AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Maths
In a class of 60 students, 30 opted for
NCC, 32 opted for NSS and 24 opted for both NCC and NSS. If one of these
students is selected at random, find the
probability that
(i) The student opted for NCC or NSS
(ii) The student has opted neither NCC
nor NSS
(iii) The student has opted NSS but not
\( \mathrm{NCC} \)
Subject: Physics
The wavelength of monochromatic light is \( 5000 A \) in air what will be its wave
number in a medium of refractive index
\( \mathbf{1 . 5} ? \)
A \( \cdot 3 \times 10^{6} m^{-1} \)
В. \( 5 \times 10^{6} m^{-1} \)
c. \( 2 \times 10^{6} m^{-1} \)
D. \( 9 \times 10^{6} m^{-1} \)
Subject: Chemistry
For a reversible reaction at \( 298 \mathrm{K} \), the
equilibrium constant K is 200. What is
the value of \( \triangle G^{0} \) at \( 298 \mathrm{K} ? \)
A . -13.13 kcal
B . -0.13 kcal
c. -3.158 kcal
D. - 0.413 kcal
Subject: Physics
If \( E_{1}, E_{2} \) and \( E_{3} \) are the kinetic energies
of a proton, \( \alpha \) -particle and deuteron
respectively, which all have the same
wavelength, then
A \( \cdot E_{1}>E_{2}>E_{3} \)
в. \( E_{1}>E_{3}>E_{2} \)
c. \( E_{3}>E_{2}>E_{1} \)
D. \( E_{3}>E_{1}>E_{2} \)
Subject: Maths
Factorize the following expression
\( 8 x^{3}-27 y^{3} \)
\( \mathbf{A} \cdot(2 x-3 y)\left(4 x^{2}+6 x y+9 y^{2}\right) \)
B \( \cdot(2 x+3 y)\left(4 x^{2}+6 x y+9 y^{2}\right) \)
\( \mathbf{c} \cdot(2 x-3 y)\left(4 x^{2}-6 x y+9 y^{2}\right) \)
D. None of these
Subject: Physics
Two sound waves emerging from a source reach a point simultaneously along two paths. When the path difference is \( 12 \mathrm{cm} \) or \( 36 \mathrm{cm} \) then there
is silence at that point. If the speed of sound in air is \( 330 \mathrm{m} / \mathrm{s} \) then calculate
least possible frequency of the source in Hz
Subject: Chemistry
\( \boldsymbol{H} \boldsymbol{C} \equiv \boldsymbol{C} \boldsymbol{H} \frac{(i) \mathbf{2} \boldsymbol{N} \boldsymbol{a}}{(i i) \mathbf{2} C \boldsymbol{O}_{2}}(\boldsymbol{A}) \frac{\boldsymbol{H}_{2} / \boldsymbol{P} \boldsymbol{d}}{\boldsymbol{B} \boldsymbol{a} \boldsymbol{S} \boldsymbol{O}_{4}}(\boldsymbol{B}) \)
What is B?
