If $24\int _{0}\frac{\pi}{4} (sin 4x- \frac{\pi}{12} + [2 sinx])dx= 2\pi +\alpha$ , where $[\cdot ]$ denotes the greatest integer function, then $\alpha$ is
equal to _______.
✓ Accepted Answer:12
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Q2nat
Let $a_{1},a_{2}, … ,a_{2024}$ be an Arithmetic Progression such that
$a_{1}+ (a_{5}+a_{10}+a_{15}+ … +a_{2020}) +a_{2024} = 2233$ . Then $a_{1}+a_{2}+a_{3}+ … +a_{2024}$ is equal to _______
✓ Accepted Answer:11132
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Q3mcq
The remainder, when $7^{103}$ is divided by 23 , is equal to :
a.
6
b.
17
c.
9
d.
14
Correct Answer
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Q4mcq
Let $f(x) =\int _{0} t(t t+ 20)dt, 1 \leq x\leq 5$ . If the range of $f$ is $[\alpha ,\beta ]$ , then $4(\alpha +\beta )$ equals :
a.
253
b.
154
c.
125
d.
157
Correct Answer
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Q5mcq
Let the function $f(x) =(x^{2} + 1) x^{2} - ax+ 2 + cos |x|$ be not differentiable at the two points $x=\alpha = 2$
and $x=\beta$ . Then the distance of the point $(\alpha ,\beta )$ from the line $12x+ 5y+ 10 = 0$ is equal to :
a.
5
b.
4
c.
3
Correct Answer
d.
2
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Q6mcq
Let the line $x+y= 1$ meet the axes of $x$ and $y$ at A and B, respectively. A right angled triangle AMN is
inscribed in the triangle OAB , where O is the origin and the points M and N lie on the lines $OB$ and $AB$ ,
respectively. If the area of the triangle $AMN$ is $\frac{4}{9}$ of the area of the triangle $OAB$ and AN : NB $=\lambda : 1$ , then
the sum of all possible value(s) of is $\lambda$ :
a.
2
Correct Answer
b.
$\frac{5}{2}$
c.
$\frac{1}{2}$
d.
$\frac{13}{6}$
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Q7mcq
Let $\alpha ,\beta (\alpha \neq \beta )$ be the values of m , for which the equations $x+y+z= 1;x+ 2y+ 4z= m$ and
$x+ 4y+ 10z=m^{2}$ have infinitely many solutions. Then the value of $\sum ^{10}_{n=1} (n^{\alpha }+n^{\beta })$ is equal to :
a.
3080
b.
560
c.
3410
d.
440
Correct Answer
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Q8mcq
If for the solution curve $y=f(x)$ of the differential equation $\frac{dy}{\,dx} + (tanx)y= \frac{2+secx}{(1+2 secx)^{2}}$ ,
$x\in ( \frac{-\pi}{2}, \frac{\pi}{2}),f(\frac{\pi}{3} )= \frac{\sqrt{3}}{10}$ , then $f(\frac{\pi}{4} )$ is equal to :
a.
$\frac{\sqrt{3}+1}{10(4+)\sqrt{3}}$
b.
$\frac{5-\sqrt{3}}{2\sqrt{2}}$
c.
$\frac{9+3\sqrt{3}}{10(4+)\sqrt{3}}$
d.
$\frac{4-\sqrt{2}}{14}$
Correct Answer
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Q9mcq
Let $A= [a_{ij}]$ be a matrix of order $3 \times 3$ , with $a_{ij} = ()\sqrt{2}^{i+j}$ . If the sum of all the elements in the third row of
$A^{2}$ is $\alpha +\beta \sqrt{2},\alpha ,\beta \in Z$ , then $\alpha +\beta$ is equal to :
a.
280
b.
224
Correct Answer
c.
210
d.
168
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Q10mcq
If $sinx+ sin^{2} x= 1,x\in (0, \frac{\pi}{2} )$ , then
$(cos^{12} x+ tan^{12} x)+ 3(cos^{10} x+ tan^{10} x+ cos^{8} x+ tan^{8} x)+(cos^{6} x+ tan^{6} x)$ is equal to :
a.
4
b.
1
c.
3
d.
2
Correct Answer
No explanation saved for this question yet.
