AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Physics
A thin convex lens of focal length \( 20 \mathrm{cm} \)
is kept in contact with a plane mirror. The focal length of the combination will
be :
A . \( 5 \mathrm{cm} \)
B. \( -10 \mathrm{cm} \)
\( \mathrm{c} .-20 \mathrm{cm} \)
D. Infinite
Subject: Maths
If \( x_{1} x_{2} x_{3} \dots x_{n}=1\left(x_{1}>0, i=\right. \)
\( 1,2, \dots . n), \) prove that \( x_{1}+x_{2}+ \)
\( \dots . . x_{n} \geq n(n \geq 2) \)
Subject: Chemistry
How many gm of solid KOH must be added to \( 100 \mathrm{ml} \) of a buffer solution,
which is 0.1 each with respect to acid \( \mathrm{H} \)
\( A \) and salt \( K A \) to make the pH of the
solution 6.0?
\( \left[\text { Given: } \mathrm{pK}_{-} \mathrm{a}(\mathrm{HA})=5\right] \)
Subject: Physics
A charge \( +q \) is fixed at each of the
points \( \boldsymbol{x}=\boldsymbol{x}_{0}, \boldsymbol{x}=\mathbf{3} \boldsymbol{x}_{0}, \boldsymbol{x}=\mathbf{5} \boldsymbol{x}_{0} \dots \dots, \infty \)
on the \( x \) -axis and charge \( -q \) is fixed at
each of the points \( \boldsymbol{x}=\mathbf{3} \boldsymbol{x}_{0}, \boldsymbol{x}= \)
\( \mathbf{4} \boldsymbol{x}_{0}, \boldsymbol{x}=\boldsymbol{6} \boldsymbol{x}_{0}, \ldots \ldots, \infty . \) Here, \( \boldsymbol{x}_{0} \) is a
positive quantity. Take the electric potential at a point due to charge \( Q \) at a distance \( r \) from it to be \( \frac{Q}{4 \pi \varepsilon_{0} r} . \) Then the potential at origin due to the above system of charges is:
A . zero
B. infinity
c. \( \frac{q}{8 \pi \varepsilon_{0} x_{0} \text { In2 }} \)
D. \( \frac{q \operatorname{In} 2}{4 \pi \varepsilon_{0} x_{0}} \)
Subject: Maths
Simplify: \( \left(\boldsymbol{x}^{2}-\boldsymbol{x}+\mathbf{1}\right)\left(\mathbf{2} \boldsymbol{x}^{2}+\mathbf{2}\right) \)
A \( \cdot 2 x^{4}-2 x^{3}+4 x^{2}-2 x+2 \)
B . \( 2 x^{4}-2 x^{3}+4 x^{5}-2 x+2 \)
c. \( 2 x^{4}+2 x^{3}+4 x^{2}-2 x+2 \)
D. \( 2 x^{4}-2 x^{3}-2 x+2 \)
Subject: Chemistry
Which of the following set contains species having same angle around the
central atom?
A. \( S F_{4}, C H_{4}, N H_{3} \)
B. \( N F_{3}, B C l_{3}, N H_{3} \)
c. \( B F_{3}, N F_{3}, A l C l_{3} \)
D. \( B F_{3}, B C l_{3}, B B r_{3} \)
Subject: Physics
A projectile shot at an angle of \( 45^{\circ} \) above the horizontal strikes the wall of a
building \( 30 m \) away at a point \( 15 m \)
above the point of projection. Initial velocity of the projectile is
\( \left(\operatorname{take} g=9.8 m / s^{2}\right) \)
\( \mathbf{A} \cdot 14 m / s \)
B. \( 14 \sqrt{2} \mathrm{m} / \mathrm{s} \)
c. \( 14 \sqrt{3} \mathrm{m} / \mathrm{s} \)
D. \( 14 \sqrt{5} \mathrm{m} / \mathrm{s} \)
Subject: Physics
In a series circuit, \( \boldsymbol{R}=\mathbf{3 0 0 \Omega}, \boldsymbol{L}= \)
\( \mathbf{0 . 9 H}, \boldsymbol{C}=\mathbf{2 . 0 \mu} \boldsymbol{F} \) and \( \boldsymbol{\omega}=\mathbf{1 0 0 0 r a d} / \boldsymbol{s} \)
The impedance of the circuit is
A . \( 1300 \Omega \)
в. \( 900 \Omega \)
\( \mathbf{c} .500 \Omega \)
D. \( 400 \Omega \)
Subject: Chemistry
Arrange the following compounds in increasing order of dipole moment.
