The radius of third stationary orbit of electron for Bohr's atom is $R$ . The radius of fourth stationary orbit will
be:
a.
$\frac{4}{3}R$
b.
$\frac{16}{9}R$
Correct Answer
c.
$\frac{3}{4}R$
d.
$\frac{9}{16}R$
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Q2mcq
The acceleration due to gravity on the surface of earth is $g$ . If the diameter of earth reduces to half of its original
value and mass remains constant, then acceleration due to gravity on the surface of earth would be :
a.
$\frac{g}{4}$
b.
$2g$
c.
$\frac{g}{2}$
d.
$4g$
Correct Answer
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Q3mcq
A plane electromagnetic wave propagating in $x$ -direction is described by
$E_{y} =(200\,V\,m^{-1})sin[1. 5 \times 10^{7}t -0. 05x]; \,$ The intensity of the wave is :
(Use $\epsilon _{0} = 8. 85 \times 10^{-12}\,C^{2}\,N^{-1}\,m^{-2}$ )
a.
$35. 4\,W\,m^{-2}$
b.
$53. 1\,W\,m^{-2}$
Correct Answer
c.
$26. 6\,W\,m^{-2}$
d.
$106. 2\,W\,m^{-2}$
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Q4mcq
Identify the physical quantity that cannot be measured using spherometer :
a.
Radius of curvature of concave surface
b.
Specific rotation of liquids
Correct Answer
c.
Thickness of thin plates
d.
Radius of curvature of convex surface
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Q5mcq
Which of the following circuits is reverse - biased ?
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Q6mcq
A train is moving with a speed of $12\,m\,s^{-1}$ on rails which are $1. 5\,m$ apart. To negotiate a curve radius $400\,m$ ,
the height by which the outer rail should be raised with respect to the inner rail is (Given, $g= 10\,m\,s^{-2}$ ):
a.
$6. 0\, cm$
b.
$5. 4\, cm$
Correct Answer
c.
$4. 8\, cm$
d.
$4. 2\, cm$
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Q7mcq
A wire of length $10\, cm$ and radius $\sqrt{7}\times 10^{-4}\,m$ connected across the right gap of a meter bridge. When a
resistance of $4. 5\,\Omega$ is connected on the left gap by using a resistance box, the balance length is found to be at
$60\, cm$ from the left end. If the resistivity of the wire is $R \times 10^{-7}\,\Omega \,m$ , then value of $R$ is :
a.
$63$
b.
$70$
c.
$66$
Correct Answer
d.
$35$
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Q8nat
The charge accumulated on the capacitor connected in the following circuit is ______$\mu$ $C$ .
(Given $C = 150\,\mu F)$
✓ Accepted Answer:400
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Q9mcq
Given below are two statements:
Statement (I) : Planck's constant and angular momentum have the same dimensions.
Statement (II) : Linear momentum and moment of force have the same dimensions.
In 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.
Both Statement I and Statement II are false
c.
Both Statement I and Statement II are true
d.
Statement I is false but Statement II is true
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Q10mcq
Two bodies of mass $4\,g$ and $25\,g$ are moving with equal kinetic energies. The ratio of magnitude of their linear
momentum is :
a.
$3 : 5$
b.
$5 : 4$
c.
$2 : 5$
Correct Answer
d.
$4 : 5$
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A rectangular loop of length $2. 5\,m$ and width $2\,m$ is placed at $60^{\circ}$ to a magnetic field of $4\,T$ . The loop is
removed from the field in $10\, sec$ . The average emf induced in the loop during this time is
a.
$-2\,V$
b.
$+2\,V$
c.
$+1\,V$
d.
$-1\,V$
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Two immiscible liquids of refractive indices $\frac{8}{5}$ and $\frac{3}{2}$ respectively are put in a beaker as shown in the figure.
