AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Maths
Find the roots of each of the
following quadratic equations by the method of completing the squares \( \sqrt{5} x^{2}+9 x+4 \sqrt{5}=0 \)
A. \( -\sqrt{7}, \frac{-17}{\sqrt{3}} \)
в. \( -\sqrt{5}, \frac{-4}{\sqrt{5}} \)
c. \( -\sqrt{5}, \frac{-14}{\sqrt{3}} \)
D. \( -\sqrt{7}, \frac{-13}{\sqrt{5}} \)
Subject: Physics
A solenoid of length \( 10 \mathrm{cm} \), diameter 1 \( \mathrm{cm}, \) number of turns 500 with relative
permeability of the core
\( 2000, \) is connected to an ac source of
frequency 50 Hz. Then, the reactance is
A . zero
B. \( 55 \Omega \)
c. \( 105 \Omega \)
D. \( 155 \Omega \)
Subject: Physics
What is the escape velocity from the
surface of the earth of radius \( R \) and
density \( \rho ? \)
\( ^{\text {A }} \cdot 2 R \sqrt{\frac{2 \pi \rho G}{3}} \)
в. \( 2 \sqrt{\frac{2 \pi \rho G}{3}} \)
c. \( 2 \pi \sqrt{\frac{R}{g}} \)
D. \( \sqrt{\frac{2 \pi G \rho}{R^{2}}} \)
Subject: Physics
A load of \( 10 k N \) is supported from a
pulley which in turn is supported by a rope of sectional area, \( 1 \times 10^{3} m m^{2} \)
and modulus of elasticity \( 10^{3} N m m^{-2} \) as shown in Fig. 5.18. Neglecting the friction at the pulley, determine the deflection of the load is \( x+0.75 m m \)
Find \( \boldsymbol{x} \)
Subject: Maths
The rate at which ice-ball melts is
proportional to the amount of ice in it. If half of it melts in 20 minutes, the
amount of ice left after 40 minutes compared to it original amount is
\( ^{A} \cdot\left(\frac{1}{8}\right) t h \)
B. \( \left(\frac{1}{16}\right) \) th
\( ^{c} \cdot\left(\frac{1}{4}\right) t h \)
D. \( \left(\frac{1}{32}\right) t h \)
Subject: Maths
Metal spheres, each of radius \( 2 \mathrm{cm}, \) are
packed into a rectangular box of internal dimensions \( 16 \mathrm{cm} \times 8 \mathrm{cm} \times 8 \)
cm. When 16 spheres are packed the box filled with preservative liquid. Find the volume of this liquid. (Give the answer to the nearest integer value)
\( \mathbf{A} \cdot 482 c m^{3} \)
В. \( 478 \mathrm{cm}^{3} \)
\( \mathrm{c} \cdot 488 \mathrm{cm}^{3} \)
D. \( 490 \mathrm{cm}^{3} \)
Subject: Physics
One gram of radium is reduced by \( 2 m g \)
in 5 years by \( \alpha \) - decay. The half life of radium is:
\( \left(\log _{10} 998=2.9991\right) \)
A. 1520.4 years
B. 1671.7 years
c. 1617.5 years
D. 1732.86 years
Subject: Chemistry
The vapour pressure of pure benzene is
\( 639.7 \mathrm{mm} \mathrm{Hg} \) and the vapour pressure of a solution of a solute in benzene at the
temperature is \( 631.9 \mathrm{mm} \) Hg. If the
molality of the solution is \( 156 \times 10^{-x} \)
then what is the value of \( x ? \)
Subject: Maths
\( f(x)=\left\{\begin{array}{ll}\frac{1-\sin ^{3} x}{3 \cos ^{2} x}, & \text { if } \quad x<\frac{\pi}{2} \\ a, \quad \text { if } x= & \frac{\pi}{2} \\ \frac{b(1-\sin x)}{(\pi-2 x)^{2}}, & \text { if } \quad x>\frac{\pi}{2}\end{array}\right. \)
so that \( f(x) \) is continuous at \( x=\frac{\pi}{2} \)
then
This question has multiple correct options
A \( a=\frac{1}{2} \)
в. \( b=4 \)
\( c \cdot a=1 \)
D. \( b=-4 \)
Subject: Maths
The function \( f(x)=2 x^{3}-15 x^{2}+ \)
\( 36 x+6 \) is strictly decreasing in the
interval
A. (2,3)
(年) (2,3,3)
в. \( (-\infty, 2) \)
c. (3,4)
(年. \( (3,4)) \)
D. \( (-\infty, 3) \cup(4, \infty) \)
E \( .(-\infty, 2) \cup(3, \infty) \)
Subject: Chemistry
\( \boldsymbol{P h}-\boldsymbol{C} \equiv \boldsymbol{C}-\boldsymbol{C H}_{3} \stackrel{\boldsymbol{H} \boldsymbol{g}^{2+} / \boldsymbol{H}^{+}}{\longrightarrow} \boldsymbol{A} \)
The product A is:
\( A \)
в.
