Define a relation R on the interval $[0, \frac{\pi}{2})$ by $xRy$ if and only if $sec^{2} x-tan^{2} y= 1$ . Then R is :
a.
both reflexive and transitive but not symmetric
b.
an equivalence relation
Correct Answer
c.
reflexive but neither symmetric not transitive
d.
both reflexive and symmetric but not transitive
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Q2nat
Let $S ={x: cos^{-1} x=\pi + sin^{-1} x+ sin^{-1}(2x+ 1)}$ . Then $\sum _{x\in \,S}(2x-1)^{2}$ is equal to ______.
✓ Accepted Answer:5
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Q3nat
Let $f : (0, \infty ) \rightarrow \rightarrow R$ be a twice differentiable function. If for some $a \neq 0,\int _{0}^{1} f(\lambda x)d\lambda = af(x),f(1) = 1$ and
$f(16) = \frac{1}{8}$ , then $16 - f' (\frac{1}{16} )$ is equal to _______.
✓ Accepted Answer:112
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Q4mcq
Let $|z_{1}-8 -2i| \leq 1$ and $|z_{2}-2 + 6i| \leq 2,z_{1},z_{2} \in C$ . Then the minimum value of $|z_{1}- z_{2}|$ is :
a.
13
b.
10
c.
3
d.
7
Correct Answer
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Q5nat
$_{2} 2 -1$
Let $S ={m \in Z: A^{m} + A^{m} = 3I -A^{-6}}$ , where $A =[ ]$ . Then $n(S)$ is equal to ______.
$1 0$
✓ Accepted Answer:2
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Q6mcq
Let $\vec{a}= 2\hat{i}- \hat{j}+ 3\hat{k}, \,\vec{b}= 3\hat{i}-5\hat{j}+ \hat{k}$ and $\vec{c}$ be a vector such that $\vec{a}\times \vec{c}= \vec{c}\times \vec{b}$ and $(\vec{a}+ \vec{c}) \cdot (\vec{b}+ \vec{c}) = 168$ .
Then the maximum value of $|\vec{c}|^{2}$ is :
a.
462
b.
77
c.
154
d.
308
Correct Answer
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Q7mcq
Let the line $x+y= 1$ meet the circle $x^{2} +y^{2} = 4$ at the points A and B . If the line perpendicular to $AB$ and
passing through the mid point of the chord $AB$ intersects the circle at $C$ and $D$ , then the area of the
quadrilateral ADBC is equal to :
a.
$\sqrt{14}$
b.
$3\sqrt{7}$
c.
$2\sqrt{14}$
Correct Answer
d.
$5\sqrt{7}$
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Q8mcq
Let $ABC$ be a triangle formed by the lines $7x-6y+ 3 = 0,x+ 2y-31 = 0$ and $9x-2y-19 = 0$ . Let the
point $(h,k)$ be the image of the centroid of $\Delta ABC$ in the line $3x+ 6y-53 = 0$ . Then $h^{2} +k^{2} +hk$ is equal
to:
a.
47
b.
37
Correct Answer
c.
36
d.
40
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Q9mcq
$| |$
The least value of n for which the number of integral terms in the Binomial expansion of $(\sqrt{7}^{3} +^{12}\sqrt{11})^{n}$ is 183,
is :
a.
2184
Correct Answer
b.
2196
c.
2148
d.
2172
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Q10mcq
The number of solutions of the equation $(\frac{9}{x} - \frac{9}{\sqrt{x}} + 2) (\frac{2}{x} - \frac{7}{\sqrt{x}} + 3)= 0$ is:
a.
2
b.
3
c.
1
d.
4
Correct Answer
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Let $L_{1} : \frac{x-1}{1} = \frac{y-2}{-1} = \frac{z-1}{2}$ and $L_{2} : \frac{x+1}{-1} = \frac{y-2}{2} = \frac{z}{1}$ be two lines. Let $L_{3}$ be a line passing through the point
$(\alpha ,\beta ,\gamma )$ and be perpendicular to both $L_{1}$ and $L_{2}$ . If $L_{3}$ intersects $L_{1}$ , then $|5\alpha -11\beta -8\gamma |$ equals :
a.