The height of each column is $6\, cm$ . A coin is placed at the bottom of the beaker. For near normal vision, the
apparent depth of the coin is $\frac{\alpha}{4} \, cm$ . The value of $\alpha$ is _______.
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A particle executes simple harmonic motion with an amplitude of $4\, cm$ . At the mean position, velocity of the
particle is $10\, cm \,s^{-1}$ . The distance of the particle from the mean position when its speed becomes $5\, cm \,s^{-1}$
is $\sqrt{\alpha}\, cm$ , where $\alpha =$ ______.
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If average depth of an ocean is $4000\,m$ and the bulk modulus of water is $2 \times 10^{9}\,N\,m^{-2}$ , then fractional
compression $\frac{\Delta V}{V}$ of water at the bottom of ocean is $\alpha \times 10^{-2}$ . The value of $\alpha$ is _______, (Given,
$g = 10\,m\,s^{-2}, \,\rho = 1000\, kg \,m^{-3}$ )
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Four particles, each of mass $1\, kg$ are placed at four corners of a square of side $2\,m$ . The moment of inertia of
the system about an axis perpendicular to its plane and passing through one of its vertex is $______\, kg \,m^{2}$ .
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Given below are two statements :
Statement (I) : Viscosity of gases is greater than that of liquids.
Statement (II) : Surface tension of a liquid decreases due to the presence of insoluble impurities.
In the light of the above statements, choose the most appropriate answer from the options given below :
a.
Statement I is correct but statement II is incorrect
b.
Statement I is incorrect but Statement II is correct
c.
Both Statement I and Statement II are incorrect
d.
Both Statement I and Statement II are correct
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$0. 08\, kg$ air is heated at constant volume through $5^{\circ}C$ . The specific heat of air at constant volume is
$0. 17\, kcal \, kg^{-1} \,^{\circ}C^{-1}$ and $1\,J = 4. 18\, joule \, cal^{-1}$ . The change in its internal energy is approximately.
a.
$318\,J$
b.
$298\,J$
c.
$284\,J$
d.
$142\,J$
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A body of mass $1000\, kg$ is moving horizontally with a velocity $6\,m\,s^{-1}$ . If $200\, kg$ extra mass is added, the
final velocity (in $m\,s^{-1}$ ) is:
a.
$6$
b.
$2$
c.
$3$
d.
$5$
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In a nuclear fission process, a high mass nuclide $(A≈236)$ with binding energy $7. 6\, MeV /$ Nucleon
dissociated into two middle mass nuclides $(A ≈118)$ , having binding energy of $8. 6\, MeV /$ Nucleon. The
energy released in the process would be _______ $MeV$ .
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Position of an ant ( $S$ in metres) moving in $Y -Z$ plane is given by $S = 2t^{2}ˆj + 5ˆk$ (where $t$ is in second). The
magnitude and direction of velocity of the ant at $t = 1\,s$ will be :
a.
$16\,m\,s^{-1}$ in y-direction
b.
$4\,m\,s^{-1}$ in $x$ -direction
c.
$9\,m\,s^{-1}$ in z-direction
d.
$4\,m\,s^{-1}$ in $y$ -direction
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A proton moving with a constant velocity passes through a region of space without any change in its velocity.
If $\vec{E}$ and $\vec{B}$ represent the electric and magnetic fields respectively, then the region of space may have :
(A) $E = 0, \,B= 0$ ; (B) $E = 0, \,B\neq 0$ ; (C) $E \neq 0, \,B= 0$ ; (D) $E \neq 0, \,B\neq 0$
Choose the most appropriate answer from the options given below :
a.
(A), (B) and (C) only
b.
(A), (C) and (D) only
c.
(A), (B) and (D) only
d.
