AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Chemistry
The value of \( ^{\prime} n^{\prime} \) in the reaction is:
\( \boldsymbol{C r}_{2} \boldsymbol{O}_{\mathbf{7}}^{2-}+\mathbf{1 4} \boldsymbol{H}^{+}++\boldsymbol{n} \boldsymbol{F} \boldsymbol{e}^{2+} \rightarrow \)
\( 2 C r^{3+}+n F e^{3+}+7 H_{2} O \)
\( A \cdot 2 \)
B. 3
\( c \cdot 6 \)
D.
Subject: Physics
A long solenoid has 200 turns per cm
and carries a current \( I \). The magnetic
field at its centre is \( 6.28 \times \)
\( 10^{-2} W b / m^{2} . \) Another long solenoid has
100 turns per cm and it carries a
current \( I / 3 . \) The value of the magnetic
field at its centre is
A \( \cdot 1.05 \times 10^{-2} \mathrm{Wb} / \mathrm{m}^{2} \)
B . \( 1.05 \times 10^{-5} \mathrm{Wb} / \mathrm{m}^{2} \)
c. \( 1.05 \times 10^{-3} \mathrm{Wb} / \mathrm{m}^{2} \)
D. \( 1.05 \times 10^{-4} \mathrm{Wb} / \mathrm{m}^{2} \)
Subject: Maths
Let \( \boldsymbol{f}(\boldsymbol{x})= \)
\( \left\{\begin{array}{ll}a \sin ^{2 n} x & \text { for } x \geq 0 \text { and } \\ b \cos ^{2 m} x-1 & \text { for } x<0 \text { and }\end{array}\right. \)
\( n \rightarrow \infty \)
\( m \rightarrow \infty \)
then -
A \( \cdot f\left(0^{-}\right) \neq f\left(0^{+}\right. \)
в. \( f\left(0^{+}\right) \neq f(0) \)
c. \( f\left(0^{-}\right)=f(0) \)
D. fis continuous at \( x=0 \)
Subject: Physics
A semiconductor has an electron
concentration of \( 8 \times 10^{13} \) per \( c m^{3} \) and \( a \)
hole concentration of \( 5 \times 10^{12} \) per \( c m^{3} \)
The electron mobility is \( 25000 c m^{2} V^{-1} s^{-1} \) and the hole mobility
is \( 100 \mathrm{cm}^{2} V^{-1} s^{-1} . \) Then
A. The semiconductor is \( n \) -type
B. The conductivity is 320 \( \mathrm{m} \) mho \( \mathrm{cm}^{-1} \)
c. Both (a) and (b)
D. None of the above
Subject: Physics
In the circuit shown in fig. the heat
produced in \( 5 \Omega \) resistor due to a current
flowing in it is 10 cal /s. The heat
produced in \( 4 \Omega \) resistor is -
A. 4 cal 1 s
B. 1 cal /s
c. 2 cal / s
D. 3 cal /s
Subject: Physics
Two homogeneous spheres \( A \) and \( B \) masses \( \mathrm{m} \) and \( 2 \mathrm{m} \) having radii \( 2 \mathrm{a} \) and a respectively are placed in touch. The distance of centre of mass from first
sphere is:
\( A \)
B. 2a
c. 3a
D. None of these
Subject: Maths
In the diagram 0 is the centre of a
circle. \( A E+E B=C E+E D O P \perp A B \) and \( 0 Q \)
\( \perp \) CD then true relation between OP and
OQ is
A. ор > \( 0 Q \)
B. op < \( 0 Q \)
\( c \cdot o p=\frac{1}{2} o Q \)
D. OP = OO
Subject: Physics
Consider a tank made of
glass(refractive index 1.5 ) with a thick bottom. It is filled with a liquid of
refractive index \( \mu . \) A student finds that,
irrespective of what the incident angle (see figure) is for a beam of light entering the liquid, the light reflected from the liquid glass interface is never completely polarized. For this to happen the minimum value of \( \mu \) is :
A \( \cdot \frac{3}{\sqrt{5}} \)
в. \( \frac{5}{\sqrt{3}} \)
c. \( \sqrt{\frac{5}{3}} \)
\( D \)
Subject: Maths
