AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Maths
Given two independent events \( A \) and \( B \) such that \( \boldsymbol{P}(\boldsymbol{A})=\mathbf{0 . 3}, \boldsymbol{P}(\boldsymbol{B})=\mathbf{0 . 6} \)
Find
(i) \( P(A \text { and not } B) \)
(ii) P(neither A nor
B)
Subject: Maths
Assertion
The equation \( 2\left(\sin ^{-1} x\right)^{2}- \)
\( 5\left(\sin ^{-1} x+2\right)=0 \)
Reason
\( \sin ^{-1}(\sin x)=x \) if \( x \epsilon[-1.57,1.57] \)
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. Assertion false but Reason is true
Subject: Chemistry
A hypothetical reaction \( \boldsymbol{A}_{2}+\boldsymbol{B}_{2} \rightarrow \)
\( 2 A B \) follows the mechanism as given
below:
\( \boldsymbol{A}_{2} \rightleftharpoons \boldsymbol{A}+\boldsymbol{A} \quad(\text { fast }) \)
\( \boldsymbol{A}+\boldsymbol{B}_{2} \rightarrow \boldsymbol{A} \boldsymbol{B}+\boldsymbol{B} \quad(\text { slow }) \)
\( A+B \rightarrow A B \quad(f a s t) \)
The order of the overall reaction is:
\( A \cdot 2 \)
B.
c. 1.5
D.
Subject: Physics
The binding energy per nucleon for the
parent nucleus is \( \mathrm{E}_{1} \) and that for the
daughter nuclei is \( \mathrm{E}_{2} \). Then
A \( \cdot \mathrm{E}_{2}=2 \mathrm{E}_{1} \)
в. \( \mathrm{E}_{1}>\mathrm{E}_{2} \)
c. \( \mathrm{E}_{2}>\mathrm{E}_{1} \)
D. \( \mathrm{E}_{1}=2 \mathrm{E}_{2} \)
Subject: Maths
If \( z^{2}+z+1=0, \) then \( \sum_{r=1}^{6}\left(z_{1}+\frac{1}{z_{2}}\right)^{2} \)
is equal to
\( A \cdot 6 \)
B. 12
\( c \cdot 18 \)
D. 24
Subject: Maths
Area of the region bounded by the curve \( \boldsymbol{y}=\boldsymbol{x}^{2} \) and \( \boldsymbol{y}=\boldsymbol{s e c}^{-1}\left[\boldsymbol{s i n}^{2} \boldsymbol{x}\right] \) (where \( [.] \)
denotes the greatest integer function) is
A \( \cdot \frac{\pi}{3} \sqrt{\pi} \)
В. \( \frac{2 \pi \sqrt{\pi}}{3} \)
c. \( \frac{4 \pi \sqrt{\pi}}{3} \)
D. \( \frac{6 \pi \sqrt{\pi}}{3} \)
E \( \cdot \frac{3 \pi \sqrt{\pi}}{2} \)
Subject: Physics
An example of nuclear fusion reaction
is :
A \( \cdot \frac{2033}{90} \mathrm{Th}+\frac{1}{0} \mathrm{n} \rightarrow \frac{23^{3} \mathrm{Th}}{ } \)
B \( \cdot \frac{27}{13} \mathrm{AI}+\frac{4}{2} \mathrm{He} \rightarrow \frac{30}{15} \mathrm{P}+\frac{1}{0} \mathrm{n} \)
\( \mathbf{c} \cdot_{2}^{3} \mathrm{He}+_{2}^{3} \mathrm{He} \rightarrow_{2}^{4} \mathrm{He}+2_{1}^{1} \mathrm{H} \)
D \( \cdot \frac{239}{92} \mathrm{U} \rightarrow_{93}^{239} \mathrm{Np}+_{-1}^{0} \mathrm{e} \)
Subject: Maths
The cost of a scooter depreciates every year by \( 15 \% \) of its value at beginning of
the year. If the present cost of the scooter is Rs. 8,\( 000 ; \) find its cost (in
Rs.) after 2 years.
