AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Physics
The graph drawn between pressure and
volume in Boyle's law experiment is
shown in figure for two different gases. If the same amount of both the gases has
been taken, then the relationship between their molecular weights will be
A \( . M_{2}<M_{1} \)
\( \mathbf{B} \cdot M_{1}<M_{2} \)
\( \mathbf{c} \cdot M_{1}=M_{2} \)
\( \mathbf{D} \cdot M_{1}^{3}=M_{2} \)
Subject: Maths
The common chord of \( x^{2}+y^{2}-4 x- \)
\( 4 y=0 \) and \( x^{2}+y^{2}=16 \) subtends at
the origin an angle to
A. \( \pi / 6 \)
в. \( \pi / 4 \)
c. \( \pi / 3 \)
D. \( \pi / 5 \)
Subject: Chemistry
The percentage hydrolysis in \( 0.003 M \)
aqueous solution of \( N a O C N\left(K_{a} \) for \right.
\( \left.\boldsymbol{H} \boldsymbol{O} \boldsymbol{C} \boldsymbol{N} \text { is } \boldsymbol{3} \boldsymbol{3} \boldsymbol{3} \times \mathbf{1 0}^{-4} \boldsymbol{M}\right) \) is:
A . \( 0.1 \% \)
B. \( 0.01 \% \)
\( c .0 .5 \% \)
D. \( 0.8 \% \)
Subject: Maths
Number of solutions of the equation \( [y+ \) \( [y]]=2 \cos x \) is
(where \( y=(1 / 3)[\sin x+[\sin x+[\sin x]]] \)
and []\( =\text { greatest integer function }) \)
\( \mathbf{A} \cdot \mathbf{0} \)
B.
\( c \cdot 2 \)
\( D \cdot \infty \)
Subject: Maths
\( \int x^{2} \tan ^{-1} x d x \)
A. \( \frac{x^{3}}{3} \tan ^{-1} x-\frac{1}{6} x^{2}+\frac{1}{6} \log \left(x^{2}+1\right) \)
B. \( \frac{x^{3}}{3} \tan ^{-1} x+\frac{1}{6} x^{2}+\frac{1}{6} \log \left(x^{2}+1\right) \)
C \( \frac{x^{3}}{3} \tan ^{-1} x-\frac{1}{3} x^{2}+\frac{1}{6} \log \left(x^{2}+1\right) \)
D. \( \frac{x^{3}}{3} \tan ^{-1} x-\frac{1}{6} x^{2}+\frac{1}{3} \log \left(x^{2}+1\right) \)
Subject: Physics
I ne retractıve index of the materıal of a
concave lens is \( \mu . \) It is immersed in a
medium of refractive index \( \mu_{1} . A \)
parallel beam of light is incident on the
lens. The path of the emergent rays
when \( \mu_{1}>\mu \) is :
\( \mathbf{A} \)
B.
\( \mathbf{c} \)
D.
Subject: Maths
\( A B C \) is a triangle. \( D \) is a point on \( A B \) such that \( A D=\frac{1}{4} A B \) and \( E \) is a point
on \( A C \) such that \( A E=\frac{1}{4} A C . \) Prove that \( D E=\frac{1}{4} B C \)
Subject: Physics
Two charge of \( +25 \times 10^{-9} \mathrm{C} \) and
\( -25 \times 10^{-9} \mathrm{C} \) are placed \( 6 \mathrm{m} \) apart.
Find the electric field intensity ratio at point \( 4 \mathrm{m} \) from the centre of the electric dipole
(i) on axial line
(ii) on equatorial line
Subject: Chemistry
The wrong option among the following
statements is :