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Let P be the foot of the perpendicular from the point $(1, 2, 2)$ on the line $L : \frac{x-1}{1} = \frac{y+1}{-1} = \frac{z-2}{2}$ . Let the line
$\vec{r}= (-\hat{i}+ \hat{j}-2\hat{k}) +\lambda (\hat{i}- \hat{j}+ \hat{k}),\lambda \in R$ , intersect the line L at Q . Then $2(PQ)^{2}$ is equal to :
a.
25
b.
19
c.
29
d.
27
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Let a circle $C$ pass through the points $(4, 2)$ and $(0, 2)$ , and its centre lie on $3x+ 2y+ 2 = 0$ . Then the length
of the chord, of the circle $C$ , whose mid-point is $(1, 2)$ , is :
a.
$\sqrt{3}$
b.
$2\sqrt{2}$
c.
$2\sqrt{3}$
d.
$4\sqrt{2}$
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If $\alpha x+\beta y= 109$ is the equation of the chord of the ellipse $\frac{x^{2}}{9} + \frac{y^{2}}{4} = 1$ , whose mid point is $( \frac{5}{2}, \frac{1}{2} )$ , then
$\alpha +\beta$ is equal to :
a.
58
b.
46
c.
37
d.
72
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Let the area enclosed between the curves $|y| = 1 - x^{2}$ and $x^{2} +y^{2} = 1$ be $\alpha$ . If $9\alpha =\beta \pi +\gamma ;\beta ,\gamma$ are
integers, then the value of $|\beta - \gamma |$ equals.
a.
27
b.
33
c.
15
d.
18
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Let $A = [a_{ij}]$ be a $2 \times 2$ matrix such that $a_{ij} \in {0, 1}$ for all $i$ and $j$ . Let the random variable X denote the
possible values of the determinant of the matrix $A$ . Then, the variance of $X$ is :
a.
$\frac{3}{4}$
b.
$\frac{5}{8}$
c.
$\frac{3}{8}$
d.
$\frac{1}{4}$
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Let a straight line $L$ pass through the point $P(2, -1, 3)$ and be perpendicular to the lines $\frac{x-1}{2} = \frac{y+1}{1} = \frac{z-3}{-2}$
and $\frac{x-3}{1} = \frac{y-2}{3} = \frac{z+2}{4}$ . If the line $L$ intersects the $yz$ -plane at the point $Q$ , then the distance between the
points $P$ and $Q$ is :
a.
$\sqrt{10}$
b.
$2\sqrt{3}$
c.
2
d.
3
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If $lim_{t\rightarrow 0\rightarrow } (\int _{0}^{1}(3x+ 5)^{t}dx)\frac{1}{t} = \frac{\alpha}{5e}(\frac{8}{5})\frac{2}{3}$ , then $\alpha$ is equal to ________
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If all the words with or without meaning made using all the letters of the word "KANPUR" are arranged as in a
dictionary, then the word at $440^{th\,}$ position in this arrangement, is :
a.
PRNAUK
b.
PRKANU
c.
PRKAUN
d.
PRNAKU
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If the set of all $a \in R$ , for which the equation $2x^{2} + (a-5)x+ 15 = 3a$ has no real root, is the interval $(\alpha ,\beta )$ ,
and $X = {x\in Z :\alpha <x<\beta }$ , then $\sum _{x\in X}x^{2}$ is equal to :
a.
2109
b.
2129
c.
2119
d.
2139
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Let $y^{2} = 12x$ be the parabola and $S$ be its focus. Let PQ be a focal chord of the parabola such that
$(SP)(SQ) = \frac{147}{4}$ . Let C be the circle described taking PQ as a diameter. If the equation of a circle $C$ is
$64x^{2} + 64y^{2} - \alpha x-64\sqrt{3}y=\beta$ , then $\beta - \alpha$ is equal to ________.
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Let $\hat{a}$ be a unit vector perpendicular to the vectors $\vec{b}= \hat{i}-2\hat{j}+ 3\hat{k}$ and $\vec{c}= 2\hat{i}+ 3\hat{j}- \hat{k}$ , and makes an angle of
$cos^{-1} (- \frac{1}{3})$ with the vector $\hat{i}+ \hat{j}+ \hat{k}$ . If $\hat{a}$ makes an angle of $\frac{\pi}{3}$ with the vector $\hat{i}+\alpha \hat{j}+ \hat{k}$ , then the value of $\alpha$
is :
a.
$\sqrt{6}$
b.
$-\sqrt{6}$
c.
$-\sqrt{3}$
d.