\( A \cdot 5780 \)
B. 6690
c. 7200
D. 7530
Subject: Chemistry
In an octahedral complex, if ligands on one axis are displaced little away from their ideal positions, the crystal field splitting of d-orbitals for this complex is as given below
\( \boldsymbol{d}_{\boldsymbol{x}^{2}-\boldsymbol{y}^{2}} \boldsymbol{d}_{z^{2}} \boldsymbol{d}_{\boldsymbol{x} \boldsymbol{y}} \boldsymbol{d}_{\boldsymbol{y} \boldsymbol{z}} \boldsymbol{d}_{\boldsymbol{x} \boldsymbol{z}} \)
The ligands are displaced on which axis/ axes:
A. x- and y
B. y-only
c. x-only
D. z-only
Subject: Physics
A metallic sphere of radius \( 18 \mathrm{cm} \) has
been given a charge of \( 5 \times 10^{-6} \) C. The
energy of the charged conductor is:
A. 0.25
J \( J \)
в. 0.6 .5
c. \( 1.2 J \)
D. 2.4J
Subject: Chemistry
An electrolysis of a oxytungsten complex ion using \( 1.10 A \) for 40 min produces \( 0.838 g \) of tungsten. What is the charge of tungsten in the material? (Atomic weight: \( \boldsymbol{W}=\mathbf{1 8 4} \) )
A . 6
B. 3
\( c .5 \)
D.
Subject: Physics
Q Type your question-
Davisson and Germer demonstrated
this by diffracting electrons
from crystals. The law governing the
diffraction from a crystal is obtained by requiring that electron waves reflected
from the planes of atoms in a crystal
interfere constructively (see figure). Electrons accelerated by potential Vare
diffracted from a crystal. If \( \boldsymbol{d}=\mathbf{1} \boldsymbol{A}^{\boldsymbol{o}} \) and
\( i=30^{\circ}, V \) should be about :
\( \left(h=6.6 \times 10^{-34} j s, m=9.1 \times\right. \)
\( \mathbf{1 0}^{-\mathbf{3 1}} \mathbf{k g}, e=\mathbf{1 . 6} \times \mathbf{1 0}^{-\mathbf{1 9}} \mathbf{c} \)
A . 2000 v
B. \( 50 v \)
c. 500 v
D. \( 1000 \mathrm{v} \)
Subject: Physics
The impedance of a circuit, when a
resistance \( R \) and an inductor of
inductance \( L \) are connected in series in
an AC circuit of frequency \( f \), is
A \( \cdot \sqrt{R+2 \pi^{2} f^{2} L^{2}} \)
B . \( \sqrt{R+4 \pi^{2} f^{2} L^{2}} \)
c. \( \sqrt{R^{2}+4 \pi^{2} f^{2} L^{2}} \)
D. \( \sqrt{R^{2}+2 \pi^{2} f^{2} L^{2}} \)
Subject: Chemistry
Assertion
Formation of petroleum occurs from hydrocarbon by the process called pyrolysis.
Reason
Hydrocarbon pyrolysis involves
exothermic reactions.
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
\( 5^{t h} \) term from the end in the expansion
of \( \left(\frac{x^{2}}{2}-\frac{2}{x^{2}}\right)^{12} \) is
B . \( 7920 x^{4} \)
c. \( 7920 x^{-4} \)
D. \( -7920 x^{4} \)
Subject: Physics
A particle executes SHM on a straight line path. The amplitude of oscillation is \( 2 \mathrm{cm} . \) When the displacement of the
particle from the mean position is \( 1 \mathrm{cm} \) the numerical value of the magnitude of
acceleration is equal to the numerical
value of the magnitude of the velocity.
The frequency of SHM is:
\( A \cdot 2 \pi \sqrt{3} \)
B. \( \frac{2 \pi}{\sqrt{3}} \)
\( c \cdot \frac{\sqrt{3}}{2 \pi} \)
D. \( \frac{1}{2 \pi \sqrt{3}} \)
Subject: Physics
Consider following statements. Choose
the correct ones:
This question has multiple correct options
A. \( \mathrm{CM} \) of a uniform semicircular disc of radius \( \mathrm{R} \) is \( 2 R \pi \)
from the centre.
