AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Chemistry
An ammonia solution has a density of
\( 0.910 \mathrm{g} \mathrm{cm}^{-3} \) and is \( 25.0 \% \mathrm{NH}_{3} \) by mass.
What is the molarity of the solution?
A . \( 12.1 \mathrm{M} \)
B. 13.4 M
c. \( 14.5 \mathrm{M} \)
D. 15.5 M
Subject: Maths
The value of \( \sin ^{-1} \)
\( \left\{\tan \left(\cos ^{-1} \sqrt{\frac{2+\sqrt{3}}{4}}+\cos ^{-1} \frac{\sqrt{12}}{4}-\right.\right. \)
is
\( \mathbf{A} \cdot \mathbf{0} \)
в. \( \frac{\pi}{2} \)
\( c \cdot-\frac{\pi}{2} \)
D.
Subject: Physics
Find the \( x \) -coordinates on the \( x \) -axis.
(excluding \( \boldsymbol{x}=\mathbf{0} \) and \( \boldsymbol{x}=\infty \)
This question has multiple correct options
A. \( x=4 \lambda \)
B . \( x=7 \lambda / 4 \)
c. \( x=5 \lambda / 4 \)
D. \( x=3 \lambda \)
Subject: Physics
r.m.s. speed of ideal gas at \( 127^{\circ} \mathrm{C} \) is \( 200 m / s, \) the r.m.s. speed of same ideal
gas at temperature \( 227^{\circ} \mathrm{C} \) is:
A. \( 100 \sqrt{5} \)
5
в. \( 200 \sqrt{5} \)
\begin{tabular}{l}
\( c \cdot 100 \sqrt{15} \) \\
\hline
\end{tabular}
D. \( 100 \sqrt{10} \)
Subject: Chemistry
Elemental analysis results obtained for cortisone, an anti-inflammatory agent,
are \( 69.98 \% \) C, \( 7.83 \mathrm{H} \) and \( 22.19 \% \) 0. What
is the empirical formula of cortisone?
A \( \cdot C_{4} H_{6} O \)
в. \( C_{18} \mathrm{H}_{22} \mathrm{O}_{3} \)
\( \mathbf{c} \cdot C_{20} H_{25} O_{4} \)
D. \( C_{12} H_{28} O_{5} \)
Subject: Physics
(a) Draw the circuit diagram of a ful
wave rectifier using \( \boldsymbol{p}-\boldsymbol{n} \) junction
diode

Explain its working and show the
output, input waveforms.
(b) Show the output waveforms (Y) for
the following inputs \( A \) and \( B \) of
(i) OR gate (ii) NAND gate
Subject: Chemistry
For a zero order reaction at \( 200 K \)
reaction complete in 5 minutes while at
\( 300 K, \) same reaction, completes in 2.5
minutes. What will be the activation
energy in calorie? \( (\boldsymbol{R}= \)
\( \mathbf{2} \text { Cal } /(\text { mol. } \boldsymbol{K}) ; \boldsymbol{l n} \mathbf{2}=\mathbf{0 . 7}) \)
Subject: Maths
A particle starts moving from rest from a fixed point in a fixed direction. The distance s from the fixed point at a time \( t \) is given by \( s=t^{2}+a t-b+17, \) where
\( a \) and \( b \) are real numbers. If the particle
comes to rest after \( 5 s \) at a distance of
\( s=25 \) units from the fixed point, then
value of \( a \) and \( b \) are respectively.