\( c \)
D.
Subject: Physics
A boy stands \( 85 \mathrm{m} \) infront of a high wall and then blows a whistle. Calculate the
time interval when he hears an echo.
(speed of sound \( =340 m s^{-1} \) )
A . \( 0.1 \mathrm{s} \)
B. \( 0.2 \mathrm{s} \)
c. \( 0.5 \mathrm{s} \)
D. 1 s
Subject: Physics
The pulleys and strings shown in the fig are smooth and of negligible mass. For the system to remain in equilibrium,
the angle \( \theta \) should be:
\( A \cdot 0^{\circ} \)
B. \( 30^{\circ} \)
\( c \cdot 45^{\circ} \)
D. \( 60^{\circ} \)
Subject: Maths
If \( z=-3+2 i, \) then \( \frac{1}{z} \) is equal to
A \( \cdot \frac{1}{13}(3+2 i) \)
B. \( -\frac{1}{13}(3+2 i) \)
c. \( \frac{1}{\sqrt{13}}(3+2 i) \)
D. \( -\frac{1}{\sqrt{13}}(3+2 i) \)
Subject: Chemistry
Statement 1: The ideal gas law does not hold under low temperatures and high
pressure. Statement 2: Interactions between
particles cannot be neglected under these conditions.
A. Statement 1 and Statement 2 are correct and Statement 2 is the correct explanation of Statement1
B. Both the Statement 1 and Statement 2 are correct, but Statement 2 is not the correct explanation of Statement 1.
c. statement 1 is correct, but statement 2 is not correct
D. Statement 1 is not correct, but Statement 2 is correct
Subject: Maths
\( L_{1} \) and \( L_{2} \) are 2 tangent \( y^{2}=16 x \) which
markes angle \( \tan ^{-1} \frac{1}{3} \) with the tangent
\( T^{\prime} \) to the same parabola at the end point of latus rectum which the ordinate then find the area of \( \triangle \) formed
\( \boldsymbol{L}_{1}, \boldsymbol{L}_{2} ? \)
Subject: Chemistry
The precipitation of \( \boldsymbol{A} \boldsymbol{g} \boldsymbol{C l}\left(\boldsymbol{K}_{s p}=\mathbf{1 . 8} \times\right. \)
\( \mathbf{1 0}^{-10} \) ) will occur when which of the
following two solutions are mixed?
A \( \cdot 10^{-4} M\left(A g^{+}\right) \) and \( 10^{-4} M\left(C l^{-}\right. \)
B . \( 10^{-5} M\left(A g^{+}\right) \) and \( 10^{-5} M\left(C l^{-}\right) \)
C. \( 10^{-5} M\left(A g^{+}\right) \) and \( 10^{-6} M\left(C l^{-}\right) \)
D. \( 10^{-10} M\left(A g^{+}\right) \) and \( 10^{-10} M\left(C l^{-}\right) \)
Subject: Physics
Which of the following complexes has the least molar conductivity in the
solution?