\( \boldsymbol{C H}_{3} \boldsymbol{C H}_{2} \boldsymbol{C H}_{3}, \boldsymbol{C H}_{3} \boldsymbol{C H}_{2} \boldsymbol{N} \boldsymbol{H}_{2}, \boldsymbol{C H}_{3} \boldsymbol{C I} \)
Subject: Chemistry
Q Type your question
Why may be members of the same family, it does mean that they will behave in similar ways.

The same things can be said about elements in a group ("family") on the periodic table. For example, fluorine and iodine are members of the halogen family, but their physical properties are different, as shown in the table below.
Melting Point \( \quad \) Boiling Point Element \( \quad\left(^{\circ} C\right) \)
\( \left(^{\circ} C\right) \)
Fluorine
\[
220
\]
\( \begin{array}{ll}\text { lodine } & +118 \\ & +184\end{array} \)
What of the following is the BEST explanation for these differences in melting and boiling point?
This question has multiple correct options
A. Fluorine has a higher value for electronegativity than iodine
B. The covalent bond in the fluorine molecule is stronger than the covalent bond in the iodine molecule
C. lodine molecules are larger and more polarizable than fluorine molecules
D. Fluorine is a nonpolar molecule, but iodine is a polar molecule
Subject: Maths
The ratio of \( j \) to \( k \) to \( l \) to \( m \) to \( p \) is 5 to 4 to 3 to 2 to \( 1 . \) If \( j=60, \) what is the
value of \( m ? \)
\( A \cdot 8 \)
B. 12
c. 24
D. 55
Subject: Physics
Determine \( V \) for \( r<R \)
A \( \cdot \frac{\rho}{6 \epsilon_{0}}\left(3 R^{2}\right) \)
В. \( \frac{\rho}{6 \epsilon_{0}}\left(r^{2}\right) \)
c. \( \frac{\rho}{6 \epsilon_{0}}\left(3 R^{2}-r^{2}\right. \)
D. \( \frac{\rho}{6 \epsilon_{0}}\left(3 R^{2}+r^{2}\right) \)
Subject: Maths
If two supplementary angles are in the ratio \( 4: 5, \) then the angles are
A. \( 80^{\circ}, 100^{\circ} \)
в. \( 85^{\circ}, 95^{\circ} \)
c. \( 40^{\circ}, 50^{\circ} \)
D. \( 60^{\circ}, 120^{\circ} \)
Subject: Physics
A solid cylinder \( C \) and a hollow pipe \( P \) of same diameter are in contact when they
are released from rest as shown in the
figure on a long incline plane. Cylinder \( C \) and pipe \( P \) roll without slipping. Determine the clear gap (in \( \mathrm{m} \) ) between them after \( 2 \sqrt{3} \) seconds.