A .10,-33
B. -10,-33
c. -8,33
D. -10,33
Subject: Physics
Find the increase in pressure required to decrease the volume of water sample
by \( 0.01 \% \). Bulk modulus of water \( = \) \( 2.1 \times 10^{9} N m^{-2} \)
A \( \cdot 4.3 \times 10^{4} N / m^{2} \)
B. \( 1.8 \times 10^{7} N / m^{2} \)
c. \( 2.1 \times 10^{5} N / m^{2} \)
D. \( 3.7 \times 10^{4} N / m^{2} \)
Subject: Chemistry
Correct order of radius of the 1 st orbit of \( \boldsymbol{H}, \boldsymbol{H} \boldsymbol{e}^{+}, \boldsymbol{L} \boldsymbol{i}^{2+} \) and \( \boldsymbol{B} \boldsymbol{e}^{\boldsymbol{3}+} \) is:
A \( \cdot H>H e^{+}>L i^{2+}>B e^{3} \)
в. \( B e^{3+}>L i^{2+}>H e^{+}>H \)
\( \mathbf{c} \cdot H e^{+}>B e^{3+}>L i^{2+}>H \)
D. \( H e^{+}>H>L i^{2+}>B e^{3} \)
Subject: Physics
The difference between I and II energy levels is
A \( \cdot 1.5 \times 10^{-18} \mathrm{J} \)
B \( .3 \times 10^{-18} J \)
c \( \cdot 6 \times 10^{-18} J \)
D. \( 12 \times 10^{-18} \mathrm{J} \)
Subject: Physics
An artificial satellite moves in a
circular orbit around the earth. Total
energy of the satellite is given by \( \boldsymbol{E} \). The
potential energy of the satellite is:
A . \( -2 E \)
в. \( 2 E \)
c. \( \frac{2 E}{3} \)
D. \( -\frac{2 E}{3} \)
Subject: Physics
\( P \) is the centre of the square \( B_{p}=? \) Four
\( \boldsymbol{L} \) shaped wires, each carrying current \( \boldsymbol{I} \)
Find the magnetic field at point \( \boldsymbol{P} \) ?
A \( \cdot 1 w b / m^{2} \)
В. \( 0 w b / m^{2} \)
\( c \cdot 2 w b / m^{2} \)
D. none of these
Subject: Maths
The range of the function \( y= \) \( \frac{1}{(2-\sin 3 x)} \) is
\( ^{\mathrm{A}} \cdot\left(\frac{1}{3}, 1\right) \)
в. \( \left[\frac{1}{3}, 1\right) \)
c. \( \left[\frac{1}{3}, 1\right] \)
D. None of these
Subject: Chemistry
The crystals of ferrous sulphate on
heating gives:
A \( . F e O+S O_{2}+H_{2} O \)
в. \( F e_{2} O_{3}+H_{2} S O_{4}+H_{2} O \)
\( \mathrm{c} \cdot F e_{2} O_{3}+S O_{2}+S O_{3} \)
Subject: Chemistry
Catalytic decomposition of nitrous
oxide by gold at \( 900^{\circ} \mathrm{C} \) at an initial pressure of \( 200 \mathrm{mm}, \) was \( 50 \% \) in 53 minutes and \( 73 \% \) in 100 minutes.
Velocity constant of the reaction is:
[Note: assume decomposition as the first order.
A \( .1 .308 \times 10^{-2} \)
В. \( 2.317 \times 10^{-2} \)
c. \( 3.208 \times 10^{-3} \)
D. none of these
Subject: Physics
If \( E_{a} \) be the electric field intensity due to a short dipole at a point on the axis
and \( E_{r} \) be that on the right bisector at the same distance from the dipole, then
A \( \cdot E_{a}=E_{r} \)
В. \( E_{a}=2 E_{r} \)
\( \mathbf{c} \cdot E_{r}=2 E_{a} \)
D. \( E_{a}=\sqrt{2} E_{r} \)
Subject: Maths
If the vector \( \vec{b} \) is colllinear with the vector \( \overrightarrow{\boldsymbol{a}}=(2 \sqrt{\mathbf{2}},-\mathbf{1}, \mathbf{4}) \) and \( |\overrightarrow{\boldsymbol{b}}|=\mathbf{1 0} \)
then:
\( \mathbf{A} \cdot \vec{a}+\vec{b}=0 \)
B . \( \vec{a}+2 \vec{b}=0 \)
Subject: Chemistry
For the reaction, \( N_{2}+3 H_{2} \rightleftharpoons 2 N H_{3} \)
the rate of change of concentration for hydrogen is \( 0.3 \times 10^{-4} M s^{-1} \)
The rate of change of concentration of
ammonia is \( \left(\operatorname{in} M s^{-1}\right) \)
A . \( -0.2 \times 10^{-4} \)
В. \( 0.2 \times 10^{-4} \)
c. \( 0.1 \times 10^{-4} \)
Subject: Chemistry
The unit of ebullioscopic constant is?