Let \( \boldsymbol{\alpha}=\boldsymbol{\pi} / \mathbf{5} \) and
\[
\begin{array}{c}
\boldsymbol{A}=\left[\begin{array}{cc}
\cos \boldsymbol{\alpha} & \sin \boldsymbol{\alpha} \\
-\sin \boldsymbol{\alpha} & \cos \boldsymbol{\alpha}
\end{array}\right] \text { and } \boldsymbol{B}=\boldsymbol{A}+ \\
\boldsymbol{A}^{2}+\boldsymbol{A}^{3}+\boldsymbol{A}^{4}, \text { then }
\end{array}
\]
This question has multiple correct options
A. singular
B. non-singular
c. skew-symmetric
D. \( |B|=1 \)
Subject: Maths
prove that
\[
\begin{array}{l}
2 \tan ^{-1}\left[\tan \frac{\alpha}{2} \tan \left(\frac{\pi}{4}-\frac{\beta}{2}\right)\right]= \\
\tan ^{-1} \frac{\sin \alpha \cos \beta}{\cos \alpha+\sin \beta}
\end{array}
\]
Subject: Maths
The middle term of \( \left(\boldsymbol{x}-\frac{1}{\boldsymbol{x}}\right)^{2 n+1} \) is
\( \mathbf{A} \cdot^{2 n+1} C_{n} \cdot x \)
B. \( 2 n+1 C_{n} \)
C \( \cdot(-1)^{n} \cdot 2^{2+1} C_{n} \)
D \( \cdot(-1)^{n} \cdot^{2 n+1} C_{n} \cdot x \)
Subject: Maths
If
\( A, B \) and \( C \) are three events such that \( P(B)=\frac{3}{4}, P\left(A \cap B \cap C^{\prime}\right)=\frac{1}{3} \) and
\( P\left(A^{\prime} \cap B \cap C^{\prime}\right)=\frac{1}{3}, \operatorname{then} P(B \cap C) \) is
equal to
A \( \cdot \frac{1}{12} \)
B.
c. \( \frac{1}{15} \)
D.
Subject: Chemistry
\( N a_{2} C O_{3} \) is widely used in softening of hard water. If 1 L of hard water required
\( 0.0106 g \) of \( N a_{2} C O_{3}, \) The hardness in
ppm (parts per million i.e., \( 10^{6} \) ml) of
\( \boldsymbol{C a} \boldsymbol{C O}_{3} \) is:
A. 0.01 ppm \( C a C O_{3} \)
B. 0.10 ppm \( C a C O_{3} \)
c. 1.00 ppm \( C a C O_{3} \)
D. \( 10.00 \mathrm{ppm} \mathrm{CaCO}_{3} \)
Subject: Chemistry
4
The IUPAC name of \( C H_{3}-C H- \)
\( \boldsymbol{C H}_{3} \)
\( C H_{2}-C H-C H O: \)
A. 4 -hydroxy - 2 - methyl pentanal
B. 2-hydroxy -4- methyl pentanal
C. 4 -hydroxy-2-methyl pentanol
D. 2-hydroxy-4- methyl pentanol
Subject: Chemistry
heated on the flame directly. It crumbled to give white powder of calcium oxide. After cooling, when water is added to it a hissing sound is heard and water started boiling. If it is allowed to stay over night, a clear solution (top layer) is taken and for this experiment below as lime water.

When carbon dioxide is bubbled into
testtube a clear solution of lime water, turbidity appears first and later a white precipitate of calcium carbonate is formed. Carbon dioxide is continued to
passed into the same solution and the solution again became clear because of
formation of calcium bicarbonate. On
heating the contents of the tube, white precipitate of calcium carbonate
reappears. Heating of calcium bicarbonate gave the following:
A. Calcium oxide and carbon dioxide
B. Calcium carbonate, water and \( C O_{2} \)
c. calcium bicarbonate and \( C O_{2} \)
D. Calcium hydroxide and carbon dioxide
Subject: Chemistry
(a) Describe how the following properties vary on descending group IA and IIA (alkali and alkaline earth
metals) and state how these properties differ between the two groups?
