AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Physics
Acceleration due to gravity as a
function of \( r \) is given by :
A \( \cdot \frac{4}{3} \pi G r(A-B r) \)
B . \( 4 \pi G r(A-B r) \)
c. \( \frac{4}{3} \pi G r\left(A-\frac{3}{4} B r\right) \)
D \( \cdot \frac{4}{3} \pi G r\left(A-\frac{3}{2} B r\right) \)
Subject: Maths
Equation of the circle which touches the line \( \mathbf{x}+\mathbf{y}-\mathbf{8}=\mathbf{0} \) and centre \( (\mathbf{3}, \mathbf{3}) \) is
A \( \cdot x^{2}+y^{2}-6 x-6 y=0 \)
B \cdot \( x^{2}+y^{2}-6 x-6 y+4=0 \)
C \( \cdot x^{2}+y^{2}-6 x-6 y+36=0 \)
D. \( x^{2}+y^{2}-6 x-6 y+16=0 \)
Subject: Chemistry
Dinitrogen pentoxide \( \left(N_{2} O_{5}\right), \) a colourless solid, is prepared by:
A . heating \( N H_{4} N O_{2} \) with an excess of oxygen
B. dehydrating \( H N O_{3} \) with \( C a O \)
C. dehydrating \( H N O_{3} \) with \( P_{4} O_{10} \)
D. heating a mixture of \( H N O_{2} \) and \( C a\left(N O_{3}\right) \)
Subject: Maths
Which of the following does NOT
represent a zero polynomial?
\( \mathbf{A} \cdot p(x)=0 \)
B \( \cdot p(x)=0 . x^{0} \)
\( \mathbf{C} \cdot p(x)=x^{0} \)
D \( \cdot p(x)=x^{0}-1 \)
Subject: Physics
Two soap bubbles of radii \( a \) and \( b \)
combine under isothermal conditions to
form a single bubble of radius \( c \) without
any leakage of air. If \( \boldsymbol{P}_{\mathbf{0}}= \)
atmospheric pressure and \( \boldsymbol{T}= \) surface
tension of soap solution, show that \( \boldsymbol{P}_{0}=\frac{\boldsymbol{4} \boldsymbol{T}\left(\boldsymbol{a}^{2}+\boldsymbol{b}^{2}-\boldsymbol{c}^{2}\right)}{\boldsymbol{c}^{3}-\boldsymbol{a}^{3}-\boldsymbol{b}^{3}} \)
Subject: Biology
Which of the following statements are
true?
This question has multiple correct options
A. In lung capillaries \( C O_{2} \) combines with water to give carbonic acid
B. In tissue capillaries, carbonic acid breaks down to
\( C O_{2} \) to water
C. In lung capillaries, the carbonic acid breaks down to \( C O_{2} \) and \( H_{2} O \)
D. It tissue capillaries, the carbonic acid combines with hydrogen ions to form the bicarbonate ions
Subject: Maths
If \( \boldsymbol{A B}=\mathbf{3} \boldsymbol{i}+\boldsymbol{j}-\boldsymbol{k} \) and \( \boldsymbol{A} \boldsymbol{C}=\boldsymbol{i}-\boldsymbol{j}+ \)
3k. If the point \( P \) on the line segment
\( B C \) is equidistant from \( A B \) and \( A C \)
then \( \boldsymbol{A P} \) is
A. \( 2 i-k \)
B. \( i-2 k \)
c. \( 2 i+k \)
D. none of these
Subject: Maths
An ink container of cylindrical shape is filled with ink upto \( 91 \% . \) Ball pen refills of length \( 12 \mathrm{cm} \) and inner diameter 2 \( \mathrm{mm} \) are filled upto \( 84 \% \). If the height and radius of the ink container are 14
\( \mathrm{cm} \) and \( 6 \mathrm{cm} \) respectively, find the number of refills that can be filled with
this ink.