\( \mathbf{A} \cdot H_{2} C=C H-C O O^{-} N a^{+} \)
\( \mathbf{B} \cdot: H_{3} C-C H_{2}-C O O^{-} N a^{+} \)
\( \mathbf{c} \cdot H_{2} C=C H-C H_{2} O H \)
\( \mathbf{D} \cdot H_{3} C-C H_{2}-C H_{2} O H \)
Subject: Maths
Consider a real valued function \( \boldsymbol{f} \) \( \boldsymbol{R} \rightarrow \boldsymbol{R} \) satisfying \( \boldsymbol{f}\left(\frac{\boldsymbol{2} \boldsymbol{x}+\boldsymbol{3} \boldsymbol{y}}{\mathbf{5}}\right)= \)
\( \frac{2 f(x)+3 f(y)}{5} \forall x, y \in R \quad \) and \( f(0)= \)
\( \mathbf{2} ; \boldsymbol{f}^{\prime}(\mathbf{0})=\mathbf{1} \)
Minimum distance of a point on graph
of \( \boldsymbol{y}=\boldsymbol{f}(\boldsymbol{x}) \) from origin is less than or
equal to
A. \( \sqrt{2} \) units
B. \( \frac{1}{2} \) units
c. \( \frac{1}{\sqrt{5}} \) units
D. \( \frac{1}{\sqrt{7}} \) units
Subject: Maths
A random variable \( X \) has the following
probability distribution:
\[
\begin{array}{cccccc}
\boldsymbol{X} & \mathbf{1} & \mathbf{2} & \mathbf{3} & \mathbf{4} & \mathbf{5} \\
\hline P(X) & k^{2} & 2 k & k & 2 k & 5
\end{array}
\]
\[
5 k^{2}
\]
Then \( P(X>2) \) is equal to
\( \mathbf{A} \cdot \frac{1}{6} \)
B. \( \frac{7}{12} \)
c. \( \frac{1}{36} \)
D. \( \frac{23}{36} \)
Subject: Chemistry
The rate constant for an isomerisation
reaction, \( \boldsymbol{A} \rightarrow \boldsymbol{B} \) is \( \mathbf{4 . 5} \times \mathbf{1 0}^{-\mathbf{3}} \boldsymbol{m} \boldsymbol{i n}^{-1} . \)
the initial concentration of \( A \) is \( 1 \mathrm{M} \), the
rate of the reaction after 1 hr will be:
A \( \cdot 3.4354 \times 10^{-3} \)
B . \( 4.4554 \times 10^{-3} \)
c. \( 5.4364 \times 10^{-3} \)
D. None of these
Subject: Physics
A solid conducting sphere having a
charge \( Q \) is surrounded by an
uncharged concentric conducting
hollow spherical shell. Let the potential difference between the surface of the
solid sphere and that of the outer surface of the hollow shell be \( V \). If the
shell is now given a charge \( -3 Q \), the
new potential difference between the
same two surfaces is:
\( \mathbf{A} \cdot V \)
B. \( 2 V \)
c. \( 4 V \)
\( \mathbf{D} \cdot-2 V \)
Subject: Chemistry
When \( 2 s-2 s, 2 p-2 p \) and \( 2 p-2 s \)
orbitals overlap, the bond strength decreases in the order:
A. \( p-p>s-s>p-s \)
в. \( p-p>p-s>s-s \)
c. \( s-s>p-p>p-s \)
D. \( s-s>p-s>p-p \)
Subject: Maths
If \( \alpha \) and \( \beta \) are two zeroes of the
polynomial \( \boldsymbol{x}^{2}-\mathbf{7} \boldsymbol{x}+\boldsymbol{k} \) where \( \boldsymbol{\alpha}-\boldsymbol{\beta}= \)
\( 5, \) find value of \( k \)
Subject: Chemistry
The catalyst used in making \( H_{2} S O_{4} \) in
contact process is :
A \( \cdot V_{2} O_{5} \)
в. \( F e_{2} O_{3} \)
\( \mathrm{c} \cdot \mathrm{Cr}_{2} \mathrm{O}_{3} \)