(i) \( (I E)_{1} a n d(I E)_{2} \)
(ii) cationic radii
(iii) rates of reaction with cold water
(b) For the same s-block elements,
discuss:
(i) the action of heat on their nitrates
(ii) the crystal structures of their chlorides, XY type only.
Subject: Maths
If \( \boldsymbol{A}=\{\mathbf{2}, \boldsymbol{4}\} \) and \( \boldsymbol{B}=\{\mathbf{3}, \mathbf{4}, \mathbf{5}\} \) then
\( (\boldsymbol{A} \cap \boldsymbol{B}) \times(\boldsymbol{A} \cup \boldsymbol{B}) \) is
A \( \cdot\{(2,2),(3,4),(4,2),(5,4)\} \)
в. \{(2,3),(4,3),(4,5)\}
\( \mathbf{c} \cdot\{(2,4),(3,4),(4,4),(4,5)\} \)
D. \{(4,2),(4,3),(4,4),(4,5)\}
Subject: Maths
A student moves \( \sqrt{2 x} k m \) east from his
residence and then moves \( x \) km north.
He then goes \( x \) km north east and finally he takes a turn of \( 90^{\circ} \) towards right and
moves a distance \( x \mathrm{km} \) and reaches his
school. What is the shortest distance of
the school from his residence?
A. \( (2 \sqrt{2}+1) x k m \)
B. \( 3 x \) km
\( \mathbf{c} \cdot 2 \sqrt{2} x k m \)
D. \( 3 \sqrt{2} x \) km
Subject: Maths
Let \( \boldsymbol{f}(\boldsymbol{x})=\boldsymbol{a} \boldsymbol{x}^{2}-\boldsymbol{b}|\boldsymbol{x}|, \) where \( \boldsymbol{a} \) and \( \boldsymbol{b} \) are
constants. Then at \( x=0, f(x) \) has
This question has multiple correct options
A. A maxima whenever \( a>0, b>0 \)
B. A maxima whenever \( a>0, b<0 \)
c. A minima whenever \( a>0, b<0 \)
D. Neither minima nor a maxima whenever \( a>0, b<0 \)
Subject: Maths
Find the value of \( k \) so that the function \( f \)
is continuous at the indicated point. \( \boldsymbol{f}(\boldsymbol{x})=\left\{\begin{array}{cc}\boldsymbol{k} \boldsymbol{x}^{2} & , \boldsymbol{x} \leq \mathbf{2} \\ \boldsymbol{3} & , \boldsymbol{x}>\mathbf{2}\end{array}\right\} \) at \( \boldsymbol{x}=\mathbf{2} \)
Subject: Physics
Two magnetic poles one of which is three
times as strong as the other exert on each other, a force equal to \( 3 \times 10^{-3} \) when
separated by a distance of \( 10 \mathrm{cm} \). The
strength of the each pole is
\( \mathbf{A} .5 \mathrm{Am}, 15 \mathrm{Am} \)
В. 30 Ат, 10 Ат
\( \mathbf{c} .20 \mathrm{Am}, 60 \mathrm{Am} \)
D. \( 50 A m, 150 A m \)
Subject: Chemistry
\( N F_{3} \) is stable. But, \( N C l_{3} \) is explosive.
Identify the reason:
A. \( N C l_{3} \) undergoes hydrolysis whereas \( N F_{3} \) does not.
B . \( N C l_{3} \) decomposes on heating and \( N F_{3} \) does not
c. \( N C l_{3} \) is a gaseous substance and \( N F_{3} \) is liquid
D. \( N C l_{3} \) undergoes sublimation while \( N F_{3} \) does not
Subject: Maths
Weight \( 50-\quad 56 \)
(in \( \mathrm{kg}) \)
Number
of 15
students
Garima collected the data regarding
weights of students of her class and prepared the above table:
A student is to be selected randomly from her class for some competition.