Subject: Chemistry
The enthalpies of formation of \( A l_{2} O_{3} \)
and \( C r_{2} O_{3} \) are \( -1596 \mathrm{kJ} \) and \( -1134 \mathrm{kJ} \)
respectively. \( \Delta H \) for the reaction,
\( \mathbf{2} \boldsymbol{A} \boldsymbol{l}+\boldsymbol{C r}_{2} \boldsymbol{O}_{3} \rightarrow \boldsymbol{2} \boldsymbol{C r}+\boldsymbol{A l}_{2} \boldsymbol{O}_{3} \) is :
B . -462 kJ
c. -1365 kJ
D. +2730 kJ
Subject: Maths
Let \( Q \) be a non empty subset of \( N \)
and \( q \) is a statement as given below:
\( \boldsymbol{q}: \) There exists an even number \( \boldsymbol{a} \in \boldsymbol{Q} \)
Negation of the statement \( \boldsymbol{q} \) will be :
A. There is no even number in the set \( Q \)
B. Every \( a \in Q \) is an odd number
c. \( (a) \) and \( (b) \) both
D. None of these
Subject: Chemistry
Temperature of a monoatomic gas is
increased from \( T_{0} \) to \( 2 T_{0} \) in three
different processes: isochoric, isobaric and adiabatic. Heat given to the gas in
these processes are \( Q_{1}, Q_{2} \) and \( Q_{3} \) respectively. Then choose the correct
option. This question has multiple correct options
A \( \cdot Q_{1}>Q_{3} \)
в. \( Q_{2}>Q_{1} \)
\( \mathbf{c} \cdot Q_{2}>Q_{3} \)
D. \( Q_{3}=0 \)
Subject: Maths
Which of the following statements is
true?
\( \mathbf{A} \cdot 6 x+3 x=9 x^{2} \)
B . \( 4(x+5)=4 x+5 \)
c. \( 4(x+5)=4 x+20 \)
D \( \cdot x(4 x+5)=4 x^{2}+5 \)
Subject: Maths
Which of the following are true or false?
a) T-distribution varies from+infinity to infinity
b)The variance of \( t \) distribution and the
variance of normal distribution become
closer and closer as the size of the
sample increases.
A. both (a) and (b) are true
B. both (a) and (b) are false
c. (a) is true but (b) is false
D. (a) is false but (b) is true
Subject: Maths
If \( \bar{a}, \bar{b}, \bar{c} \) are non-coplanar vectors and if \( \bar{d} \) is such that \( \bar{d}=\frac{1}{x}(\bar{a}+\bar{b}+\bar{c}) \) and
\( \overline{\boldsymbol{d}}=\frac{\mathbf{1}}{\boldsymbol{y}}(\overline{\boldsymbol{b}}+\overline{\boldsymbol{c}}+\overline{\boldsymbol{d}}) \) where \( \mathbf{x} \) and \( \mathbf{y} \) are non
zero real numbers, then \( \frac{1}{x y}(\bar{a}+\bar{b}+ \) \( \overline{\boldsymbol{c}}+\overline{\boldsymbol{d}})= \)
B. \( -\bar{a} \)
\( c . \overline{0} \)
D . \( 2 \bar{a} \bar{a} \bar{a} \)
Subject: Maths
A bag contains 4 red balls, 6 blue balls and 3 black balls. A ball is draw at
random from the bag. What is the
probability that the ball drawn is not
blue?