D. \( C r O_{3} \)
Subject: Maths
A vehicle registration number consists
of 2 letters of English alphabet followed by 4 digits, where the first digit is not zero. Then, the total number of vehicles
with distinct registration numbers is
A \( \cdot 26^{2} \times 10^{4} \)
В. 26 \( P_{2} \times \) 10 \( P_{4} \)
c. \( 26 P_{2} \times 9 \times 10 P_{3} \)
D . \( 26^{2} \times 9 \times 10^{3} \)
Subject: Maths
If \( a, b, c \) are non-zero, unequal rational
numbers, then the roots of the equation \( a b c^{2} x^{2}+\left(3 a^{2}+b^{2}\right) c x-6 a^{2}-a b+ \)
\( 2 b^{2}=0 \) are
A . rational
B. imaginary
C. irrational
D. none of these
Subject: Maths
If \( y=a \cos (\log x)+b \sin (\log x), \) then
A. \( x^{2} \frac{d^{2} y}{d x^{2}}+x \frac{d y}{d x}+y=0 \)
B. \( \quad x^{2} \frac{d^{2} y}{d x^{2}}-x \frac{d y}{d x}-y=0 \)
c. \( x^{2} \frac{d^{2} y}{d x^{2}}+x \frac{d y}{d x}-y=0 \)
D. \( x^{2} \frac{d^{2} y}{d x^{2}}+x \frac{d y}{d x}+x y=0 \)
Subject: Chemistry
The ionization energy of the ground state of hydrogen atom is \( 2.18 \times 10^{-18} \)
J. The energy of an electron in its second orbit would be:
В. \( -2.18 \times 10^{-18} \mathrm{J} \)
c. \( -4.36 \times 10^{-18} \mathrm{J} \)
D. \( -5.45 \times 10^{-19} \mathrm{J} \)
Subject: Physics
A point object is placed on the principal axis of the convex lens of focal length
\( 20 \mathrm{cm} \) at a distance \( 40 \mathrm{cm} \) to the left on
it. The diameter of the lens is \( 10 \mathrm{cm} \). If
the eye is placed 60cm to the right of the lens at a distance h below the
principal axis, then max value of 'h' to
see the image is
A . \( 1.5 \mathrm{cm} \)
B. 2.5 \( \mathrm{cm} \)
c. \( 3 \mathrm{cm} \)
D. \( 5 \mathrm{cm} \)
Subject: Physics
A small piece of space junk is at rest in outer space. A very small asteroid strikes it, exerting a force on it that is NOT directed through the piece of space junk's center of mass. Which of the following describes the motion of the piece of space junk DURING the asteroid strike?
A. Because the asteroid is small, the space junk remains at rest
B. The piece of space junk spins, but does NOT move linearly
c. The piece of space junk moves at constant velocity linearly, but does NOT spin
D. The piece of space junk accelerates linearly, but does NOT spin
E. The piece of space junk accelerates linearly, AND spins
Subject: Maths
\( \lim _{x \rightarrow 3} \frac{\sqrt{3 x}-3}{\sqrt{2 x-4}-\sqrt{2}} \) is equal to.
A \( \cdot \frac{1}{\sqrt{2}} \)
B. \( \sqrt{3} \)
\( c \cdot \frac{1}{2 \sqrt{2}} \)
D. \( \frac{\sqrt{3}}{2} \)
Subject: Chemistry
toppr 5
Q Type your question-
1. \( \boldsymbol{C} \boldsymbol{l}_{2}, \boldsymbol{F} \boldsymbol{e} \boldsymbol{l}_{3} \)
III. \( \boldsymbol{H} \boldsymbol{B} \boldsymbol{r}, \) Heat
\( A \)
B.
