AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Maths
Distance between plane \( 3 x+4 y- \)
\( \mathbf{2 0}=\mathbf{0} \) and point \( (\mathbf{0}, \mathbf{0},-\mathbf{7}) \) is
A. 4 units
B. 3 units
c. 2 units
D. 1 units
Subject: Chemistry
In the given sequence of reactions, predict \( (\boldsymbol{X}) \)
\( (\boldsymbol{X}) \frac{\boldsymbol{K O H}}{\boldsymbol{H}_{2} \boldsymbol{O}}(\boldsymbol{Y}) \frac{\boldsymbol{A l}_{2} \boldsymbol{O}_{3}}{4 \boldsymbol{3} \boldsymbol{3} \boldsymbol{K}}(\boldsymbol{Z}) \stackrel{[\boldsymbol{O}]}{\longrightarrow} \)
\( 2 m o l C H_{3} C O O H \)
\( \mathbf{A} \cdot C H_{3} C H_{2} C H(I) C H_{3} \)
в. \( C H_{3} C H_{2} C H_{2} C H_{2} I \)
c. \( C H_{3} C H(I) C H(I) C H_{3} \)
D. \( C H_{3} C H(I) C H_{2} C H_{2} I \)
Subject: Maths
If the line \( 3 x-4 y=\lambda \) cuts the circle
\( x^{2}+y^{2}-4 x-8 y-5=0 \) in two
points then limits of \( \lambda \) are
A . [-35,15]
В . (-35,15)
c. (-35,10)
D. (-35,15]
Subject: Chemistry
Assertion
\( N_{2} O \) supports combustion more
vigorously than air
Reason
Both nitrogen and oxygen contribute for combustion
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect
Subject: Chemistry
The rate equation for a reaction, \( \boldsymbol{A} \longrightarrow \)
\( B \) is \( r=k[A]^{0} . \) If the initial
concentration of the reactant is \( a \)
mol.dm \( ^{-3} \), the half-life period of the
reaction is:
A \( \cdot \frac{a}{2 k} \)
в. \( \frac{k}{a} \)
c. \( \frac{a}{k} \)
D. \( \frac{2 a}{k} \)
Subject: Maths
If \( t \) is a parameter,then \( \boldsymbol{x}=\boldsymbol{a}\left(\boldsymbol{t}+\frac{\mathbf{1}}{\boldsymbol{t}}\right) \)
and \( y=b\left(t-\frac{1}{t}\right) \) represent
A. An ellipse
B. A circle
c. A pair of straight lines
D. A hyperbola
Subject: Maths
The solution of \( \frac{d y}{d x}=\frac{y^{2}}{x y-x^{2}} \)
A. \( y=c e^{x y} \)
B. \( y=\frac{e^{\frac{y}{x}}}{c} \)
c. \( \log y=x y+c \)
D. \( \log x=x y+c \)
Subject: Maths
If \( P(A)=\frac{1}{3}, P(B)=\frac{1}{2} \) and \( A, B \) are
mutually exclusive, find \( \boldsymbol{P}\left(\boldsymbol{A}^{\prime} \cap \boldsymbol{B}^{\prime}\right) \)
A \( \cdot \frac{5}{6} \)
B.
\( c \cdot \frac{1}{5} \)
D.
Subject: Chemistry
Coordination compounds have great
importance in biological systems. In
this context which of the
following statement(s) is/are incorrect?
A. Chlorophyll is a green pigment in plants and contains calcium
B. Haemoglobin is the red pigment of blood and contains iron
C. Cyanocobalamin is \( B_{12} \) and contains cobalt
D. Carboxypeptidase A is an enzyme and contains zinc
Subject: Physics
\( A, B \) and \( C \) are parallel conductors of
equal lengths carrying currents \( \boldsymbol{I}, \boldsymbol{I} \) and
\( 2 I \) respectively. Distance between \( A \)
and \( B \) is \( x . \) Distance between \( B \) and \( C \)
is also \( x . F_{1} \) is the force exerted by \( B \) on
\( A . F_{2} \) is the force exerted by \( C \) on \( A \)
Choose the correct answer.
\( \mathbf{A} \cdot F_{1}=2 F_{2} \)
B . \( F_{2}=2 F_{1} \)
\( \mathbf{c} \cdot F_{1}=F_{2} \)
D. \( F_{1}=-F_{2} \)
Subject: Maths
Find a value of \( \boldsymbol{x} \) if \( \left|\begin{array}{cc}\boldsymbol{x} & \boldsymbol{2} \\ \boldsymbol{1} \boldsymbol{8} & \boldsymbol{x}\end{array}\right|=\left|\begin{array}{cc}\boldsymbol{6} & \boldsymbol{2} \\ \boldsymbol{1} \boldsymbol{8} & \boldsymbol{6}\end{array}\right| \)
Subject: Chemistry
In Period 3 of the Periodic Table, element
B is placed to the left of element A. On the basis of this information, choose
the correct word from the brackets of
complete the following statement.