A \( \cdot \frac{6}{13} \)
в. \( \frac{3}{13} \)
\( c \cdot \frac{7}{13} \)
D. None
Subject: Maths
If \( \lim _{x \rightarrow 0}(\cos x+a \sin b x)^{\frac{1}{x}}=e^{2} \) then
the possible values of \( ^{\prime} a^{\prime} \&^{\prime} b^{\prime} a r e: \)
This question has multiple correct options
A \( . a=1, b=2 \)
В. \( a=2, b=1 \)
c. \( a=3, b=2 / 3 \)
D. \( a=2 / 3, b=3 \)
Subject: Biology
The correct representation of the given
alphabets is
A. A- muscle; B- tendon; C-ligament; D- ulna
B. A-ligament; B- - muscle; C- radius; D- tendon
C. A-ligament; B- muscle; C- tendon; D- radius
D. A- tendon; B- muscle; C- ligament; D- radius
E. A- tendon; B- muscle; C-ligament; D- ulna
Subject: Chemistry
If " \( n " \) number of \( \boldsymbol{H}_{3} \boldsymbol{P} \boldsymbol{O}_{4} \) molecules are
polymerized to produce chain molecule and ring molecule separately, then the number of \( \boldsymbol{P}-\boldsymbol{O}-\boldsymbol{P} \) linkages formed
is, respectively:
A \( . n \) and \( (n-1) \)
в. \( (n-1) \) and \( (n-1) \)
c. \( (n-1) \) and \( n \)
D. \( n \) and \( n \)
Subject: Physics
If electric field between plates of a
parallel plate capacitor is \( 2 N C^{-1} \) and
charge on two plates are \( 10 \mathrm{C} \) and \( 3 \mathrm{C} \)
then force on one of the plates is
A. 20 N
B. 30 N
c. \( \frac{60}{7} N \)
D. \( \frac{7}{2} N \)
Subject: Physics
Ocean thermal energy is a useful
source of energy when temperature difference between surface and depth of \( 2 \mathrm{km} \) is :
A \( \cdot \) Less than \( 10^{\circ} C \)
B. More than \( 10^{\circ} \mathrm{C} \)
c. Less than \( 20^{\circ} \mathrm{C} \)
D. More than \( 20^{\circ} \mathrm{C} \)
Subject: Chemistry
Electromagnetic radiation of wavelength \( 242 \mathrm{nm} \) is just sufficient to ionise the sodium atom. Calculate the
ionisation energy of sodium atom? \( (c= \)
\( 3 \times 10^{8} \mathrm{ms}^{-1}, \mathrm{h}=6.626 \times 10^{-34} \mathrm{Js} \)
A \( \cdot 5.6 \times 10^{-19} k J \)
В . \( 6.9 \times 10^{-18} k J \)
c. \( 8.2 \times 10^{-19} \mathrm{J} \)
D. 495 kJ
Subject: Maths
If \( \boldsymbol{f}(\boldsymbol{x})=\boldsymbol{x}^{2}+\frac{\boldsymbol{x}^{2}}{\left(1+\boldsymbol{x}^{2}\right)}+\frac{\boldsymbol{x}^{2}}{\left(1+\boldsymbol{x}^{2}\right)^{2}}+ \)
\( +\frac{x^{2}}{\left(1+x^{2}\right)^{n}}+\ldots . \) then at \( x=0 \)
A \( \cdot f(x) \) has no limit
B . \( f(x) \) is discontinuous
C . \( f(x) \) is continuous but not differentiable
D \cdot \( f(x) \) is differentiable
Subject: Chemistry
\( \boldsymbol{V}\left(\boldsymbol{H} \boldsymbol{C O}_{3}\right)+\boldsymbol{V}\left(\boldsymbol{P} \boldsymbol{O}_{4}\right)+\boldsymbol{V}(\boldsymbol{C l}) \) is
divisible by :
\( (V(X) \text { shows valency of } X) \)
\( A \cdot 2 \)
B. 3
\( c \cdot 4 \)
D. 5
Subject: Physics
respectively, constitute an electric
dipole. Distance \( A B=2 a, 0 \) is the mid point of the dipole and OP is
perpendicular to AB. A charge Q is placed at \( P \) where \( O P=y \) and \( y>>2 a . \) The charge \( Q \) experiences and electrostatic
force F. If \( Q \) is now moved along the
equatorial line to \( P^{\prime} \) such that \( O P^{\prime}= \) \( \left(\frac{y}{3}\right) \) the force on \( Q \) will be close to \( L \) \( \left(\frac{y}{3}>>2 a\right) \)
\( A \cdot \frac{F}{3} \)
в. зF
\( c . \) 9F
D. 27
Subject: Maths
If \( \boldsymbol{y}=\tan ^{-1}\left(\frac{1+\boldsymbol{x}^{2}}{1-\boldsymbol{x}^{2}}\right) \) then \( \frac{\boldsymbol{d} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}}=? \)
A. \( \frac{2 x}{\left(1+x^{4}\right)} \)
B. \( \frac{-2}{\left(1+x^{4}\right)} \)
c. \( \frac{x}{\left(1+x^{4}\right)} \)
D. none of these
Subject: Physics
In figure a certain mass of gas traces
three path 1,2,3 from state \( A \) to the state
B.If work done by the gas along the three
paths are \( W_{1}, W_{2}, W_{3} \) respectively,then:
A \( . W_{1} \)
в. \( W_{1}=W_{2}=W_{3} \)
c. \( W_{1}>W_{2}>W_{3} \)
D. cannot say
Subject: Physics
An a.c. generator consists of a coil of
10,000 turns and of area \( 100 \mathrm{cm}^{2} . \) The
coil rotates at an angular speed of 140 rpm in a uniform magnetic field of
\( 3.6 \times 10^{-2} \mathrm{T} . \) Find the maximum value
of the emf induced.