$\sqrt{3}$
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If the domain of the function $log_{5}(18x- x^{2} -77)$ is $(\alpha ,\beta )$ and the domain of the function
$log_{(x-1)}( \frac{2x^{2}+3x-2}{x^{2}-3x-4})$ is $(\gamma ,\delta )$ , then $\alpha ^{2} +\beta ^{2} +\gamma ^{2}$ is equal to :
a.
195
b.
179
c.
186
d.
174
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Let integers $a, b \in [-3, 3]$ be such that $a + b \neq 0$ . Then the number of all possible ordered pairs (a, b), for
$z+ 1 \omega \omega ^{2}$
which $\frac{z-a}{z+b} = 1$ and $\omega z+\omega ^{2} 1 = 1,z\in C$ , where $\omega$ and $\omega ^{2}$ are the roots of $x^{2} +x+ 1 = 0$ , is
$\omega ^{2} 1 z+\omega$
equal to ________.
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Let $S =N\cup {0}$ . Define a relation $R$ from $S$ to $R$ by : $R ={(x,y) : log =xlog \frac{2}{5}),x\in \,S,y\in R}$
$_{e}y_{e}($
Then, the sum of all the elements in the range of $R$ is equal to :
a.
$\frac{10}{9}$
b.
$\frac{3}{2}$
c.
$\frac{5}{2}$
d.
$\frac{5}{3}$
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Bag 1 contains 4 white balls and 5 black balls, and Bag 2 contains $n$ white balls and 3 black balls. One ball is
drawn randomly from Bag 1 and transferred to Bag 2. A ball is then drawn randomly from Bag 2. If the
probability, that the ball drawn is white, is $29/45$ , then $n$ is equal to :
a.
6
b.
3
c.
5
d.
4
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Two concave refracting surfaces of equal radii of curvature and refractive index 1.5 face each other in air as
shown in figure. A point object O is placed midway, between P and B . The separation between the images of
$O$ , formed by each refracting surface is :
a.
0.214 R
b.
0.411 R
c.
0.124 R
d.
0.114 R
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An electric dipole is placed at a distance of 2 cm from an infinite plane sheet having positive charge density $\sigma _{o}$
. Choose the correct option from the following.
a.
Potential energy and torque both are maximum.
b.
Torque on dipole is zero and net force is directed
away from the sheet.
c.
Torque on dipole is zero and net force acts
towards the sheet.
d.
Potential energy of dipole is minimum and torque
is zero.
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A plane electromagnetic wave propagates along the $+x$ direction in free space. The components of the electric
field, $\vec{E}$ and magnetic field, $\vec{B}$ vectors associated with the wave in Cartesian frame are
a.
$E_{x}, \,B_{y}$
b.
$E_{y}, \,B_{z}$
c.
$E_{z}, \,B_{y}$
d.
$E_{y}, \,B_{x}$
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Two cars $P$ and $Q$ are moving on a road in the same direction. Accleration of car $P$ increases linearly with
time whereas car $Q$ moves with a constant accleration. Both cars cross each other at time $t= 0$ , for the first
time. The maximum possible number of crossing(s) (including the crossing at $t= 0)$ is ________.
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Two bodies A and B of equal mass are suspended from two massless springs of spring constant $k_{1}$ and $k_{2}$ ,
respectively. If the bodies oscillate vertically such that their amplitudes are equal, the ratio of the maximum
velocity of $A$ to the maximum velocity of $B$ is
a.
$\frac{k_{1}}{k_{2}}$
b.
$\sqrt{\,} \frac{k_{1}}{k_{2}}$
c.
$\sqrt{\,} \frac{k_{2}}{k_{1}}$
d.
$\frac{k_{2}}{k_{1}}$
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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) : With the increase in the pressure of an ideal gas, the volume falls off more rapidly in an
isothermal process in comparison to the adiabatic process. Reason (R) : In isothermal process, $PV =$ constant,
while in adiabatic process $PV^{\gamma } =$ constant. Here $\gamma$ is the ratio of specific heats, P is the pressure and V is the
volume of the ideal gas. In the light of the above statements, choose the correct 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 true but (R) is false
d.
(A) is false but (R) is true
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Two identical symmetric double convex lenses of focal length $f$ are cut into two equal parts $L_{1},L_{2}$ by $AB$
plane and $L_{3},L_{4}$ by $XY$ plane as shown in figure respectively. The ratio of focal lengths of lenses $L_{1}$ and $L_{3}$
is
a.
1:1
b.
1:2
c.
1:4
d.