B. \( \mathrm{CM} \) of a uniform semicircular ring of radius \( 2 R / 3 \) is \( 4 R / 3 \pi \) from the centre.
C. \( \mathrm{CM} \) of a solid hemisphere of radius \( \mathrm{R} \) is \( 4 R / 3 \pi \) from the centre.
D. \( \mathrm{CM} \) of a solid hemisphere shell of radius \( \mathrm{R} \) is \( R / 2 \) from the centre.
Subject: Physics
The electric flux passing through a hemispherical surface of radius \( \mathrm{R} \)
placed in an electric field E with its axis parallel to the filed is :
\( \mathbf{A} \cdot \pi R^{2} E \)
В. \( 2 \pi R^{2} E \)
c. \( 2 \pi R E \)
\( \mathbf{D} \cdot 2 \pi R^{3} E \)
Subject: Chemistry
The mole of \( \operatorname{gases} N H_{3}, C O_{2} \) and \( H_{2} \) adsorbed by \( 1 g \) charcoal at \( 300 K \) and
1 atm pressure shows the order:
A. \( C O_{2}>H_{2}>N H_{3} \)
в. \( N H_{3}>C O_{2}>H_{2} \)
c. \( H_{2}>C O_{2}>N H_{3} \)
D. \( C O_{2}>N H_{3}>H_{2} \)
Subject: Physics
What is the recoil velocity of the gun of mass \( 8 \mathrm{kg} \) when a bullet of mass \( 10 \mathrm{g} \) is fired from it with a velocity of \( 400 \mathrm{m} / \mathrm{s} ? \)
\( \mathbf{A} \cdot 5 \mathrm{m} / \mathrm{s} \)
B. \( 2 \mathrm{m} / \mathrm{s} \)
c. \( 50 \mathrm{m} / \mathrm{s} \)
D. \( 0.5 \mathrm{m} / \mathrm{s} \)
Subject: Chemistry
Law of multiple proportions is illustrated by which one of the following pairs?
A \( . H_{2} S \) and \( S O_{2} \)
B. \( N H_{3} \) and \( N O_{2} \)
c. \( N_{2} O \) and \( N O \)
D. \( N_{2} S \) and \( N a_{2} O \)
Subject: Physics
\( \ln L-C-R \operatorname{series} \) circuit, the
capacitor is changed from \( C \) to \( 4 C \). For
the same resonant frequency, the inductance should be changed from
\( \boldsymbol{L} \) to
A \( .2 L \)
в. \( \frac{L}{2} \)
c. \( \frac{L}{4} \)
D. \( 4 L \)
Subject: Chemistry
\( \boldsymbol{H}_{2}(\boldsymbol{g})+\boldsymbol{C l}_{2}(\boldsymbol{g})=\boldsymbol{2} \boldsymbol{H} \boldsymbol{C l}(\boldsymbol{g}) \)
\( \Delta H(298 K)=-22.06 \mathrm{kcal} . \) For this
reaction, \( \Delta U \) is equal to:
A \( .-22.06+2 \times 10^{-3} \times 298 \times 2 \mathrm{kcal} \)
В. \( -22.06+2 \times 298 \) kcal
c. \( -22.06-2 \times 298 \times 4 \) kcal
D. -22.06 kcal
Subject: Chemistry
\( \boldsymbol{C} \boldsymbol{a}_{2} \boldsymbol{B}_{6} \boldsymbol{O}_{11}+\boldsymbol{2} \boldsymbol{N} \boldsymbol{a}_{2} \boldsymbol{C O}_{3} \rightarrow \boldsymbol{X}+ \)
\( 2 C a C O_{3}+2 N a_{2} B O_{2} . \) The compound \( x \)
in the above reaction is :
A. \( N a_{2} B_{4} O_{7} \)
в. \( H B O_{2} \)
c. \( H_{3} B O_{3} \)
D. \( H_{2} B_{4} O_{7} \)
Subject: Maths
Initially, equation of ellipse was \( 3 x^{2}+ \)
\( 4 y^{2}=12 . \) Keeping major axis constant
ellipse is bulge to form circle (with major axis as diameter). Its eccentricity
changes at a rate \( 0.1 / \) sec. Time taken to form this circle is
A . 2 sec
B. 3 sec
c. 5 sec
D. 7 sec
Subject: Physics
A \( 12 \Omega \) resistor and a \( 0.21 H \) inductor
are connected in series to an a.c source
operating at \( 20 ~ V, 50 \) cycle/second.
