AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Chemistry
Assertion: According to the principle of common ion effect, the solubility of
\( H g C l_{2} \) is expected to be less in an
aqueous solution of \( K I \) than in water.
\( H g I_{2} \) dissolves in an aqueous
solution of \( K I \) to form a clear solution.
Reason: lodide ion, \( \boldsymbol{I}^{-} \) is highly
polarizable.
A. Both Assertion and Reason are correct and Reason is the correct explanation of Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation of Assertion
c. Assertion is correct but Reason is not correct
D. Assertion is not correct but Reason is correct
E. Both Assertion and Reason are not correct
Subject: Maths
In figure, \( P O Q \) is a line. Ray \( O R \) is
perpendicular to line \( P Q . O S \) is another
ray lying between rays \( O P \) and \( O R \) Prove that \( \angle R O S=\frac{1}{2}(\angle Q O S- \)
\( \angle P O S) \)
Subject: Maths
Statement \( 1: \sim(\mathbf{p} \leftrightarrow \sim \mathbf{q}) \) is equivalent
to \( \mathbf{p} \leftrightarrow \mathbf{q} \)
Statement \( 2: \sim(\mathbf{p} \leftrightarrow \sim q) \) is a
tautology
A. Both Statement 1 and Statement 2 are true and
Statement 2 is a correct explanation for statement 1
B. Both Statement 1and Statement 2 are true and Statement 2 is not a correct explanation for Statement
1
C. Statement 1 is true but statement 2 is false
D. Statement 1 is false but Statement 2 is true
Subject: Physics
Match The following:
\begin{tabular}{ll|l|l} 
& Column-1 & & Column-2 \\
\hline \( \mathrm{A} \) & Audible range & \( \mathrm{p} \) & Faster transmission of sound \\
\hline \( \mathrm{B} \) & Infrasonic range & \( \mathrm{q} \) & Slower transmission of sound \\
\hline \( \mathrm{C} \) & Ultrasonic range & \( \mathrm{r} \) & Less than \( 20 \mathrm{Hz} \) \\
\( \mathrm{E} \) & Denser medium & \( \mathrm{s} \) & \( 20 \mathrm{Hz}-20 \mathrm{kHz} \) \\
& & & \\
Rarer medium & \( \mathrm{t} \) & More than \( 20 \mathrm{kHz} \)
\end{tabular}
Subject: Maths
Which one of the following functions is
not one-one?
\( \mathbf{A} \cdot f:(-1, \infty) \rightarrow R \) given by \( f(x)=x^{2}+2 x \)
B \( \cdot g:(2, \infty) \rightarrow R \) given by \( g(x)=e^{x^{3}-3 x+2} \)
C \( . h: R \rightarrow R \) given by \( h(x)=2^{x(x-1)} \)
D \( \quad \phi:(-\infty, 0) \rightarrow R \) given by \( \phi(x)=\frac{x^{2}}{x^{2}+1} \)
Subject: Physics
A vector \( \overline{\boldsymbol{m}} \) of magnitude \( 2 \sqrt{101} \) in the
direction of internal bisector of the
angle between the vector \( \bar{b}=8 \hat{i}-6 \hat{j}- \) \( 6 \hat{k} \) and \( \bar{c}=4 \hat{i}-3 \hat{j}+4 \hat{k} \) is
\( A \)
B . \( 16 \hat{i}-12 \hat{j}+2 \hat{k} \)
\( \frac{-16 \hat{i}+12 \hat{j}+2 \hat{k}}{5} \)
D . \( 16 \hat{i}+12 \hat{j}+2 \hat{k} \)
Subject: Physics
A person traveling on a straight line
moves with a uniform velocity \( v_{1} \) for a
distance \( x \) and with uniform velocity \( v_{2} \)
for the next equal time. The average velocity \( v \) is given by
A \( \cdot v=\frac{v_{1}+v_{2}}{2} \)
B. \( v=\sqrt{v_{1} v_{2}} \)
c. \( v=\frac{v_{1} v_{2}}{v_{1}+v_{2}} \)
D. \( v=\frac{v_{1}+v_{2}}{v_{1} v_{2}} \)
Subject: Physics
An electron of mass \( M_{e}, \) initially at rest moves through a certain distance in a uniform electric field in time \( t_{1} . A \)
proton of mass \( M_{p} \) also intially at rest,
takes time \( t_{2} \) to move through an equal distance in this uniform electric field.