A \( \cdot C O C I_{3} \cdot 3 N H_{3} \)
в. \( C O C I_{3} .4 N H_{3} \)
c. \( \operatorname{COCI}_{3} .5 \mathrm{NH}_{3} \)
D. \( C O C I_{3} .6 N H_{3} \)
Subject: Physics
Two blocks of masses \( 10 \mathrm{kg} \) and \( 4 \mathrm{kg} \) are connected by a spring of negligible mass and placed on a frictionless horizontal surface.An impulse gives a velocity of \( 14 \mathrm{m} / \mathrm{s} \) to the heavier block in
the direction of the lighter block.the velocity of the center of mass is :
\( A \cdot 5 m / s \)
B. 20 \( \mathrm{m} / \mathrm{s} \)
\( c \cdot 30 m / s \)
D. \( 10 \mathrm{m} / \mathrm{s} \)
Subject: Maths
Find the volume of a hemisphere whose radius is \( \left.7 \mathrm{cm} . \text { (use } \pi=\frac{22}{7}\right) \)
A \( \cdot 112.66 \mathrm{cm}^{3} \)
в. \( 718.66 \mathrm{cm}^{3} \)
c. \( 12.66 \mathrm{cm}^{3} \)
D. \( 132.66 \mathrm{cm}^{3} \)
Subject: Chemistry
The degree of dissociation of
\[
\boldsymbol{P C l}_{5}(\boldsymbol{g}) \rightleftharpoons \boldsymbol{P C l}_{3}(\boldsymbol{g})+\boldsymbol{C l}_{2}(\boldsymbol{g})
\]
with increase in
pressure at equilibrium.
A . increases
B. decreases
c. first increases and then decreases
D. first decreases and then increases
Subject: Maths
Use the digits 11,9,7 to form the smallest and the largest mixed number. Then find their sum giving your answer as a mixed number.
A \( \cdot 18 \frac{8}{9} \)
в. \( 20 \frac{8}{77} \)
c. \( _{18} \frac{42}{99} \)
D. \( _{19} \frac{52}{77} \)
Subject: Biology
toppr
Q туре your question
produced in liver cells. The production of AAT is dependent upon various hormonal stimuli. Human liver cells were cultured;
nalf the cultured cells were used to
measure the amount of AAT mRNA
present, and half were used to measure
the amount of AAT present.

Measurements were taken at five-minute
ntervals following hormonal stimulation of the cells. Figure 1 shows the results of
this experiment. This experiment was
repeated by the addition of an inhibitor of protein synthesis along with the hormone and its result is shown in figure
2. The figure 2 shows that the AAT is a/an
Figure
Minutes after hormone added
Figure 2
A. Protein
B. Hormon
c. Lipid
D. Inhibito
E. Amino acid
Subject: Physics
An electric motor is a device to convert
electrical energy into mechanical energy. The motor shown below has a rectangular coil \( (15 \mathrm{cm} \times 10 \mathrm{cm}) \) with
100 turns placed in a uniform magnetic
fleld \( B=2.5 T . \) When a current is
passed through the coil, lt completes 50 revolutions in one second. the power
output of the motor is \( 1.5 k W \). The
current rating of the coil should be
\( A \cdot 1 A \)
B. 2 A
\( c \cdot 3 A \)
\( D \cdot 4 A \)
Subject: Physics
A block of \( A \) of \( \operatorname{mass} M_{A}=1 \) kg is kept
on a smooth horizontal surface and
attached by a light thread to another
block B of mass \( M_{B}=2 k g . \) Block B is
resting on ground, and thread and pulley are massless and frictionless. A
bullet of mass \( m=0.25 \mathrm{kg} \) moving
horizontally with velocity of \( u= \)
\( 200 m / s \) penetrates through block \( A \)
and comes out with a velocity of 100 \( \mathrm{m} / \mathrm{s} \)
Subject: Chemistry
List -1
A) Antiferromagnetic
\( N i F e_{2} O_{4} \)
B) Covalent crystal
2) \( M n O \)
C) Ferrimagnetic
3)
Diamond
The correct match is :
A. A-2, B-3, C- -
B. A-3, B-2, C-1
c. A-1, B-2, C-3
D. A-1, B-3, C-2
Subject: Physics
Displacement versus time curve for a
particle executing SHM is as shown in
figure.