Subject: Maths
\( |f| z_{1}|=2,| z_{2}|=3,| z_{3} \mid=4 \) and \( \mid z_{1}+ \)
\( z_{2}+z_{3} \mid=5, \) then \( \mid 4 z_{2} z_{3}+9 z_{3} z_{1}+ \)
\( \mathbf{1 6 z}_{1 \mathbf{z}_{2}} \mid= \)
A . 20
B. 24
\( c \cdot 48 \)
D. 120
Subject: Chemistry
Impure \( \boldsymbol{N} \boldsymbol{i}+\boldsymbol{4} \boldsymbol{C} \boldsymbol{O} \stackrel{\boldsymbol{6} \boldsymbol{0}-\boldsymbol{8} \boldsymbol{0}^{o} \boldsymbol{C}}{\longrightarrow} \)
\( N i(C O)_{4} \stackrel{180^{0} C}{\longrightarrow} N i+4 C O \)
The above process of purification of the metal is known as:
A. van arkel process
B. pyrometallurgy
c. mond process
D. zone refining
Subject: Chemistry
What is 'boiling point'? Derive a relation between \( \triangle H \) and \( \triangle U \)
for a chemical reaction Draw neat
labelled diagram of calomel electrode Resistance and conductivity of a cell
containing \( 0.001 M K C l \) solution at
\( 298 K \) are \( 1500 \Omega \) and \( 1.46 \times \)
\( 10^{-4} \)S.cm\( ^{-1} \) respectively. What is the
cell constant?
Subject: Physics
How is the distance related with time
for the motion under uniform
acceleration such as the motion of a
freely falling body starting from rest?
\( \mathbf{A} \cdot S \propto t^{2} \)
в. \( S \propto t \)
c. \( s \propto \frac{1}{t^{2}} \)
D. \( s \propto \frac{1}{t} \)
Subject: Maths
\( \int_{-1}^{1} \frac{e^{x}+1}{e^{x}-1} d x \) equals
\( \mathbf{A} \cdot \ln \left(e^{x}+1\right) \)
B \( \cdot \ln \left(e^{x}-1\right) \)
\( c \cdot 1 \)
D.
Subject: Physics
Two second wave travel out from a
common point have frequencies \( 30 \mathrm{Hz} \)
and \( 40 \mathrm{Hz} \) respectively where phase difference between the after 0.8 second.
\( ? \)
A . zero
B. \( \frac{\pi}{4} \)
c. \( \frac{5 \pi}{2} \)
D. \( 5 \pi \)
Subject: Chemistry
Consider the ester benorylate (an
analgesic) shown below.
The correct statement regarding the
rate of base-catalyzed hydrolysis of
benorylate is:
This question has multiple correct options
A . a nitro group substitution at \( C 4 \$ \) will increase the rate
B. a methoxy group substitution at \( C 4 \) will decrease the rate
c. a nitro group substitution at \( C 4 \) will decrease the rate
D. a methoxy group substitution at \( C 4 \) will increase the rate
Subject: Physics
A jet of water is projected at an angle
\( \theta=45^{\circ} \) with horizontal from point \( A \)
which is situated at a distance \( x=O A \)
\( =(a) 1 / 2 m,(b) 2 m \) from a vertical wall.
If the speed of projection is \( v_{0}= \)
\( \sqrt{10} m s^{-1}, \) find point \( P \) of striking of
the water jet with the vertical wall.
Subject: Physics
Two particle of equal mass \( m \) and
charge \( q \) are placed at a distance of
16cm. They do not experience any force.
The value of \( \frac{\boldsymbol{q}}{\boldsymbol{m}} \) is :
A. \( \sqrt{\frac{\pi \varepsilon_{0}}{G}} \)
в. \( L \)
c. \( \sqrt{\frac{G}{\pi \varepsilon_{0}}} \)
D. \( \sqrt{4 \pi \varepsilon_{0} G} \)
Subject: Physics
A wagon of mass 10 tons moving at a
speed of 12 kmph collides with another
wagon of mass 8 tons moving on the same track in the same direction at a
speed of \( 10 \mathrm{kmph} \). If the speed of the first wagon decreases to 8 kmph. Find the speed of the other after collision
A. \( 18 \mathrm{kmph} \)
B. 25 kmph
c. \( 5 \mathrm{kmph} \)
D. \( 15 \mathrm{kmph} \)
Subject: Physics
Match List-I with List- II and select the
answer using the codes given below the
lists:
\begin{tabular}{lll|l} 
List-I & \multicolumn{3}{l} { List-II } \\
A. & Microscope & 1. & To see objects on the surface by an observer in a trench \\
B. & Telescope & 2. & To see small objects \\
C. & Periscope & 3. & To see distant objects \\
D. & Camera & 4. & To take photographs of objects
\end{tabular}
\( A \)
\( \begin{array}{llll}2 & 1 & 4 & 3\end{array} \)
B. \( 1 \quad 2 \quad 3 \quad 4 \)
\( \begin{array}{llll}\mathbf{c} \cdot 2 & 3 & 4 & 1\end{array} \)
\( \begin{array}{ll}\text { D. } 2 & \text { (年) } 3\end{array} \)
Subject: Maths
Find the mean deviation about mean for
the data in \( \mathrm{Ex} 9 \) and 10 .