A . \( K \) kg mol \( ^{-1} \) or \( K(\text { molality })^{-1} \)
B . mol kg \( K^{-1} \) or \( K^{-1} \) (molality)
c. \( k g \) mol \( ^{-1} K^{-1} \) or \( K^{-1} \) (molality) \( ^{-1} \)
D. \( K \) mol \( k g^{-1} \) or \( K(\text { molality }) \)
Subject: Biology
Assertion
The common name of Exocetus is flying
fish.
Reason
Exocetus has wing like pectoral fins.
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: Physics
A car is moving with speed \( 30 m s^{-1} \) on a
circular path of radius \( 500 \mathrm{m} \). Its speed
is increasing at a rate of \( 2 m s^{-2}, \) what is the acceleration of the car?
A \( \cdot 2 m s^{-2} \)
B. \( 2.7 m s^{-2} \)
c. \( 1.82 m s^{-2} \)
D. \( 9.82 m s^{-2} \)
Subject: Maths
\( (\vec{a} \cdot \vec{i})^{2}+(\vec{a} \cdot \vec{\jmath})^{2}+(\vec{a} \cdot \vec{k})^{2} \) is equal to
A \( \left.\left.\cdot|\vec{a}|^{2}\right|^{2}\right|^{\vec{l}} \)
B. 3
c \( \cdot|\vec{a} \cdot(\vec{i}+\vec{j}+\vec{k})|^{2} \)
D. None of these
Subject: Chemistry
Coconut charcoal, having adsorbed \( A r \) \( \mathrm{Kr} \) and \( \mathrm{Xe} \) is brought into contact with
charcoal maintained at \( 77 \mathrm{K} \). The
following gas diffuses into the latter:
\( A \cdot A r \)
B. Kr
\( c \cdot x e \)
D. al
Subject: Physics
Electric field intensity in free space at a
distance ' \( r^{\prime} \) outside the charged
conducting sphere of radius ' \( \boldsymbol{R}^{\prime} \) in
terms of surface charge density '\sigma' is :
A \( \cdot \frac{\sigma}{\epsilon_{0}}\left[\frac{R}{r}\right]^{2} \)
В. \( \frac{\epsilon_{0}}{\sigma}\left[\frac{R}{r}\right]^{2} \)
c. \( \frac{R}{r}\left[\frac{\sigma}{\epsilon_{0}}\right]^{2} \)
D. \( \frac{R}{\sigma}\left[\frac{r}{\epsilon_{0}}\right]^{2} \)
Subject: Physics
Which of these does not represent a
wave equation
A \( . y=\operatorname{Asin}(\omega t-k x) \)
B. \( y=\operatorname{Asin}(\omega t+k x) \)
c. \( y=A \cos (\omega t-k x) \)
D. \( y=A(\omega t-k x) \)
Subject: Physics
The amplitude of a particle in SHM is \( 5 \mathrm{cms} \) and its time period is \( \pi . \) At a displacement of \( 3 \mathrm{cm} \) from its mean
position the velocity in cm/sec will be:
\( A \cdot 8 \)
B. 12
\( c \cdot 2 \)
D. 16
Subject: Chemistry
Oxygen is more electronegative than
sulphur, yet \( H_{2} S \) is acidic while \( H_{2} O \) in
neutral. This is because
A. water is a highly associated compound
B. \( H-S \) bond is weaker than \( H-O \) bond
c. \( H_{2} S \) is a gas while \( H_{2} O \) is a liqiud
D. the molecular weight of \( H_{2} S \) is more than that of \( H_{2} O \)
Subject: Physics
Assertion
The Sl unit of weight is Newton.