20
b.
18
c.
25
d.
16
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The number of 6-letter words, with or without meaning, that can be formed using the letters of the word
MATHS such that any letter that appears in the word must appear at least twice, is _______.
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Let M and m respectively be the maximum and the minimum values of
$1 + sin^{2} x cos^{2} x 4 sin 4x$
$f(x) = sin^{2} x 1 + cos^{2} x 4 sin 4x ,x\in R$ Then $M^{4} - m^{4}$ is equal to :
$sin^{2} x cos^{2} x 1 + 4 sin 4x$
a.
1280
b.
1295
c.
1215
d.
1040
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Let the ellipse $E_{1} : \frac{x^{2}}{a^{2}} + \frac{y^{2}}{\,b^{2}} = 1, a > b$ and $E_{2} : \frac{x^{2}}{\,A^{2}} + \frac{y^{2}}{\,B^{2}} = 1, \,A < B$ have same eccentricity $\frac{1}{\sqrt{3}}$ . Let the
product of their lengths of latus rectums be $\frac{32}{\sqrt{3}}$ , and the distance between the foci of $E_{1}$ be 4. If $E_{1}$ and $E_{2}$
meet at $A,B,C$ and $D$ , then the area of the quadrilateral $ABCD$ equals :
a.
$\frac{12\sqrt{6}}{5}$
b.
$6\sqrt{6}$
c.
$\frac{18\sqrt{6}}{5}$
d.
$\frac{24\sqrt{6}}{5}$
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Consider an A. P. of positive integers, whose sum of the first three terms is 54 and the sum of the first twenty
terms lies between 1600 and 1800. Then its $11^{th\,}$ term is :
a.
90
b.
84
c.
122
d.
108
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Let P be the set of seven digit numbers with sum of their digits equal to 11 . If the numbers in P are formed by
using the digits 1,2 and 3 only, then the number of elements in the set $P$ is :
a.
173
b.
164
c.
158
d.
161
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Let $x_{1},x_{2}, … ,x_{10}$ be ten observations such that $\sum _{i=1} (x_{i}-2) = 30,\sum _{i=1} (x_{i}- \beta ) = 98,\beta > 2$ , and their
variance is $\frac{4}{5}$ . If $\mu$ and $\sigma ^{2}$ are respectively the mean and the variance of $2 (x_{1}-1) + 4\beta$ ,
$2 (x_{2}-1) + 4\beta , … . , 2 (x_{10}-1) + 4\beta$ , then $\frac{\beta \mu}{\sigma ^{2}}$ is equal to :
a.
100
b.
120
c.
110
d.
90
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Let [t] be the greatest integer less than or equal to t. Then the least value of $p \in N$ for which
$lim_{x\rightarrow 0\rightarrow }_{+}(x([\frac{1}{x} ]+[\frac{2}{x} ]+ … +[\frac{p}{x}])- x^{2}([\frac{1}{x^{2}}]+[\frac{2^{2}}{x^{2}}]+ … +[\frac{9^{2}}{x^{2}}]))\geq 1$ is equal to ________.
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Two parabolas have the same focus $(4, 3)$ and their directrices are the $x$ -axis and the $y$ -axis, respectively. If
these parabolas intersects at the points $A$ and $B$ , then $(AB)^{2}$ is equal to :
a.
392
b.
384
c.
192
d.