(i) The element B would have(lower/higher) metallic character
than \( A \)
(ii) The element A would probably have(lesser/higher) electron affinity than B.
(iii) The element A would have(greater/smaller) atomic size than
B.
Subject: Chemistry
The incorrect statements among the
following are:
This question has multiple correct options
A. \( N C l_{5} \) does not exist while \( P C l_{5} \) does
B. Pb prefers to form tetravalent compounds
C. The three \( C-O \) bond are not equal in the carbonate
ion
D. Both \( O_{2}^{+} \) and \( N O \) are paramagnetic
Subject: Chemistry
In the following gaseous phase first order reaction
\( \boldsymbol{A}(\boldsymbol{g}) \rightarrow \boldsymbol{2} \boldsymbol{B}(\boldsymbol{g})+\boldsymbol{C}(\boldsymbol{g}) \)
initial pressure was found to be 400
\( \mathrm{mm} \) of \( \mathrm{Hg} \) and it changed to \( 1000 \mathrm{mm} \) of \( H g \) after \( \$ \$ 20 \$ 4 \) min. Then:
This question has multiple correct options
A. half life for \( A \) is 10 min
B. rate constant is \( 0.0693 \mathrm{min}^{-1} \)
c. partial pressure of \( C \) at 30 min is 350 mm of \( H g \)
D. total pressure after 30 min is 1100 mm of \( H g \)
Subject: Physics
An object is said to be in equilibrium
when:
1. there is no net force acting on the
object
2. the total clockwise moments about
any point is equal to the total anti-
clockwise moments about the same
point
3. the object moves with constant
velocity
A . 1 only
B. 2 only
c. 1 and 2 only
D. 1,2 and 3
Subject: Maths
Two dice each numbered from 1 to 6 are
thrown together. Let \( A \) and \( B \) be two
events given by
\( A: \) even number on the first die
\( B: \) number on the second die is greater
than 4
Find the value of \( \boldsymbol{P}(\boldsymbol{A} \cap \boldsymbol{B}) \)
A \( \cdot \frac{1}{2} \)
B. \( \frac{1}{4} \)
\( c \cdot \frac{2}{3} \)
D. \( \frac{1}{6} \)
Subject: Maths
Let \( \boldsymbol{P}(\boldsymbol{n}): \boldsymbol{2}^{n}>\boldsymbol{n}, \forall \boldsymbol{n} \in \boldsymbol{N} \) and \( \boldsymbol{2}^{k}> \)
\( k, \forall n=k, \) then which of the following is
true \( \forall k \geq 2 ? \)
\( \mathbf{A} \cdot 2^{k}>5 k>1 \)
В \( \cdot 2^{k+1}>2 k>k+1 \)
C \( \cdot 2^{k}>2(k+1)>k \)
D. None of these.
Subject: Maths
If \( f(x)=l x \) and \( a, b, c \) are in A.P. \( k, l \) are
constants. Then \( \boldsymbol{f}(\boldsymbol{a}-\boldsymbol{k}), \boldsymbol{f}(\boldsymbol{b}-\boldsymbol{k}), \) and
\( f(c-k) \) are in
A . A.
в. с.
c. н.