\( c \)
\( D \)
Subject: Maths
The function \( \boldsymbol{f}: \boldsymbol{N} \rightarrow \boldsymbol{N}, \) where \( \boldsymbol{N} \) is
the set of natural numbers, defined by \( f(x)=7 x+11 \) is
A. injective
B. surjective
c. bijective
D. none of these
Subject: Chemistry
NaCN used in the froth flotation method
for the purification of ore is:-
A. \( Z n S \) which contain \( P b S \)
B. \( C u_{2} S \) which contain \( F e_{e} S_{3} \)
c. \( P b S \) which contain \( Z n S \)
D. \( P b S \) which contain \( S i O_{2} \)
Subject: Physics
A ray of light strikes a transparent rectangular slab of refractive index \( \sqrt{2} \) at an angle of incidence of \( 45^{\circ} . \) The angle between the reflected and refracted rays is :
A \( .75^{\circ} \)
В. \( 90^{\circ} \)
\( c \cdot 105 \)
D. \( 120^{\circ} \)
Subject: Physics
If the ionization energy of hydrogen
atom is \( 13.6 e V \) then the wavelength of the radiation required to excite the
electron in \( L i^{++} \) from first to third Bohr
orbit is approximately
A . \( 1140 A \)
В. \( 914 A \)
c. \( 11.4 A \)
D. \( 134 A \)
Subject: Chemistry
Molecule(s) possessing two-centre-two electron bonds and three-centre-two
electron bonds would include:
A. \( B_{2} H_{6} \) and \( S i F_{4} \)
B. \( X e F_{6} \) and \( B F_{6} \)
\( \mathbf{c} \cdot B_{2} H_{6} \) and \( X e F_{6} \)
D. \( B_{2} H_{6} \) alone
Subject: Chemistry
Which buffer solution comprising of the
following has its \( p H \) value greater than
\( 7 ? \)
A \( \cdot C H_{3} C O O H+C H_{3} C O O N a \)
в. \( H C O O H+H C O O K \)
c. \( C H_{3} C O O N H_{4} \)
D. \( N H_{4} O H+N H_{4} C l \)
Subject: Chemistry
Write the main product formed when propanal reacts with the following
reagents:
(i) 2 moles of \( C H_{3} O H \) in presence of
dry \( \boldsymbol{H} \boldsymbol{C l} \)
(ii) Dilute \( N a O H \)
(iii) \( H_{2} N-N H_{2} \) followed by heating
with \( K O H \) in ethylene glycol
Subject: Maths
Which of the following is not a
quadratic equation?
A \( \cdot 2(x-1)^{2}=4 x^{2}-2 x+1 \)
B. \( \left(x^{2}+1\right)^{2}=x^{2}+3 x+9 \)
\( \mathbf{C} \cdot\left(x^{2}+2 x\right)^{2}=x^{4}+3+4 x^{3} \)
D \( \cdot x^{2}+9=3 x^{2}-5 x \)
Subject: Chemistry
A polar bond is formed between two
atoms of different electronegativity. A polar molecule results when there is
only one polar bond, or more than one polar bond within it is not sufficiently symmetrically oriented to cancel the effects of the others.
Select the correct order of boiling point.
\( \mathbf{A} \cdot H_{2} O<H F \)
в. \( H_{2} O>H F \)
\( \mathbf{c} \cdot H F=H_{2} O \)
D. None of these
Subject: Biology
Which one of the following statements
is correct with respect to salt water balance inside the body of living organisms?
A. When water is not available camels do not produce urine but store urea in tissues
B. Salmon fish excretes lot of stored salt through gill membrane in fresh water.
c. Paramecium discharges concentrated salt solution by contractile vacuoles.
D. The body fluids of fresh water animals are generally hypotonic to surrounding water.
Subject: Chemistry
Arrange the following hydrides of group 16 elements in order of increasing
stability:
A. \( H_{2} S<H_{2} O<H_{2} T e>H_{2} S e \)
в. \( H_{2} O<H_{2} T e<H_{2} S e<H_{2} S \)
c. \( H_{2} O<H_{2} S<H_{2} S e<H_{2} T e \)
D. \( H_{2} T e<H_{2} S e<H_{2} S<H_{2} O \)
Subject: Chemistry
In the cyanide extraction process of
silver from argentite ore, the oxidising
and reducing agents used are:
A. \( O_{2} \) and \( C O \) respectively
B. \( O_{2} \) and \( Z n \) dust respectively
C. \( H N O_{3} \) and \( Z n \) dust respectively
D. \( H N O_{3} \) and \( C O \) respectively
Subject: Maths
The solution of differential equation
\( \boldsymbol{x}^{2} \boldsymbol{y} \boldsymbol{d} \boldsymbol{x}-\left(\boldsymbol{x}^{3}+\boldsymbol{y}^{3}\right) \boldsymbol{d} \boldsymbol{y}=\mathbf{0} \) is
A \( \cdot-\frac{1}{3} \frac{x^{3}}{y^{3}}+\log y=C \)
B. \( -\frac{1 x^{3}}{3 y^{3}}-\log y=C \)
\( ^{\mathbf{c}} \cdot \frac{x^{3}}{y^{3}}+\log y=C \)
D. None of these
Subject: Chemistry
Assertion
In Lewis structures of \( N F_{3} \) and \( C O_{3}^{2-} \)
nitrogen and carbon occupy the central position whereas fluorine and oxygen
occupy the terminal positions.