96
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Let $\vec{a}= \hat{i}+ 2\hat{j}+ \hat{k}$ and $\vec{b}= 2\hat{i}+ 7\hat{j}+ 3\hat{k}.$ Let $L_{1} : \vec{r}= (-\hat{i}+ 2\hat{j}+ \hat{k}) +\lambda \vec{a},\lambda \in R$ and
$L_{2} : \vec{r}= (\hat{j}+ \hat{k}) +\mu \vec{b},\mu \in R$ be two lines. If the line $L_{3}$ passes through the point of intersection of $L_{1}$ and $L_{2}$ ,
and is parallel to $\vec{a}+ \vec{b}$ , then $L_{3}$ passes through the point :
a.
$(5, 17, 4)$
b.
$(2, 8, 5)$
c.
$(8, 26, 12)$
d.
$(-1, -1, 1)$
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Let $y=y(x)$ be the solution of the differential equation
$cosx(log_{e}(cosx))^{2}dy + (sinx-3ysinxlog_{e}(cosx))dx= 0,x\in (0, \frac{\pi}{2})$ . If $y( \frac{\pi}{4})= \frac{-1}{log_{e}2}$ , then $y( \frac{\pi}{6})$ is
equal to :
a.
$\frac{1}{log_{e}(3)-log_{e}(4)}$
b.
$\frac{2}{log_{e}(3)-log_{e}(4)}$
c.
$\frac{1}{log_{e}(4)-log_{e}(3)}$
d.
$-\frac{1}{log_{e}(4)}$
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$log_{5}128 log_{4}5_{2}$
Let $A = [a_{ij}] =[ ]$ . If $A_{ij}$ is the cofactor of $a_{ij}, C_{ij} =\sum _{k=1} a_{ik}A_{jk}, 1 \leq i,j\leq 2$ , and
$log_{5}8 log_{4}25$
$C = [C_{ij}]$ , then $8|C|$ is equal to :
a.
288
b.
222
c.
242
d.
262
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At the interface between two materials having refractive indices $n_{1}$ and $n_{2}$ , the critical angle for reflection of
an em wave is $\theta _{1C}$ . The $n_{2}$ material is replaced by another material having refractive index $n_{3}$ such that the
critical angle at the interface between $n_{1}$ and $n_{3}$ materials is $\theta _{2C}$ . If $n_{3} > n_{2} > n_{1}; \frac{n_{2}}{n_{3}} = \frac{2}{5}$ and
$sin\theta _{2C}-sin\theta _{1C} = \frac{1}{2}$ , then $\theta _{1C}$ is
a.
$sin^{-1} (\frac{1}{6} )$
b.
$sin^{-1} ( \frac{1}{3})$
c.
$sin^{-1} (\frac{-5}{6} )$
d.
$sin^{-1} ( \frac{2}{3})$
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The fractional compression $(\frac{\Delta V}{V})$ of water at the depth of 2.5 km below the sea level is ______ $%$ . Given, the
Bulk modulus of water $= 2 \times 10^{9}\,N\,m^{-2}$ , density of water $= 10^{3} kgm^{-3}$ , acceleration due to gravity
$= g = 10\,m\,s^{-2}$ .
a.
1.25
b.
1.0
c.
1.75
d.
1.5
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The maximum speed of a boat in still water is $27\,km/h$ . Now this boat is moving downstream in a river
flowing at $9\,km/h$ . A man in the boat throws a ball vertically upwards with speed of $10\,m/s$ . Range of the ball
as observed by an observer at rest on the river bank, is _______ cm. (Take $g = 10\,m/s^{2}$ )
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A body of mass ' $m$ ' connected to a massless and unstretchable string goes in verticle circle of radius ' $R$
'under gravity $g$ . The other end of the string is fixed at the center of circle. If velocity at top of circular path is
$n\sqrt{gR}$ , where, $n⩾ 1$ , then ratio of kinetic energy of the body at bottom to that at top of the circle is
a.
$\frac{n^{2}}{n^{2}+4}$
b.
$\frac{n^{2}+4}{n^{2}}$
c.
$\frac{n+4}{n}$
d.