The probability of selection of the
student is the highest whose weight (in
kg) is in the interval
A. \( 44-49 \)
B. \( 56-61 \)
c. \( 50-55 \)
D. \( 62-67 \)
Subject: Maths
Let \( \boldsymbol{f}:(\boldsymbol{0}, \infty) \rightarrow \boldsymbol{R} \) and \( \boldsymbol{g}: \boldsymbol{R} \rightarrow \boldsymbol{R} \) be
defined by \( f(x)=\sqrt{x} \) and \( g(x)=x \) Find \( \boldsymbol{f}+\boldsymbol{g}, \boldsymbol{f}-\boldsymbol{g}, \boldsymbol{f} \boldsymbol{g} \) and \( \frac{\boldsymbol{f}}{\boldsymbol{g}} \)
Subject: Physics
Assertion
A rocket moves forward by pushing the
surrounding air backwards.
Reason
It derives the necessary thrust to move forward according to Newton's third law of motion.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Assertion is incorrect but Reason is correct
Subject: Chemistry
The solubility of a sparingly soluble salt
\( A . B_{y} \) in water at \( 25^{\circ} \mathrm{C} 1.4 \times 10^{4} \) M. The
solubility product is \( 1.1 \times 10^{11} . \) The
possibilities are:
A. \( x=1, y=2 \)
в. \( x=2, y=1 \)
c. \( x=1, y=3 \)
D. \( x=3, y=1 \)
Subject: Chemistry
Which of the following statement(s)
is/are wrong?
A. The malting point of trans-but-2-ene is greater than that of the cis-isomer due to symmetrical packing in the crystal lattice of the trans-form.
B. The boiling point of cis-but-2-ene is greater than that of the trans-isomer due to steric strain in the cisisomer because of van der Waals repulsion force of large group on the same side of the double bond and the cis-isomer becomes less stable because of the increasing repulsive force
C. The boiling point of the cis-isomer is greater than that of the trans-isomer due to the relatively high polarity of the cis-isomer compared to its trans-isomer
D. Refer Image
The boiling point of
is greter than that
Subject: Chemistry
Make the correct pairs from below
mentioned \( X \) and \( Y \)
\[
\boldsymbol{X}
\]
a) Dehydrating agent
1) Sulphur dioxide gas
b) In preparation of fire
2) Concentrated crackers \( \quad \) sulphur acid
c) Weak bleaching agent
3 ) Dihydrogen gas
d) Lightest gas
4) Sulphur
\( \mathbf{A} \cdot(a-2),(b-4),(c-1),(d-3) \)
B \( \cdot(a-3),(b-2),(c-4),(d-1) \)
C \( .(a-4),(b-3),(c-1),(d-2) \)
D. \( (a-3),(b-1),(c-2),(d-4) \)
Subject: Maths
Let \( P(2,-4) \) and \( Q(3,1) \) be two given
points. Let \( R(x, y) \) be a point such that
\( (x-2)(x-3)+(y-1)(y+4)=0 \)
area of \( \triangle P Q R \) is \( \frac{13}{2}, \) then the number
of possible positions of \( \boldsymbol{R} \) are
A .2
B. 3
\( c \cdot 4 \)
D. None of these
Subject: Physics
A hole is made at the bottom of a tank
filled with water (density \( \left.=10^{3} k g / m^{3}\right) \)
If the total pressure at the bottom of the \( \operatorname{tank} \) is \( 3 \operatorname{atm}\left(1 a t m=10^{5} N / m^{2}\right) \)
then the velocity of efflux is
\( \mathbf{A} \cdot \sqrt{400} \mathrm{m} / \mathrm{s} \)
B. \( \sqrt{200} \mathrm{m} / \mathrm{s} \)
c. \( \sqrt{600} \mathrm{m} / \mathrm{s} \)
D. \( \sqrt{500} \mathrm{m} / \mathrm{s} \)
Subject: Chemistry
There are two old wells in the area where
Punita lives. Her grandmother says that about fifteen-twenty years ago there was water in these wells. The wells
could have dried up because:
Water is being pumped up from under the ground with the help of electric
motors.
The lakes in which rainwater used to
collect are no longer there.
The soil around trees and parks is now covered with cement.
Is there some other reason for this?