The phase angle between current and source voltage is
A . \( 30^{\circ} \)
В . \( 40^{\circ} \)
\( c \cdot 80^{\circ} \)
D. \( 90^{\circ} \)
Subject: Physics
Assertion
\( \mathbf{3} \boldsymbol{H} \) isotopes does not undergo fusion of
the type \( _{1}^{3} H+_{1}^{2} H \rightarrow \) as it is rarely
found in nature.
Reason
\( \mathbf{3} \boldsymbol{H} \) has half life of \( \approx \mathbf{1 2} \boldsymbol{y} \boldsymbol{e} \boldsymbol{a} \boldsymbol{r} \boldsymbol{s} \)
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: Chemistry
The sum of coordination number and
oxidetion number of the metal M in the
\( \operatorname{complex}\left[M(e n)_{2}\left(C_{2} O_{4}\right)\right] \) CI (where en
is ethylenediamine) is:
\( A \cdot 6 \)
B. 7
\( c \cdot 8 \)
D.
Subject: Physics
An equiconvex lens is made from glass of refractive index \( 1.5 . \) If the radius of
each surface is changed from 5 \( \mathrm{cm} \) to
\( 6 c m, \) then the power:
A. Remains unchanged
B. Increases by 3.33 D
c. Decreases by 3.33 D
D. Decreases by \( 5.5 D \)
Subject: Physics
A metal rod of uniform thickness and of
length \( 1 m \) is suspended at its \( 25 c m \)
division with the help of a string. The rod remains horizontally straight when a block of mass \( 2 k g \) is suspended to
the rod at its \( 10 \mathrm{cm} \) division from same
end. The mass of the rod is:
A. \( 0.4 \mathrm{kg} \)
B. \( 0.8 \mathrm{kg} \)
c. \( 1.2 \mathrm{kg} \)
D. \( 1.6 \mathrm{kg} \)
Subject: Chemistry
The solubility products of \( A g C l \) and \( A g I \) are \( 1.1 \times 10^{-10} \) and \( 1.6 \times 10^{-16} \)
respectively. If \( A g N O_{3} \) is added drop by drop the solution containing both chloride and iodide ions, then
precipitated first is:
\( A \cdot A g I \)
в. \( A g N O_{3} \)
c. \( A g C l \)
D. Both \( A g I \) and \( A g C l \)
Subject: Biology
A man was infested with germs and
was taken to the hospital. On
pathological tests, it was found that he
had
a. A low number of RBC
b. A high number of WBC and a low
number of RBC
c. A low number of WBC
d. \( A \) high number of platelets Which of the following alternative is
correct?