Reason
Weight is the force of gravity with which
a body is attracted towards the earth.
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 is incorrect but Reason is correct
Subject: Chemistry
Freshly prepared pure dilute solution of
sodium in liquid ammonia:
This question has multiple correct options
A. shows copper-bronze colour
B. occupy larger volume than that from the sum of the volumes of \( N a \) and \( N H_{3}(1) \)
C . reduced the \( G e H_{4} \) to \( G e H_{2}^{-} \)
D. produced sodium amide and hydrogen gas with rusty iron wire.
Subject: Biology
Assertion
In a woman after hysterectomy, the
ovarian cycle is stopped
Reason
Because \( F S H \) is not secreted.
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 equilibrium constant for the
following reaction is \( 1.6 \times 10^{5} \) at \( 1024 \mathrm{K} \)
\( \boldsymbol{H}_{2}(\boldsymbol{g})+\boldsymbol{B} \boldsymbol{r}_{2}(\boldsymbol{g}) \rightleftharpoons \boldsymbol{2} \boldsymbol{H} \boldsymbol{B} \boldsymbol{r}(\boldsymbol{g}) \)
Find the equilibrium pressure of \( \boldsymbol{H}_{2} \) gas if 10.0 bar of HBr is introduced into a
sealed container at \( 1024 \mathrm{K} \)
A \( .2 .8 \times 10^{3} \)
B. \( 5.2 \times 10^{-3} \)
c. \( 2.5 \times 10^{-2} \)
D. \( 2 \times 10^{-3} \)
Subject: Maths
Find the value of \( \mathrm{m} \) and \( \mathrm{n} \) using cross multiplication method:
\( 3 m+n=15 \) and \( m+2 n=10 \)
\( A \cdot(4,3) \)
B. (-4,3)
\( c \cdot(-4,-3) \)
D. (4,-3)
Subject: Maths
Which of the following is/are correct?
This question has multiple correct options
A. Parabola is symmetric with respect to the axis of the parabola.
B. Length of latus rectum of a parabola, \( y^{2}=4 a x \) is \( 4 a \)
C. A line through the focus and perpendicular to the directrix is called the axis of the parabola.
D. The point of intersection of a parabola with the axis is called the vertex of the parabola.
Subject: Physics
The distance between the object and its
image formed by a plane mirror appears to be \( 24 \mathrm{cm} . \) What is the distance
between the mirror and the object?
A. \( 24 \mathrm{cm} \)
B. 12 \( \mathrm{cm} \)
\( c \cdot 48 \mathrm{cm} \)
D. 36 cm
Subject: Physics
The coefficients of self induction of two
coils are \( L_{1}=8 \mathrm{mH} \) and \( L_{2}=2 \mathrm{mH} \)
respectively. The current rises in the two coils at the same rate. The power given to the two coils at any instant is same. The ratio of induced emf's in the coils
will be :
A. \( \frac{V_{1}}{V_{2}}=4 \)
B. \( \frac{V_{1}}{V_{2}}=\frac{1}{4} \)
c. \( \frac{V_{1}}{V_{2}}=\frac{1}{2} \)
D. \( \frac{V_{1}}{V_{2}}=\frac{1}{3} \)
Subject: Maths
\( \mathbf{f} \boldsymbol{A}=\left[\begin{array}{ll}\mathbf{1} & \mathbf{0} \\ \mathbf{0} & \mathbf{1}\end{array}\right] ; \boldsymbol{B}=\left[\begin{array}{ll}\boldsymbol{a} & \boldsymbol{c} \\ \boldsymbol{b} & \boldsymbol{d}\end{array}\right], \) then show
that \( (A . B)^{-1}=B^{-1} . A^{-1} \)
Subject: Physics
There is a fixed potential difference
between the two ends of a
potentiometer. Two cells are connected
in series in such a way that in one
arrangement they help each other where as in the second arrangement they oppose each other. The balance point for these two combinations is obtained at
\( 120 \mathrm{cm} \) and \( 60 \mathrm{cm} \) length respectively. The ratio of the emf of the cell is:
A \( \cdot 2: \)
B. 3:
\( c \cdot 1: 1 \)
D. 4:
Subject: Maths
The image of the point (-1,3,4) in the
plane \( \boldsymbol{x}-\mathbf{2} \boldsymbol{y}=\mathbf{0} \) is
\( ^{\mathbf{A}} \cdot\left(-\frac{17}{3},-\frac{19}{3}, 4\right) \)
В. (15,11,4)
\( ^{\mathbf{C}} \cdot\left(-\frac{17}{3},-\frac{19}{3}, 1\right) \)
D. \( \left(\frac{9}{5},-\frac{13}{5}, 4\right) \)
Subject: Maths
STATEMENT - 1: Dependent events are those in which the outcome of one does not affect and is not affected by the
other.