2:1
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A point charge causes an electric flux of $-2 \times 10^{4}Nm^{2}C^{-1}$ to pass through a spherical Gaussian surface of 8.0
cm radius, centred on the charge. The value of the point charge is : (Given $\epsilon _{0} = 8.85 \times 10^{-12}C^{2}\,N^{-1}\,m^{-2}$ )
a.
$15.7 \times 10^{-8}C$
b.
$17.7 \times 10^{-8}C$
c.
$-15.7 \times 10^{-8}C$
d.
$-17.7 \times 10^{-8}C$
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A cup of coffee cools from $90^{\circ }C$ to $80^{\circ }C$ in t minutes when the room temperature is $20^{\circ }C$ . The time taken by
the similar cup of coffee to cool from $80^{\circ }C$ to $60^{\circ }C$ at the same room temperature is :
a.
$\frac{13}{10} t$
b.
$\frac{10}{13}t$
c.
$\frac{5}{13} t$
d.
$\frac{13}{5}t$
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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) :
Three identical spheres of same mass undergo one dimensional motion as shown in figure with initial
velocities $v_{A} = 5\,m/s,v_{B} = 2\,m/s,v_{C} = 4\,m/s$ . If we wait sufficiently long for elastic collision to happen,
then $v_{A} = 4\,m/s,v_{B} = 2\,m/s$ , $v_{C} = 5\,m/s$ will be the final velocities. Reason (R): In an elastic collision
between identical masses, two objects exchange their velocities. 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 but (R) is NOT the
correct explanation of (A)
c.
Both (A) and (R) are true and (R) is the correct
explanation of (A)
d.
(A) is true but (R) is false
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A sand dropper drops sand of mass $m(t)$ on a conveyer belt at a rate proportional to the square root of speed
$(v)$ of the belt, i.e. $\frac{dm}{dt} \propto \sqrt{v}$ . If P is the power delivered to run the belt at constant speed then which of the
following relationship is true?
a.
$P \propto \sqrt{v}$
b.
$P \propto v$
c.
$P^{2} \propto v^{5}$
d.
$P^{2} \propto v^{3}$
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A poly-atomic molecule ( $C_{V} = 3R,C_{P} = 4R$ , where $R$ is gas constant) goes from phase space point
$A(P_{A} = 10^{5}\,Pa, \,V_{A} = 4 \times 10^{-6}\,m^{3})$ to point $B(P_{B} = 5 \times 10^{4}\,Pa, \,V_{B} = 6 \times 10^{-6}\,m^{3})$ to point
$C(P_{C} = 10^{4} Pa, V_{C} = 8 \times 10^{-6}\,m^{3})$ . A to B is an adiabatic path and $B$ to $C$ is an isothermal path. The net
heat absorbed per unit mole by the system is :
a.
$500R(ln 3 + ln 4)$
b.
$450R(ln 4 -ln 3)$
c.
$500R ln 2$
d.
$400R ln 4$
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A parallel plate capacitor consisting of two circular plates of radius 10 cm is being charged by a constant
current of 0.15 A . If the rate of change of potential difference between the plates is $7 \times 10^{8}\,V/s$ then the
integer value of the distance between the parallel plates is $($ Take, $\epsilon _{0} = 9 \times 10^{-12} \frac{\,F}{\,m},\pi = \frac{22}{7})$ ________ $\mu m$ .
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A convex lens made of glass (refractive index $= 1.5$ ) has focal length 24 cm in air. When it is totally
immersed in water (refractive index $= 1.33$ ), its focal length changes to
a.
24 cm
b.
96 cm
c.
48 cm
d.
72 cm
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Two planets, $A$ and $B$ are orbiting a common star in circular orbits of radii $R_{A}$ and $R_{B}$ , respectively, with
$R_{B} = 2R_{A}$ . The planet $B$ is $4\sqrt{2}$ times more massive than planet $A$ . The ratio $( \frac{L_{B}}{L_{A}})$ of angular momentum
$(L_{B})$ of planet $B$ to that of planet $A(L_{A})$ is closest to integer ________.
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The magnetic field inside a 200 turns solenoid of radius 10 cm is $2.9 \times 10^{-4}Tesla$ . If the solenoid carries a
current of 0.29 A , then the length of the solenoid is ________ $\pi cm$ .
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Match List - I with List - II.
List - I List - II
(A) Magnetic induction (I) Ampere meter $^{2}$
(B) Magnetic intensity (II) Weber
(C) Magnetic flux (III) Gauss
(D) Magnetic moment (IV) Ampere/meter
a.