$\frac{n}{n+4}$
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Two projectiles are fired with same initial speed from same point on ground at angles of $(45^{\circ } - \alpha )$ and
$(45^{\circ } +\alpha )$ , respectively, with the horizontal direction. The ratio of their maximum heights attained is :
a.
$\frac{1-tan\alpha}{1+tan\alpha}$
b.
$\frac{1-sin 2\alpha}{1+sin 2\alpha}$
c.
$\frac{1+sin 2\alpha}{1-sin 2\alpha}$
d.
$\frac{1+sin\alpha}{1-sin\alpha}$
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An electric dipole of mass m, charge q, and length $l$ is placed in a uniform electric field $\vec{E}= E_{0}\hat{i}$ . When the
dipole is rotated slightly from its equilibrium position and released, the time period of its oscillations will be:
a.
$\frac{1}{2\pi}\sqrt{\,} \frac{ml}{2qE_{0}}$
b.
$2\pi \sqrt{\,} \frac{\,ml}{qE_{0}}$
c.
$\frac{1}{2\pi}\sqrt{\,} \frac{2\,ml}{qE_{0}}$
d.
$2\pi \sqrt{\,} \frac{\,ml}{2qE_{0}}$
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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) : Choke coil is simply a coil having a large inductance but a small resistance. Choke coils are
used with fluorescent mercury-tube fittings. If household electric power is directly connected to a mercury
tube, the tube will be damaged. Reason (R): By using the choke coil, the voltage across the tube is reduced by
a factor $(R/\sqrt{R^{2}+\omega ^{2}L^{2}})$ , where $\omega$ is frequency of the supply across resistor $R$ and inductor L . If the choke
coil were not used, the voltage across the resistor would be the same as the applied voltage. In the light of the
above statements, choose the most appropriate answer from the options given below :
a.
$(A)$ is true but (R) is false
b.
Both (A) and (R) are true and (R) is the correct
explanation of (A)
c.
(A) is false but (R) is true
d.
Both $(A)$ and $(R)$ are true but $(R)$ is not the
correct explanation of $(A)$
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$\,List - I\, \,List - II\,$
$\,Electric field inside (distance\,r> 0\,from center)\,$
$\,(A)\,\,of a uniformly charged spherical shell with\, \,(I)\,\sigma /\epsilon _{0}$
$\,surface charge density\,\sigma , and radius R.\,$
$\,Electric field at distance r>0 from a uniformly\,$
$\,(B)\,\,charged infinite plane sheet with surface\, \,(II)\,\sigma /2\epsilon _{0}$
Match List - I with List - II. $\,charge density\,\sigma .$ Choose
$\,Electric field outside (distance r>0 from center)\,$
$\,(C)\,\,of a uniformly charged spherical shell with\, \,(III)\,0$
$\,surface charge density\,\sigma , and radius R.\,$
$\,Electric field between\,2\,oppositely charged\,$
$\,(D)\,\,infinite plane parallel sheets with uniform\, \,(IV)\, \frac{\sigma R^{2}}{\epsilon _{0}r^{2}}$
$\,surface charge density\,\sigma .$
the correct answer from the options given below :
a.
(A)-(III), (B)-(II), (C)-(IV), (D)-(I)
b.
(A)-(IV), (B)-(II), (C)-(III), (D)-(I)
c.
(A)-(II), (B)-(I), (C)-(IV), (D)-(III)
d.
(A)-(IV), (B)-(I), (C)-(III), (D)-(II)
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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) : Emission of electrons in photoelectric effect can be suppressed by applying a sufficiently
negative electron potential to the photoemissive substance. Reason (R) : A negative electric potential, which
stops the emission of electrons from the surface of a photoemissive substance, varies linearly with frequency
of incident radiation. 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.
(A) is true but (R) is false
c.
Both $(A)$ and $(R)$ are true and $(R)$ is the correct
explanation of $(A)$
d.