(B), (C) and (D) only
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Two long, straight wires carry equal currents in opposite directions as shown in figure. The separation between
the wires is $5. 0\, cm$ . The magnitude of the magnetic field at a point $P$ midway between the wires is $_____ \mu T$
. (Given: $\mu _{0} = 4\pi \times 10^{-7}\,T\,m\,A^{-1}$ )
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A particle starts from origin at $t = 0$ with a velocity $5ˆi\,m\,s^{-1}$ and moves in $x -y$ plane under action of a force
which produces a constant acceleration of $(3ˆi + 2ˆj)\,m\,s^{-2}$ . If the $x$ -coordinate of the particle at that instant is
$84\,m$ , then the speed of the particle at this time is $\sqrt{\alpha}\,m\,s^{-1}$ . The value of $\alpha$ is _______.
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A convex lens of focal length $40\, cm$ forms an image of an extended source of light on a photoelectric cell. A
current $I$ is produced. The lens is replaced by another convex lens having the same diameter but focal length
$20\, cm$ . The photoelectric current now is
a.
$\frac{I}{2}$
b.
$4I$
c.
$2I$
d.
$I$
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An electric charge $10^{-6} \mu C$ is placed at origin $(0, \,0) m$ of $X -Y$ co-ordinate system. Two points $P$ and $Q$ are
situated at $(\sqrt{3}, \,\sqrt{3})\,m$ and $(\sqrt{6}, \,0)\,m$ respectively. The potential difference between the points $P$ and $Q$
will be :
a.
$\sqrt{3}\,V$
b.
$\sqrt{6}\,V$
c.
$0\,V$
d.
$3\,V$
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Two coils have mutual inductance $0. 002\,H$ . The current changes in the first coil according to the relation
$i=i_{0}sin\omega t$ , where $i_{0} = 5\,A$ and $\omega = 50\pi rad \,s^{-1}$ . The maximum value of $emf$ in the second coil is $\frac{\pi}{\alpha}\,V$ .
The value of $\alpha$ is
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A thin metallic wire having cross sectional area of $10^{-4}\,m^{2}$ is used to make a ring of radius $30\, cm$ . A positive
charge of $2\pi \,C$ is uniformly distributed over the ring, while another positive charge of $30\, pC$ is kept at the
centre of the ring. The tension in the ring is $_______\,N$ ; provided that the ring does not get deformed (neglect
the influence of gravity).
(Given, $\frac{1}{4\pi \epsilon _{0}} = 9 \times 10^{9}$ SI units)
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Consider the following data for the given reaction
$2 HI_{(g)} H_{2(\,g)}+ I_{2(\,g)}$
$HI(mol\vec{L}^{-1}) \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,0. 005 \,\,\,\,\,\,\,\,\,0. 01\,\,\,\,\,\,\,\,\, 0. 02$
Rate $(molL^{-1} \,s^{-1})\,\,\,\,\,\,7. 5 \times 10^{-4}\,\,\,\,\,\,3. 0 \times 10^{-3}\,\,\,\,\,\,\,1. 2 \times 10^{-2}$
The order of the reaction is __________.
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The ascending order of acidity of $- OH$ group in the following compounds is :
(A) $Bu \,-\, OH$
Choose the correct answer from the options given below :
a.
$(A)\, < \,(D)\, < \,(C)\, < \,(B)\, < \,(E)$
b.
$(C)\, < \,(A)\, < \,(D)\, < \,(B)\, < \,(E)$
c.
$(C)\, < \,(D)\, < \,(B)\, < \,(A)\, < \,(E)$
d.
$(A)\, < \,(C)\, < \,(D)\, < \,(B)\, < \,(E)$
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Yellow compound of lead chromate gets dissolved on treatment with hot $NaOH$ solution. The product of lead
formed is a :
(1) Tetraanionic complex with coordination number (2) Neutral complex with coordination number four
six
(3) Dianionic complex with coordination number six (4) Dianionic complex with coordination number
four
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Among the following, total number of meta directing functional groups is (Integer based)
$-OCH_{3}, -NO_{2}, -CN, -CH_{3}-NHCOCH_{3}$ , $-COR, -OH, -COOH, -Cl$
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If three moles of an ideal gas at $300\,K$ expand isothermally from $30 dm^{3}$ to $45 dm^{3}$ against a constant
opposing pressure of $80 kPa$ , then the amount of heat transferred is __________J.