A. bonly
B. a and d
c. conly
D. donly
Subject: Physics
A \( 20 \mathrm{kg} \) box is on the floor of a truck. The coefficient of static friction
between the box and the truck floor is
0.3 and the coefficient of sliding friction is 0.2. The magnitude and direction of the frictional force acting on the box when the truck is accelerating at \( 2 m s^{-2} \) is:
A. \( 100 \mathrm{N} \) backward
B. 100 N forward
c. \( 60 \mathrm{N} \) forward
D. 60 N backward
Subject: Physics
A right triangular plate \( A B C \) of mass \( m \)
is free to rotate in the vertical plane about a fixed horizontal axis through \( \mathbf{A} \) It is supported by a string such that the side \( A B \) is horizontal. The reaction at the
support \( A \) is :
\( A \cdot \frac{m}{3} \)
B. \( \frac{2 m g}{3} \)
\( c \cdot \frac{m g}{2} \)
D. \( m g \)
Subject: Maths
Let \( \left|z_{i}\right|=i, i=1,2,3,4 \) and
\( \mid 16 z_{1} z_{2} z_{3}+9 z_{1} z_{2} z_{4}+4 z_{1} z_{3} z_{4}+z_{2} z_{3} z_{4} \)
\( 48, \) then the value of \( \left|\frac{1}{z_{1}}+\frac{4}{\bar{z}_{2}}+\frac{9}{\bar{z}_{3}}+\frac{16}{\bar{z}_{4}}\right| \)
A . 1
B. 2
\( c \cdot 4 \)
\( D \)
Subject: Chemistry
toppr
Q Type your ques
The cleavage of \( C-O \) bond takes place
under drastic conditions with excess of
hydrogen halide, \( \boldsymbol{R}-\boldsymbol{O}-\boldsymbol{R}+ \)
\( 2 H X \rightarrow H X \rightarrow 2 R X+H_{2} O \)
If hydrogen halide is not taken in excess, then one molecule each of
alcohol and alkyl halide are formed, \( \boldsymbol{R}-\boldsymbol{O}-\boldsymbol{R}+\boldsymbol{H} \boldsymbol{I} \stackrel{^{373} \boldsymbol{H}} \boldsymbol{R}-\boldsymbol{O} \boldsymbol{H}+\boldsymbol{R}- \)
I. The order of reactivity of hydrogen
halides towards the above mentioned
reaction depends on the bond strength of halogenated acids. Weaker is the \( \boldsymbol{H}-\boldsymbol{X} \) bond, greater is its reactivity. In
case of unsymmetrical ethers, the site of cleavage is such that the halide is formed from the alkyl group which is tertiary, so that the halide formed is tertiary halide.
Indicate whether the following statements / reactions are true or false.
The order of hydrogen halide reactivity is \( \boldsymbol{H} \boldsymbol{I}<\boldsymbol{H} \boldsymbol{B r}<\boldsymbol{H} \boldsymbol{C l} \)
A. True
B. False
Subject: Chemistry
Which of the following complex ion is expected to absorb light in the visible
region?
\( \mathbf{A} \cdot\left[T i(e n)_{3}\right]^{4+} \)
B \( \cdot\left[S c\left(N H_{3}\right)_{4}\left(H_{2} O\right)_{2}\right]^{3+} \)
c. \( \left[C r O_{4}\right]^{2} \)
D \cdot \( \left[Z n(C N)_{2}\right]^{2} \)
Subject: Maths
Put in the form \( A+i B \)
\( \frac{(\cos x+i \sin x)(\cos y+i \sin y)}{[\cot u+i](1+i \tan v)} \)
\( \mathbf{A} \cdot \sin u \cos v[\cos (x+y-u-v)-i \sin (x+y-u-v)] \)
B \( \cdot \sin u \cos v[\cos (x+y-u-v)+i \sin (x+y-u-v)] \)
\( \mathbf{C} \cdot \sin v \cos u[\cos (x+y-u-v)+i \sin (x+y-u-v)] \)
\( \mathbf{D} \cdot \sin v \cos u[\cos (x+y-u-v)-i \sin (x+y-u-v)] \)
Subject: Physics
A body of mass \( 5 k g \) is taken from a
height of \( 5 m \) to \( 10 m . \) Find the increase