Explain
Subject: Maths
O is any point inside a triangle ABC. The bisector of \( \angle A O B, \angle B O C \) and \( \angle C O A \)
meet the sides, \( A B, B C \) and \( C A \) in point D, E and F respectively, therefore,
\( A D \times B E=D B \times F A \)
A. True
B. False
Subject: Maths
State which of the following are not the
probability distributions of a random
variable. Give reasons for your answer.
\( (i) \)
\begin{tabular}{|c|l|l|l|}
\hline \( \mathrm{X} \) & 0 & 1 & 2 \\
\hline \( \mathrm{P}(\mathrm{X}) \) & 0.4 & 0.4 & 0.2 \\
\hline
\end{tabular}
(ii) \begin{tabular}{|c|l|l|l|c|l|}
\hline \( \mathrm{X} \) & 0 & 1 & 2 & 3 & 4 \\
\hline \( \mathrm{P}(\mathrm{X}) \) & 0.1 & 0.5 & 0.2 & -0.1 & 0.3 \\
\hline
\end{tabular}
(iii) \begin{tabular}{|c|r|l|l|}
\hline \( \mathrm{Y} \) & -1 & 0 & 1 \\
\hline \( \mathrm{P}(\mathrm{Y}) \) & 0.6 & 0.1 & 0.2 \\
\hline
\end{tabular}
(iv) \begin{tabular}{|c|l|l|l|l|l|}
\hline \( \mathrm{Z} \) & 3 & 2 & 1 & 0 & -1 \\
\hline \( \mathrm{P}(\mathrm{Z}) \) & 0.3 & 0.2 & 0.4 & 0.1 & 0.05 \\
\hline
\end{tabular}
Subject: Maths
If \( \vec{a}=a_{1} \hat{i}+a_{2} \hat{j}+a_{3} \hat{k}, \vec{b}=b_{1} \hat{i}+b_{2} \hat{j}+ \)
\( b_{3} \hat{k}, \vec{c}=c_{1} \hat{i}+c_{2} \hat{j}+c_{3} \hat{k} \) and \( \vec{c} \) is a unit
vector orthogonal to the plane of \( \vec{a}, \vec{b} \) and the angle between \( \vec{a} \) and \( \vec{b} \) is \( \frac{\pi}{3} \)
then \( |\vec{c}|^{2}= \)
\( \mathbf{A} \cdot \mathbf{0} \)
B.
c. \( \frac{3}{4}\left(a_{1}^{2}+a_{2}^{2}+a_{3}^{2}\right)\left(b_{1}^{2}+b_{2}^{2}+b_{3}^{2}\right) \)
D \( \cdot \frac{3}{4}\left(C_{1}^{2} a_{1}^{2}+b_{1}^{2}+\mathrm{X} a_{2}^{2}+b_{2}^{2}+c_{2}^{2}\right) \)
Subject: Chemistry
The hydrolysis of sodium carbonate
involves the reaction between:
A. sodium ion and water
B. \( N a^{+} \) and \( O H^{-} \)
\( \mathrm{c} \cdot \mathrm{CO}_{3}^{2-} \) and water
D. \( C O_{3}^{2-} \) and \( H^{+} \)
Subject: Physics
The focal length of the objective and eye piece of a compound microscope are \( 1 \mathrm{cm} \) and \( 5 \mathrm{cm} \) respectively. An object
is placed at a distance of \( 1.1 \mathrm{cm} \) from objective. If final image is formed by at least distance vision, the magnifying
power is:
\( \mathbf{A} \cdot 60 \)
B. 50
c. 40
D. None of these
Subject: Physics
Assertion
In a varying magnetic field the induced currents exhibit diamagnetic-like repulsion effects. A conductive object
will experience a repulsion force.