Subject: Physics
A current \( I=5.0 A \) flows along a thin
wire shaped as shown in figure above. The radius of a curved part of the wire is equal to \( R=120 m m \), the angle
\( 2 \varphi=90^{\circ} . \) Find the magnetic induction
of the field at the point \( O \) in \( \mu T . \) If the
answer is \( X \) then enter \( \frac{X}{7} \)
Subject: Chemistry
Identify the correct balanced chemical equation from the following:
\( \mathbf{A} \cdot S O_{3}+H_{2} O \longrightarrow H_{2} S O_{4} \)
B . \( 6 N a O H+12 S \longrightarrow N a_{2} S_{5}+ \)
\( N a_{2} S_{2} O_{3}+3 H_{2} O \)
\( \begin{array}{llll}\text { c. } C u & + & 2 S & \rightarrow & C u S_{2}\end{array} \)
D. \( S+4 H N O_{3} \longrightarrow H_{2} S O_{4}+4 N O_{2}+ \)
\( 2 H_{2} O \)
Subject: Chemistry
The number of oxidation states is
exhibited by the actinoids more than by the lanthanide. The main reason for this
is:
A. more energy difference between 5 f and 6 d orbital than that between 4 f and 5 d orbitals.
B. the lesser energy difference between 5 and \( 6 d \) orbital than between \( 4 f \) and \( 5 d \) orbitals
C. the greater metallic character of the lanthanoids than that of the corresponding actinoids
D. more active nature of the actinoids
Subject: Maths
Find the number of relations from
\( \{\boldsymbol{m}, \boldsymbol{o}, \boldsymbol{t}, \boldsymbol{h}, \boldsymbol{e}, \boldsymbol{r}\} \) to \( \{\boldsymbol{c}, \boldsymbol{h}, \boldsymbol{i}, \boldsymbol{l}, \boldsymbol{d}\} \)
A . 30
B . \( 30^{2} \)
\( c \cdot 2^{30} \)
D. 60
Subject: Physics
A solid rectangular block of mass \( 200 k g \) has the dimensions \( l=2 m, b= \)
\( 1 m, h=0.5 m . \) It lies on a horizontal
floor on sides \( l \) and \( b \). The minimum
work needed to turn it so that it lies
on the sides \( b \) and \( h \) is:
A . zero
B. \( 1500 J \)
c. \( 3000 J \)
D. \( 2000 J \)
Subject: Biology
Complete the paragraph given below by filling in the blanks.

Blood flows twice in heart. In pulmonary circulation, the oxygenated blood is
carried to from
of heart through The oxygenated blood from lings is carried back to
of the heart through This oxygenated blood
from heart is carried to all systems
through and the deoxygenated blood from the systems below and above the heart is supplied to of
heart through

Hence it is
called double circulation.
Subject: Chemistry
As per de Broglie's formula a
macroscopic particle of mass \( 100 g \) and
moving at a velocity of \( 100 \mathrm{cm} s^{-1} \) will have a wavelength of :
A \( \cdot 6.6 \times 10^{-29} \mathrm{cm} \)
B . \( 6.6 \times 10^{-30} \mathrm{cm} \)
c. \( 6.6 \times 10^{-31} \mathrm{cm} \)
D. \( 6.6 \times 10^{-32} \mathrm{cm} \)
Subject: Physics
What does the sign of magnification indicates \( \left(\boldsymbol{m}=\frac{-\boldsymbol{v}}{\boldsymbol{u}}\right) ? \)
a) Negative sign indicates image is real and inverted.
b) Positive sign indicates image is erect and virtual.
c) Positive sign indicates image is virtual.