At what points the velocity of the
particle is zero?
\( A \cdot A, C, E \)
B. В, D, F
\( c \cdot A, D, F \)
D. \( \mathrm{C}, \mathrm{E}, \mathrm{F} \)
Subject: Physics
Two wires are kept tight between the
same pair supports. The tensions in the wires are in the ration \( 2: 1, \) the radii are
in the ratio 3: 1 and the densities are in
the ratio \( 1: 2 . \) The ratio of their
fundamental frequencies is
A .2: 3
B. 2: 4
c. 2: 5
D. 2: 6
Subject: Physics
The resistances of the four arms \( P, Q, R \) and \( \sin \) a Wheatstone's bridge are 10
ohm, 30 ohm, 30 ohm and 90 ohm, respectively. The e.m.f. and internal resistance of the cell are 7 volt and 5 ohm respectively. If the galvanometer
resistance is 50 ohm, the current drawn
from the cell will be
A . \( 1.0 \mathrm{A} \)
B. 0.2 A
\( c \cdot 0.1 \mathrm{A} \)
D. 2.0 A
Subject: Physics
A hollow conducting sphere is placed in
an electric field produced by a point
charge as shown. Let \( V_{A}, V_{B}, V_{C} \) be the
electric potentials at points \( A, B, C \)
respectively and \( V_{0} \) is the potential at
centre 0 due to induced charge on shell.
This question has multiple correct options
A \( . V_{0}=0 \)
В. \( V_{A}>V_{B}>V_{C} \)
\( \mathbf{c} \cdot V_{4}=V_{B}=V_{O} \)
\( \mathbf{D} \cdot V_{A}<V_{B}<V_{C} \)
Subject: Physics
A motor car is traveling at \( 30 m s^{-1} \) on a circular road of radius \( 500 \mathrm{m} \). It is
increasing speed at the rate of \( 2 m s^{-2} \) The acceleration of car is :
A \( .2 m s^{-2} \)
В. 2.7 \( m s^{-2} \)
\( c \cdot 3 m s^{-2} \)
D. 3.7 \( m s^{-2} \)
Subject: Physics
Three capacitors, \( 3 \mu F, 6 \mu F \) and \( 6 \mu F \) are connected in series to a source of
120V. The potential difference, in
volts, across the \( 3 \mu F \) capacitor will be
A . 24
B. 30
\( c \cdot 40 \)
\( D \cdot 60 \)
Subject: Maths
If \( \triangle \mathrm{ABC} \) and \( \triangle \mathrm{AMP} \) are right triangles, right-angled at \( \mathrm{B} \) and \( \mathrm{M} \) respectively and \( \angle M A P=\angle B A C \)
Prove that
(i) \( \triangle A B C \sim \triangle A M P \)
(ii) \( \frac{\boldsymbol{C A}}{\boldsymbol{P A}}=\frac{\boldsymbol{B C}}{\boldsymbol{M P}} \)
Subject: Maths
In the number \( 0.257, \) which of the
following does the digit 7 represent??
A \( \cdot 7 \times \frac{1}{10} \)
в. \( 7 \times \frac{1}{100} \)
c. \( _{7 \times \frac{1}{1000}} \)
D. \( 7 \times \frac{1}{10000} \)
E \( \cdot 7 \times \frac{1}{100000} \)
Subject: Maths
If the differential equation of a body of mass \( m \) falling from rest subjected to the force of gravity and an air resistance proportional to the square of the velocity is given by \( m v \frac{d v}{d x}=k a^{2}- \) \( k v^{2}, \) then it can be proved that \( \frac{2 k x}{m}= \) \( \log \left(\frac{\boldsymbol{a}^{2}}{\boldsymbol{a}^{2}-\boldsymbol{v}^{2}}\right), \) where \( \boldsymbol{m} \boldsymbol{g}=\boldsymbol{k} \boldsymbol{a}^{2} \)
A. True
B. False
Subject: Chemistry
In a container a mixture is prepared by mixing of three samples of hydrogen, helium ion \( \left(H e^{+}\right) \) and lithium ion
\( \left(L i^{2+}\right) \) In sample all the hydrogen atoms are in 1 st excited state and al
the He ions are in third excited state
and all the \( \left(L i^{2+}\right) \) ions are in fifth
excited state Find the total number of
spectral lines observed in the emission
spectrum of such a sample, when the electrons return back upto the ground
state
Subject: Maths
A multiple choice examination has 5 questions. Each question has three alternative answers of which exactly one is correct. The probability that a
student will get 4 or more correct answers just by guessing is
A \( \cdot \frac{13}{3^{5}} \)
в. \( \frac{11}{3^{5}} \)
c. \( \frac{10}{3^{5}} \)
D. \( \frac{17}{3^{5}} \)
Subject: Chemistry
The enthalpy of dissociation of \( \boldsymbol{H}_{3} \) is
\( 954 k J / m o l \) and that of \( P_{2} H_{4} \) is \( 1.485 M J \) mol \( ^{-1} . \) What is the bond
enthalpy of the \( P-P \) bond?