in its potential energy. Take \( \boldsymbol{g}= \) \( 10 m s^{-2} \)
A . \( 50 J \)
в. \( 150 J \)
\( c .250 J \)
D. \( 300 J \)
Subject: Physics
The torque equation for a pendulum bob
making an angle \( \theta \) with the vertical is
given by
\( \mathbf{A} \cdot d^{2} \theta / d t^{2}=-(g / L) \cos \theta \)
B \( \cdot d^{2} \theta / d t^{2}=-(g / L) \sin \theta \)
\( \mathbf{c} \cdot d^{2} \theta / d t^{2}=-(g / L)^{2} \sin \theta \)
D. \( \left.d^{2} \theta / d t^{2}=-\sqrt{(} g / L\right) \sin \theta \)
Subject: Chemistry
A red coloured mixed oxide \( (X) \) on
treatment with concentrate \( \boldsymbol{H} \boldsymbol{N} \boldsymbol{O}_{3} \)
gives a compound (Y). (Y) with HCI, produces a chloride compound (z) which can also be produced by treating
(X) with concentrate HCl. Compounds \( (X),(Y) \) and \( (Z) \) will be :
A. \( M n_{3} O_{4}, M n O_{2}, M n C l_{2} \)
в. \( P b_{3} O_{4}, P b O_{2}, P b C l_{2} \)
\( \mathrm{c} \cdot \mathrm{Fe}_{3} \mathrm{O}_{4}, \mathrm{Fe}_{2} \mathrm{O}_{3}, \mathrm{FeCl}_{2} \)
D. \( F e_{3} O_{4}, F e_{2} O_{3}, F e C l_{3} \)
Subject: Chemistry
The main source of lead is PbS. It is
converted to Pb by:-
(i) \( P b S \frac{a i r}{\Delta} P b O+S O_{2} \frac{C}{\Delta} P b+C O_{2} \)
(ii) \( P b S \frac{a i r}{\Delta} P b O+P b S \stackrel{\Delta}{\longrightarrow} P b+S O_{2} \)
Self reduction process is:
\( A \)
B. i
c. both
D. none
Subject: Maths
If \( \left|\frac{z_{1}}{z_{2}}\right|=1 \) and \( \arg \left(z_{1} z_{2}\right)=0, \) then
A \( . z_{1}=z_{2} \)
В \( \cdot\left|z_{2}\right|^{2}=z_{1} z_{2} \)
\( \mathbf{c} \cdot z_{1} z_{2}=1 \)
D. \( z_{1}=-z_{2} \)
Subject: Physics
The inductive reactance of a coil of
\( 0.2 H \) inductance at a frequency of
\( \mathbf{6 0} \boldsymbol{H} \boldsymbol{z} \) is:
A . \( 7.54 \Omega \)
в. \( 0.754 \Omega \)
c. \( 75.4 \Omega \)
D. \( 7.54 \times 10^{-3} \Omega \)
Subject: Maths
\( \left|\begin{array}{ccc}1 & a & a^{2}-b c \\ 1 & b & b^{2}-c a \\ 1 & c & c^{2}-a b\end{array}\right| \) is equal to
\( A \)
B . \( \sum a^{2}(b-c) \)
c. \( 2 \sum a^{2}(b-c) \)
D. \( -2 \sum a b(a-b) \)
Subject: Physics
A force \( F=(5 \hat{i}+3 \hat{j}) \) newtons is applied over a particle which displaces it from its origin to the point \( r=(2 \hat{i}- \)
1 \( \hat{\boldsymbol{j}} \) ) metres. The work done on the
particle is
A. -7 joules
B. +13 joules
c. +7 joules
D. +11 joules
Subject: Chemistry
The potential of the following cell at
\( 25^{\circ} C \) is:
\( \boldsymbol{P t}\left|\begin{array}{c|c|c}\boldsymbol{H}_{2} & \boldsymbol{H} \boldsymbol{N} \boldsymbol{O}_{3} & \boldsymbol{N a O H} & \boldsymbol{H}_{2} \\ (\boldsymbol{1} \boldsymbol{a} \boldsymbol{t m}) & \boldsymbol{0} . \boldsymbol{1} \boldsymbol{M} & \mid & \left(\boldsymbol{1 0}^{-3} \boldsymbol{M}\right)\end{array}\right|(\boldsymbol{1} \boldsymbol{a} \boldsymbol{t m}) \)
A. \( -0.059 V \)
B. \( 0.059 V \)
\( c .-0.59 V \)
D. \( 0.5 V \)
Subject: Maths
If a line makes angles \( \frac{\pi}{12}, \frac{5 \pi}{12} \) with \( \boldsymbol{o} \boldsymbol{y}, \boldsymbol{o} \boldsymbol{z} \) respectively where \( \boldsymbol{0}=(\boldsymbol{0}, \boldsymbol{0}, \boldsymbol{0}) \)