\( \begin{array}{lll}\text { Income per day } & \text { No of persons } \\ 0-100 & 4 \\ 100-200 & 8 \\ 200-300 & 9 \\ 300-400 & 10 \\ 400-500 & 7 \\ 500-600 & 5 \\ 600-700 & 4 \\ 700-800 & 3\end{array} \)
Subject: Maths
Find the modulus and amplitude of \( -2 i \)
A \( \cdot|z|=2 ; \operatorname{amp}(z)=-\frac{3 \pi}{2} \)
В \( \cdot|z|=2 i ; a m p(z)=\frac{\pi}{2} \)
c. \( |z|=2 ; a m p(z)=\frac{\pi}{2} \)
D \( \cdot|z|=2 ; \operatorname{amp}(z)=-\frac{\pi}{2} \)
Subject: Maths
Show that the points
\( \boldsymbol{A}(\mathbf{1}, \mathbf{1}, \mathbf{1}), \boldsymbol{B}(\mathbf{1}, \mathbf{2}, \mathbf{3}) \) and \( \boldsymbol{C}(\mathbf{2},-\mathbf{1}, \mathbf{1}) \) are
vertices of an isosceles triangle.
Subject: Maths
Of the 1000 inhabitants of a town, \( 60 \% \) are males of which \( 20 \% \) are literate. If
among all the inhabitants, \( 25 \% \) are
literate, then what percent of the females of the town are literate?
A . 22.5
в. 27.5
c. 32.5
D. 37.5
Subject: Maths
Find the equation of the plane which contains the line of intersection of the planes \( \vec{r} \cdot(\hat{i}+2 \widehat{j}+3 \widehat{k})-4= \)
\( \mathbf{0}, \overrightarrow{\boldsymbol{r}} \cdot(2 \hat{\boldsymbol{i}}+\hat{\boldsymbol{j}}-\widehat{\boldsymbol{k}})+\boldsymbol{5}=\boldsymbol{0} \) and which is
perpendicular to the plane \( \vec{r} \cdot(5 \hat{i}+3 \widehat{j}-6 \widehat{k})+8=0 \)
Subject: Maths
Find the sum of the following series to \( n \)
terms:
\( 1 \times 2+2 \times 3+3 \times 4+4 \times 5+\dots \)
A \( \cdot \frac{n}{4}(n-1)(n+2) \)
B \( \cdot \frac{n}{3}(n-1)(n-2) \)
c. \( \frac{n}{2}(n-1)(n+1) \)
D \( \cdot \frac{n}{3}(n+1)(n+2) \)
Subject: Physics
The armature of a dc motor has \( 20 \Omega \)
resistance. It draws a current of \( 1.5 \mathrm{A} \)
when run by a \( 220 \mathrm{V} \) dc supply. The value of the back emf induced in it is
\( A \cdot 150 V \)
B. 170 V
c. \( 180 v \)
D. \( 190 \mathrm{v} \)
Subject: Chemistry
Choose the correct combination among thefollowing
A) A mixture of weak acid and its salt of strong base acts as acidic buffer.
B) As number of moles of acid or base required to change the \( p^{H} \) of the buffer
by one unit increases, the quality of buffer increases.
C) Buffer action is maximum at \( \boldsymbol{p}^{\boldsymbol{H}}= \)
\( P^{K a} \) in case of acidic buffer.