\( A \cdot a, b \)
в. b,
\( c . \) a,
D. a, b, c
Subject: Physics
A particle executing SHM according to
the equation \( \boldsymbol{x}=\mathbf{5} \cos \left[\mathbf{2} \boldsymbol{\pi} \boldsymbol{t}+\frac{\pi}{4}\right] \) in \( \mathbf{S} \)
units. The displacement and acceleration of the particle at \( t=1.5 \) s is:
A \( .-3.0 m, 100 m s^{-2} \)
B . \( +2.54 m, 200 m s^{-2} \)
c. \( -3.54 m, 140 m s^{-2} \)
D. \( -3.55 m, 120 m s^{-2} \)
Subject: Physics
At what distance ( from the left) on the
bottom face of the block will the normal
reaction act when \( F \) acts at the height \( \frac{\boldsymbol{H}}{\mathbf{2}} \) ? (here, assume no toppling happens)
A \( \cdot \frac{\mu_{k} H}{2} \)
в. \( \frac{b-\mu_{k} H}{2} \)
c. \( _{b-} \frac{\mu_{k} H}{2} \)
D. \( \frac{H}{2 \mu_{k}} \)
Subject: Maths
If all the fractions \( \frac{3}{5}, \frac{1}{8}, \frac{8}{11}, \frac{4}{9}, \frac{2}{7}, \frac{5}{7} \) and
\( \frac{5}{4} \) are arranged in descending order of
\( \overline{\mathbf{1 2}} \)
their values which one will be the third?
A \( \cdot \frac{1}{8} \)
B. \( \frac{3}{5} \)
c. \( \frac{5}{12} \)
D. \( \frac{8}{11} \)
Subject: Chemistry
Which of the following is/are true
regarding rancidity?

This question has multiple correct options
A. On keeping for long time, the oxidation of oils and fats, changes the taste and odour of food.
B. To prevent rancidity, food is stored in air tight containers.
C. Rancidity can also be prevented by addition of antioxidants.
D. To prevent rancidity, packed food items are flushed with an inert gas like nitrogen.
Subject: Physics
A positive charge \( q \) at origin is moving with velocity \( v_{0} \hat{j} \). Magnetic field at point
\( (a,-a) \) is
A. zero
B. \( \frac{\mu_{0} q v_{0}}{16 \sqrt{2} \pi a^{2}} \hat{k} \)
c. \( \frac{-\mu_{0} q v_{0}}{8 \sqrt{2} \pi a^{2}} \hat{k} \)
D. \( \frac{-\mu_{0} q v_{0}}{4 \sqrt{2} \pi a^{2}} \hat{k} \)
Subject: Physics
If \( A \) and \( B \) are two perpendicular vectors given by \( \bar{A}=5 \bar{i}+7 \bar{j}+3 \bar{k}, \) and \( 4 \bar{B}= \)
\( 2 \bar{i}+2 \bar{j}+c \bar{k}, \) then the value of \( c \) is:
\( A \cdot-2 \)
B. 8
\( c .-7 \)
\( D \cdot-8 \)
Subject: Maths
\( \boldsymbol{f}(\boldsymbol{x})=([\boldsymbol{x}]-[-\boldsymbol{x}]) \boldsymbol{s i n}^{-1}|\boldsymbol{x}-\mathbf{1}| \)
Which of the following statements is/are correct?