then the angle made by that line with ox
is
A \( \cdot 45^{\circ} \)
B. \( 90^{\circ} \)
\( c \cdot 60^{\circ} \)
D. \( 30^{\circ} \)
Subject: Maths
The equation of circle at center (3,4) and radius 5
A. \( x^{2}+y^{2}-6 x-8 y=0 \)
B . \( x^{2}+y^{2}+3 x+4 y+5=0 \)
C. \( x^{2}+y^{2}+6 x+8 y=0 \)
D. None
Subject: Physics
A convex lens of focal length \( 20 \mathrm{cm} \) is
cut into two equal parts so as to obtain
two plano convex lenses as shown in the fig (a). The two parts are then put in contact as shown in fig (b). The focal length of the combination is
A. zero
B . 5cm
c. \( 10 \mathrm{cm} \)
D. 20cm
Subject: Physics
A point initially at rest moves along \( x- \) axis. Its acceleration varies with time
as \( a=(6 t+5) m / s^{2} . \) If it starts from
origin, the distance covered in \( 2 s \) is.
A. \( 20 m \)
в. 18 т
\( \mathrm{c} \cdot 16 \mathrm{m} \)
D. 25
Subject: Chemistry
Which of the following behaviour is true regarding the coefficient of viscosity \( (\eta) \) of a liquid?
A. Plot of \( \eta \) versus \( T \) is linear
B. Plot of \( \eta \) versus \( \frac{1}{T} \) is linear
c. \( \eta=\frac{E}{R T} \)
D. Plot log of \( \eta \) versus \( \frac{1}{T} \) is linear
Subject: Maths
If \( t_{5}, t_{10} \) and \( t_{25} \) are \( 5^{t h}, 10^{t h} \) and \( 25^{t h} \)
terms of an AP respectively, then the value of \( \left|\begin{array}{ccc}\boldsymbol{t}_{5} & \boldsymbol{t}_{10} & \boldsymbol{t}_{25} \\ \mathbf{5} & \mathbf{1 0} & \mathbf{2 5} \\ \mathbf{1} & \mathbf{1} & \mathbf{1}\end{array}\right| \) is
A . -40
B.
\( c \cdot-1 \)
D. 0
E. 40
Subject: Physics
In the figure, the cross-sectional area of
the smaller tube is \( a \) and that of the
larger tube is \( 2 a . \) A block of mass \( m \) is
kept in the smaller tube having the
same base area \( a \), as that of the tube
The difference between water levels of
the two tubes is
A \( \cdot \frac{P_{0}}{\rho g}+\frac{m}{a \rho} \)
в. \( \frac{P_{0}}{\rho g}+\frac{m}{2 a \rho} \)
c. \( \frac{m}{a \rho} \)
D. \( \frac{m}{20} \)
Subject: Physics
at the earth's surface is \( 10 m s^{-2} \) and at
the surface of Mars is \( 4.0 m s^{-2} . \) A \( 60 k g \)
passenger goes from the earth to Mars
in a spaceship moving with a constant
velocity. Neglect all other objects in the
sky. Which part of the figure best
represents the weight (net gravitational force) of the passenger as a function of
time?
\( A \cdot A \)
B. \( B \)
\( c \)
\( D \)
Subject: Physics
Ray \( A O \) in medium \( I \) emerges as \( O B \) in
medium \( I I \) then refractive index of
medium \( I I \) with respect to medium \( I \)
is:
\( A \)
в. \( \frac{\partial \vec{O} A \times N_{1}^{\rightarrow} O}{O B \times N_{2} \vec{\rightarrow}} \)
c. \( \frac{\overrightarrow{A O} \cdot \overrightarrow{O P}}{\overrightarrow{O B} \cdot \overrightarrow{O P}} \)
D \( \frac{\overrightarrow{O A} \times \overrightarrow{O P}}{\overrightarrow{O B} \times \overrightarrow{O P}} \)
Subject: Chemistry
Assertion
\( \boldsymbol{H}_{2}+\boldsymbol{O}_{2} \) fuel cell gives a constant
voltage throughout its life.