A. All are correct
B. A only correct
c. B only correct
D. A only false
Subject: Maths
The area bounded by the curves \( x+ \)
\( \mathbf{2}|\boldsymbol{y}|=\mathbf{1} \) and \( \boldsymbol{x}=\mathbf{0} \) is?
A \( \cdot \frac{1}{4} \)
в. \( \frac{1}{2} \)
\( c .1 \)
D. 2
Subject: Physics
Find the electric field at a distance \( x \)
from the centre inside the shell.
\( \mathbf{A} \cdot E=0 \)
в. \( \quad E=\frac{Q}{4 \pi \epsilon_{0} a^{2}} \)
c. \( _{E}=\frac{Q}{4 \pi \epsilon_{0} x^{2}} \)
D. \( _{E}=\frac{Q}{4 \pi \epsilon_{0}(a-x)^{2}} \)
Subject: Maths
The points on the curve \( 12 y=x^{3} \) whose
ordinate and abscissa change at the
same rate, are
A \( \cdot(-2,-2 / 3),(2,2 / 3) \)
в. \( (-2,2 / 3),(2 / 3,2) \)
c. \( (-2,-2 / 3) \) only
D. \( (2 / 3,2) \) only
Subject: Chemistry
Assertion
Size of the hydrated ion is in order \( \boldsymbol{L} \boldsymbol{i}^{+}>\boldsymbol{N} \boldsymbol{a}^{+}>\boldsymbol{K}^{+}>\boldsymbol{R} \boldsymbol{b}^{+} \geq \boldsymbol{C} \boldsymbol{s}^{+} \)
which is just reverse of ionic size
Reason
Greater the charge or charge density smaller the ionic size, greater the hydration hence, greater the size of the hydrated 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 not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect
Subject: Maths
If \( \sum_{i=1}^{18}\left(x_{i}-8\right)=9 \) and
\( \sum_{i=1}^{18}\left(x_{i}-8\right)^{2}=45, \) then standard
deviation of \( x_{1}, x_{2}, \dots, x_{18} \) is
A \( \cdot \frac{4}{9} \)
B. \( \frac{9}{4} \)
\( c \cdot \frac{3}{2} \)
D. \( \frac{3}{4} \)
Subject: Chemistry
Arrange the following compounds in increasing order of their property as indicated:
(i) \( \boldsymbol{F}-\boldsymbol{C H}_{2} \boldsymbol{C O O H}, \boldsymbol{O}_{2} \boldsymbol{N}- \)
\( \boldsymbol{C H}_{2} \boldsymbol{C O O H}, \boldsymbol{C H}_{3} \boldsymbol{C O O H}, \boldsymbol{H C O O H}- \)
acid character
(ii) Acetone, Acetaldehyde, Benzaldehyde, Acetophenone reactivity towards addition of \( \boldsymbol{H} \boldsymbol{C} \boldsymbol{N} \)
Subject: Maths
If \( y=\tan ^{-1}\left(\frac{2^{x}}{1+2^{2 x+1}}\right), \) then \( \frac{d y}{d x} \) at
\( \boldsymbol{x}=\mathbf{0} \) is \( ? \)
\( A \cdot-\frac{1}{5} \)
B. 2
\( c \cdot \epsilon 2 \)
D. none of these
Subject: Maths
The value of
\( \sum_{n=1}^{9999} \frac{1}{(\sqrt{n}+\sqrt{n+1})(\sqrt[4]{n}+\sqrt[4]{n+1})} \)
is
\( \mathbf{A} \cdot \mathbf{9} \)
B. 99
\( c .999 \)
D. 9999
Subject: Biology
Three water samples namely river water, untreated sewage water and secondary effluent discharged from a sewage treatment plant were subjected to BOD test. The samples were labelled \( A, B \) and \( C ; \) but the laboratory attendant did not note which was which
The BOD values of the three samples \( A, B \) and \( C \) were recorded as \( \mathbf{2 0} \boldsymbol{m g} / \boldsymbol{L}, \mathbf{8 m g} / \boldsymbol{L} \) and \( \mathbf{4 0 0} \boldsymbol{m g} / \boldsymbol{L} \)
respectively. Which sample of the water is most polluted? Can you assign the correct label to each assuming the river water is relatively clean?