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$NaCl$ reacts with conc. $H_{2}SO_{4}$ and $K_{2}Cr_{2}O_{7}$ to give reddish fumes (B), which react with $NaOH$ to give
yellow solution (C). (B) and (C) respectively are ;
a.
$CrO_{2}Cl_{2}, \, Na_{2}CrO_{4}$
b.
$Na_{2}CrO_{4}, \, CrO_{2}Cl_{2}$
c.
$CrO_{2}Cl_{2}, \, KHSO_{4}$
d.
$CrO_{2}Cl_{2}, \, Na_{2}Cr_{2}O_{7}$
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The number of electrons present in all the completely filled subshells having $n = 4$ and $s = + \frac{1}{2}$ is ____
(Where $n =$ principal quantum number and $s =$ spin quantum number)
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Consider the following complex ions
$P\, = \,[FeF_{6}]^{3-}$ , $Q\, = \,[V(H_{2}O)\,_{6}]^{2+}$ , $R\, = \,[Fe(H_{2}O)_{6}]^{2+}$
The correct order of the complex ions, according to their spin only magnetic moment values (in B.M.) is :
a.
$R\, < \,Q\, < \,P\,$
b.
$R\, < \,P < \,Q$
c.
$Q\, < \,R\, < \,P\,$
d.
$Q\, < \,P\, < \,R$
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The mass of silver (Molar mass of $Ag : 108 gmol^{-1}$ ) displaced by a quantity of electricity which displaces
$5600\, mL$ of $O_{2}$ at S.T.P. will be _____ g.
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$3-$ Methylhex-2-ene on reaction with $HBr$ in presence of peroxide forms an addition product (A). The number
of possible stereoisomers for ' $A$ ' is ________.
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Given below are two statements :
Statement (I): Aqueous solution of ammonium carbonate is basic.
Statement (II): Acidic/basic nature of salt solution of a salt of weak acid and weak base depends on $K_{a}$ and
$K_{b}$ value of acid and the base forming it.
In the light of the above statements, choose the most appropriate answer from the options given below :
a.
Both Statement I and Statement II are correct
b.
Statement I is correct but Statement II is
incorrect
c.
Both Statement I and Statement II are incorrect
d.
Statement I is incorrect but Statement II is
correct
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Given below are two statements :
Statement (I): p-nitrophenol is more acidic than m-nitrophenol and o-nitrophenol.
Statement (II): Ethanol will give immediate turbidity with Lucas reagent.
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.
Both Statement I and Statement II are true
c.
Both Statement I and Statement II are false
d.
Statement I is false but Statement II is true
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-
Mass of methane required to produce $22\,g$ of $CO$ after complete combustion is g. (Given Molar mass in g mol
1
, $C = 12. 0$ , $H = 1. 0$ , $O = 16. 0)$
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Given below are two statements :
Statement (I): The 4f and 5f - series of elements are placed separately in the Periodic table to preserve the
principle of classification.
Statement (II): s-block elements can be found in pure form in nature.
In light of the above statements, choose the most appropriate 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.
Statement I is true but Statement II is false
d.
Both Statement I and Statement II are false
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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): Melting point of Boron $(2453\,K)$ is unusually high in group $13$ elements.
Reason (R): Solid Boron has very strong crystalline lattice.
In the light of the above statements, choose the most appropriate answer from the options given below ;
a.
Both (A) and (R) are correct but (R) Is not the
correct explanation of (A)
b.
Both (A) and (R) are correct and (R) is the
correct explanation of (A)
c.
(A) is true but (R) is false
d.