A. The decreasing order of the value of the heat of combustion is :
B. cycloalakanes are planar
C. cyclopropane has a higher heat of combustion per methylene group \( \left(C H_{2}\right) \) than that of cyclobutane.
D. with the exception of cyclopropane, cycloalkanes are non-planar
Subject: Physics
An electric dipole of moment 'p' is placed in an electric field of intensity 'E'. The dipole acquires a position such that the axis of the dipole makes an angle 0 with the direction of the field. Assuming that the potential energy of the dipole to be zero when \( \theta=90^{0} \), the torque and
the potential energy of the dipole will respectively be:
A. \( p E \sin \theta, 2 p E \cos \theta \)
B. \( p E \cos \theta,-p E \sin \theta \)
c. \( p E \sin \theta,-p E \cos \theta \)
D. \( p E \sin \theta,-2 p E \cos \theta \)
Subject: Physics
A cricket ball is thrown up with a speed
of \( 19.6 m s^{-1} . \) The maximum height it
can reach is
\( \mathbf{A} \cdot 9.8 m \)
в. \( 19.6 \mathrm{m} \)
c. \( 29.4 m \)
D. 39.2 \( m \)
Subject: Chemistry
A solution containing \( 62 g \) ethyl glycol
in \( 250 g \) water is cooled to \( -10^{\circ} \mathrm{C} \). If \( K_{f} \)
for water is \( 1.86 K k g m o l^{-1}, \) the
amount of water \( (\text { in } g \) ) separated as ice is:
A . 32
B. 48
\( c \cdot 16 \)
D. 64
Subject: Biology
A large quantity of urban sewage is drained into nearby village river. Which among the given conditions would happen after mixing of sewage into the river?
(i) Biochemical oxygen demand (BOD) of receiving water body increases.
(ii) Dissolved oxygen of receiving water body decreases.
(iii) It will not cause mortality among fishes and other aquatic creatures.
(iv) It will lead to the nutrient
enrichment of receiving water body.
A \( \cdot \) (i), (ii) and (iii)
B. (i), (ii) and (iv)
C. (ii) and (iii) only
D. (iii) and (iv) only
Subject: Chemistry
groups, e.g.
\( O \)
\( -\boldsymbol{C H O} \)
\[
\begin{array}{ccc} 
& \| & , & \| \\
- & \boldsymbol{C} & -\boldsymbol{R}- & \boldsymbol{C} & -\boldsymbol{O} \boldsymbol{R}
\end{array}
\]
\( N,-N O_{2} \) activates nucleophilic attack
in halobenzene. The order of reactivity of
these groups is:
A.
\[
\begin{array}{c}
0 \\
-N O_{2}>-C \equiv N>\quad\|\quad \quad>\quad\| \\
0 \\
-\quad C \quad-H \quad-\quad C \quad-R \\
-\quad C \quad-O R
\end{array}
\]
B.
\[
\begin{array}{l}
\|\quad>\quad\| \\
C \quad-H \quad-\quad C
\end{array}
\]
11
\[
>-C \equiv
\]
\[
\begin{array}{c}
-C-H \\
N>-N O_{2}
\end{array}
\]
\( -C-R-C-O R \)
\( c \)
\[
\begin{aligned}
-C \equiv N>-N O_{2}>& 0 \\
-& C-H-C-R
\end{aligned}
\]
\( O \)
11
\[
-C \quad O R
\]
D.
\[
\begin{array}{rl}
0 & 0 \\
\| & >-N O_{2}>-C \equiv N> \\
- & C \\
0 & -H & \| \\
& \| \\
- & C
\end{array}
\]
Subject: Maths
The angles of a triangle are in \( A . P . . \) The number of degree in the least is to be the number of radians in the greatest
as \( 60: \pi . \) Then the greatest angle is
A \( \cdot 120^{\circ} \)
В. \( 90^{\circ} \)
\( \mathrm{c} \cdot 135^{\circ} \)
D. \( 105^{\circ} \)
Subject: Physics
The intrinsic conductivity of
germanium at \( 27^{\circ} \mathrm{C} \) is \( 2.13 \mathrm{mho} / \mathrm{m} \)
and mobilities of electrons and holes
are 0.38 and \( 0.18 m^{2} / V s \) respectively. The density of charge carriers is
\( \mathbf{A} \cdot 2.37 \times 10^{19} / m^{3} \)
B. \( 3.28 \times 10^{19} / m^{3} \)
C. \( 7.83 \times 10^{19} / m^{3} \)
D. \( 8.47 \times 10^{19} / m^{3} \)
Subject: Chemistry
Which statement is correct about the
following reaction?