Neglecting the effect of gravity, the ratio \( t_{2} / t_{1} \) is nearly equal to:
A . 1
в. \( \sqrt{\frac{M_{p}}{M_{e}}} \)
c. \( \sqrt{\frac{M_{e}}{M_{p}}} \)
D. 1836
Subject: Chemistry
A solution containing 7 g of a solute (molar mass 210 g \( m o l^{-1} \) ) in 350 g of acetone raised the boiling point of
acetone from \( 56^{\circ} \mathrm{C} \) to \( 56.3^{\circ} \mathrm{C} \). The value
of ebullioscopic constant of acetone in \( \mathrm{K} \mathrm{kg} \operatorname{mol}^{-1} \) is :
A . 2.66
B. 3.15
c. 4.12
D. 2.86
Subject: Chemistry
The equilibrium constant of a reaction
at \( 298 K \) and \( 1000 K \) is \( 5 \times 10^{-3} \) and
\( 2 \times 10^{-3} \) respectively. The \( \Delta H \) for the
reaction is:
A. positive
B. negative
c. either positive or negative
D. zero
Subject: Physics
An electric dipole is situated in an
electric field of uniform intensity whose dipole moment is p and moment of inertia is I. if the dipole is displaced then the angular frequency of its oscillation is
A \( \cdot\left(\frac{p E}{I}\right)^{1 / 2} \)
B. \( \left(\frac{p E}{I}\right)^{3 / 2} \)
\( ^{\mathrm{c}} \cdot\left(\frac{I}{p E}\right)^{1 / 2} \)
D. \( \left(\frac{p}{I E}\right)^{1 / 2} \)
Subject: Physics
A man running on a horizontal road at
\( 8 k m p h \) find that rain is falling vertically. He increases the speed to
\( 12 k m p h \) and find the drops make an
angle \( 30^{\circ} \) with the vertical
A. The speed of rain is \( 8 \sqrt{3} k m p h \)
B. The speed of rain is \( 8 \sqrt{112} k m p h \)
c. speed of rain wrt man is \( 8 k m p h \)
D. Speed of rain wrt man is \( 8 \sqrt{3} k m p h \)
Subject: Physics
Two moles of helium gas are taken over
the cycle \( A B C D A, \) as show in the \( P-T \)
diagram. Assuming the gas to be ideal
the work done on the gas in taking it from state \( A \) to \( B \) is :
\( \mathbf{A} \cdot 200 R \)
B. \( 300 R \)
c. \( 400 R \)
\( \mathbf{D} \cdot 500 R \)
Subject: Physics
A cord is used to raise a block of mass
\( m \) vertically through a distance \( d \) at a
constant downward acceleration \( \boldsymbol{g} / \mathbf{4} \) The work done by the cord is:
\( \mathbf{A} \cdot m g d / 4 \)
в. \( 3 M g d / 4 \)
c. \( -3 M g d / 4 \)
D. \( M g d \)
Subject: Biology
Choose the type of enzyme involved in
the following reaction.
\( \boldsymbol{S}-\boldsymbol{G}+\boldsymbol{S}^{\prime} \longrightarrow \boldsymbol{S}+\boldsymbol{S}^{\prime}-\boldsymbol{G} \)
A. Dehydrogenase
B. Transferase
c. Hydrolase
D. Lyase
E. Isomerase
Subject: Chemistry
Rate expression of a chemical change is \( -\frac{\boldsymbol{d} \boldsymbol{x}}{\boldsymbol{d} \boldsymbol{t}}=\boldsymbol{k}[\boldsymbol{A}]^{2}[\boldsymbol{B}]^{1}[\boldsymbol{C}]^{0} . \) The order of
reaction is:
\( A \cdot 3 \)
B . 2
c. 1
D.