Subject: Maths
\( A(1,-1,-1), B(2,1,-2) \) and \( C(-5,2,-6) \) are the
position vectors of the vertices of triangle \( A B C \) The length of the bisector
of its internal angle at \( A \) is:
A. \( \frac{\sqrt{10}}{4} \)
B. \( \frac{3 \sqrt{10}}{4} \)
c. \( \sqrt{10} \)
D. none
Subject: Physics
A planet is moving in an elliptical path around the sun as shown in
figure.Speed of planet in position \( P \) and
\( \mathrm{Q} \) are \( \boldsymbol{v}_{1} \) and \( \boldsymbol{v}_{2} \) respectively with \( \boldsymbol{S} \boldsymbol{P}= \)
\( r_{1} \) and \( S Q=r_{2} \) then \( v_{1} / v_{2} \) is equal to
then
A \( \cdot \frac{r_{1}}{r_{2}} \)
в. \( \frac{r_{2}}{r_{1}} \)
c. consonant
D.
Subject: Chemistry
From the stability constant
hypothetical values \( ), \) given below,
predict which is the strongest ligand?
\( \mathbf{A} \)
\[
C u^{2+}+4 N H_{3} \rightleftharpoons\left[C u\left(N H_{3}\right)_{4}\right]^{2+}, K=4.5 \times 10^{11}
\]
\( B \)
\[
C u^{2+}+4 C N^{-} \rightleftharpoons\left[C u(C N)_{4}\right]^{2-}, K=2.0 \times 10^{27}
\]
\( \mathbf{c} \)
\[
C u^{2+}+2 e n \rightleftharpoons\left[C u(e n)_{2}\right]^{2+}, K=3.0 \times 10^{15}
\]
D.
\[
C u^{2+}+4 H_{2} O \rightleftharpoons\left[C u\left(H_{2} O\right)_{4}\right]^{2+}, K=9.5 \times 10^{8}
\]
Subject: Chemistry
Which is right combination?
(a) Hydrate isomerism\( \left[\boldsymbol{C o}\left(\boldsymbol{H}_{2} \boldsymbol{O}\right)_{3} \boldsymbol{C l}_{3}\right] \boldsymbol{3} \boldsymbol{H}_{2} \boldsymbol{O} \) and
\( \left[\boldsymbol{C o}\left(\boldsymbol{H}_{2} \boldsymbol{O}\right)_{6}\right] \boldsymbol{C l}_{3} \)
(b) lonisation isomerism-
\( \left[\boldsymbol{C o}\left(\boldsymbol{N} \boldsymbol{H}_{3}\right)_{5} \boldsymbol{B r}\right] \boldsymbol{S O}_{4} \) and
\( \left[\boldsymbol{C o}\left(\boldsymbol{N} \boldsymbol{H}_{3}\right)_{5} \boldsymbol{S} \boldsymbol{O}_{4}\right] \boldsymbol{B} \boldsymbol{r} \)
(c) Geometrical isomerism- \( M C l_{2} B r_{2} \)
\( A \cdot a \) and \( b \)
B. b and c
c. a and c
D. a , b and c
Subject: Chemistry
Thermal decomposition of a \( M n \) compound \( (X) \) at \( 513 K \) results in
compound \( Y, M n O_{2} \) and a gaseous
product. \( M n O_{2} \) reacts with \( N a C l \) and
concentrated \( H_{2} S O_{4} \) to give a pungent
\( \operatorname{gas} Z \)
\( X, Y \) and \( Z, \) respectively.