\( \mathrm{ZnO}+\mathrm{CO} \rightarrow \mathrm{Zn}+\mathrm{CO}_{2} \)
A. zno is being oxidized
B. co is being reduced
\( \mathrm{C} \cdot \mathrm{CO}_{2} \) is being oxidized
D. zno is being reduced
Subject: Physics
When a beam of white light parallel to the principal axis is refracted through a convex lens, then the rays converge to the principal axis. If a screen is placed at a sufficient distance from the focus-
point perpendicular to the principal axis then the image on the screen will be
A. A sharp white point
B. A sharp violet point or red point
c. A circular spot whose edges are violet and central portion red
D. A circular spot whose edges are red and central portion violet
Subject: Maths
If \( A \) is symmetric and \( B \) is skew
symmetric matrix, then which of the following is/are correct? This question has multiple correct options
A \( \cdot A B A^{T} \) is skew symmetric matrix
B. \( A B^{T}+B A^{T} \) is symmetric matrix
c. \( (A+B)(A-B) \) is symmetric
D. \( (A+I)(B-I) \) is skew symmetric
Subject: Maths
Construct a quadrilateral PQRS such
that \( \boldsymbol{P Q}=\mathbf{3 . 5} \boldsymbol{c m}, \boldsymbol{Q} \boldsymbol{R}= \)
\( 4.5 c m, R S=4 c m, \angle Q=110^{\circ} \) and
\( \angle R=80^{\circ} \)
Subject: Physics
Calculate the maximum speed with which a car can be driven safely along a curved road of radius \( 30 m \) and banked
at \( 30^{\circ} \) with the horizontal. Given, \( g= \)
\( 9.8 m s^{-2} \)
A \( \cdot 13.03 \mathrm{ms}^{-1} \)
B . \( 12.08 \mathrm{ms}^{-1} \)
\( \mathbf{c} \cdot 15.08 m s^{-1} \)
D. \( 14.02 \mathrm{ms}^{-1} \)
Subject: Physics
Assertion
A stationary charged particle in a magnetic field does not experience a force.
Reason
The force acting on a charged particle does not depend on velocity of the
particle
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
At what temperature does the average transnational kinetic energy of a molecule in a gas become equal to kinetic energy of an electron accelerated from rest through a
potential difference of 1 volt? \( (k= \)
\( \left.1.38 \times 10^{-23} J / K\right) \)
A . \( 3770 K \)
в. \( 7370 K \)
c. \( 7730 K \)
D. \( 7330 K \)
Subject: Physics
toppr
\( Q \)
electrostatic field is maintained in
a direction normal to the common axis
of the coils. A narrow beam of (single
species) charged particles al
accelerated through \( 15 k V \) enters this region in a direction perpendicular to both the axis of the coils and the
electrostatic field. If the beam remains
undeflected when the electrostatic field
is \( 9.0 \times 10^{-5} V m^{-1}, \) make a simple
guess as to what the beam contains. Why is the answer not unique?

Consider two parallel co-axial circular coils of equal radius \( R \), and number of turns \( N, \) carrying equal currents in the same direction, and separated by a distance \( R \) Show that the field on the
axis around the mid-point between the coils is uniform over a distance that is
small as compared to \( R \), and is given by, \( \boldsymbol{B}=\mathbf{0 . 7 2} \frac{\boldsymbol{\mu}_{0} \boldsymbol{N I}}{\boldsymbol{R}} \)
[Such an arrangement to produce a nearly uniform magnetic field over a small region is known as Helmholtz coils \( ] \)
Subject: Maths
\( \frac{\boldsymbol{A} \boldsymbol{x}-\mathbf{1}}{\left(\mathbf{1}-\boldsymbol{x}+\boldsymbol{x}^{2}\right)(\boldsymbol{x}+\mathbf{2})}=\frac{\boldsymbol{x}}{\mathbf{1}-\boldsymbol{x}+\boldsymbol{x}^{2}}- \)
\( \frac{1}{x+2} \Rightarrow A= \)
\( A \cdot 3 \)
B. 2
\( c \cdot 4 \)
\( D \)
Subject: Chemistry
A certain buffer solution contains equal
concentration of \( \boldsymbol{X}^{-} \) and \( \boldsymbol{H} \boldsymbol{X} . \) The \( \boldsymbol{K}_{\boldsymbol{b}} \)
for \( X^{-} \) is \( 10^{-10} . \) The \( p H \) of the buffer is:
A . 4
B. 7
c. 10
D. 14
Subject: Physics
The graph between two temperature
scales \( A \) and \( B \) is shown in figure.