Subject: Maths
\( \int \frac{\boldsymbol{x}^{2}+\mathbf{1}}{\boldsymbol{x}^{4}+\mathbf{1}} \boldsymbol{d} \boldsymbol{x}= \)
\( \mathbf{A} \cdot \frac{1}{\sqrt{2}} \tan ^{-1}\left(\frac{x^{2}+1}{\sqrt{2 x}}\right)+c \)
\( \mathbf{B} \cdot \tan ^{-1}\left(\frac{x^{2}+1}{\sqrt{2 x}}\right)+c \)
\( \mathbf{C} \cdot \frac{1}{\sqrt{2}} \tan ^{-1}\left(\frac{x^{2}-1}{\sqrt{2 x}}\right)+c \)
\( \mathbf{D} \cdot \tan ^{-1}\left(\frac{x^{2}-1}{\sqrt{2 x}}\right)+c \)
Subject: Chemistry
Which of the following is/are not
correct?
\( \mathbf{A} \cdot S i O_{2} \) is used as acid flux
B. The distance between the layers in graphite is \( 3.35 \times \) \( 10^{-8} \mathrm{cm} \)
C \( . S i O_{2} \) reacts with \( N a_{2} C O_{3} \) and liberates CO.
D. The hybridization of \( C \) in graphite is \( S p^{2} \).
Subject: Physics
In a Fresnel's bi-prism experiment, the fringe of width 0.05 mm is observed on
a screen at a distance of \( 1.5 m \) from the
source. When a convex lens is placed between the source and the screen, for
two positions of the lens image of interfering sources are produced on the screen. The separation between the two
images being 0.04 and \( 0.01 m m \) respectively. The wavelength of light used is
\( \mathbf{A} \cdot 6.67 n m \)
B. \( 0.667 n m \)
\( c .667 n m \)
D. \( 667 A^{\circ} \)
Subject: Physics
Match the following
List - I 1 \( t-1 \) The in
a) Relative velocity
and separation are approach e) Interaction
between bodies sity of app
are same
b) Bodies stick together
f) Newton's ॥I 1 law
\( c \)
Force g) Coefficient
of restitution \( = \)
1 1
d) Recoil of the gun h) Coefficient
of restitution \( = \)
0
¡) Binding
energy A er
\( A \cdot a-g ; b-h ; c-e ; d-f \)
B. \( a-h ; b-g ; c-f ; d-e \)
\( C \cdot a-g ; b-e ; c-f ; d-h \)
D. \( a-e ; b-f ; c-g ; d-i \)
Subject: Maths
The areas of two similar triangles are
45 sq. \( \mathrm{cm} \) and 80 sq.cm. The sum of their perimeters is \( 35 \mathrm{cm} . \) Find the perimeter of each triangle in cm.
\( \mathbf{A} \cdot 15,20 \)
B. 13,22
c. 17,18
D. None of these
Subject: Chemistry
The correct order of reducing abilities of
hydrides of \( V \) group elements is:
A. \( N H_{3}<P H_{3}<A s H_{3}<S b H_{3}<B i H_{3} \)
В. \( N H_{3}>P H_{3}>A s H_{3}>S b H_{3}>B i H_{3} \)
c. \( N H_{3}<P H_{3}>A s H_{3}>S b H_{3}>B i H_{3} \)
D. \( S b H_{3}>B i H_{3}>A s H_{3}>N H_{3}>P H_{3} \)
Subject: Chemistry
Aluminium oxide may be electrolysed
at \( 1000^{\circ} \mathrm{C} \) to furnish aluminium metal.
The cathode reaction is \( A l^{3+}+3 e^{-} \rightarrow \)
Al. To prepare \( 5.12 \mathrm{kg} \) of aluminium
metal by this method would require:
A \( \cdot 5.49 \times 10^{1} C \) of electricity
B . \( 5.49 \times 10^{4} C \) of electricity
c. \( 1.83 \times 10^{7} C \) of electricity
D. \( 5.49 \times 10^{7} C \) of electricity
Subject: Chemistry
Which facts are revealed from
Avogadro's law for ideal gases?