A. \( 213 k J / \) mol
в. \( -213 k J / \) тод
c. \( 2757 k J / \) mol
D. None of these
Subject: Maths
The coordinates of two consecutive
vertices \( A \) and \( B \) of a regular hexagon
\( A B C D E F \) are (1,0) and (2,0)
respectively. The equation of the diagonal \( C E \) is
A. \( \sqrt{3} x+y=4 \)
B . \( x+\sqrt{3} y+4=0 \)
c. \( x+\sqrt{3} y=4 \)
D. None of these
Subject: Maths
Find the real number \( \boldsymbol{x} \) if \( (\boldsymbol{x}-\mathbf{2} \boldsymbol{i})(\mathbf{1}+ \)
\( i) \) is purely imaginary.
\( A \cdot 2 \)
B. -2
\( c \cdot 4 \)
D. -4
Subject: Chemistry
IUPAC name of the given compound is:
\[
\begin{array}{c}
\mathrm{H}_{3} \mathrm{C}-\mathrm{CH}-\mathrm{CH}_{2}-\mathrm{CH}-\mathrm{CH}-\mathrm{CH}_{2}-\mathrm{CH}_{3} \\
\mathrm{OH}
\end{array}
\]
A. 5 -ethylheptane-2.4-diol
B. 3-ethylheptane-4,6-diol
C . 4-ethyl-1-methylhexane-1,3-diol
D. none of these
Subject: Physics
A man turns on rotating table with an
angular speed \( \omega . \) He is holding two equal masses at arms length. Without moving his arms, he just drops the two masses. How will his angular speed change?
A. less than \( \omega \)
B. more than \( \omega \)
c. it will be equal to
D. it will be more than \( \omega \) if the dropped mass is more than \( 9.8 \mathrm{Kg} \) and it will be less than \( \omega \) if the mass dropped is less than \( 9.8 \mathrm{Kg} \)
Subject: Chemistry
Assertion
Sulphuric acid is more viscous than
water.
Reason
Concentrated sulphuric acid has a great affinity for water
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect
Subject: Maths
If \( \boldsymbol{P}(\boldsymbol{A})=\frac{\mathbf{7}}{\mathbf{1 3}}, \boldsymbol{P}(\boldsymbol{B})=\frac{\mathbf{9}}{\mathbf{1 3}}, \boldsymbol{P}(\boldsymbol{A} \cup \boldsymbol{B})= \)
2
- then find \( (\mathrm{A} \mid \mathrm{B}) \) 13
Subject: Physics
If \( \overrightarrow{\boldsymbol{A}}=\mathbf{5} \hat{\boldsymbol{i}}+\mathbf{7} \hat{\boldsymbol{j}}-\boldsymbol{3} \hat{\boldsymbol{k}} \) and \( \overrightarrow{\boldsymbol{B}}=\mathbf{1 5} \hat{\boldsymbol{i}}+ \)
\( 21 \hat{j}+a \hat{k} \) are parallel vectors then the
value of \( \boldsymbol{a} \) is:
\( A \cdot-3 \)
B. 9
\( c \cdot-9 \)
D. 3
Subject: Maths
Let \( \boldsymbol{O}= \) Set of odd natural numbers \( = \)
\( \{1,3,5,7,9, \dots\} \) and \( E=\operatorname{set} \) of even
natural numbers \( =\{2,4,6,8,10, \dots \dots .\} \)
Then show that \( 0.1 \notin E \)
Subject: Chemistry
The compounds shown below have similar weights but significantly different boiling points. Match the compound with its boiling point.