Reason
Eddy currents produced in conductor will produce magnetic field to oppose the varying magnetic field according to faradays law
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
\( \frac{\mathbf{2 2}}{\boldsymbol{x}+\boldsymbol{y}}+\frac{\mathbf{1 5}}{\boldsymbol{x}-\boldsymbol{y}}=\mathbf{5} \)
\( \frac{\mathbf{5 5}}{\boldsymbol{x}+\boldsymbol{y}}+\frac{\mathbf{4 5}}{\boldsymbol{x}-\boldsymbol{y}}=\mathbf{1 4} \)
A. \( x=-8, y=3 \)
в. \( x=-3, y=8 \)
c. \( x=8, y=3 \)
D. \( x=8, y=-3 \)
Subject: Maths
If \( f(x)=\frac{\tan x}{\tan x} \) then
A \( \cdot \lim _{x \rightarrow 0} f(x) \) does not exists
B \( \cdot \lim _{x \rightarrow 0} f(x) \) exists
c. \( f(x) \) has fundamental period \( \pi \)
D. all of these
Subject: Maths
The third term from the end in the
expansion of \( \left(\frac{3 x}{5}-\frac{5}{2 x}\right)^{8} \) is
A \( \cdot \frac{35451}{15 x^{4}} \)
в. \( \frac{45455}{16 x^{4}} \)
c. \( \frac{39372}{15 x^{4}} \)
D. \( \frac{39375}{16 x^{4}} \)
Subject: Physics
The earth is considered as a short
magnet with its centre coinciding with the geometric centre of earth. The angle of dip \( \phi \) related to the magnetic latitude
\( \alpha \lambda \) as
\( ^{\mathbf{A}} \cdot \tan \phi=\frac{1}{2 \tan \alpha} \)
B. \( \tan \lambda=\tan \phi \)
c. \( \tan \lambda=2 \tan \phi \)
D. \( \tan \phi=2 \tan \lambda \)
Subject: Chemistry
For a reversible reaction, \( A \stackrel{\boldsymbol{K}_{1}}{\dot{\boldsymbol{K}}_{2}} \boldsymbol{B}, \) Ist
order in both the directions, the rate of
reaction is given by:
\( \mathbf{A} \cdot K_{1}[A] \)
\( \mathbf{B} \cdot-K_{2}[B] \)
\( \mathbf{c} \cdot K_{1}[A]+K_{2}[B] \)
\( \mathbf{D} \cdot K_{1}[A]-K_{2}[B] \)
Subject: Maths
If a unit vector \( \vec{a} \) makes an angle \( \frac{\pi}{3} \) with \( \hat{i}, \frac{\pi}{4} \) with \( \hat{j} \) and an accute angle \( \theta \) with \( \hat{k}, \) then find \( \theta \) and hence, the
components of \( \overrightarrow{\boldsymbol{a}} \).
A \( \cdot \frac{\pi}{3} ; \vec{a}=\frac{1}{2} \hat{i}-\frac{1}{\sqrt{2}} \hat{j}+\frac{1}{2} \hat{k} \)
B \( \cdot \frac{\pi}{3} ; \vec{a}=\frac{-1}{2} \hat{i}+\frac{1}{\sqrt{2}} \hat{j}+\frac{1}{2} \hat{k} \)
C \( \cdot \frac{\pi}{3} ; \vec{a}=\frac{1}{2} \hat{i}+\frac{1}{\sqrt{2}} \hat{j}+\frac{1}{2} \hat{k} \)
D \( \cdot \frac{\pi}{3} ; \vec{a}=\frac{1}{2} \hat{i}+\frac{1}{\sqrt{2}} \hat{j}-\frac{1}{2} \hat{k} \)
Subject: Chemistry
The osmotic pressure of equimolar
solutions of
a) \( A l_{2}\left(S O_{4}\right)_{3}, \) b) \( K C l \) and
c) sugar will be:
\( \mathbf{A} \cdot b>a>c \)
В . \( a>b>c \)
\( \mathbf{c} . c>b>a \)
\( \mathbf{D} \cdot b>c>a \)
Subject: Maths
Suppose \( A=\frac{d y}{d x} \) when \( x^{2}+y^{2}=4 \) at \( (\sqrt{2}, \sqrt{2}), B=\frac{d y}{d x} \) when \( \sin y+\sin x= \)
\( \sin x-\sin y \) at \( (\pi, \pi) \) and \( C=\frac{d y}{d x} \) when
\( 2 e^{x y}+e^{x} e^{y}-e^{x}-e^{y}=e^{x y+1} \operatorname{at}(1,1) \)
then \( (A+B+C) \) has the value equal
to
\( A \)
в.