\( \mathbf{A} \cdot K_{2} M n O_{4}, K M n O_{4} \) and \( S O_{2} \)
B . \( K_{2} M n O_{4}, K M n O_{4} \) and \( C l_{2} \)
c. \( K_{3} M n O_{4}, K_{2} M n O_{4} \) and \( C l_{2} \)
D. \( K M n O_{4}, K_{2} M n O_{4} \) and \( C l_{2} \)
Subject: Physics
Assertion
If a positively charged particle is placed in front of a spherical uncharged conductor. The number of lines of forces
terminating on the sphere will be more than those emerging from it.
Reason
The surface charge density at a point on the sphere nearest to the point charge will be negative and maximum in magnitude compared to other points on the sphere
A. If both Assertion and Reason are correct and Reason is 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: Physics
A circuit consists of three batteries of
\( \operatorname{emf} \boldsymbol{E}_{1}=\mathbf{1} \boldsymbol{V}, \boldsymbol{E}_{2}=\mathbf{2} \boldsymbol{V} \) and \( \boldsymbol{E}_{3}=\mathbf{3} \boldsymbol{V} \)
and internal resistances \( 1 \Omega, 2 \Omega \) and
1 \( \Omega \) respectively which are connected in parallel as shown in the figure. The
potential difference between points \( \boldsymbol{P} \)
and \( Q \) is:
A \( .1 .0 V \)
B. \( 2.0 V \)
c. \( 2.2 V \)
D. 3.0 \( V \)
Subject: Maths
The angle between vectors \( (\bar{M} \times \bar{N}) \) and \( (\overline{\boldsymbol{N}} \times \overline{\boldsymbol{M}}) \) is then
\( \mathbf{A} \cdot 0^{\circ} \)
B . \( 60^{\circ} \)
\( c .90^{\circ} \)
D. \( 180^{\circ} \)
Subject: Physics
Section-A Section-B
a) Incompressible liquid
e) Density constant
b) Turbulent flow
f) Stream lines
c) Tube of flow
g) Constant
d) Fluid flux rate in laminar
h) Reynold's no \( > \) flow 2000
\( A \cdot a-f ; b-e ; c-g ; d-h \)
B. \( a-e ; b-h ; c-f ; d-g \)
\( \mathbf{c} \cdot \mathrm{a}-\mathrm{g} ; \mathrm{b}-\mathrm{f} ; \mathrm{c}-\mathrm{e} ; \mathrm{d}-\mathrm{h} \)
D. \( a-h ; b-g ; c-e ; d-f \)
Subject: Maths
The vector \( \overrightarrow{O A} \) where \( O \) is origin is \( \operatorname{given} \) by \( \overrightarrow{O A}=2 \hat{i}+2 \hat{j} . \) Now it is
rotated by \( 45^{\circ} \) anticlockwise about \( O \)
What will be the new vector?
A \( \cdot 2 \sqrt{2} \hat{j} \)
is \( \sqrt{2} \) is \( \sqrt{2} \)
в. 2 ई
\( c \cdot 2 \hat{\imath} \)
D. \( 2 \sqrt{2} \hat{\imath} \)
Subject: Maths
\( A B C \) and \( A B D \) are two triangles on
the same base \( A B . \) If line-segment
\( C D \) is bisected by \( A B \) at \( O, \) show \( \operatorname{that} \boldsymbol{a r}(\boldsymbol{A B C})=\boldsymbol{a r}(\boldsymbol{A B D}) \)
Subject: Maths
The value of \( 108^{\circ} \) in circular measure
is
A \( \cdot 5 \pi^{c} / 3 \)
в. \( 3 \pi^{c} / 5 \)
c. \( \pi^{c} / 5 \)
D. \( 6 \pi^{c} / 7 \)
Subject: Chemistry
Correct order of reducing agent, in \( V^{2+} \)
or \( C o^{2+} \) is:
A \( \cdot V^{2+}=C o^{2+} \)
B. \( V^{2+}<C o^{2+} \)
\( \mathbf{c} \cdot V^{2+}>C o^{2} \)
D. none of these
Subject: Chemistry
Given \( A \leftrightharpoons B . K_{f} \) is the equilibrium
constant and \( K_{b} \) is the equilibrium constant for backward reaction. Find