This question has multiple correct options
A. The distance between molecules is much large than the actual dimension of molecules
B. Equal number of molecules of different gases under identical conditions of temperatures and pressure occupy the same volume.
C. Saturated vapours obey gas laws
D. 1 mole of a gas contains \( 6.023 \times 10^{23} \) molecules of
gases.
Subject: Maths
The sum of all the coefficient of those
terms in the expansion of \( (a+b+c+d)^{8} \) which contains \( b \) but
not \( \boldsymbol{c} \) is
\( \mathbf{A} \cdot 6305 \)
B \( \cdot 4^{8}-3^{8} \)
C. Number of ways of forming 8 digit numbers using digits 1,2,3 each number as atleast one 3
D. Number of ways of forming 4 digit numbers using digits 1,2,3 each number as atleast one 3
Subject: Maths
Let \( f(x) \) be a continous and differentiable function on \( [0,1], \) such
that \( f(0) \neq 0 \) and \( f(1)=0 . \) We can
conclude that there exists \( c \in(0,1) \)
such that
A \( \cdot c . f^{\prime}(c)-f(c)=0 \)
B. \( f^{\prime}(c)+c . f(c)=0 \)
c. \( f^{\prime}(c)-c . f(c)=0 \)
D. \( c . f^{\prime}(c)+f(c)=0 \)
Subject: Biology
Considering mode of asexual reproduction, match the Column I with I and select the correct option.
\( \begin{array}{ll}\text { Column I } & \text { Column II } \\ \text { a. Yeast } & \text { i. Fragmentation } \\ \text { b. Penicillium } & \text { ii. Zoospores } \\ \text { c. Filamentous algae } & \text { iii. Budding } \\ \text { d. Chlamydomonas } & \text { iv.Conidia }\end{array} \)
\( A \)
\( a-i i i, b-i v, c-i, d-i i \)
в. \( a-i i, b-i i i, c-i, d-i v \)
c. \( a-i v, b-i i i, c-i i, d-i \)
D. \( a-i i i, b-i i, c-i, d-i v \)
Subject: Maths
Find \( (\boldsymbol{a}+\boldsymbol{b})^{4}-(\boldsymbol{a}-\boldsymbol{b})^{4} \). Hence,
evaluate \( (\sqrt{\mathbf{3}}+\sqrt{\mathbf{2}})^{4}-(\sqrt{\mathbf{3}}-\sqrt{\mathbf{2}})^{4} \)
Subject: Physics
A beam of light passes from air into a substance \( X \). If the angle of incident be
\( 72^{\circ} \) and the angle of refraction be \( 40^{\circ} \)
calculate the refractive index of
substance \( X \). (Given: \( \sin 72^{\circ}=0.951 \)
and \( \left.\sin 40^{\circ}=0.642\right) \)
Subject: Physics
A capacitor of capacitance \( C=4 \mu F \) is
connected as shown in figure. If internal resistance of the cell is \( 0.5 . \) The charge
on the capacitor plates is
A. zero
3. \( 8 \mu \) C
\( c \cdot 4 \mu C \)
\( D \cdot 6 \mu C \)
Subject: Maths
\( \operatorname{tet} f(\theta)=\left|\begin{array}{ccc}\cos \frac{\theta}{2} & 1 & 1 \\ 1 & \cos \frac{\theta}{2} & -\cos \frac{\theta}{2} \\ -\cos \frac{\theta}{2} & 1 & -1\end{array}\right| \)
\( f(\pi)+f(-\pi) \) is equal to
A. The maximum value of \( f(\theta) \)
B. The minimum value of \( f(\theta) \)
c. Average value of the range of \( f(\theta) \)
D. None of these
Subject: Physics
\( \ln \) an A.C circuit, the resistance \( \boldsymbol{R}= \)
\( 0.2 \Omega . \) At a certain instant, \( V_{A}-V_{B}= \)
\( 0.5 V, I=0.5 A, \) and the current is
increasing at the rate of \( \frac{\Delta I}{\Delta t}=8 A / s \) The inductance of the coil is:
A . \( 0.05 H \)
в. \( 0.1 \mathrm{H} \)
\( c .0 .2 H \)
D. none of these
Subject: Physics
A plane has a takeoff speed of \( 88.3 m / s \)
and requires \( 1365 m \) to reach that speed. Determine the acceleration of
the plane.