STATEMENT - 2 : Dependent events are
those in which the outcome of one
affects and is affected by the other.
A. Statement - 1 is True, Statement - 2 is True, Statement 2 is a correct explanation for Statement- -
B. Statement-1 is True, Statement- 2 is True: Statement 2 is NOT a correct explanation for Statement-
c. statement- 1 is True, Statement - 2 is False
D. Statement - 1 is False, Statement- 2 is True
Subject: Physics
A metallic rod \( C D \) rests on a thick
metallic wire \( P Q R S \) with arms \( P Q \) and
\( R S \) parallel to each other, at a distance
\( l=40 \mathrm{cm}, \) as shown in following figure.
A uniform magnetic field \( B=0.1 T \)
acts perpendicular to the plane of this paper, pointing inwards (i.e., aways
from the reader). The rod is now made to
slide towards right, with a constant
velocity of \( \boldsymbol{v}=\mathbf{5 . 0} \boldsymbol{m} \boldsymbol{s}^{-1} \)
How much emf is induced between the
two ends of the rod \( C D ? \)
Subject: Physics
Heat energy required to raise the
temperature of a body of mass \( m \) in \( \mathrm{kg} \)
by \( \Delta t k \) is
A \( \cdot \frac{m c}{\Delta t} \) Joule
B. \( \frac{m \Delta t}{c} \) Joule
c. \( \frac{c}{m \Delta t} J \)
\( \mathbf{D} \cdot m c \Delta t \)
Subject: Physics
Which of the following statement
related to hysteresis loop is incorrect?
A. The curve of B against H for a ferromagnetic material is called hysteresis loop
B. The area of B-H curve is a measure of power dissipated per cycle per unit area of the specimen
C. Coercitivity is a measure of the magnetic field required to destroy the residual magnetism of ferromagnetic material
D. The retentivity of a specimen is the measure of magnetic field remaining in the specimen when the magnetising field is removed
Subject: Physics
The binding energy per nucleon of \( ^{16} \mathrm{O} \) is
\( 7.97 M e V \) and that of \( 17 O \) is \( 7.75 M e V \)
The energy in MeV required to remove a
neutron from \( ^{17} \) O is:
A . 3.52
в. 3.64
c. 4.23
D. 7.86
E . 1.68
Subject: Physics
An electron beam passes through a
magnetic field of \( 2 \times 10^{-3} W b / m^{2} \) and
an electric field of \( 1.0 \times 10^{4} V / m \) both
acting simultaneously. The path of electron remains undeviating. The speed of electron if the electric field is removed, and the radius of electron path will be respectively.