Between upper fixed point and lower
fixed point, there are 150 equal
divisions on scale \( A \) and 100 on scale \( B \)
The relationship for conversion between the two scales in given by:
A \( \cdot \frac{t_{A}-180}{100}=\frac{t_{B}}{150} \)
в. \( \frac{t_{A}-30}{150}=\frac{t_{B}}{100} \)
c. \( \frac{t_{B}-180}{150}=\frac{t_{A}}{100} \)
D. \( \frac{t_{B}-40}{100}=\frac{t_{A}}{180} \)
Subject: Chemistry
Which of the following combinations of \( 0.20 M \) aqueous solutions will form a precipitate on mixing?
I. \( A g N O_{2} \) and \( H C l \)
Il. \( B a C_{2} H_{2} O_{2} \) and \( M g S O_{4} \)
III. \( \boldsymbol{K} \boldsymbol{I} \) and \( \boldsymbol{P b}\left(\boldsymbol{N} \boldsymbol{O}_{3}\right)_{2} \)
A. I only
B. I and II only
c. I and III only
D. II and III only
E . ।, II, and III
Subject: Chemistry
Which of the following changes occurs
when excess of \( C O_{2} \) gas is passed into
a clear solution of lime water?
A . A white precipitate containing both \( C a C O_{3} \) and \( C a\left(H C O_{3}\right)_{2} \) is formed
B . Initially a white precipitate of \( C a C O_{3} \) is formed which changes into soluble \( C a\left(H C O_{3}\right)_{2} \) on passing excess \( C O_{2} \) gas
C. A white precipitate of \( C a\left(H C O_{3}\right)_{2} \) is formed
D. A white precipitate of \( C a C O_{3} \) is formed
Subject: Physics
In a circuit shown, the average power dissipated in the resistor is (assume
diode to be ideal)
A \( \cdot \frac{E_{0}^{2}}{2 R} \)
в. \( \frac{E_{0}^{2}}{4 R} \)
c. \( \frac{E_{0}^{2}}{R} \)
D. zero
Subject: Maths
What is the degree of the polynomial \( \boldsymbol{p}(\boldsymbol{x})=\mathbf{5} \boldsymbol{x}^{3}-\boldsymbol{8} \boldsymbol{x}^{2}+\boldsymbol{4} \boldsymbol{x} ? \)
\( A \cdot 3 \)
B . 2
\( c \cdot 1 \)
D.
Subject: Physics
The graph describes an airplane's
acceleration
(a) -time ( \( t \) ) during its
take-off run. The airplane's velocity
when it lifts off at \( t=20 s \) is
A \( \cdot 40 \mathrm{ms}^{-} \)
B. \( 50 \mathrm{ms}^{-1} \)
\( \mathrm{c} \cdot 90 \mathrm{ms}^{-} \)
D. \( 180 \mathrm{ms}^{-1} \)
Subject: Maths
Assertion
The area bounded by the curve \( y= \) \( \sin ^{-1} x \& \) the line \( x=0 \&|y|=\frac{\pi}{2} \) is \( \sqrt{2} \)
square units.
Reason
The domain \& principal value branch of \( y=\sin ^{-1} x \operatorname{are}[-1,1] \&\left[\frac{-\pi}{2}, \frac{\pi}{2}\right] \)
respectively
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: Maths
The vector \( \vec{P} \) makes \( 120^{\circ} \) with the \( x- \)
axis and the vector \( \vec{Q} \) makes \( 30^{\circ} \) with \( \boldsymbol{y}- \) axis. What is the resultant vector?
A. \( P+Q \)
в. \( P-Q \)
c. \( \sqrt{P^{2}+Q^{2}} \)
D. \( \sqrt{P^{2}-Q^{2}} \)
Subject: Physics
A stone tied to the end of a string \( 80 \mathrm{cm} \) long is whirled in a horizontal circle
with a constant speed. If the stone makes 14 revolutions in 25 s, the magnitude of acceleration is :
A \( \cdot 20 m s^{-2} \)
В \( \cdot 12 m / s^{2} \)
c. \( 27.53 m s^{-2} \)
\( \mathbf{D} \cdot 8 m s^{-2} \)
Subject: Maths
If \( \boldsymbol{I}=\int \sqrt{\frac{\mathbf{5}-\boldsymbol{x}}{\mathbf{5}+\boldsymbol{x}}} \boldsymbol{d} \boldsymbol{x}, \) then \( \boldsymbol{I} \) equals
A \( \cdot 5 \sin ^{-1}\left(\frac{x}{5}\right)+\sqrt{25-x^{2}}+C \)
B. \( 10 \sin ^{-1}\left(\frac{x}{5}\right)+\sqrt{25-x^{2}}+C \)
c. \( 5 \sin ^{-1}\left(\frac{x}{5}\right)-\sqrt{25-x^{2}}+C \)
D. none of these
Subject: Chemistry
What concentration of \( \boldsymbol{F}- \)
\( \boldsymbol{C H}_{2} \boldsymbol{C O O H},\left(\boldsymbol{K}_{a}=\mathbf{2 . 6} \times \mathbf{1 0}^{-3}\right) \) is
needed so that \( \left[\boldsymbol{H}^{+}\right]=\mathbf{2} \times \mathbf{1 0}^{-\mathbf{3}} \) ?