(Boiling points \( \left.\left(^{o} C\right) 28,57,100,141\right) \)
A. Methyl acetate=100, 2-butanol=141, 2-methyl butane=28, Propanoic acid=57
B. Methyl acetate=57, 2-butanol=100, 2-methyl butane=28, Propanoic acid=141
c. Methyl acetate=28, 2-butanol=100, 2-methyl butane=57, Propanoic acid=141
D. Methyl acetate=141, 2-butanol=57, 2-methy butane=28, Propanoic acid=100
Subject: Physics
The temperature coefficient of
resistance of conductor varies as
\( \boldsymbol{\alpha}(\boldsymbol{T})=\boldsymbol{3} \boldsymbol{T}^{2}+\boldsymbol{2} \boldsymbol{T} . \) If \( \boldsymbol{R}_{0} \) is resistance at
\( T=0 \) and \( R \) is resistance at \( T, \) then
A \( . R=R_{0}(6 T+2) \)
B . \( R=2 R_{0}(3+2 T) \)
C \( . R=R_{0}\left(1+T^{2}+T^{3}\right) \)
D. \( R=R_{0}\left(1-T+T^{2}+T^{3}\right) \)
Subject: Maths
If \( \boldsymbol{x}=\boldsymbol{a} \cos ^{3} \boldsymbol{\theta} \) and \( \boldsymbol{y}=\boldsymbol{a} \sin ^{3} \boldsymbol{\theta}, \) then find
the value of \( \frac{d^{2} y}{d x^{2}} \) at \( \theta=\frac{n}{6} \)
Subject: Chemistry
Which of the following is/are disproportionation reactions?
This question has multiple correct options
\( ^{\mathbf{A}} \cdot_{H_{2}} O_{2} \rightarrow H_{2} O+\frac{1}{2} O_{2} \)
B . \( H N O_{3}+H C l \rightarrow N O+C l_{2}+H_{2} O \)
c. \( 3 C l O^{-} \rightarrow C l O_{3}^{-}+2 C l^{-} \)
D. \( C l_{2}+H_{2} O \rightarrow H C l+H C l O \)
Subject: Chemistry
Select the correct orders of bond angles.
This question has multiple correct options
\( \mathbf{A} \cdot H-\hat{P}-H\left(P H_{3}\right)<F-\hat{P}-F\left(P F_{3}\right) \)
B \( \cdot F-\hat{N}-F\left(N F_{3}\right)<H-\hat{N}-F\left(N H_{3}\right) \)
\( \mathbf{c} \cdot F-\hat{O}-F\left(O F_{3}\right)<H-\hat{O}-H\left(H_{2} O\right)<C l-\hat{O}- \)
\( \mathrm{Cl}\left(\mathrm{O} \mathrm{Cl}_{2}\right) \)
D. \( H-\hat{P}-H\left(P H_{3}\right)>F-\hat{P}-F\left(P F_{3}\right) \)
Subject: Physics
The velocity of the block at the midpoint
between \( B \) to \( C \) will be :
A. \( \frac{\sqrt{2 g h}}{2} \)
B. \( \sqrt{2 g h} \)
\( \mathbf{c} \cdot \sqrt{g h} \)
\( D \cdot \frac{\sqrt{g h}}{2} \)
Subject: Physics
A block of wood floats in water with \( \frac{4}{5} \) th of its volume submerged, but it just floats in another liquid. The density of
liquid is? \( \left(\operatorname{in} \mathrm{kg} / m^{3}\right) \)
\( \mathbf{A} \cdot 750 \)
в. 800
c. 1000
D. 1250
Subject: Physics
Two blocks \( A \) and \( s \) of masses \( 100 k g \)
and \( 20 k g \) respectively, separated by a
distance of 5 in are kept on a smooth
surface. A mass of 60kg is then added
to the block \( A . \) Now, in order to
experience same attractive force as before, the two blocks should be separated by a distance of :