(A) is false but (R) is true
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From the given list, the number of compounds with $+4\,$ oxidation state of Sulphur
$SO_{3}, H_{2}SO_{3}, SOCl_{2}, SF_{4}, BaSO_{4}, H_{2}\,S_{2}O_{7}$
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The portion of the line $4x+ 5y= 20$ in the first quadrant is trisected by the lines $L_{1}$ and $L_{2}$ passing through
the origin. The tangent of an angle between the lines $L_{1}$ and $L_{2}$ is :
a.
$\frac{8}{5}$
b.
$\frac{25}{41}$
c.
$\frac{2}{5}$
d.
$\frac{30}{41}$
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$2 0 1 1$
$[ ] [ ]$
Let $A = 1 1 0 , \,B = [B_{1} B_{2} B_{3}]$ , where $B_{1}$ , $B_{2}, \,B_{3}$ are column matrices, and $AB_{1} = 0$ ,
$[1 0 1] [0]$
$2 3$
$[ ] [ ]$
$AB_{2} = 3 , AB_{3} = 2$
$[0] [1]$
If $\alpha = |B|$ and $\beta$ is the sum of all the diagonal elements of $B$ , then $\alpha ^{3} +\beta ^{3}$ is equal to
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The distance, of the point $(7, -2, 11)$ from the line $\frac{x-6}{1} = \frac{y-4}{0} = \frac{z-8}{3}$ along the line $\frac{x-5}{2} = \frac{y-1}{-3} = \frac{z-5}{6}$ , is :
a.
$12$
b.
$14$
c.
$18$
d.
$21$
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If $\alpha$ satisfies the equation $x^{2} +x+ 1 = 0$ and $(1 +\alpha )^{7} = A + B\alpha + C\alpha ^{2}, \,A, \,B, C \geq 0$ , then
$5(3\,A -2\,B -C)$ is equal to
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The least positive integral value of $\alpha$ , for which the angle between the vectors $\alpha ˆi -2ˆj + 2ˆk$ and $\alpha ˆi + 2\alpha ˆj -2ˆk$
is acute, is _____.
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If $A$ denotes the sum of all the coefficients in the expansion of $(1 -3x+ 10x^{2})^{n}$ and $B$ denotes the sum of all
the coefficients in the expansion of $(1 +x^{2})^{n}$ , then :
a.
$A = B^{3}$
b.
$3\,A = B$
c.
$B = A^{3}$
d.
$A = 3\,B$
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Let $x=x(t)$ and $y=y(t)$ be solutions of the differential equations $\frac{dx}{dt} + ax = 0$ and $\frac{dy}{dt} + by = 0$
respectively, $a, b \in R$ . Given that $x(0) = 2\,; \,y(0) = 1$ and $3\,y(1) = 2\,x(1)$ , the value of $t$ , for which
$x(t) =y(t)$ , is :
a.
$log\frac{2}{3} 2$
b.
$log_{4}3$
c.
$log_{3}4$
d.
$log\frac{4}{3} 2$
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If the shortest distance between the lines $\frac{x-4}{1} = \frac{y+1}{2} = \frac{z}{-3}$ and $\frac{x-\lambda}{2} = \frac{y+1}{4} = \frac{z-2}{-5}$ is $\frac{6}{\sqrt{5}}$ , then the sum of all
possible values of $\lambda$ is :
a.
$5$
b.
$8$
c.
$7$
d.
$10$
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$\{\frac{a(7x-12-x^{2})}{b|x^{2}-7x+12|} , x < 3$
Consider the function $f(x) = \frac{sin(x-3)}{x-[x]}$ ,where $[x]$ denotes the greatest integer less than or equal
$2 , x > 3$
$\{$
$b , x = 3$
to $x$ . If $S$ denotes the set of all ordered pairs $(a, \,b)$ such that $f(x)\,$ is continuous at $x = 3$ , then the number of
elements in $S$ is :
a.