A \( \cdot 3.86 m / s^{2} \)
B. \( 2.86 m / s^{2} \)
c. \( 2.8 m / s^{2} \)
D. \( 2.6 \mathrm{m} / \mathrm{s}^{2} \)
Subject: Maths
Let mean value of \( \boldsymbol{f}(\boldsymbol{x})=\frac{1}{\boldsymbol{x}+\boldsymbol{c}} \) over
interval (0,2) is \( \frac{1}{2} \ell n 3 \) then positive
values of \( c \) is
A . 12
в. 1
\( c \cdot 2 \)
\( D \cdot \frac{3}{3} \)
Subject: Maths
The sum to \( n \) terms of the services \( \frac{3}{1^{2}}+ \) \( \frac{5}{1^{2}+2^{2}}+\frac{7}{1^{2}+2^{2}+3^{2}}+\dots \dots \) is
A \( \cdot \frac{3 n}{n+1} \)
В. \( \frac{6 n}{n+1} \)
c. \( \frac{g n}{n+1} \)
D. \( \frac{12 n}{n+1} \)
Subject: Chemistry
The structures of two compounds
and \( (I I) \) are given below. Which statement is correct?
\( \boldsymbol{F}_{2} \boldsymbol{C}=\boldsymbol{C}=\boldsymbol{C} \boldsymbol{F}_{2}(\boldsymbol{I}) \) and \( \boldsymbol{F}_{2} \boldsymbol{C}=\boldsymbol{C}= \)
\( \boldsymbol{C}=\boldsymbol{C} \boldsymbol{F}_{2}(\boldsymbol{I} \boldsymbol{I}) \)
A. Reductive ozonolysis of both gave the same product
B. Reductive ozonolysis of both gave different products
c. Reductive and oxidative ozonolysis of both gave different products.
D. Reductive and oxidative ozonolysis of (I) gave the same product but of \( (I I) \) gave different products.
Subject: Physics
A tennis racket can be idealized as a
uniform ring of mass \( \mathrm{M} \) and radius \( \mathrm{R} \) attached to a uniform rod also of mass
M and length L. The rod and the ring are coplanar, and the line of the rod passes through the centre of the ring. The moment of inertia of the object (racket) about an axis through the centre of the ring and perpendicular to its plane is
A \( \cdot \frac{1}{12} M\left(6 R^{2}+L^{2}\right) \)
B \cdot\frac{12 } { 1 2 } M ( 1 8 R ^ { 2 } + L ^ { 2 } )
C \( \cdot \frac{1}{3} M\left(6 R^{2}+L^{2}+3 L R\right) \)
D. None of these
Subject: Chemistry
Over a number of years the average pH
of a stream changes from a pH of 6.9 to a pH of 5.9 due to acid rain. Which statement is true about the pH of the
stream?
A. The pH of the stream now is one times more acidic than it was years ago
B. The stream now has 10 times more hydroxide ions than it did years ago
c. The pH of the stream is now 10 times more acidic than it was years ago
D. The stream is more basic now than it was years ago
E. The concentration of hydronium ion in the stream has decreased over the years
Subject: Biology
Study the graph which shows results of
three different experiments \( P, Q \) and \( R \)
Concentrate on graphs \( \mathrm{P} \) and \( \mathrm{Q} \) and
answer the following questions?
What is the difference between the
Curves?