Reason
In Lewis representation, the least electronegative atom occupies the central position in the molecule/ion.
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 wire of fixed length is wound on a solenoid of length I and radius r. Its self inductance is found to be L. Now, if
same wire is wound on a solenoid of
ength \( \frac{l}{2} \) and radius \( \frac{r}{2}, \) then self inductance will be
A . 2L
в. \( \frac{L}{2} \)
c. \( 3 L \)
D. 4L
Subject: Physics
Assertion
Each of the plates of a parallel-plate capacitor is given equal positive charge
Q. The charges on the facing surfaces will be same.
Reason
A negative charge (-Q) will be induced on each of the facing surfaces.
A. If both Assertion and Reason are correct and Reason the correct explanation of Assertion
B. If both Assertion and Reason are correct, but Reason is not the correct explanation of Assertion
c. If Assertion is correct but Reason is incorrect
D. If Assertion is incorrect but Reason is correct
Subject: Maths
If \( \vec{e}=l \hat{i}+m \hat{j}+n \hat{k} \) is a unit vector,
then the maximum value of \( l m+ \)
\( m n+n l \) is
A. \( -\frac{1}{2} \)
B.
c. 1
D. \( \frac{3}{2} \)
Subject: Chemistry
A metal \( M \) forms a sulphate which is
isomorphous with \( M g S O_{4} .7 H_{2} O . \) If
\( 0.6538 \mathrm{g} \) of metal \( M \) displaced 2.16 g of silver from silver nitrate solution, then
the atomic weight of the metal \( M \) is:
A . 32.61
B. 56.82
c. 65.38
D. 74.58
Subject: Chemistry
\( \boldsymbol{C C l}_{3} \boldsymbol{C H O}+\boldsymbol{N O} \longrightarrow \boldsymbol{C H C l}_{3}+ \)
\( N O+C O \)
The rate of the reaction above is equal
to rate \( =\boldsymbol{k}\left[\boldsymbol{C C l}_{3} \boldsymbol{C H O}\right][\boldsymbol{N O}] \)
If the concentration is expressed in mol \( \mathrm{L}^{-1}, \) find the unit of \( k ? \)
A \( \cdot \mathrm{Lmol}^{-1} \mathrm{s}^{-1} \)
B. molL \( ^{-1} \mathrm{s}^{-1} \)
c. \( L^{2} \) mol \( ^{-2} s^{-1} \)
D. s \( ^{-1} \)
Subject: Physics
Assertion
In interference, all the fringes are of
same width.
Reason
In interference, fringe width is independent of the position of fringe.
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: Biology
Assertion
Mass or bulk flow is the movement of
substances in bulk from source to sink
as a result of pressure differences.
Reason
Water, minerals and food are generally moved by mass flow.
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
Given standard electrode potentials:
\( F e^{3+}+3 e^{-} \rightarrow F e ; E^{0}=-0.036 V \)
\( F e^{2+}+2 e^{-} \rightarrow F e ; E^{0}=-0.440 V \)
The standard electrode potential \( E^{o} \) for
\( F e^{3+}+e \rightarrow F e^{2+} \) is:
A. \( 0.476 v \)
B. 0.404 v
c. \( 0.40 v \)
D. +0.772 V
Subject: Physics
If earth is a homogeneous solid sphere
of mass \( M \) and radius \( R \), then
gravitational self potential energy of earth is
\( ^{\mathrm{A}} \cdot-\frac{G M^{2}}{R} \)
в. \( -\frac{G M^{2}}{2 R} \)
c. \( -\frac{3 G M^{2}}{5 R} \)
D. None of these
Subject: Physics
A tube of flow is shown in the figure.