the equilibrium constant \( \boldsymbol{K} \)
A. \( K_{f} / K_{b} \)
в. \( K_{b} / K_{f} \)
\( \mathbf{c} \cdot K_{b} \times K_{f} \)
D. \( K_{b}+K_{f} \)
Subject: Physics
The number of beats produced per second by two tuning fork when sounded together is \( 4 . \) One of them has a frequency of \( 250 \mathrm{Hz} \) and if waxed, number of beats become 6. The
frequency of the other tuning fork is
A . 254 \( \mathrm{H} \)
B. 252 нz
c. 248 н на
D. 246 нz
Subject: Physics
A rubber rope of length \( 8 m \) is hung
from the ceiling of a room. What is the increase in length of rope due to its own weight? (Given : Young's modulus of elasticity of rubber \( =\mathbf{5} \times \mathbf{1 0 6} N / \boldsymbol{m} \)
and density of rubber \( =1.5 \times \) \( \left.\mathbf{1 0}^{3} \mathbf{k g} / \boldsymbol{m}^{3} . \text { Take } \boldsymbol{g}=\mathbf{1 0} \boldsymbol{m} / \boldsymbol{s}^{2}\right) \)
A \( .1 .5 \mathrm{mm} \)
B. \( 6 m m \)
c. \( 24 m m \)
D. \( 96 m m \)
Subject: Chemistry
Balance the following chemical
equation \( \boldsymbol{H}_{2} \boldsymbol{O}_{2}+\boldsymbol{O}_{3} \rightarrow \boldsymbol{H}_{2} \boldsymbol{O}+\boldsymbol{O}_{2} \)
Indicating the changes in oxidation numbers of oxygen, find the equivalent
weight of \( \boldsymbol{H}_{2} \boldsymbol{O}_{2} \) for this reaction.
Subject: Physics
In the basic \( C s C l \) crystal structure,
\( C s^{+} \) and \( C l^{-} \) ions are arranged in a bcc
configuration as shown in the figure. The net electrostatic force exerted by
the eight \( C s^{+} \) ions on the \( C l^{-} \) ion is :
\( ^{A} \cdot \frac{1}{4 \pi \varepsilon_{0}} \frac{4 e^{2}}{3 a^{2}} \)
B. \( \frac{1}{4 \pi \varepsilon_{0}} \frac{16 e^{2}}{3 a^{2}} \)
c. \( 1 \frac{32 e^{2}}{3 a^{2}} \)
\( D \)
Subject: Chemistry
Ammonia forms the complexion
\( \left[\boldsymbol{C u}\left(\boldsymbol{N} \boldsymbol{H}_{3}\right)_{4}\right]^{2+} \) with copper ions in the
alkaline solution because:
A. in acidic solutions, protons coordinate with ammonia molecules
B. in acidic solutions, hydration protects copper ions.
c. in alkaline solutions, insoluble \( C u(O H)_{2} \) is precipitated which is soluble in excess of any alkali
D. copper hydroxide is an atmospheric substance.
Subject: Maths
The vector \( (\cos \alpha \cos \beta) \vec{i}+ \)
\( (\cos \alpha \sin \beta) \vec{j}+\sin \alpha \vec{k} \) is
A. Null vector
B. unit vector
C . parallel to \( (\vec{i}+\vec{j}+\vec{k}) \)
D. a vector parallel to \( (2 \vec{i}+\vec{j}-\vec{k}) \)
Subject: Chemistry
Assertion
\( \boldsymbol{H}_{2} \boldsymbol{O} \) is the only hydride of group- 16 which is liquid at ordinary temperature.
Reason

In ice, each oxygen atom is surrounded by two covalent bonds and two hydrogen bonding.
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 ball of mass \( 0.1 \mathrm{kg} \) strikes a wall normally with a speed of \( 30 m s^{-1} \) and
rebounds with a speed of \( 20 m s^{-1} . \) The impulse of the force exerted by the wall on the ball is
A. \( 1 N s \)
в. 5 Ns
\( c .2 N s \)
D. 3 Ns