в. \( 2.6 \times 10^{-3} M \)
c. \( 5.2 \times 10^{-3} M \)
D. \( 3.53 \times 10^{-3} M \)
Subject: Biology
B-DNA which is right-handed double helix contains \( _{-1-} \) base pairs per
turn of the helix and each turn is
long.
A. \( 10,3.4 \AA \)
B. 10,34 ,
c. \( 11,20 \dot{A} \)
D. 11,34 , \( \dot{A} \)
Subject: Maths
If \( \boldsymbol{A}=\cos ^{2} \boldsymbol{x}+\frac{\mathbf{1}}{\cos ^{2} \boldsymbol{x}}, \boldsymbol{B}=\cos \boldsymbol{x}- \)
\( \frac{1}{\cos x} \forall x \neq(2 n \pm 1) \frac{\pi}{2}, \) then the
minimum value of \( \frac{\boldsymbol{A}}{\boldsymbol{B}} \) is
A \( \cdot \sqrt{2} \)
B. \( 2 \sqrt{2} \)
c. \( \frac{1}{\sqrt{2}} \)
D. None of these
Subject: Chemistry
Solubility product constants \( \left(\boldsymbol{K}_{s p}\right) \) of
salts of types \( M X, M X_{2}, M_{3} X \) at
temperature \( \boldsymbol{T} \) are \( \boldsymbol{4} \cdot \boldsymbol{0} \times \boldsymbol{1 0}^{-8}, \boldsymbol{3} \cdot \boldsymbol{2} \times \)
\( 10^{-4} \) and \( 2.7 \times 10^{-13} \) respectively.
Solubility \( \left(\operatorname{mol} d m^{-3}\right) \) of the salts at
temperature \( \boldsymbol{T} \) are in the order:
A \( . M X>M X_{2}>M_{3} X \)
B. \( M_{3} X>M X_{2}>M X \)
c. \( M X_{2}>M_{3} X>M X \)
D. \( M X>M_{3} X>M X_{2} \)
Subject: Maths
A particle moves along the \( x \) -axis obeying the equation \( \boldsymbol{x}=\boldsymbol{t}(\boldsymbol{t}-\mathbf{1})(\boldsymbol{t}- \)
2), where \( x \) is in meter and \( t \) is in
second
Find the acceleration of the particle when its velocity is zero.
Subject: Chemistry
Assertion
In the reaction,
\( \left.\left.2 C u_{2} O_{(s)}+C u_{2} S_{(} s\right) \rightarrow 6 C u_{(} s\right)+ \)
\( \boldsymbol{S} \boldsymbol{O}_{2(\boldsymbol{g})} \)
copper acts as a reductant and sulphur
acts as an oxidant
Reason
The given reaction is not a redox
reaction
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
Assertion
The properties of phosphorus should be closer to those of sulfur than to those of
nitrogen.
Reason
Phosphorus and nitrogen are in the same row of the periodic table.
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
Which of the following reactions will
yield 2,2 -dibromopropane?