A. The fluid particles must be accelerated from \( A \) to \( B \)
B. Fluid particles may accelerate from \( A \) to \( B \)
C. The fluid particles must be decelerated from \( A \) to \( B \)
D. The fluid particles may be decelerated from \( B \) to \( A \)
Subject: Maths
Find the values of \( x, \) if \( \left|\begin{array}{ll}\mathbf{3} & \boldsymbol{x} \\ \boldsymbol{x} & \mathbf{1}\end{array}\right|=\left|\begin{array}{ll}\mathbf{3} & \mathbf{2} \\ \mathbf{4} & \mathbf{1}\end{array}\right| \)
Subject: Physics
A body is moving down into a well through a rope passing over a fixed pulley of radius \( 10 \mathrm{cm} . \) Assume that
there is no slipping between rope \( \& \) pulley, calculate the angular velocity and angular acceleration of the pulley at an instant when the body is going down at a speed of \( 20 \mathrm{cm} / \mathrm{s} \) and has an
acceleration of \( 4.0 m / s^{2} \)
Subject: Physics
A monochromatic beam of light falls on Young's double slit experiment
apparatus as shown in figure. A thin
sheet of glass is inserted .in front of
lower slit \( S_{2} \)
The central bright fringe can be
obtained:
\( A \cdot A t O \)
B. Above \( O \)
c. Below \( O \)
D. Anywhere depending on angle \( \theta \), thickness of plate \( t \), and refractive index of glass \( \mu \)
Subject: Maths
A function \( f(X) \) which satisfies the relation \( \boldsymbol{f}(\boldsymbol{X})=\boldsymbol{e}^{\boldsymbol{x}}+\int_{0}^{1} \boldsymbol{e}^{\boldsymbol{x}} \boldsymbol{f}(\boldsymbol{t}) \boldsymbol{d} \boldsymbol{t}, \) then
\( \boldsymbol{f}(\boldsymbol{X}) \) is
A \( \cdot \frac{e^{x}}{2-e} \)
B \( \cdot(e-2) e^{x} \)
\( c \cdot 2 e^{x} \)
D. \( \frac{e^{x}}{2} \)
Subject: Chemistry
The outer most electronic configuration of the most electronegative element is:
\( A \cdot n s^{2} n p^{3} \)
B. \( \mathrm{ns}^{2} \mathrm{np}^{4} \)
\( c \cdot n s^{2} n p^{5} \)
D. \( \mathrm{ns}^{2} \mathrm{np}^{6} \)
Subject: Maths
\( \int \frac{1}{\left(1+x^{2}\right) \sqrt{\left[p^{2}+q^{2}\left(\tan ^{-1} x\right)^{2}\right]}} d x \)
A \( \cdot \frac{1}{q} \log [t-\sqrt{p^{2}+t^{2}}] \) where \( t=q \tan ^{-1} x \)
B. \( \frac{1}{t} \log [t+\sqrt{p^{2}+t^{2}}] \) where \( t=q \tan ^{-1} x \)
c. \( \frac{1}{q} \log [t+\sqrt{p^{2}+t^{2}}] \) where \( t=q \tan ^{-1} x \)
D. \( \frac{1}{q} \log [t+\sqrt{p^{2}-t^{2}}] \) where \( t=q \tan ^{-1} x \)
Subject: Chemistry
Water and chlorobenzene are
immiscible liquids. Their mixture boils
at \( 89^{\circ} \mathrm{C} \) under a reduced pressure of
\( 7.7 \times 10^{4} \) Pa. The vapour pressure of
pure water at \( 89^{\circ} \mathrm{C} \) is \( 7 \times 10^{4} \mathrm{Pa} \)
Weight percent of chlorobenzene in the distillate is:
A . 50
B. 60
c. 79
D. 38.46
Subject: Physics
Consider a hypothetical annihilation of a stationary electron with a stationary positron. What is the wavelength of the resulting radiation?