(Note : [.] denotes the greatest integer function)
This question has multiple correct options
A. \( f(x) \) is continuous at \( x=1 \)
B. \( f(x) \) is differentiable at \( x=1 \)
c. \( f(x) \) is not differentiable at \( x=1 \)
D. \( f(x) \) is discontinuous at \( x=1 \)
Subject: Physics
The temperature of a body is 3000 K. The wavelength corresponding to maximum emission of radiation will be
\( A \cdot 1 M \)
в. \( 1 \dot{A} \)
\( \mathrm{c} \cdot 9.76 \times 10^{-7} \mathrm{m} \)
D . \( 48.8 \times 10^{-7} \mathrm{m} \)
Subject: Physics
A thin uniform metallic rod of mass \( M \)
and length \( L \) is rotated with a angular
velocity \( \omega \) in a horizontal plane about a
vertical axis passing through one of its ends. The tension in the middle of the
rod is :
A \( \cdot \frac{1}{2} M L \omega^{2} \)
B \( \cdot \frac{1}{4} M L \omega^{2} \)
c. \( \frac{1}{8} M L \omega^{2} \)
D. \( \frac{3}{8} M L \omega^{2} \)
Subject: Chemistry
\( \boldsymbol{P h}-\boldsymbol{C H}(\boldsymbol{O H}) \boldsymbol{C H}_{3} \stackrel{\boldsymbol{S O C l}_{2}}{\longrightarrow} \boldsymbol{P h C l}- \)
\( \quad \) Specific Rotaion \( =+\boldsymbol{5 0}^{o} \)
\( \boldsymbol{C H}_{3} \)
What is the specific rotation of the product?
A. \( +50^{\circ} \)
B. \( +60^{\circ} \)
\( c .-60^{\circ} \)
D. zero
Subject: Maths
A vector equation of the line of
intersection of the planes \( \boldsymbol{r}=\boldsymbol{b}+ \)
\( \boldsymbol{\lambda}_{1}(\boldsymbol{b}-\boldsymbol{a})+\boldsymbol{\mu}_{1}(\boldsymbol{a}+\boldsymbol{c}) \)
\( \boldsymbol{r}=\boldsymbol{c}+\boldsymbol{\lambda}_{2}(\boldsymbol{b}-\boldsymbol{c})+\boldsymbol{\mu}_{1}(\boldsymbol{a}+\boldsymbol{b}) \boldsymbol{a}, \boldsymbol{b}, \boldsymbol{c} \)
being non-coplanar vectors is.
A \( \cdot r=a+\mu_{1}(b+c) \)
B . \( r=b+\mu_{1}(a+2 c) \)
C . \( r=a+\mu_{1}(b+2 c) \)
D. \( r=b+\mu_{1}(a+c) \)
Subject: Chemistry
The yield of the products in the reaction, \( \boldsymbol{A}_{2(\boldsymbol{g})}+\mathbf{2} \boldsymbol{B}_{(\boldsymbol{g})} \rightleftharpoons \boldsymbol{C}_{(\boldsymbol{g})}+\boldsymbol{Q} \boldsymbol{k} \boldsymbol{J} \) would be
higher at :
A. high temperature and high pressure
B. high temperature and low pressure
C. low temperature and high pressure
D. low temperature and low pressure
Subject: Chemistry
The triad of nuclei that is isotonic is:
\( \mathbf{A} \cdot_{6}^{14} C, \frac{15}{7} N,_{9}^{17} F \)
В . \( _{6}^{12} C, \frac{14}{7} N, \) ' \( _{19}^{9} F \)
\( \mathbf{C} \cdot_{6}^{14} C, \frac{14}{7} N,_{9}^{17} F \)
\( \mathbf{D} \cdot_{6}^{14} C, \frac{14}{7} N, \frac{19}{9} F \)
Subject: Biology
Assertion
Chloroplast is a cell organelle.
Reason
An organelle is a distinct part of a cell
which has a particular structure and
function.