Both $(A)$ and $(R)$ are true but $(R)$ is not the
correct explanation of $(A)$
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Let u and $v$ be the distances of the object and the image from a lens of focal length $f$ . The correct graphical
representation of $u$ and $v$ for a convex lens when $|u| >$ , is
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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) : Electromagnetic waves carry energy but not momentum. Reason ( $R$ ): Mass of a photon is zero.
In the light of the above statements, choose the most appropriate answer from the options given below :
a.
Both (A) and (R) are true and (R) is the correct
explanation of $(A)$
b.
Both $(A)$ and $(R)$ are true but $(R)$ is not the
correct explanation of $(A)$
c.
(A) is false but (R) is true
d.
(A) is true but ( $R$ ) is false
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The coordinates of a particle with respect to origin in a given reference frame is $(1, 1, 1)$ meters. If a force of
$\vec{F}= \hat{i}- \hat{j}+ \hat{k}$ acts on the particle, then the magnitude of torque (with respect to origin) in z-direction is
______.
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Two light beams fall on a transparent material block at point 1 and 2 with angle $\theta _{1}$ and $\theta _{2}'$ respectively, as
shown in figure. After refraction, the beams intersect at point 3 which is exactly on the interface at other end of
the block. Given : the distance between 1 and 2, $d = 4\,cm\sqrt{3}$ and $\theta _{1} =\theta _{2} = cos^{-1} (\frac{n_{2}}{2n_{1}})$ , where refractive
index of the block $n_{2} >$ refractive index of the outside medium $n_{1}$ , then the thickness of the block is ________
cm.
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In a hydraulic lift, the surface area of the input piston is $6\,cm^{2}$ and that of the output piston is $1500\,cm^{2}$ . If 100
N force is applied to the input piston to raise the output piston by 20 cm, then the work done is _______ kJ.
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Consider a long straight wire of a circular cross-section (radius a) carrying a steady current I. The current is
uniformly distributed across this cross-section. The distances from the centre of the wire's cross-section at
which the magnetic field [inside the wire, outside the wire] is half of the maximum possible magnetic field,
any where due to the wire, will be
a.
$[a/4, 3a/2]$
b.
$[a/4, 2a]$
c.
$[a/2, 2a]$
d.
$[a/2, 3a]$
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A container of fixed volume contains a gas at $27^{\circ }C$ . To double the pressure of the gas, the temperature of gas
should be raised to ______ $^{\circ }C$ .
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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) : Time period of a simple pendulum is longer at the top of a mountain than that at the base of the
mountain. Reason (R): Time period of a simple pendulum decreases with increasing value of acceleration due
to gravity and vice-versa. In the light of the above statements, choose the most appropriate answer from the
options given below :
a.
Both $(A)$ and $(R)$ are true and $(R)$ is the correct
explanation of $(A)$
b.
(A) is true but (R) is false
c.
(A) is false but (R) is true
d.
Both $(A)$ and $(R)$ are true but $(R)$ is not the
correct explanation of $(A)$
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As shown below, bob $A$ of a pendulum having massless string of length ' $R$ ' is released from $60^{\circ }$ to the
vertical. It hits another bob $B$ of half the mass that is at rest on a friction less table in the center. Assuming
elastic collision, the magnitude of the velocity of bob A after the collision will be (take g as acceleration due to
gravity.)
a.
$\frac{4}{3}\sqrt{Rg}$
b.
$\frac{2}{3}\sqrt{Rg}$
c.
$\sqrt{Rg}$
d.
$\frac{1}{3}\sqrt{Rg}$
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A coil of area A and N turns is rotating with angular velocity $\omega$ in a uniform magnetic field $\vec{B}$ about an axis
perpendicular to $\vec{B}$ . Magnetic flux $\phi$ and induced $emf\epsilon$ across it, at an instant when $\vec{B}$ is parallel to the plane
of coil, are :
a.
$\phi = AB,\epsilon = 0$
b.
$\phi = 0,\epsilon = 0$
c.