A \( \cdot 10 \times 10^{6} m / s, 2.43 \)
В. \( 2.5 \times 10^{6} \mathrm{m} / \mathrm{s}, 0.43 \)
c. \( 5 \times 10^{6} \mathrm{m} / \mathrm{s}, 1.43 \)
D. None of these
Subject: Maths
The equation ot the line passing through the point (1,-2,3) and paralle to the \( \operatorname{linex}-y+2 z=5 \) and \( 3 x+y+ \)
\( z=6 \) is
A \( \cdot \frac{x-1}{-3}=\frac{y+2}{5}=\frac{z-3}{4} \)
B. \( \frac{x-1}{1}=\frac{y+2}{-1}=\frac{z-3}{2} \)
\( \mathbf{c} \cdot \frac{x-1}{3}=\frac{y+2}{1}=\frac{z-3}{6} \)
D. \( \frac{x-1}{3}=\frac{y+2}{-1}=\frac{z-3}{2} \)
Subject: Maths
If \( \boldsymbol{A}=\left[\begin{array}{lll}\boldsymbol{a} & \boldsymbol{0} & \boldsymbol{0} \\ \boldsymbol{0} & \boldsymbol{a} & \boldsymbol{0} \\ \boldsymbol{0} & \boldsymbol{0} & \boldsymbol{a}\end{array}\right], \) then the value of
\( |\boldsymbol{A}||\mathbf{A} \mathbf{d} \mathbf{j} \boldsymbol{A}| \)
A \( \cdot a^{3} \)
в. \( a^{6} \)
\( c \cdot a^{9} \)
\( D \cdot a^{2} \)
Subject: Chemistry
Balance the following in basic medium:
\( \boldsymbol{F} \boldsymbol{e}_{3} \boldsymbol{O}_{4}+\boldsymbol{M} \boldsymbol{n} \boldsymbol{O}_{4}^{-} \rightarrow \boldsymbol{F} \boldsymbol{e}_{2} \boldsymbol{O}_{3}+\boldsymbol{M} \boldsymbol{n} \boldsymbol{O}_{2} \)
A \( \cdot 6 F e_{3} O_{4}+2 M n O_{4}^{-}+H_{2} O \rightarrow 9 F e_{2} O_{3}+2 M n O_{2} \)
\( 2 O H^{-} \)
B. \( 6 F e_{3} O_{4}+4 M n O_{4}^{-}+H_{2} O \rightarrow 9 F e_{2} O_{3}+5 M n O_{2}+ \)
\( O H^{-} \)
\( \mathrm{c} \cdot 6 \mathrm{Fe}_{3} \mathrm{O}_{4}+\mathrm{MnO}_{4}^{-}+\mathrm{H}_{2} \mathrm{O} \rightarrow 9 \mathrm{Fe}_{2} \mathrm{O}_{3}+3 \mathrm{MnO}_{2}+ \)
\( 2 O H^{-} \)
D. None of these
Subject: Physics
Four particles, each of mass \( \mathrm{m}, \) are placed at the four corners of a square of side 'a'. Force exerted by this system on another particle of mass \( \mathrm{m} \) placed at the midpoint of a side of square is -
A \( \cdot \frac{16 G m^{2}}{5 \sqrt{5 a^{2}}} \)
в. \( \frac{16 G m^{2}}{5 \sqrt{3 a^{2}}} \)
c. \( \frac{16 G m^{2}}{5 a} \)
D. zero
Subject: Physics
The velocity of a particle moving along a straight line increases according to
the linear law \( v=v_{0}+k x, \) where \( k \) is a
constant. Then
This question has multiple correct options
A. the acceleration of the particle is \( k\left(v_{0}+k x\right) \)
B the particle takes a time \( \frac{1}{k} \log _{e}\left(\frac{v_{1}}{v_{0}}\right) \) to attain a velocity \( v_{1} \)
c. velocity varies linearly with displacement with slope of velocity displacement curve equal to \( k \).
D. the acceleration of the particle is zero.
Subject: Maths
The area of quadrilateral which the straight line cuts off from the given triangle is:
A \( \cdot \frac{3+\tan \theta}{1-\tan \theta} \)
B. \( \frac{3+5 \tan \theta}{1+\tan \theta} \)
c. \( \frac{3+2 \tan \theta}{1+\tan \theta} \)
D. \( \frac{3+\tan \theta}{1+\tan \theta} \)
Subject: Maths
If the points \( (0,0),(3, \sqrt{3}),(p, q) \) form
an equilateral triangle and \( \boldsymbol{q}_{1}, \boldsymbol{q}_{2} \) are
the two values of \( \boldsymbol{q} \) then \( \boldsymbol{q}_{1}+\boldsymbol{q}_{2}=? \)
A \( \cdot 2 \sqrt{3} \)
B. \( \sqrt{3} \)
\( c \cdot-\sqrt{3} \)
D.