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: Physics
The S.I. unit of universal gas constant is
A. \( W a t t K^{-1} m o l^{-1} \)
B. \( N K^{-1} \) mol \( ^{-1} \)
c. \( J K^{-1} m o l^{-1} \)
D. \( \operatorname{erg} K^{-1} \)mol\( ^{-1} \)
Subject: Chemistry
White phosphorous catches fire in air to produce dense white fumes. This is due to the formation of
\( \mathbf{A} \cdot P_{4} O_{10} \)
в. \( P H_{3} \)
\( \mathrm{c} \cdot \mathrm{H}_{3} \mathrm{PO}_{3} \)
D. \( H_{3} P O_{2} \)
Subject: Maths
The value of \( \int \cos (\log x) d x \) is
A \( \cdot \frac{1}{2}[\sin (\log x)+\cos (\log x)]+C \)
B. \( \frac{x}{2}[\sin (\log x)+\cos (\log x)]+C \)
c. \( \frac{x}{2}[\sin (\log x)-\cos (\log x)]+C \)
D \( \cdot \frac{1}{2}[\sin (\log x)-\cos (\log x)]+C \)
Subject: Maths
Construct a quadrilateral \( A B C D \) in
which \( \boldsymbol{A B}=\mathbf{6} \mathrm{cm}, \boldsymbol{B C}=\mathbf{8} \mathrm{cm}, \boldsymbol{C D}= \)
\( \mathbf{5} \mathrm{cm}, \boldsymbol{A} \boldsymbol{D}=\mathbf{4} \mathrm{cm} \) and diagonal \( \boldsymbol{A} \boldsymbol{C}= \)
\( 4.5 \mathrm{cm} \)
Subject: Physics
A convex lens forms a real image of a
point object at a distance of \( 50 \mathrm{cm} \) from the convex lens. A concave lens is
placed. \( 10 \mathrm{cm} \) behind the convex lens on the image side. On placed a plane mirror an the image side and facing the concave lens. It is observed that the
final image now coincides with the
object itself. The focal length of the concave lens is:
A. \( 50 \mathrm{cm} \)
B. 20 cm
\( c .40 \mathrm{cm} \)
D. 25 cm
Subject: Chemistry
A buffer solution with \( p H=9 \) is to be
prepared by mixing \( N H_{4} C l \) and
\( N H_{4} O H . \) Calculate the number of
moles of \( N H_{4} C l \) that should be added
to 1 liter of
\( \mathbf{1} \boldsymbol{M} \boldsymbol{N} \boldsymbol{H}_{\mathbf{4}} \boldsymbol{O} \boldsymbol{H} \cdot \boldsymbol{K}_{\boldsymbol{b}}\left(\boldsymbol{N} \boldsymbol{H}_{4} \boldsymbol{O} \boldsymbol{H}\right)=\mathbf{1 . 8} \times \)
\( 10^{-5} \)
Subject: Physics
An unbanked curve has a radius of \( 60 m \)
Coefficient of friction between the tyre
of truck and road is \( 0.75 . \) The distance
between two front wheel of truck is \( 2 m \)
If the truck exceeds the speed of safe
limit, then select the correct statement and justify your asnwer.
1) Inner wheels leave the ground first.
2) Outer wheels leave the ground first.
Subject: Maths
\( \ln \triangle P Q R, \angle P \) is right angle. \( A, B \) are
mid points of \( \boldsymbol{R} \boldsymbol{P} \) and \( \boldsymbol{R} \boldsymbol{Q} \)
\( \boldsymbol{R} \boldsymbol{P}=\boldsymbol{3}, \boldsymbol{R} \boldsymbol{Q}=\mathbf{5} . \) Find length of \( \boldsymbol{A} \boldsymbol{B} \)
4
3
\( c .3 \)
\( D \)
Subject: Chemistry
A volume of 100 ml of water gas
containing some \( C O_{2} \) was mixed with
\( 100 m l \) of oxygen and mixture exploded. The volume after an explosion was 100 ml. On introducing \( N a O H \) the volume was reduced to 52.5 ml. If
the volume ratio of \( C O, H_{2} \) and \( C O_{2} \) in
the original sample is \( a b: c d: 2 \)
calculate the value of \( ^{\prime} a b c d^{\prime} \)
Subject: Chemistry
Assertion
The value of the van der Waals' constant
\( a^{\prime} \) is larger for ammonia than for
nitrogen.
Reason
Hydrogen bonding is present in ammonia.