A. The temperature has increased at
B. The rate of photosynthesis increased faster in \( Q \) and in \( P \)
C. The rate of photosynthesis lowered in \( Q \) and
D. The temperature has lowered at \( Q \)
Subject: Chemistry
The molecular formula of Magnesium
(II) acetate is:
\( \mathbf{A} \cdot M g\left(C H_{3} C O O\right) \)
в. \( M g_{2}\left(C H_{3} C O O\right)_{3} \)
c. \( M g\left(C H_{3} C O O\right)_{2} \)
D. \( M g\left(C H_{3} C O O\right)_{3} \)
Subject: Maths
\( A B C \) is an isosceles triangle such that
\( A B=A C . D \) is the mid point of \( A C . A \)
circle is drawn taking \( B D \) as diameter which intersects \( A B \) at point \( E \).then
\( \boldsymbol{A C}=\mathbf{3 A E} \)
A. True
B. False
Subject: Maths
If \( \overline{\boldsymbol{a}}=\mathbf{2} \overline{\mathbf{i}}-\mathbf{3} \overline{\mathbf{j}}+\overline{\mathbf{k}}, \overline{\boldsymbol{b}}=_{-} \overline{\mathbf{i}}+\overline{\mathbf{k}}, \overline{\boldsymbol{c}}= \)
\( 2 \bar{j}-\bar{k}, \) then the area of the parallelogram is having diagonals \( \bar{a}+\bar{b} \) and \( \bar{b}+\bar{c}(\text { in square units }) \) is
A \( \cdot \sqrt{21} \)
B. \( \frac{\sqrt{21}}{2} \)
c. \( \sqrt{19} \)
D. \( \frac{\sqrt{19}}{2} \)
Subject: Chemistry
Which of the following reactions
involves oxidation and reduction?
\( \mathbf{A} \cdot N a B r+H C l \rightarrow N a C l+H B r \)
B. \( H B r+A g N O_{3} \rightarrow A g B r+H N O_{3} \)
\( \mathbf{c} \cdot H_{2}+B r_{2} \rightarrow 2 H B r \)
D. \( N a_{2} O+H_{2} S O_{4} \rightarrow N a_{2} S O_{4}+H_{2} O \)
Subject: Physics
two equal drops of water each of radius
\( \boldsymbol{r} \) are falling through air with a steady velocity \( 8 c m / s \). the two drops combine
to form a big drop. The terminal velocity of big drop will be:
A \( \cdot \quad_{8(2)} \frac{2}{3} \mathrm{cm} / \mathrm{s} \)
в. \( \quad \frac{2}{3} \mathrm{cm} \)
c. \( \quad 4(2)^{\frac{2}{3}} c m \)
D. 32 cm / \( s \)
Subject: Maths
\( f(x)=x^{3}+a x^{2}+b x+c \) has a max.
at \( x=-1 \) and \( \min . \) at \( x=3 . \) Determine
the constants \( a, b, c \)
\( \mathbf{A} \ldots a=-3, b=-3, c=0 \)
В \( \ldots a=-3, b=-9, c=3 \)
\( \mathbf{c} \ldots a=-3, b=9, c=9 \)
D \( \ldots a=3, b=9, c=-3 \)
Subject: Maths
A land surveyor records the various
treatments of a field in his
measurement book as given below. The
area of the field surveyed is (all reading
are in meters):
\( A \cdot 6000 \) sq. \( m \)
B. 7000 sq. \( m \)
c. 7500 sq. \( m \)
D. 8250 sq.
Subject: Physics
sources of light of wavelength \( \lambda \) are placed on the dotted line in front of a large screen. The source emit waves in
phase with each other. The distance
between \( S_{1} \) and \( S_{2} \) is \( ^{\prime} d^{\prime} \) while their
distance from the screen is much
larger. Then,
(a) If \( d=7 \lambda / 2, O \) will be minima
(b) If \( d=4.3 \lambda \), there will be total of 8
minima on y-axis
(c) If \( d=7 \lambda, O \) will be maxima.
(d) If \( d=\lambda \), there will be only one
maxima on the screen.