(A)-(I), (B)-(II), (C)-(III), (D)-(IV)
b.
(A)-(III), (B)-(IV), (C)-(I), (D)-(II)
c.
(A)-(III), (B)-(II), (C)-(I), (D)-(IV)
d.
(A)-(III), (B)-(IV), (C)-(II), (D)-(I)
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Three equal masses $m$ are kept at vertices (A, B, C) of an equilateral triangle of side a in free space. At $t= 0$ ,
$------$
they are given an initial velocity $\vec{V}_{A} =V_{0}A\vec{C}, \vec{V}_{B} =V_{0}B\vec{A}$ and $\vec{V}_{C} =V_{0}C\vec{B}$ . Here, $A\vec{C},C\vec{B}$ and $B\vec{A}$ are unit
vectors along the edges of the triangle. If the three masses interact gravitationally, then the magnitude of the
net angular momentum of the system at the point of collision is :
a.
$3amV_{0}$
b.
$\frac{3}{2}$ a $mV_{0}$
c.
$\frac{\sqrt{3}}{2}$ a $mV_{0}$
d.
$\frac{1}{2}$ a $mV_{0}$
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A capacitor, $C_{1} = 6\mu \,F$ is charged to a potential difference of $V_{0} = 5\,V$ using a 5 V battery. The battery is
removed and another capacitor, $C_{2} = 12\mu \,F$ is inserted in place of the battery. When the switch 'S' is closed,
the charge flows between the capacitors for some time until equilibrium condition is reached. What are the
charges $(q_{1}$ and $q_{2})$ on the capacitors $C_{1}$ and $C_{2}$ when equilibrium condition is reached.
a.
$q_{1} = 10\mu C, q_{2} = 20\mu C$
b.
$q_{1} = 30\mu C, q_{2} = 15\mu C$
c.
$q_{1} = 20\mu C, q_{2} = 10\mu C$
d.
$q_{1} = 15\mu C, q_{2} = 30\mu C$
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A physical quantity $Q$ is related to four observables $a,b,c,d$ as follows : $Q = \frac{ab^{4}}{\,cd}$ where,
$a = (60 \pm 3)Pa; b = (20 \pm 0.1)m; c = (40 \pm 0.2)Nsm^{-2}$ and $d = (50 \pm 0.1)m$ , then the percentage error in
Q is $\frac{x}{1000}$ , where $x=$ ________ .
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Identify the homoleptic complexes with odd number of d electrons in the central metal : (A) $[FeO_{4}]^{2-}$ (B)
$[Fe(CN)_{6}]^{3-}$ (C) $[Fe(CN)_{5}NO]^{2-}$ (D) $[CoCl_{4}]^{2-}$ (E) $[Co(H_{2}O)_{3}\,F_{3}]$ Choose the correct answer from the
options given below :
a.
(A), (B) and (D) only
b.
(C) and (E) only
c.
(B) and (D) only
d.
(A), (C) and (E) only
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$O_{2}$ gas will be evolved as a product of electrolysis of : (A) an aqueous solution of $AgNO_{3}$ using silver
electrodes. (B) an aqueous solution of $AgNO_{3}$ using platinum electrodes. (C) a dilute solution of $H_{2}SO_{4}$ using
platinum electrodes. (D) a high concentration solution of $H_{2}SO_{4}$ using platinum electrodes. Choose the correct
answer from the options given below :
a.
(A) and (C) only
b.
(B) and (C) only
c.
(A) and (D) only
d.
(B) and (D) only
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In the sulphur estimation, 0.20 g of a pure organic compound gave 0.40 g of barium sulphate. The percentage
of sulphur in the compound is ______ $\times 10^{-1}%$ . (Molar mass : $O = 16, \,S = 32, Ba = 137$ in $gmol^{-1}$ )
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Consider the following low-spin complexes $K_{3}[Co(NO_{2})_{6}], K_{4}[Fe(CN)_{6}]$ ,
$K_{3}[Fe(CN)_{6}], Cuu_{2}[Fe(CN)_{6}]\,and\,Zn_{2}[Fe(CN)_{6}]$ The sum of the spin-only magnetic moment values of
complexes having yellow colour is. _____ B.M. (answer in nearest integer)
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For hydrogen like species, which of the following graphs provides the most appropriate representation of E vs
Z plot for a constant n ? [E: Energy of the stationary state, Z : atomic number, $n =$ principal quantum number]
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Given below are two statements : Statement (I) : NaCl is added to the ice at $0^{\circ }C$ , present in the ice cream box
to prevent the melting of ice cream. Statement (II) : On addition of NaCl to ice at $0^{\circ }C$ , there is a depression in
freezing point. In the light of the above statements, choose the correct answer from the options given below :
a.