D. A.G.P
Subject: Maths
Let \( \boldsymbol{f}(\boldsymbol{x})=\sin \boldsymbol{x}+\cos \boldsymbol{x}+\tan \boldsymbol{x}+ \)
\( \arcsin x+\arccos x+\arctan x . \) If \( \mathrm{M} \) and
\( \mathrm{m} \) are maximum and minimum values
of \( f(x) \) then their arithmetic mean is
equal to
A \( \cdot \frac{\pi}{2}+\cos 1 \)
B . \( \frac{\pi}{2}+\sin 1 \)
C \( \cdot \frac{\pi}{4}+\tan 1+\cos 1 \)
D. \( \frac{\pi}{4}+\tan 1+\sin 1 \)
Subject: Maths
Consider the following frequency distribution:
\( \begin{array}{lllll}\text { Class } & 0- & 6- & 12- & 1 \\ & 5 & 11 & 17 & 2\end{array} \)
Frequency 13 10 15
The upper limit of the median class is
A. 17
в. 17.5
c. 18
D. 18.5
Subject: Physics
f a piece of metal is heated to an absolute temperature \( T \) and then put in
an enclosure at absolute temperature \( t \)
then the heat generated in the atmosphere will be proportional to
A \( \cdot(T-t)^{4} \)
B . \( T^{4}-t^{4} \)
\( c \cdot T^{2}-t^{2} \)
D. \( T^{3}-t^{3} \)
Subject: Physics
Two trains \( A \) and \( B \) which are \( 100 \mathrm{km} \)
apart are travelling towards each other on different tracks with the initial speed
of \( 50 \mathrm{km} / \mathrm{h} \) for both. The train \( \mathrm{A} \)
accelerates at \( 20 \mathrm{kmh}^{-2} \) and the train \( \mathrm{B} \)
retards at the rate \( 20 k m h^{-2} \) The
distance covered by the train A when they cross each other is approximately:
A. \( 45 \mathrm{km} \)
B. 55 km
\( c . \) 150 \( \mathrm{km} \)
D. \( 162 \mathrm{km} \)
Subject: Maths
The solution of the equation \( \frac{d y}{d x}+ \)
\( \boldsymbol{x}(\mathbf{2} \boldsymbol{x}+\boldsymbol{y})=\boldsymbol{x}^{3}(\boldsymbol{2} \boldsymbol{x}+\boldsymbol{y})^{3}-\boldsymbol{2} \) is \( (C \)
being arbitrary constant):
A \( \cdot \frac{1}{2 x+x y}=x^{2}+1+C e^{x} \)
B. \( \frac{1}{(2 x+y)^{2}}=x^{2}+1+C e^{x^{2}} \)
c. \( \frac{1}{2 x+y}=x+1+C e^{-x^{2}} \)
D. \( \frac{1}{(2 x+y)^{2}}=x^{2}+1+C \)
Subject: Chemistry
Match the column
Column -II Column-I
\( (A) \)
(i) Citric acid Acetobacter aceti (1)
(B) (ii)Latic \( d \) Clostridium butylicum acid
(C) Aspergillus r Acetic acid Por Is niger (iii) tC acid dot
(D) Lactobacillus \( \quad \) (iv) Butyric ric acid
\( \mathbf{A} \)
\( A-(i i), B-(i), C-(i i i), D-(i v) \)
B. A-(iii), B-(ii), C-(i), D-(iv)
C \( . A-(\text { iii) }, B-(i v), C-(i), D-(i i) \)
D. \( A-(\text { iv }), B-(\text { iii) }, C-(i i), D-(i) \)
Subject: Physics
What is the force in \( y \) direction if the
plate is given a constant velocity ' \( u \) ' in
the direction of \( v ? \)
A \( \cdot \rho A(v-u)^{2} \sin 2 \theta \)
В \( \cdot_{\rho A}(v-u)^{2} \sin \theta \)
c. \( \rho A\left(v^{2}-u^{2}\right) \sin \theta \)
D. None of these
Subject: Chemistry
Geometrical isomerism can be shown
by:
A \( \cdot\left[A g(C N)\left(N H_{3}\right)\right. \)
в. \( _{N a_{2}}\left[C d\left(N O_{2}\right)_{4}\right] \)
\( \mathbf{c} \cdot\left[P t C l_{4} I_{2}\right] \)
D. \( \left[P t C l\left(N H_{3}\right)_{3}\right]\left[A u(C N)_{4}\right] \)
Subject: Maths
Which of the following is/are true regarding the following linear equation:
\( \boldsymbol{x}+\mathbf{5} \boldsymbol{y}+\mathbf{2}=\mathbf{0} \)
A. It passes through (0,-0.4) and \( m=-0.2 \)
B. It passes through (0,0.4) and \( m=0.2 \)
C. It passes through (0,-0.2) and \( m=-0.4 \)
D. It passes through (0,0.2) and \( m=0.4 \)
Subject: Physics
A geostationary satellite is orbiting the earth at a height \( 6 \mathrm{R} \) above the surface of earth, where \( R \) is the radius of the
earth. The time period of another satellite at a height of \( 2.5 \mathrm{R} \) from the surface of earth in hour is
В. \( 1.5 \sqrt{2} h \)
c. \( 6 \sqrt{2} h \)
D. \( 12 \sqrt{2} h \)
Subject: Physics
Assertion
On a rainy day it is difficult to drive a
car or bus at high speed.
Reason
The value of coefficient of friction is
lowered due to wetting of the surface.
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
Prove: \( \tan ^{-1}\left(\frac{\sqrt{1+x}-\sqrt{1-x}}{\sqrt{1+x}+\sqrt{1-x}}\right)= \)
\( \frac{\pi}{4}-\frac{1}{2} \cos ^{-1} x,-\frac{1}{\sqrt{2}} \leq x \leq 1 \)
[Hint: \( p u t x=\cos 2 \theta] \)
Subject: Maths
If \( A D, B E \) and \( C F \) are the medians of \( \angle \)
ABC, then which one of the following
statements is
correct?