Which is the set of correct statement:
A. \( a, b \) and \( c \)
B. \( b, c \) and \( d \)
c. \( a, b, c \) and \( d \)
D. \( a, c \) and \( d \)
Subject: Maths
Using properties of determinant, prove
\[
\text { that }\left|\begin{array}{lll}
\boldsymbol{b}+\boldsymbol{c} & \boldsymbol{a}-\boldsymbol{b} & \boldsymbol{a} \\
\boldsymbol{c}+\boldsymbol{a} & \boldsymbol{b}-\boldsymbol{c} & \boldsymbol{b} \\
\boldsymbol{a}+\boldsymbol{b} & \boldsymbol{c}-\boldsymbol{a} & \boldsymbol{c}
\end{array}\right|=\mathbf{3} \boldsymbol{a} \boldsymbol{b} \boldsymbol{c}-\boldsymbol{a}^{3}-
\]
\( b^{3}-c^{3} \)
Subject: Physics
What is the angle between vector \( \vec{A}= \) \( \hat{\mathbf{i}}+\hat{\mathbf{j}}+\sqrt{\mathbf{2}} \hat{\boldsymbol{k}} \) and the z-axis :
A \( \cdot 0^{\circ} \)
B . 45
\( c \cdot 60 \)
D. \( 90^{\circ} \)
Subject: Maths
If the foot of the perpendicular from the origin to a plane is \( (1,2,3), \) then the equation of the plane is
A. \( 3 x+2 y+z=14 \)
B. \( x+2 y+3 z=14 \)
c. \( x+\frac{y}{2}+\frac{z}{3}=1 \)
D. \( x+2 y+3 z=6 \)
Subject: Maths
Two numbers are selected at random
from the number \( 1,2, \ldots, n . \) Let \( p \) denote the probability that the difference
between the first and second is not less
than \( m \) (where \( 0<m<n \) ). If \( n=25 \)
and \( \boldsymbol{m}=\mathbf{1 0}, \) find \( \mathbf{5} \boldsymbol{p} \)
Subject: Maths
If \( \boldsymbol{R} \) be a relation \( < \) from \( \boldsymbol{A}=\{\mathbf{1}, \mathbf{2}, \mathbf{3}, \mathbf{4}\} \)
to \( B=\{1,3,5\} \) i.e., \( (a, b) \in \mathrm{R} \) if \( a<b \)
then find \( R O R^{-1} \)
Subject: Maths
Let \( A \) be a non-empty set such that \( A \times \) \( A \) has 9 elements among which are
found (-1,0) and \( (0,1), \) then
\( \mathbf{A} \cdot A=\{-1,0\} \)
В \( \cdot A=\{0,1\} \)
C \( \cdot A=\{-1,0,1\} \)
D \( \cdot A=\{-1,1\} \)
Subject: Chemistry
The maximum number of \( 90^{\circ} \) angles between the bond pair-bond pair of
electrons is observed in:
A \( \cdot d s p^{2} \)
B. \( s p^{3} d \) hybridization
c. \( d s p^{3} \) hybridization
D. \( s p^{3} d^{2} \) hybridization
Subject: Chemistry
Identify the correct order of reactivity of metals among the following.