\( c \cdot-3 \)
D.
Subject: Physics
A player kicks a ball at a speed of 20 \( m s^{-1} \) so that its horizontal range is
maximum. Another player 24 m away in the direction of kick starts running in the same direction at the same instant
of hit. If he has to catch the ball just before it reaches the ground, he should run with a velocity equal to (Take \( g=10 \) \( m s-2) \)
A \( \cdot 2 \sqrt{2} \mathrm{ms}^{-1} \)
B. \( 4 \sqrt{2} \mathrm{ms}^{-1} \)
\( c \cdot 6 \sqrt{2} m s^{-1} \)
D. \( 10 \sqrt{2} \mathrm{ms}^{-1} \)
Subject: Maths
Let \( ^{*} \) be a binary operation on the set \( \boldsymbol{Q} \)
of rational numbers as follows:
\( \boldsymbol{a} * \boldsymbol{b}=\frac{\boldsymbol{a} \boldsymbol{b}}{\boldsymbol{4}} \)
Find which of the binary operations are commutative and which are
associative.
Subject: Physics
Current is flowing through a conductor
and creates a magnetic field. Assume
that this is the only source of the
magnetic field. Reversing a current in a straight conductor with no change to
the magnitude(ampere value) will
cause a
A. Reduction in the magnetic field
B. Disappearance of the magnetic field
C. Reversal of the direction of the magnetic field
D. Reversal and reduction of the magnetic field
Subject: Maths
Find the coordinates of the point \( \boldsymbol{P} \) where the line through \( \boldsymbol{A}(\mathbf{3},-\mathbf{4},-\mathbf{5}) \)
and \( B(2,-3,1) \) crosses the plane
passing through three points \( \boldsymbol{L}(\mathbf{2}, \mathbf{2}, \mathbf{1}), \boldsymbol{M}(\mathbf{3}, \mathbf{0}, \mathbf{1}) \) and \( \boldsymbol{N}(\mathbf{4},-\mathbf{1}, \mathbf{0}) \)
Also, find the ratio in which \( P \) divides
the line segment \( \boldsymbol{A B} \)
Subject: Chemistry
Assertion
\( C l_{2} \) gas bleaches the articles
permanently.
Reason
\( C l_{2} \) is a strong reducing agent.
Read the above assertion and reason
and choose the correct option regarding
¡t.
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
In a class of 100 students, 60 students
drink tea, 50 students drink coffee and
30 students drink both. A student from
class is selected at random, find the
probability that student takes at least one of the two drinks (i.e. tea or coffee or both)
\( A \cdot 1 \)
5
B. \( \frac{2}{5} \)
\( c \cdot \frac{3}{5} \)
D. \( \frac{4}{5} \)
Subject: Maths
In the figure given, \( O \) is the centre of the
circle. \( A B \) and \( C D \) are two chords of the
circle. \( O M \) is perpendicular to \( A B \) and \( O N \) is perpendicular to \( C D . A B= \)
\( \mathbf{2 4} c \boldsymbol{m}, \boldsymbol{O} \boldsymbol{M}=\mathbf{5} \boldsymbol{c m}, \boldsymbol{O} \boldsymbol{N}=\mathbf{1 2} c \boldsymbol{m} . \) Finc
the
Length of chord \( C D \)
Subject: Physics
If one mole of an ideal gas goes through the process \( A \rightarrow B \) and \( B \rightarrow C . \) Given
that \( T_{A}=400 K, \) and \( T_{c}=400 K . \) If
\( \frac{P_{A}}{P_{B}}=\frac{1}{5}, \) then find the heat supplied to the gas.
A . 2059.2 J
в. 3659.23
c. 2225.2 J
D. 2659.23
Subject: Chemistry
In the given graph.