$\phi = 0,\epsilon = NAB\omega$
d.
$\phi = AB,\epsilon = NAB\omega$
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If $\lambda$ and $K$ are de Broglie wavelength and kinetic energy, respectively, of a particle with constant mass. The
correct graphical representation for the particle will be
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Consider $I_{1}$ and $I_{2}$ are the currents flowing simultaneously in two nearby coils 1 & 2, respectively. If $L_{1} =$ self
inductance of coil $1, M_{12} =$ mutual inductance of coil 1 with respect to coil 2, then the value of induced emf in
coil 1 will be Options
$|||$
Given below are some nitrogen containing compounds
Each of them is treated with HCl separately. 1.0 g of the most basic compound will consume _______ mg of
HCl. (Given molar mass in $gmol^{-1}C : 12, H : 1, O : 16, Cl : 35.5$ )
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The correct increasing order of stability of the complexes based on $\Delta _{o}$ value is : I. $[Mn(CN)_{6}]^{3-}$ II.
$[Co(CN)_{6}]^{4-}$ III. $[Fe(CN)_{6}]^{4-}$ IV. $[Fe(CN)_{6}]^{3-}$
a.
$IV < III < II < I$
b.
$I < II < IV <$ III
c.
III $<$ II $<$ IV $<$ I
d.
II $<$ III $<$ I $<$ IV
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Total number of nucleophiles from the following is :
$NH_{3}, PhSH, (H_{3}C)_{2}\,S, H_{2}C = CH_{2}, O H, H^{\ominus }_{3}O^{\oplus }, (CH_{3})_{2}CO,\rightleftharpoons NCH_{3}$
a.
7
b.
4
c.
6
d.
5
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Given below are two statements : Statement ( $I$ ): The radii of isoelectronic species increases in the order.
$Mg^{2+} < Na^{+} < F^{-} < O^{2-}$ Statement (II): The magnitude of electron gain enthalpy of halogen decreases in
the order. $Cl > F > Br > I$ In the light of the above statements, choose the most appropriate answer from the
options given below :
a.
Statement I is incorrect but Statement II is
correct
b.
Statement I is correct but Statement II is
incorrect
c.
Both Statement I and Statement II are incorrect
d.
Both Statement I and Statement II are correct
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An element ' $E'$ has the ionisation enthalpy value of $374\,kJ\,mol^{-1}$ . ' $E$ ' reacts with elements $A, B, C$ and D
with electron gain enthalpy values of $-328, -349, -325$ and $-295\,kJ\,mol^{-1}$ , respectively. The correct order
of the products EA, EB, EC and ED in terms of ionic character is :
a.
$ED > EC > EB > EA$
b.
$EA > EB > EC > ED$
c.
$EB > EA > EC > ED$
d.
$ED > EC > EA > EB$
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Choose the correct statements. (A) Weight of a substance is the amount of matter present in it. (B) Mass is the
force exerted by gravity on an object. (C) Volume is the amount of space occupied by a substance. (D)
Temperatures below $0^{\circ }C$ are possible in Celsius scale, but in Kelvin scale negative temperature is not possible.
(E) Precision refers to the closeness of various measurements for the same quantity. Choose the correct answer
from the options given below :
a.
(A), (D) and (E) Only
b.
(C), (D) and (E) Only
c.
(A), (B) and (C) Only
d.
(B), (C) and (D) Only
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If $a_{0}$ is denoted as the Bohr radius of hydrogen atom, then what is the de-Broglie wavelength $(\lambda )$ of the
electron present in the second orbit of hydrogen atom? [n : any integer]
a.
$\frac{8\pi a_{0}}{n}$
b.
$\frac{2a_{0}}{n\pi}$
c.
$\frac{4n}{\pi a_{0}}$
d.