Subject: Physics
A uniform solid cylindrical roller of mass 'm' is being pulled on a horizontal surface \( F \) parallel to the surface and applied at its centre. If the acceleration
of the cylinder is 'a' and it is rolling
without slipping then the value of 'F' is
A . ma
B . \( \frac{5}{3} m a \)
\( c \cdot 2 m a \)
\( D \cdot \frac{3}{2} m a \)
Subject: Physics
A machine raises a load of \( \mathbf{7 5 0} \boldsymbol{N} \)
through a height of \( 16 m \) in \( 5 s . \) Calculate
energy spent by machine:
A. \( 12000 k J \)
в. \( 12 k J \)
c. \( 1200 J \)
D. \( 120 k J \)
Subject: Maths
In a hot water heating system, there is a
cylindrical pipe of length 28 m and diameter \( 5 \mathrm{cm} . \) Find the total radiating surface in the system.
A \( \cdot 4.4 m^{2} \)
B . \( 2.4 m^{2} \)
c. \( 4.1 \mathrm{m}^{2} \)
D. \( 3.4 m^{2} \)
Subject: Chemistry
Which of the following is a true statement for the acids of phosphorus:
\( \boldsymbol{H}_{3} \boldsymbol{P} \boldsymbol{O}_{2}, \boldsymbol{H}_{3} \boldsymbol{P} \boldsymbol{O}_{3} \) and \( \boldsymbol{H}_{3} \boldsymbol{P} \boldsymbol{O}_{4} ? \)
A. The order of their acidic strength is \( H_{3} P O_{4}> \) \( H_{3} P O_{3}>H_{3} P O_{2} \)
B. All of them are reducing in nature.
c. All of them are tribasic acids
D. The geometry of phosphorus is tetrahedral in all the three
Subject: Maths
Bag \( I \) contains 3 red and 4 black balls
and Bag \( I I \) contains 4 red and 5 black
balls. One ball is transferred from Bag \( \boldsymbol{I} \) and Bag \( I I \) and then a ball is drawn
from Bag \( I I . \) The ball so drawn is found
to be red in colour. Find 310 times the
probability that the transferred ball is
black.
Subject: Physics
A particle of mass \( 0.5 \mathrm{kg} \) is executing SHM along a straight line. Its path length is \( 10 \mathrm{cm} \) and time period is 8s. TE
when its phase angle is \( \frac{\pi}{6} \) radian is
B. 0.964x10-4 J
c. \( 3.856 \times 10^{-4} \) j
D. 4.324x10-4 J
Subject: Maths
The position vectors of \( \mathbf{A}, \mathbf{B} \) are \( \mathbf{a}, \mathbf{6} \) respectively. The position vector of \( \mathbf{C} \) is \( \frac{5 \bar{a}}{3}-\bar{b} . \) Then 3
\( \mathbf{A} \cdot \mathrm{C} \) is inside the \( \Delta O A B \)
B. \( C \) is outside the \( \Delta O A B \) but inside the angle OAB
C. \( \mathrm{C} \) is outside the \( \Delta O A B \) but inside the angle \( \mathrm{OBA} \)
D. None of these
Subject: Physics
If a magnet is suspended at an angle \( 30^{\circ} \)
to the magnetic meridian, the dip needle
makes an angle of \( 60^{\circ} \) with the horizontal
The true value of dip is :
A \( \cdot \tan ^{-1}(2 / 3) \)
B \( \cdot \tan ^{-1}(3 / 2) \)
c. \( \tan ^{-1}(3) \)
D. \( \tan ^{-1}(2) \)
Subject: Maths
Let \( f: N \rightarrow N \) defined by \( f(n)= \)
\( \left\{\begin{array}{cc}\frac{n+1}{2} & \text { if } n \text { is odd } \\ \frac{n}{2} & \text { if } n \text { is even }\end{array}\right. \)
then \( \boldsymbol{f} \) is.