Subject: Maths
The condition for the vectors \( \vec{a}, \vec{b}, \vec{c}, \vec{d} \) to be the sides of a parallelogram taken in order is
A . \( \vec{a}+\vec{b}=\vec{c}+\vec{d} \)
В . \( \vec{a}+\vec{b}=\vec{c}+\vec{d}=0 \)
c. \( \vec{a}+\vec{c}=\vec{b}+\vec{d} \)
D . \( \vec{a}+\vec{c}=\vec{b}+\vec{d}=0 \)
Subject: Maths
The solution of \( \frac{d y}{d x}+2 y \tan x=\sin x \)
given that \( \boldsymbol{y}=\mathbf{0}, \boldsymbol{x}=\frac{\boldsymbol{\pi}}{\mathbf{3}} \) is
A \( \cdot y=\cos x-2 \cos ^{2} x \)
B . \( y=-\cos x+2 \cos ^{2} x \)
c. \( y=\cos x-\cos ^{2} x \)
D. \( y=2 \cos x-2 \cos ^{2} x \)
Subject: Maths
\( A \) and \( B \) are two independent witnesses
is a case. The probability that \( A \) will speak truth is \( x \) and the probability that \( B \) will speak the truth is \( y . A \) and \( B \) agree in a certain statement. The
probability that the statement is true is
A \( \cdot \frac{x y}{1-x y} \)
в. \( \frac{x y}{1-x-y+2 x y} \)
c. \( \frac{2 x y}{x-y} \)
D. \( \frac{x y}{1-x-y} \)
Subject: Physics
In the circuit shown in the figure, the
A.C. source gives a voltage \( V=20 \cos \)
\( (2000 \mathrm{t}) \) volt. Neglecting source resistance, select correct alternative(s).
This question has multiple correct options
A. The reading of voltmeter is 0 V
B. The reading of voltmeter is 5.6
C. The reading of ammeter is 1.4 A
D. The reading of ammeter is 0.47 A
Subject: Maths
The function \( f(x)=\left\{\begin{array}{cc}\frac{e^{1 / x}-1}{e^{1 / x}+1} & x \neq 0 \\ 0, & x=0\end{array}\right. \)
is
A. continuous at \( x=0 \)
B. discontinuous at \( x=0 \)
c. discontinuous at \( x=0 \) but can be made continuous at
\( x=0 \)
D. None of these
Subject: Chemistry
\( X \frac{H_{2} \text { along with boiling xylene}}{P d / B a S O_{4}} C H_{3} C H O \)
In the above reaction \( \boldsymbol{X} \) is:
A \( \cdot C H_{3} C O O H \)
в. \( C H_{3} \) СОС\( l \)
c. \( C H_{3} C O C H_{3} \)
D. \( C H_{3} C H_{2} \) ОН
Subject: Physics
A 20 g ball is fired horizontally toward a 100 g ball that is hanging motionless from a 1.0 -m-long string. The balls undergo a head-on, elastic collision, after which the 100 g ball swings out to a maximum angle of 50
degrees. Determine the initial speed of the 20 g ball.
A. \( 8.4 \mathrm{m} / \mathrm{s} \)
B. \( 4.2 \mathrm{m} / \mathrm{s} \)
c. \( 2.1 \mathrm{m} / \mathrm{s} \)
D. \( 16.8 \mathrm{m} / \mathrm{s} \)
Subject: Chemistry
Which reaction sequence below can
convert \( p \) -bromoaniline into \( p \)
bromophenol?
\( A \)
\[
\mathbf{h}_{2} \mathrm{N}-\langle\sqrt{\quad}\rangle=\mathrm{Br} \frac{\mathrm{NaNO}_{2}}{\mathrm{HCl}, \mathrm{H}_{2} \mathrm{O}, 0^{\circ} \mathrm{C}}
\]
B.