Both Statement I and Statement II are false
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 true
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Given below are two statements : Statement (I) : On nitration of m-xylene with $HNO_{3}, H_{2}SO_{4}$ followed by
oxidation, 4-nitrobenzene-1,3-dicarboxylic acid is obtained as the major product. Statement (II) : $-CH_{3}$ group
is o/p-directing while $-NO_{2}$ group is m-directing group. In the light of the above statements, choose the
correct answer from the options given below :
a.
Both Statement I and Statement II are false
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 true
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Isomeric hydrocarbons $\rightarrow \rightarrow$ negative Baeyer's test (Molecular formula $C_{9}H_{12}$ ) The total number of
isomers from above with four different non-aliphatic substitution sites is -
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0.1 M solution of KI reacts with excess of $H_{2}SO_{4}$ and $KIO_{3}$ solutions. According to equation
$5I^{-} + IO^{-}_{3} + 6H^{+} \rightarrow 3I\rightarrow_{2}+ 3H_{2}O$ Identify the correct statements : (A) 200 mL of KI solution reacts with
0.004 mol of $KIO_{3}$ (B) 200 mL of KI solution reacts with 0.006 mol of $H_{2}SO_{4}$ (C) 0.5 L of KI solution
produced 0.005 mol of $I_{2}$ (D) Equivalent weight of $KIO_{3}$ is equal to ( $\frac{\,Molecular weight\,}{5}$ ) Choose the correct
answer from the options given below :
a.
(A) and (D) only
b.
(C) and (D) only
c.
(B) and (C) only
d.
(A) and (B) only
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Given below are two statements : Statement (I): In partition chromatography, stationary phase is thin film of
liquid present in the inert support. Statement (II) : In paper chromatography, the material of paper acts as a
stationary phase. 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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In the Claisen-Schmidt reaction to prepare, dibenzalacetone from 5.3 g of benzaldehyde, a total of 3.51 g of
product was obtained. The percentage yield in this reaction was ______ %.
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Identify the essential amino acids from below : (A) Valine (B) Proline (C) Lysine (D) Threonine (E) Tyrosine
Choose the correct answer from the options given below :
a.
(A), (C) and (E) only
b.
(A), (C) and (D) only
c.
(C), (D) and (E) only
d.
(B), (C) and (E) only
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First ionisation enthalpy values of first four group 15 elements are given below. Choose the correct value for
the element that is a main component of apatite family :
a.
$1402\,kJ\,mol^{-1}$
b.
$834\,kJ\,mol^{-1}$
c.
$1012\,kJ\,mol^{-1}$
d.
$947\,kJ\,mol^{-1}$
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Given below are two statements : Statement (I) : It is impossible to specify simultaneously with arbitrary
precision, both the linear momentum and the position of a particle. Statement (II) : If the uncertainty in the
measurement of position and uncertainty in measurement of momentum are equal for an electron, then the
uncertainty in the measurement of velocity is $⩾ \sqrt{\frac{h}{\pi}} \times \frac{1}{2\,m}$ . 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.
Both Statement I and Statement II are true
d.
Statement I is true but Statement II is false
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Consider the equilibrium $CO(\,g) + 3H_{2}(\,g)\rightleftharpoons CH_{4}(\,g) + H_{2}O(\,g)$ If the pressure applied over the system
increases by two fold at constant temperature then (A) Concentration of reactants and products increases. (B)
Equilibrium will shift in forward direction. (C) Equilibrium constant increases since concentration of products
increases. (D) Equilibrium constant remains unchanged as concentration of reactants and products remain
same. Choose the correct answer from the options given below :
a.
(A), (B) and (C) only
b.
(A) and (B) only
c.
(A), (B) and (D) only
d.
(B) and (C) only
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Drug $X$ becomes ineffective after $50%$ decomposition. The original concentration of drug in a bottle was
$16mg/mL$ which becomes $4mg/mL$ in 12 months. The expiry time of the drug in months is __________
Assume that the decomposition of the drug follows first order kinetics.
a.
2
b.
6
c.
12
d.
3
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