81}$
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Given that the inverse trigonometric function assumes principal values only. Let $x$ , $y$ be any two real numbers
in $[-1, 1]$ such that $cos^{-1} x-sin^{-1} y=\alpha , \frac{-\pi}{2} \leq \alpha \leq \pi$ .
Then, the minimum value of $x^{2} +y^{2} + 2xysin\alpha$ is
a.
0
b.
-1
c.
$\frac{1}{2}$
d.
$-\frac{1}{2}$
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Consider the function $f :R\rightarrow \rightarrow R$ defined by $f(x) = \frac{2x}{\sqrt{1+9x^{2}}}$ . If the composition of
$f, (f^{\circ} f^{\circ} f^{\circ} \cdots \circ f)(x) = \frac{2^{10}x}{\sqrt{1+9\alpha x^{2}}}$ , then the value of $\sqrt{3\alpha + 1}$ is equal to ______
$ $
$10\,times\,$
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Let $y=y(x)$ be the solution of the differential equation $(x+y+ 2)^{2}dx=dy,y(0) = -2$ . Let the maximum
and minimum values of the function $y=y(x)$ in $[0, \frac{\pi}{3} ]$ be $\alpha$ and $\beta$ , respectively. If
$(3\alpha +\pi )^{2} +\beta ^{2} =\gamma +\delta \sqrt{3},\gamma ,\delta \in Z$ , then $\gamma +\delta$ equals ______
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Let three real numbers $a,b,c$ be in arithmetic progression and $a+ 1,b,c+ 3$ be in geometric progression. If
$a> 10$ and the arithmetic mean of $a,b$ and $c$ is 8, then the cube of the geometric mean of $a,b$ and $c$ is
a.
128
b.
316
c.
120
d.
312
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Consider a triangle $ABC$ having the vertices $A(1, 2), B(\alpha ,\beta )$ and $C(\gamma ,\delta )$ and angles $\angle ABC = \frac{\pi}{6}$ and
$\angle BAC = \frac{2\pi}{3}$ . If the points $B$ and $C$ lie on the line $y=x+ 4$ , then $\alpha ^{2} +\gamma ^{2}$ is equal to ________
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$1 3$
Let $A$ be a $2 \times 2$ symmetric matrix such that $A[ ]=[ ]$ and the determinant of $A$ be 1 . If $A^{-1} =\alpha A+\beta I$ ,
$1 7$
where $I$ is an identity matrix of order $2 \times 2$ , then $\alpha +\beta$ equals _______
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For $\lambda > 0$ , let $\theta$ be the angle between the vectors $\vec{a}= \hat{i}+\lambda \hat{j}-3\hat{k}$ and $\vec{b}= 3\hat{i}- \hat{j}+ 2\hat{k}$ . If the vectors $\vec{a}+ \vec{b}$
and $\vec{a}- \vec{b}$ are mutually perpendicular, then the value of (14 cos $\theta )^{2}$ is equal to
a.
50
b.
40
c.
25
d.
20
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Let $\vec{a}= \hat{i}+ \hat{j}+ \hat{k}, \vec{b}= 2\hat{i}+ 4\hat{j}-5\hat{k}$ and $\vec{c}=x\hat{i}+ 2\hat{j}+ 3\hat{k},x\in R$ . If $\vec{d}$ is the unit vector in the direction of
$\vec{b}+ \vec{c}$ such that $\vec{a}\cdot \vec{d}= 1$ , then $(\vec{a}\times \vec{b}) \cdot \vec{c}$ is equal to
a.
11
b.
3
c.
9
d.
6
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Let $C$ be a circle with radius $\sqrt{10}$ units and centre at the origin. Let the line $x+y= 2$ intersects the circle $C$
at the points $P$ and $Q$ . Let $MN$ be a chord of $C$ of length 2 unit and slope -1. Then, a distance (in units)
between the chord PQ and the chord $MN$ is
a.
$3 - \sqrt{2}$
b.
$\sqrt{2}+ 1$
c.
$\sqrt{2}-1$
d.
$2 - \sqrt{3}$
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Consider a line $L$ passing through the points $P(1, 2, 1)$ and $Q(2, 1, -1)$ . If the mirror image of the point
$A(2, 2, 2)$ in the line $L$ is $(\alpha ,\beta ,\gamma )$ , then $\alpha +\beta + 6\gamma$ is equal to _______
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$\frac{72^{x}-9^{x}-8^{x}+1}{\sqrt{2}-\sqrt{1+cosx}}, x\neq 0$
If the function $f(x) ={$ is continuous at $x= 0$ , then the value of $a^{2}$ is equal to
$alog_{e}2 log_{e}3 ,x= 0$
a.
968
b.
1152
c.
746
d.
1250
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Let $S ={sin^{2} 2\theta :(sin^{4} \theta + cos^{4} \theta )x^{2} + (sin 2\theta )x+(sin^{6} \theta + cos^{6} \theta )= 0$ has real roots $}$ . If $\alpha$ and $\beta$ be the
smallest and largest elements of the set $S$ , respectively, then $3((\alpha -2)^{2} + (\beta -1)^{2})$ equals _________
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Let a relation $R$ on $N \times N$ be defined as: $(x_{1},y_{1})R (x_{2},y_{2})$ if and only if $x_{1} \leq x_{2}$ or $y_{1} \leq y_{2}$ . Consider the
two statements: (I) $R$ is reflexive but not symmetric. (II) $R$ is transitive Then which one of the following is
true?
a.
Both (I) and (II) are correct.
b.
Only (II) is correct.
c.
Neither (I) nor (II) is correct.
d.
Only (I) is correct.
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Let $f :R\rightarrow \rightarrow R$ be a thrice differentiable function such that $f(0) = 0,f(1) = 1,f(2) = -1,f(3) = 2$ and
$f(4) = -2$ . Then, the minimum number of zeros of $(3f'f'' +ff^{'''})(x)$ is _______
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In a tournament, a team plays 10 matches with probabilities of winning and losing each match as $\frac{1}{3}$ and $\frac{2}{3}$
respectively. Let $x$ be the number of matches that the team wins, and $y$ be the number of matches that team
loses. If the probability $P(|x- y| \leq$ 2) is $p$ , then $3^{9}p$ equals ______
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Let $f(x) = 3\sqrt{x-2}+ \sqrt{4 -x}$ be a real valued function. If $\alpha$ and $\beta$ are respectively the minimum and the
maximum values of $f$ , then $\alpha ^{2} + 2\beta ^{2}$ is equal to
a.
42
b.
38
c.
24
d.
44
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