$2$
b.
Infinitely many
c.
$4$
d.
$1$
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Let the area of the region ${(x,y) :x-2y+ 4 \geq 0$ , $x+ 2y^{2} \geq 0,x+ 4y^{2} \leq 8,y\geq 0}$ be $\frac{m}{n}$ , where $m$ and $n$
are coprime numbers. Then $m + n$ is equal to ______.
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If $a=_{x}lim_{\rightarrow 0\rightarrow } \frac{\sqrt{1}+\sqrt{1+x^{4}}-\sqrt{2}}{x^{4}}$ and $b=_{x}lim_{\rightarrow 0\rightarrow } \frac{sin^{2}x}{\sqrt{2}-\sqrt{1+cosx}}$ , then the value of $ab^{3}$ is :
a.
$36$
b.
$32$
c.
$25$
d.
$30$
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A fair die is tossed repeatedly until a six is obtained. Let $X$ denote the number of tosses required and let
$a = P(X = 3), b = P(X \geq 3)$ and $c = P(X \geq 6 |X > 3)$ . Then $\frac{b+c}{a}$ is equal to
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$cosx -sinx 0$
$[ ]$
Consider the matrix $f(x) = sinx cosx 0$ . Given below are two statements :
$[ 0 0 1]$
Statement I: $f(-x)$ is the inverse of the matrix $f(x)$ .
Statement II: $f(x)\,f(y) =f(x+y)$ .
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 false
c.
Statement I is true but Statement II is false
d.
Both Statement I and Statement II are true
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If the solution of the differential equation $(2x+ 3y-2)dx+ (4x+ 6y-7)dy= 0, \,y(0) = 3$ , is
$\alpha x+\beta y+ 3 log_{e}|2x+ 3y- \gamma | = 6$ , then $\alpha + 2\beta + 3\gamma$ is equal to ______.
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If $(a, \,b)$ be the orthocentre of the triangle whose vertices are $(1, 2), (2, 3)$ and $(3, 1)$ , and
$I_{1} =\int _{a}^{b} xsin(4x -x^{2})dx, I_{2} =\int _{a}^{b} sin(4x -x^{2})dx$ , then $36\frac{I_{1}}{I_{2}}$ is equal to :
a.
$72$
b.
$88$
c.
$80$
d.
$66$
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Let the set of all $a\in R$ such that the equation $cos 2x+asinx= 2a-7$ has a solution be $[p, \,q]$ and
$r= tan 9^{\circ}-tan 27^{\circ}-\frac{1}{cot 63^{\circ}} + tan 81^{\circ}$ , then $pqr$ is equal to ________.
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If $\vec{a}= ˆi+ 2ˆj+ˆk, \,\vec{b}= 3(ˆi- ˆj+ ˆk)$ and $\vec{c}$ be the vector such that $\vec{a}\times \vec{c}= \vec{b}$ and $\vec{a}\cdot \vec{c}= 3$ , then
$\vec{a}\cdot ((\vec{c}\times \vec{b})- \vec{b}- \vec{c})$ is equal to
a.
$32$
b.
$24$
c.
$20$
d.
$36$
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Let for a differentiable function $f : (0, \infty ) \rightarrow \rightarrow R$ , $f(x) - f(y) \geq log_{e}( \frac{x}{y})+x- y, \forall x,y\in (0, \infty )$ . Then
$\sum ^{20}_{n=1} f'(\frac{1}{n^{2}})$ is equal to
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Let $a_{1}, a_{2}, . . . , a_{10}$ be $10$ observations such that $\sum ^{10}_{k=1} a_{k} = 50$ and $\sum _{\forall k<j}a_{k}\cdot a_{j} = 1100$ . Then the standard
deviation of $a_{1}, a_{2}, … , a_{10}$ is equal to :
a.
$5$
b.
$\sqrt{5}$
c.
$10$
d.
$\sqrt{115}$
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