$\frac{4\pi a_{0}}{n}$
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At temperature T, compound $AB_{2(\,g)}$ dissociates as $AB_{2(\,g)} \rightleftharpoons AB_{(g)}+ \frac{1}{2}\,B_{2(\,g)}$ having degree of dissociation
$x$ (small compared to unity). The correct expression for $x$ in terms of $K_{p}$ and p is
a.
$\sqrt{\,} ^{4} \frac{2K_{p}}{p}$
b.
$\sqrt{\,} ^{3} \frac{2K_{p}}{p}$
c.
$\sqrt{\,} ^{3} \frac{2\,K^{2}_{p}}{p}$
d.
$\sqrt{K}_{p}$
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$A_{2}k_{1}\,A + A\,(fast)\,$
$k_{-1}$
The reaction $A_{2}+ B_{2} \rightarrow 2AB\rightarrow$ follows the mechanism $k_{2}$ The overall order of the
$-A + B_{2} \rightarrow \rightarrow AB+ B\,(slow)\,$
$A + B \rightarrow AB\,(fast)\,\rightarrow$
reaction is :
a.
2
b.
2.5
c.
3
d.
1.5
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The molar mass of the water insoluble product formed from the fusion of chromite ore $(FeCr_{2}O_{4})$ with
$Na_{2}CO_{3}$ in presence of $O_{2}$ is _______ $gmol^{-1}$ .
Numerical answer locked.
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$\,List - I\, \,List - II\,$
$\,(Complex)\, \,(Hybridisation & Magnetic characters)\,$
$(A) [MnBr_{4}]^{2-} (I) d^{2}s^{3}\,& diamagnetic$
Match List - I with List - II.
$(B) [FeF_{6}]^{3-} (II) sp^{3}\,d^{2}\,& paramagnetic$
$(C) [Co(C_{2}O_{4})_{3}]^{3-} (III) sp^{3}\,& diamagnetic$
$(D) [Ni(CO)_{4}] (IV) sp^{3}\,& paramagnetic$
Choose the correct answer from the options given below :
a.
(A) $-(IV), (B) -(II), (C) -(I), (D) -(III)$
b.
$(A) -(III), (B) -(I), (C) -(II), (D) -(IV)$
c.
(A) $-(IV), (B) -(I), (C) -(II), (D) -(III)$
d.
$(A) -(III), (B) -(II), (C) -(I), (D) -(IV)$
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The molar conductivity of a weak electrolyte when plotted against the square root of its concentration, which
of the following is expected to be observed ?
a.
A small decrease in molar conductivity is
observed at infinite dilution.
b.
Molar conductivity decreases sharply with
increase in concentration.
c.
A small increase in molar conductivity is
observed at infinite dilution.
d.
Molar conductivity increases sharply with
increase in concentration.
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J of energy is transferred as heat to 0.5 mol of Argon gas at 298 K and 1.00 atm. The final temperature and the
change in internal energy respectively are: Given : $R = 8.3\,J\,K^{-1}\,mol^{-1}$
a.
378 K and 500 J
b.
368 K and 500 J
c.
348 K and 300 J
d.
378 K and 300 J
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1.24 g of $AX_{2}$ (molar mass $124\,g\,mol^{-1}$ ) is dissolved in 1 kg of water to form a solution with boiling point of
$100.0156^{\circ }C$ , while $25.4\,g^{\circ }$ of $AY_{2}$ (molar mass $250\,g\,mol^{-1}$ ) in 2 kg of water constitutes a solution with a
boiling point of $100.0260^{\circ }C$ . $K_{b}(H_{2}O) = 0.52\,K\,kg\,mol^{-1}$ Which of the following is correct ?
a.
$AX_{2}$ is fully ionised while $AY_{2}$ is completely
unionised.
b.
$AX_{2}$ is completely unionised while $AY_{2}$ is fully
ionised.
c.
$AX_{2}$ and $AY_{2}$ (both) are completely unionised.
d.
$AX_{2}$ and $AY_{2}$ (both) are fully ionised.
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