A \( \cdot \lambda=\frac{h}{2 m_{c} c} \)
B. \( \lambda=\frac{2 h}{m_{c} c^{2}} \)
c. \( \lambda=\frac{h}{2 m_{c} c^{2}} \)
D. None of these
Subject: Maths
Find differential equation
corresponding to \( y=c(x-c)^{2}, \) where \( c \)
is arbitrary constant.
A \( \cdot y^{\prime 3}=4 y\left(x y^{\prime}-2 y\right) \)
В \( \cdot y^{\prime 3}=4 y\left(x y^{\prime}+2 y\right) \)
c. \( y^{\prime 3}=-8 y\left(x y^{\prime}-2 y\right) \)
D \( \cdot y^{\prime 2}=-12 y\left(x y^{\prime}-2 y\right) \)
Subject: Physics
An electric dipole is placed at the origin and is directed along the \( x \) -axis. At a point \( P, \) far away from the dipole,the electric field is parallel to the y-axis. OP makes an angle \( \theta \) with the \( x \) -axis. Then,
A \( \cdot \tan \theta=\sqrt{3} \)
B. \( \tan \theta=\sqrt{2} \)
\( \mathbf{c} \cdot \tan \theta=1 \)
D. \( \tan \theta=\frac{1}{\sqrt{2}} \)
Subject: Maths
The product \( 2^{\frac{1}{4}} \cdot 4^{\frac{1}{16}} \cdot 8^{\frac{1}{48}} \cdot 16^{\frac{1}{128}} \cdot \ldots \) to \( \infty \)
is equal to?
A .2
B. \( 2^{\frac{1}{2}} \)
c. 1
D. \( 2^{\frac{1}{4}} \)
Subject: Maths
Assertion
If \( a>0 \) and \( b^{2}-4 a c<0, \) then the value of the integral \( \int \frac{d x}{a x^{2}+b x+c} \) will be of the type \( \mu \tan ^{-1} \frac{x+A}{B}+C \)
where \( A, B, C, \mu \) are constants.
Reason
If \( a>0, b^{2}-4 a c<0, \) then \( a x^{2}+b x+ \)
\( C \) can be written as sum of two squares.
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 electronic configuration of gadolinium (At. no.64) is:
A \( \cdot[X e] 4 f^{8}, 5 d^{0}, 6 s^{2} \)
B . \( [X e] 4 f^{7}, 5 d^{1}, 6 s^{2} \)
C . \( [X e] 4 f^{3}, 5 d^{5}, 6 s^{2} \)
D . \( [X e] 4 f^{6}, 5 d^{2}, 6 s^{2} \)
Subject: Maths
In Figure \( 5, \) rectangle \( A B C D \) is
inscribed in a circle. If the radius of the
circle is 1 and \( A B=1 \), find the area of
the shaded region.