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: Physics
The maximum and minimum distance
of a comet from the sun are \( 8 \times 10^{12} m \)
and \( 1.6 \times 10^{12} \) m. If its velocity when
nearest to the sun is \( 60 m / s \), what will
be its velocity in \( m / s \) when it is
farthest:
A . 12
B. 60
\( c \cdot 112 \)
D. 6
Subject: Physics
A battery has four cells in parallel, each has an e.m.f \( 1.5 V \) and internal
resistance \( 0.8 \Omega . \) The current delivered
by it to a load of \( 2.8 \Omega \) is
A. \( 0.2 A \)
B. 0.4A
c. \( 0.5 \mathrm{A} \)
D. \( 0.6 A \)
Subject: Chemistry
The following is not an appropriate reaction for the preparation of tert. butyl ethyl ether \( \boldsymbol{C}_{2} \boldsymbol{H}_{5} \boldsymbol{O} \boldsymbol{N} \boldsymbol{a}+\left(\boldsymbol{C} \boldsymbol{H}_{3}\right)_{3} \boldsymbol{C}-\boldsymbol{C l} \rightarrow \)
\( \left(\boldsymbol{C H}_{3}\right)_{3} \boldsymbol{C}-\boldsymbol{O}-\boldsymbol{C}_{2} \boldsymbol{H}_{5} \)
Write a suitable reaction for the
preparation of tert., butyl ethyl ether
Justify your answer in both cases.
Subject: Maths
\( \int \frac{\sin x+4 \sin 3 x+6 \sin 5 x+3 \sin 7 x}{\sin 2 x+3 \sin 4 x+3 \sin 6 x} \)
equals.
\( \mathbf{A} \cdot-2 \sin x+c \)
B. \( 2 \sin x+c \)
c. \( 2 \cos x+c \)
D. \( -2 \cos x+c \)
Subject: Maths
Let \( [x] \) denote the greatest integer part of a real number x. If
\( \boldsymbol{M}=\sum_{n=1}^{40}\left[\frac{\boldsymbol{n}^{2}}{\mathbf{2}}\right] \)
then m equals
A . 5700
B. 5720
\( c .5740 \)
D. 11060
Subject: Physics
Statement A : A neutron travelling with a velocity collides head on an atom of
atomic mass number \( A \) at rest. The
fraction of the total energy retained by neutron is \( \left(\frac{A-1}{A+1}\right)^{2} \)
Statement B : The kinetic energy
conserves during an elastic collision
\( A \cdot A \) and \( B \) are true
B. A is true but B is false
c. A is false but B is true
D. A and B are false
Subject: Physics
Energy released in the nuclear fusion
reaction is :
\( _{1} \mathbf{H}^{2}+_{1} \mathbf{H}^{3} \rightarrow_{2} \mathbf{H} \mathbf{e}^{4}+_{0} \mathbf{n}^{1} \)
Atomic mass of some species are given
below.
\( _{1} \mathbf{H}^{2}=\mathbf{2 . 0 1 4},_{1} \mathbf{H}^{3}=\mathbf{3 . 0 1 6} \)
\( _{2} \mathbf{H e}^{4}=\mathbf{4 . 0 0 3},_{0} \mathbf{n}^{1}=\mathbf{1 . 0 0 9} \mathbf{a m u} \)
A . \( 8.30 \mathrm{eV} \)
B. \( 16.758 \mathrm{MeV} \)
c. \( 500 \mathrm{J} \)
D. \( 4 \times 10^{6} \) kcal
Subject: Maths
The equation \( _{-}-_{-}-_{-}--_{-}- \) and \( 2 x+ \)
\( 2=0 \) have the same solution.
A \( . x-1=0 \)
B . \( x+1=0 \)
c. \( x-2=0 \)
D. \( x+2=0 \)
Subject: Physics
A spherical ball contracts in volume by \( 0.01 \% \) when subjected to a normal
uniform pressure of 100 atm. The Bulk
modulus of its material is
A . \( 1.01 \times 10^{11} \mathrm{Nm}^{-2} \)
В. \( 1.01 \times 10^{12} \mathrm{Nm}^{-2} \)
c. \( 1.01 \times 10^{10} N m^{-2} \)
D. \( 1.01 \times 10^{13} \mathrm{Nm}^{-2} \)