A. \( C H_{3}-C \equiv C H+2 \mathrm{HBr} \rightarrow \)
B. \( C H_{3} C H=C H B r+\mathrm{HBr} \rightarrow \)
c. \( C H \equiv C H+2 \mathrm{HBr} \rightarrow \)
D. \( C H_{3}-C H=C H_{2}+ \) HBr \( \longrightarrow \)
Subject: Maths
The volume of the greatest sphere that can be cut off from a cylindrical log of wood of base radius \( 1 \mathrm{cm} \) and height 5
\( \mathrm{cm} \) is :
A \( \cdot \frac{4}{3} \pi \)
в. \( \frac{10}{3} \pi \)
c. \( 5 \pi \)
D. \( \frac{20}{3} \pi \)
Subject: Maths
\( (p, q) \) is a point such that \( p \) and \( q \) are integers \( p \geq 50 \) and the equation \( p x^{2}+q x+1=0 \) has real roots. The
square of the least distance of the point from the origin is \( S \)
Find \( \frac{\boldsymbol{S}-\mathbf{2 2 5}}{\mathbf{5 0 0}} \)
Subject: Chemistry
Which of the following reactions does not take place during rusting?
A \( \cdot H_{2} C O_{3} \rightleftharpoons 2 H^{+}+C O_{3}^{2} \)
B. \( 4 F e^{2+}+O_{2(d r y)} \rightarrow F e_{2} O_{3} \)
C. \( 4 F e^{2+}+O_{2}+4 H_{2} O \rightarrow 2 F e_{2} O_{3}+8 H^{+} \)
D. \( F e_{2} O_{3}+x H_{2} O \rightarrow F e_{2} O_{3} \cdot x H_{2} O \)
Subject: Chemistry
Assertion
Dumas method is more applicable to nitrogen containing organic compounds than Kjeldahl's method.
Reason
Kjeldahl's method does not give satisfactory results for compounds in which \( \mathrm{N} \) is linked to 0 atom.
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
As many as different
combination of water are possible from \( 1 H^{1},_{1} H^{2},_{1} H^{3} \) and \( _{8} O^{16},_{8} O^{17} \) and \( _{8} O^{18} \)
A \( \cdot 12 \)
B. 32
\( c \cdot 18 \)
D. 15
Subject: Physics
Two coaxial solenoids of different radii
carry current I in the same direction. Let \( \vec{F}_{1} \) be the magnetic force on the inner solenoid due to the outer one and \( \vec{F}_{2} \) be
the magnetic force on the outer
solenoid due to the inner one. Then
\( A \cdot \vec{F}_{1}=\vec{F}_{2}=0 \)
B . \( \vec{F}_{1} \) is radially inwards and \( \vec{F}_{2} \) is radially outwards
C \( \cdot \vec{F}_{1} \) is radially inwards \( \vec{F}_{2}=0 \)
D. \( \vec{F}_{1} \) radially outwards and \( \vec{F}_{2}=0 \)
Subject: Physics
Assertion
Current flows in a conductor only when there is an external electric field within
the conductor.
Reason
The drift velocity of the electron is
directly proportional to the electric field
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
The distance between the line \( \vec{r}=2 \vec{i}- \) \( \mathbf{2} \overrightarrow{\boldsymbol{j}}+\boldsymbol{3} \overrightarrow{\boldsymbol{k}}+\boldsymbol{\lambda}(\overrightarrow{\boldsymbol{i}}-\overrightarrow{\boldsymbol{j}}+\boldsymbol{4} \overrightarrow{\boldsymbol{k}}) \) and the plane
\( \vec{r} \cdot(\vec{i}+5 \vec{j}+\vec{k})=5 \) is
A \( \cdot \frac{10}{3 \sqrt{3}} \)
в. \( \frac{10}{9} \)
c. \( \frac{10}{3} \)
D.
Subject: Maths
A cylindrical bucket, \( 32 \mathrm{cm} \) high and with radius of base \( 18 \mathrm{cm} \), is filled with sand. This bucket is emptied on the ground and a conical heap of sand is formed. If the height of the conical heap is \( 24 \mathrm{cm} . \) Find the radius and slant
height of the heap.
Subject: Chemistry
Assertion
Bis(dimethylglyoximato)nickel(II) can show geometrical isomerism.
Reason
Tetrahedral complexes with chiral structures exhibit optical isomerism.
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: Maths
The number of ordered pair \( (x, y) \) such
that \( 0 \leq x \leq 2 \pi \) and satisfying the inequality \( 2^{\sec ^{2} x} \sqrt{y^{2}-2 y+2} \leq 2 \) is
A .2
B. 3
c. 1
D. None of these
Subject: Maths
Let \( n \) be a natural number and \( X= \)
\( \{1,2, \dots \dots, n\} . \) For subsets \( A \) and \( B \) of
\( X, \) we denote \( A \Delta B \) to be the set of all
those elements of \( X \) which belong to
exactly one of \( A \) and \( B . \) Let \( F \) be a
collection of subsets of \( X \) such that for
any two distinct elements \( A \) and \( B \) in \( F \)
the \( \operatorname{set} A \Delta B \) has at least two elements.