A. Many-one and onto
B. One-one and not onto
c. onto but not one-one
D. Neither one-one nor onto
Subject: Physics
\( 50 W / m^{2} \) energy density of sunlight is normally incident on the surface of a
solar panel. Some part of incident energy \( (25 \%) \) is reflected from the surface and the rest is absorbed. The
force exerted on \( 1 m^{2} \) surface area will
be close to? \( \left(c=3 \times 10^{8} m / s\right) \)
\( \mathbf{A} \cdot 15 \times 10^{-8} \mathrm{N} \)
B . \( 35 \times 10^{-8} \) N
c. \( 10 \times 10^{-8} \mathrm{N} \)
D. \( 20 \times 10^{-8} \mathrm{N} \)
Subject: Maths
If the position vectors ofthe vertices \( A \) B, C of a triangle ABC are \( 7 \widehat{j}+ \) \( \mathbf{1 0} \widehat{\boldsymbol{k}},-\hat{\mathbf{i}}+\mathbf{6} \widehat{\mathbf{j}}+\mathbf{6} \widehat{\boldsymbol{k}} \) and \( -\mathbf{4} \hat{\mathbf{i}}+\mathbf{9} \hat{\mathbf{j}}+\mathbf{6} \widehat{\boldsymbol{k}} \)
respectively, the triangle is
A . equilateral
B. isosceles
c. scalene
D. right angled and isoscele
Subject: Physics
A square plate of edge \( a / 2 \) is cut out
from a uniform square plate of edge \( ^{\prime} a^{\prime} \) as shown in figure. The mass of the
remaining portion is \( M . \) The moment of inertia of the shaded portion about an axis passing through' \( O^{\prime} \) (center of the square of side a) and perpendicular to
plane of the plate is:
\( ^{A} \cdot \frac{9}{64} M a^{2} \)
в. \( \frac{3}{16} M a^{2} \)
c. \( \frac{5}{12} M a^{2} \)
D. \( \frac{M a^{2}}{6} \)
Subject: Maths
If \( f(x)=(x-a)^{2 n}(x-b)^{2 m+1} \)
where \( m \cdot n \in N, \) then
A. \( x=a \) is a point of minimum
B. \( x=a \) is a point of maximum
c. \( x=a \) is not a point of maximum or minimum
D. No value of k satisfies the requirement
Subject: Physics
A metal piece of mass \( 160 g \) lies in equilibrium inside a glass of water. The pieces touch the glass at small number of point. If the density of the metal is \( 8000 \mathrm{kg} / \mathrm{m}^{3} \) then the normal force exerted by the bottom of the glass on the metal piece is
\( A \cdot 2 N \)
В. 8 N
c. \( 0.16 N \)
D. 1.4
Subject: Chemistry
When \( N a C l \) solution is added to
\( \boldsymbol{F} \boldsymbol{e}(\boldsymbol{O} \boldsymbol{H})_{3} \) sol then:
A \( \cdot\left[F e(O H)_{3}\right] F e^{3+} \) is formed
В \cdot \( \left[\mathrm{Fe}(\mathrm{OH})_{3}\right] \mathrm{Cl}^{-} \) is formed
C \( \cdot \operatorname{Fe}(O H)_{3} \) is coagulated
D・ \( \left[\operatorname{Fe}(O H)_{3}\right] N a^{+} \) is formed
Subject: Physics
\( ^{23} N a \) is the more stable isotope of \( N a \)
By which process \( _{11}^{24} N a \) can undergo radioactive decay?
\( \mathbf{A} \cdot \beta^{-}-e m i s s i o n \)
B. \( \alpha \) - emission
c. \( \beta^{+}- \) emission
D. None of these