\( \mathbf{A} \cdot 0.091 \)
B. 0.285
c. 0.614
D. 0.705
E . 0.732
Subject: Chemistry
Find the number of acid(s) which are
having pyro prefix in its name from the
following:
\( \boldsymbol{H}_{4} \boldsymbol{P}_{2} \boldsymbol{O}_{7}, \boldsymbol{H}_{4} \boldsymbol{P}_{2} \boldsymbol{O}_{5}, \boldsymbol{H}_{2} \boldsymbol{S}_{2} \boldsymbol{O}_{7}, \boldsymbol{H}_{2} \boldsymbol{S} \boldsymbol{O}_{5} \)
Subject: Maths
Construct a \( \triangle A B C \) in which \( A B= \)
\( 4 \mathrm{cm}, \angle B=60^{\circ} \) and altitude \( C L= \)
\( 3 \mathrm{cm} . \) Construct a \( \triangle A D E \) similar to
\( \triangle A B C \) such that each side of \( \triangle A D E \)
is \( \frac{3}{2} \) times that of the corresponding
side of \( \triangle A B C \)
Subject: Chemistry
Assertion
Butene can be converted into butane
Reason
The addition reaction of hydrogen gas to an alkene will form and alkane
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 wavelength of light is 8000 A. The no. of photon required to provide 20 J of energy is approximately:
A \( \cdot 4.56 \times 10^{18} \)
B . \( 8 \times 10^{19} \)
c. \( 7 \times 10^{19} \)
D. \( 4 \times 10^{7} \)
Subject: Physics
An electric dipole ( dipole moment p) is
placed at a radial distance \( r>>a \) ( Where a
is dipole length) from an infinite line of
charge having linear charge density \( +\lambda \)
dipole moment vector is aligned along the radial vector \( \vec{r} \) force experienced by
the dipole is:-
A \( \cdot \frac{\lambda p}{2 \pi \varepsilon_{o} r^{2}}, \) attractive
B. \( \frac{\lambda p}{2 \pi \varepsilon_{o} r^{3}}, \) attractive
C \( \cdot \frac{\lambda p}{2 \pi \varepsilon_{o} r^{2}}, \) repulsive
D. \( \frac{\lambda p}{2 \pi \varepsilon_{o} r^{3}}, \) repulsive
Subject: Physics
The figure shows capillary tube of
radius \( r \) dipped into water. The
atmospheric pressure is \( P_{0} \) and the
capillary rise of water is \( h . s \) is the
surface tension for water-glass. Initially, \( h=10 \mathrm{cm} . \) If the capillary tube
is now inclined at \( 45^{\circ}, \) the length of water rising in the tube will be
\( \mathbf{A} \cdot 10 \mathrm{cm} \)
в. \( 10 \sqrt{2} \mathrm{cm} \)
c. \( \frac{10}{\sqrt{2}} c m \)
D. None of these
Subject: Maths
Let three matrices \( \boldsymbol{A}=\left[\begin{array}{ll}\mathbf{2} & \mathbf{1} \\ \mathbf{4} & \mathbf{1}\end{array}\right] ; \boldsymbol{B}= \)
\( \left[\begin{array}{ll}\mathbf{3} & \mathbf{4} \\ \mathbf{2} & \mathbf{3}\end{array}\right] \) and \( \boldsymbol{C}=\left[\begin{array}{cc}\mathbf{3} & -\mathbf{4} \\ -\mathbf{2} & \mathbf{3}\end{array}\right] \) then find
\( \operatorname{tr}(A)+\operatorname{tr}\left(\frac{A B C}{2}\right) \operatorname{tr}\left(\frac{A(B C)^{2}}{4}\right)+ \)
\( \operatorname{tr}\left(\frac{A(B C)^{3}}{8}\right)+\ldots+\infty, \) where \( t r(A) \)
represents trace of matrix \( \boldsymbol{A} \)
\( \mathbf{A} \cdot \mathbf{6} \)
B.
c. 12
D. 15
Subject: Physics
Masses of \( 1 g, 2 g, 3 g \ldots .100 g \)
are suspended from the \( 1 \mathrm{cm}, 2 \mathrm{cm}, 3 \mathrm{cm} \) \( \ldots .100 \mathrm{cm} \) marks of a light metre scale. The system will be supported in equilibrium at :
\( \mathbf{A} \cdot 60 \mathrm{cm} \)
в. \( 67 \mathrm{cm} \)
\( \mathrm{c} .55 \mathrm{cm} \)
D. \( 72 \mathrm{cm} \)