Reason
In this fuel cell, \( H_{2} \) reacts with \( O H^{-} \) ions, yet the overall concentration of
\( O H^{-} \) ions does not change.
A. assertion is true, reason is true; reason is correct explanation for assertion.
B. assertion is true, reason is true; reason is NOT a correct explanation for assertion
c. assertion is true, reason is false
D. assertion is false, reason is true
Subject: Chemistry
Lassaigne's test for the detection of nitrogen will fail in the case of:
A. \( N H_{2} C O N H_{2} \)
B. \( N H_{2} C O N H_{2} . H C l \)
c. \( N H_{2} N H_{2} \)
D. \( C_{6} H_{5} N H N H_{2} .2 H C l \)
Subject: Maths
Write the element \( a_{21} \) of the matrix
\( \boldsymbol{A}=\left[\boldsymbol{a}_{i j}\right]_{2 \times 2} \) whose elements \( \boldsymbol{a}_{i j} \) are
\( \operatorname{given} \) by \( a_{a j}=e^{2 i x} \cos j x \)
Subject: Chemistry
Assertion
Molar conductivity increases with
decrease in concentration.
Reason
Conductivity always decreases with
decrease in concentration.
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
A bag \( A \) contains 2 white and 3 red balls
and a bag \( B \) contains 4 white and 5 red
balls. One ball is drawn at random from
one of the bags and is found to be red. The probability that it was drawn from \( \operatorname{bag} B \) is \( \frac{25}{X}, \) then find the value of \( X \)
Subject: Physics
Two particles of mass \( m_{1} \) and \( M_{2} \)
approach each other due to their mutual gravitational attraction only.
Then
A. Accelerations of both the particles are equal
B. Accelerations of the particles of mass \( m_{1} \) is proportional to \( m_{1} \)
c. Accelerations of the particles of mass \( m_{1} \) is proportional to \( m_{2} \)
D. Accelerations of the particles of mass \( m_{1} \) is inversely
proportional to \( m_{1} \)
Subject: Chemistry
\( P h-\stackrel{0}{C}-O H \stackrel{S O C l_{2}}{\longrightarrow}(A) \underset{P d-B a S O_{4}}{C}(B) \)
Product (B) is:
A.
\[
P h-C_{-} H
\]
в. \( P h-C H_{2}-O H \)
c. \( P h-C H_{2}-C l \)
D. \( P h-C H=C H_{2} \)
Subject: Physics
The sun subtends an angle of \( (1 / 2)^{\circ} \) at earth.The image of the sun is obtained on a screen using a converging lens of focal length \( 1.5 \mathrm{cm} . \) The diameter of the image will be :
A. \( 0.13 \mathrm{mm} \)
B. \( 0.9 \mathrm{mm} \)
\( c .1 .8 \mathrm{mm} \)
D. 0.6 mm
Subject: Chemistry
Mixture of \( \boldsymbol{N a I}(\boldsymbol{s})+\boldsymbol{K}_{2} \boldsymbol{C r}_{2} \boldsymbol{O}_{7}(\boldsymbol{s})+ \)
conc. \( H_{2} S O_{4} \) when heated in a test
tube dark vapours evolve
A. \( I_{2} \)
в. \( N a_{2} \)
\( \mathrm{c} \cdot H_{2} \)
D. All the above
Subject: Physics
A ball is projected vertically upwards with a velocity of \( 25 m s^{-1} \) from the
bottom of a tower. A boy who is standing at the top of a tower sees it passes by him in the upward direction. He sees
ball again at same height after 3 sec when it is falling. Then the height of the tower is : \( \left(\boldsymbol{g}=\mathbf{1 0} \boldsymbol{m} \boldsymbol{s}^{-2}\right) \)
A . \( 5 m \)
в. \( 10 m \)
c. \( 15 m \)
D. \( 20 m \)