A. \( C u<F e<Z n<A l<N a \)
B. \( F e<Z n<C u<N a<A l \)
c. \( Z n<C u<F e<A l<N a \)
D. \( C u<Z n<A l<N a<F e \)
\( e \)
Subject: Chemistry
The compound(s) which generate(s) \( N_{2} \) gas upon thermal decomposition below
\( 300^{\circ} \mathrm{C} \) is/are:
This question has multiple correct options
A. \( N H_{4} N O_{3} \)
B. \( \left(N H_{4}\right)_{2} C r_{2} O_{7} \)
c. \( B a\left(N_{3}\right)_{2} \)
D. \( M g_{3} N_{2} \)
Subject: Physics
\( n \) elastic balls are placed at rest on a
smooth horizontal plane which is circular at the ends with radius \( r \) as
shown in the figure. The masses of the balls are \( m, \frac{m}{2}, \frac{m}{2^{2}} \ldots \ldots \frac{m}{2^{n-1}} \)
respectively. What is the minimum velocity which should be imparted to
the first ball of mass \( m \) such that \( n^{t h} \)
ball completes the vertical circle:
A \( \cdot\left(\frac{3}{4}\right)^{n-1} \sqrt{5} g r \)
В \( \cdot\left(\frac{4}{3}\right)^{n-1} \sqrt{5 g r} \)
c. \( \left(\frac{3}{2}\right)^{n-1} \sqrt{5 g r} \)
D \( \cdot\left(\frac{2}{3}\right)^{n-1} \sqrt{5 g r} \)
Subject: Maths
f \( 2 x-Y=\left[\begin{array}{ccc}3 & -3 & 0 \\ 3 & 3 & 2\end{array}\right] \) and \( 2 Y+X= \)
\( \left[\begin{array}{ccc}\mathbf{4} & \mathbf{1} & \mathbf{5} \\ -\mathbf{1} & \mathbf{4} & -\mathbf{4}\end{array}\right] \)
then find \( X \) and \( Y \)
Subject: Maths
If \( z_{1} \) and \( z_{2} \) are two complex numbers,
then \( R e\left(z_{1} z_{2}\right) \) is:
\( \mathbf{A} \cdot \operatorname{Re}\left(z_{1}\right) \operatorname{Re}\left(z_{2}\right) \)
B \( \cdot \operatorname{Re}\left(z_{1}\right) \cdot \operatorname{Re}\left(z_{2}\right)-\operatorname{Im}\left(z_{1}\right) \cdot \operatorname{Im}\left(z_{2}\right) \)
\( \mathbf{c} \cdot \operatorname{Im}\left(z_{1}\right) \cdot \operatorname{Re}\left(z_{2}\right) \)
D. \( \operatorname{Re}\left(z_{1}\right) . \operatorname{Im}\left(z_{2}\right) \)
Subject: Chemistry
Assertion \( : H C O_{3}^{-} \) can act as a Bronsted acid or a Bronsted base.
Reason \( : H C O_{3}^{-} \) can donate a proton to
form \( C O_{3}^{2-} \) or accept a proton to form
\( \boldsymbol{H}_{2} \boldsymbol{C} \boldsymbol{O}_{3} \)
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Assertion is incorrect but Reason is correct
E. Both Assertion and Reason are incorrect
Subject: Chemistry
mole of amino cobalt chloride on
treating with an excess of \( A g N O_{3} \)
solution gives 2 moles of \( A g C l \)
precipitate. The number of \( C l^{-} \) ions
which satisfies both primary and secondary valency of cobalt in the complex is:
A .2
B. 3
\( c . \)
D.
Subject: Physics
Two poles of same strength attract each other with a force of magnitude \( F \) when
placed at the corners of an equilateral triangle. If a north pole of the same
strength is placed at the third vertex, it experiences a force of magnitude
A. \( F \sqrt{3} \)
в. \( F \)
c. \( F \sqrt{2} \)
D. \( 2 F \)
Subject: Physics
Assertion
The formula connecting \( u, v \) and \( f \) for \( a \) spherical mirror is valid only for mirrors whose sizes are very small compared to their radii of curvature.
Reason
Laws of reflection are strictly valid for plane surfaces, but not for large spherical surfaces.
A. Statement-1 is True, Statement-2 is True; Statement - is a correct explanation for Statement-
B. Statement-1 is True, Statement-2 is True; Statement - 2 is NOT a correct explanation for Statement-1.
C. Statement- -1 is True, Statement-2 is False
D. Statement-1 is False, Statement-2 is True.
Subject: Physics
A stream lined body falls through air from a height on the surface of a liquid.
Let \( d \) and \( D \) denote the densities of the
materials of the body and the liquid
respectively. If \( D>d \), then the time
after which the body will be
instantaneously at rest is:
A \( \cdot \sqrt{\frac{2 h}{g}} \)
B. \( \sqrt{\frac{2 h}{g} \frac{D}{d}} \)
c. \( \sqrt{\frac{2 h}{g} \frac{d}{D}} \)
D. \( \frac{d}{(D-d)} \sqrt{\frac{2 h}{g}} \)