The slope of line \( A B \) gives the information of the:
A value of \( \frac{E_{a}}{2.303} \)
B. value of \( \frac{2.30}{E_{0}} \)
c. value of \( -\frac{E_{a}}{2.303 R} \)
'D value of \( -\frac{E_{a}}{2303 R T} \)
Subject: Maths
If \( U=\cot ^{-1} \sqrt{\cos 2 \theta}-\tan ^{-1} \sqrt{\cos 2 \theta} \)
then \( \sin U \) is equal to
\( A \cdot \sin ^{2} \theta \)
B. \( \cos ^{2} \theta \)
\( \mathbf{c} \cdot \tan ^{2} \theta \)
\( \mathbf{D} \cdot \tan ^{2} 2 \theta \)
Subject: Chemistry
Select the correct order of polarising
power of cation.
\( \mathbf{A} \cdot N a^{+}>M g^{+2}>A l^{+3}>S i^{+4} \)
B \( \cdot S i^{4+}>A l^{3+}>M g^{2+}>N a^{+} \)
\( \mathbf{C} \cdot A l^{3+}>M g^{2+} S i^{4+}>N a^{+} \)
D. \( M g^{2+}>A l^{3+}>S i^{4+}>N a^{+} \)
Subject: Chemistry
Structure of methyl propyl ether (methoxypropane) is:
A \( \cdot C H_{3}-C H_{2}-C H_{3} \)
в. \( C H_{3}-\underset{O}{\|}-O H \)
c. \( C H_{3}-O-C_{3} H_{7} \)
D. \( C H_{3}-C-C H_{3} \)
॥
监
\( o \)
E \( \cdot C H_{3}-C H_{2}-N H_{2} \)
Subject: Physics
The hydraulic press shown in the figure is used to raise the mass \( M \) through a height of \( 0.5 \mathrm{cm} \) by performing \( 500 \mathrm{J} \) of work at the small piston. The diameter
of the large piston is \( 10 \mathrm{cm} \), while that of
the smaller one is \( 2 c m \). The mass \( M \) is
A. \( 100 k g \)
В. \( 10^{6} k g \)
\( \mathbf{c} \cdot 10^{3} k g \)
D. None of these
Subject: Chemistry
If the shortest wavelength in Lyman series of hydrogen atom is \( A \), then the longest wavelength in Paschen series of
\( \boldsymbol{H} \boldsymbol{e}^{+} \) is :
A \( \cdot \frac{36 A}{7} \)
в. \( \frac{5 A}{9} \)
c. \( \frac{36 A}{5} \)
D. \( \frac{9 A}{5} \)
Subject: Maths
Let \( \triangle \boldsymbol{a}=\left|\begin{array}{ccc}\boldsymbol{a}-\mathbf{1} & \boldsymbol{n} & \boldsymbol{6} \\ (\boldsymbol{a}-\mathbf{1})^{2} & \boldsymbol{2} \boldsymbol{n}^{2} & \boldsymbol{4} \boldsymbol{n}-\boldsymbol{2} \\ (\boldsymbol{a}-\mathbf{1})^{3} & \boldsymbol{3} \boldsymbol{n}^{3} & \boldsymbol{3} \boldsymbol{n}^{2}-\boldsymbol{3} \boldsymbol{n}\end{array}\right| \)
Then \( \sum_{a-1}^{n} \triangle a \) is equal to
\( \mathbf{A} \cdot \mathbf{0} \)
В \( \cdot(a-1) \sum n^{2} \)
c. \( (a-1) n \sum n \)
D. None of these
Subject: Physics
Which of the following is the most
precise measurement?
A. \( 3 \times 10^{-3} \mathrm{m} \)
B . \( 0.0030 m \)
c. \( 30 \times 10^{-4} \mathrm{m} \)
D. \( 300 \times 10^{-5} \mathrm{m} \)
Subject: Chemistry
Why does \( H^{+} \) always get associated
with other atoms or molecules?
A. lonisation enthalpy of hydrogen resembles that of alkali metals.
B. Its reactivity is similar to halogens.
c. It resembles both alkali metals and halogens.
D. Loss of an electron from hydrogen atom results in a nucleus of very small size as compared to other atoms or ions. Due to small size it cannot exist freely