Show that \( F \) has at most \( 2^{n-1} \) elements
Find all such collections \( \boldsymbol{F} \) with \( \mathbf{2}^{n-1} \)
elements.
Subject: Maths
\( L \lim _{n \rightarrow \infty} t \frac{1}{n}\left[\frac{1}{n+1}+\frac{2}{n+2}+\ldots+\frac{3 n}{4 n}\right] \)
A. \( 3-\ln 4 \)
B. \( 3+\ln 4 \)
c. \( 3 \ln 4 \)
D. None of these
Subject: Maths
The equation of the ellipse having
vertices at (±5,0) and foci (±4,0) is
\( ^{A} \cdot \frac{x^{2}}{25}+\frac{y^{2}}{16}=1 \)
B. \( 9 x^{2}+25 y^{2}=225 \)
c. \( \frac{x^{2}}{9}+\frac{y^{2}}{25}=1 \)
D. \( 4 x^{2}+5 y^{2}=20 \)
Subject: Physics
An electric heater operating at \( 220 \mathrm{V} \) boils \( 5 l \) of water in 5 minutes. If it is
used on a \( 110 \mathrm{V} \) line, it will boil the
same amount of water in:
A . 10 minutes
B. 20 minutes
c. 5 minutes
D. 1 minute
Subject: Chemistry
An excess of \( \mathrm{AgNO}_{3} \) is added to \( 100 \mathrm{ml} \) of
a \( 0.1 \mathrm{M} \) solution of
dichlorotetraaquachromium (III) chloride
The number of mol of AgCl precipitate would be:
A. 0.001
B. 0.002
c. 0.003
D. 0.01
Subject: Maths
Reduce each of the following differentia equations to the variables separable
\( i \) ) \( 1+\frac{d y}{d x}= \)
form and hence solve.
\( \operatorname{cosec}(\boldsymbol{x}+\boldsymbol{y}) \)
ii) \( (x-y)^{2} \frac{d y}{d x}=a^{2} \)
Subject: Physics
A radio capacitor of variable capacitance is made of \( n \) parallel plates each of area
\( A \) and separated from each other by a
distance \( d \). The alternate plates are connected together. The capacitance of
the combination is:
A \( \cdot \frac{n A \epsilon_{0}}{d} \)
в. \( \frac{(n-1) A \epsilon_{0}}{d} \)
c. \( \frac{(2 n-1) A \epsilon_{0}}{d} \)
D. \( \frac{(n-2) A \epsilon_{0}}{d} \)
Subject: Chemistry
\( 2 N O B r(g) \rightleftharpoons 2 N O(g)+B r_{2}(g) . \) If
nitrosyl bromide \( (N O B r) \) is \( 33.33 \% \)
dissociated at \( 25^{\circ} \mathrm{C} \) and a total
pressure of 0.28 atm. Calculate \( K_{p} \) for the dissociation at this temperature
Subject: Chemistry
For the reaction \( \boldsymbol{A}+\boldsymbol{B} \rightarrow \) product, it is
found that the order of \( A \) is 1 and the order of \( B \) is \( \frac{1}{2}, \) the concentration of both \( A \) and \( B \) are increased four times,
the rate will increase by a factor of
\( A \cdot 16 \)
B. 8
\( c \cdot 6 \)
D. 4
Subject: Maths
Find the principal argument of the complex number \( \sin \frac{6 \pi}{5}+ \)
\( i\left(1+\cos \frac{6 \pi}{5}\right) \)
A \( \cdot \arg (z)=\frac{9 \pi}{10},|z|=-2 \cos \frac{3 \pi}{5} \)
B. \( \arg (z)=\frac{\pi}{10},|z|=-2 \cos \frac{3 \pi}{5} \)
c. \( \arg (z)=\frac{9 \pi}{10},|z|=2 \cos \frac{3 \pi}{5} \)
D. \( \arg (z)=\frac{9 \pi}{10},|z|=-2 \cos \frac{2 \pi}{5} \)