\( c \)
\( \mathrm{H}_{2} \mathrm{N} \longrightarrow\langle\underbrace{\mathrm{o}}_{\mathrm{Pyridine}} \mathrm{N}_{2} \mathrm{O}=\frac{\mathrm{NaOH}}{\mathrm{B}} \)
\( D \)
Subject: Maths
Find the shortest distance between the \( \operatorname{lines} \bar{r}=4 \bar{i}-\bar{j}+\lambda(\bar{i}+2 \bar{j}-5 \bar{k}) \) and
\( \overline{\boldsymbol{r}}=\overline{\boldsymbol{i}}-\overline{\boldsymbol{j}}+2 \overline{\boldsymbol{k}}+\boldsymbol{\mu}(\overline{\boldsymbol{i}}+\mathbf{2} \overline{\boldsymbol{j}}-\mathbf{5} \overline{\boldsymbol{k}}) \)
A. \( \sqrt{220} \)
B. \( \frac{\sqrt{221}}{\sqrt{30}} \)
c. 432
D. \( \sqrt{33} \)
Subject: Chemistry
In which pair(s) is/are the stronger bond found in the first species? This question has multiple correct options
A \( \cdot O_{2}^{-}, O_{2} \)
в. \( N_{2}, N_{2} \)
c. \( N O^{+}, N O^{-} \)
D. \( C O, O_{2}^{2+} \)
Subject: Chemistry
The correct order of increasing \( \boldsymbol{C}-\boldsymbol{O} \)
bond length in \( C O, C O_{3}^{-2} \) and \( C O_{2} \) is:
A \( \cdot C O_{3}^{-2}<C O_{2}<C O \)
в. \( C O_{2}<C O_{3}^{-2}<C O \)
c. \( C O<C O_{3}^{-2}<C O_{2} \)
D. \( C O<C O_{2}<C O_{3}^{-2} \)
Subject: Physics
In an experiment to determine the
specific heat capacity of a solid, following observations were made:
Mass of calorimeter + stirrer= \( \boldsymbol{x} \boldsymbol{k} \boldsymbol{g} \)
Mass of water= \( \boldsymbol{y} \boldsymbol{k} \boldsymbol{g} \)
Initial temperature of water \( =t_{1}^{o} C \)
Mass of solid \( =\boldsymbol{z} \boldsymbol{k} \boldsymbol{g} \)
Temperature of solid= \( t_{2}^{o} \boldsymbol{C} \)
Temperature of mixture \( =t^{o} C \) Specific heat capacity of calorimeter
and water are \( c_{1} \) and \( c_{2} \) respectively.
Express the specific heat capacity c of the solid in terms of the above data
A \( \cdot \frac{\left(x c_{1}+y c_{2}\right)\left(t-t_{1}\right)}{z\left(t_{2}-t\right)} \)
B. \( \frac{\left(x c_{1}+y c_{2}\right)\left(t-t_{2}\right)}{z\left(t_{1}-t\right)} \)
c. \( \frac{\left(x c_{1}+y c_{2}\right)\left(t+t_{2}\right)}{z\left(t_{1}+t\right)} \)
D. \( \frac{\left(x c_{1}+y c_{2}\right)\left(t+t_{1}\right)}{z\left(t_{2}+t\right)} \)
Subject: Chemistry
The change in volume \( V \) with respect to
an increase in pressure P has been
shown in the adjoining figure for a non-
ideal gas at four different temperatures
\( T_{1}, T_{2}, T_{3} \) and \( T_{4} . \) The critical
temperature of the gas is:
A \( \cdot T_{1} \)
\( \mathbf{B} \cdot T_{2} \)
\( c \cdot T_{3} \)
\( \mathbf{D} \cdot T_{4} \)
Subject: Chemistry
A metal ion \( M^{n+} \) having \( d^{4} \) valence electronic configuration combines with three bidentate ligands to form a complex compound. Assuming \( \triangle \boldsymbol{a}>\boldsymbol{p} \)
(i) Write the electronic configuration of
\( \boldsymbol{d}^{4} \) ion.
(ii) What type of hybridisation will \( M^{n+} \) ion has?
(iii) Name the type of isomerism exhibited by this complex.