\( \mathbf{A} \cdot(A D+B E+C F)=(A B+B C+C D) \)
B \( \cdot(A D+B E+C D)>\frac{3}{4}(A B+B C+C A) \)
\( \mathbf{c} \cdot(A D+B E+C F)>\frac{3}{4}(A B+B C+C A) \)
D. \( (A D+B E+C F)=\frac{1}{2}(A B+B C+C A) \)
Subject: Physics
A cloud carries a charge of 1000 C at a potential of \( 5 \mathrm{kV} \). If the cloud discharge,
the amount of energy released:
A \( .5 \times 10^{6} J \)
В. \( 2.5 \times 10^{6} J \)
\( c \cdot 10^{7} J \)
D \( .5 \times 10^{3} J \)
Subject: Chemistry
Which of the regents will convert a nitrile to corresponding aldehyde?
A \( \cdot\left(\text { i) } L i A l H_{4} \text { (ii) } H_{3} O^{+}\right. \)
B . (i) \( D I B A L-H \) (ii) \( H_{3} O^{+} \)
c. \( N a O H, H_{2} O, \) Heat
D. \( N a B H_{4} \)
Subject: Chemistry
In the following reaction Phenol\( \stackrel{Z n d u s t}{\rightarrow} X \frac{C H_{3} C l}{a n h . A l c l_{3}} \)
\( \boldsymbol{Y}^{\boldsymbol{a l k} \cdot \boldsymbol{K} \underline{M n} \boldsymbol{O}_{4} / \triangle} \boldsymbol{Z} \)
The product \( Z \) is:
A. toulene
B. benzaldehyde
c. benzoic acid
D. benzene
Subject: Chemistry
Assertion
limiting line in the Balmer series has a wavelength of \( 364.4 \mathrm{nm} \)
Reason
limiting line is obtained for a jump of electron from \( n= \) infinity
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect
Subject: Chemistry
A metal oxide \( M O_{(s)} \) can be reduced by carbon or carbon monoxide
successfully when the line in Ellingham
diagram for reaction (i):
A. lies above the line for one of the reactions (ii) to (iv)
B. intersects the line for one of the reactions
(ii) to (iv)
(ii) to (iv)
c. lies below the line for one of the reactions
D. may lie above or below the line for one of the reactions
(ii) to
(iv) depending upon the temperature
Subject: Maths
If \( \lim _{x \rightarrow 1} \frac{x^{4}-1}{x-1}=\lim _{x \rightarrow k} \frac{x^{3}-k^{3}}{x^{2}-k^{2}}, \) then find
the value of \( k \)
\( A \cdot \frac{5}{3} \)
B. \( -\frac{8}{3} \)
\( c \cdot \frac{8}{3} \)
D. None of these
Subject: Physics
The Poissons ratio of a material is \( 0.4 . \) If
a force is applied to a wire of this material, there is a decrease of the
cross-sectional area by \( 2 \% \). The percentage increase in its length is
A . \( 3 \% \)
в. 2.5\%
c. \( 1 \% \)
D. 0.5\%
Subject: Physics
An ideal gas is compressed isothermally until its pressure is doubled and then allowed to expand adiabatically to regain its original volume \( \left(\gamma=1.4 \text { and } 2^{-1.4}=0.38\right) . \) The ratio of the final to initial pressure is
A . 0.76: 1
B. 1: 1
\( c .0 .66: 1 \)
D. 0.86: 1
Subject: Chemistry
The role of metal written on arrows in the given chemical reactions is :
\( \mathrm{cH}_{3} \mathrm{CooH}+\mathrm{cH}_{3} \mathrm{cH}_{2} \mathrm{oH} \frac{\mathrm{Conc.} \mathrm{H}_{2} \mathrm{s} \mathrm{O}_{4}}{\longrightarrow} \mathrm{cH}_{3} \mathrm{cooc}_{2} \mathrm{H}_{5}+\mathrm{H}_{2} \mathrm{O} \)
\( \mathrm{cH}_{3} \mathrm{cH}_{2} \mathrm{o} \) н \( \frac{\mathrm{Alk}_{4} \mathrm{KMn}_{4}}{\mathrm{Heat}} \)
A. catalyst
B. oxidising agent
c. reducing agent
D. dehydrating agent
Subject: Physics
toppr
Q Type your question_
given data?
Times \( 0 \quad 10 \)
20
30
\( (s) \)
stanc \( \begin{array}{llll}\text { 0 } & \text { 40 } & \text { 80 } & \text { 120 }\end{array} \) \( (m) \) ne 0
\( A \)
B.
\( c \)
\( D \)
Subject: Maths
The function \( \boldsymbol{f}(\boldsymbol{x})=\frac{\boldsymbol{x}}{1+\boldsymbol{x} \tan \boldsymbol{x}} \) has
A. one point of minimum in the interval \( (0, \pi / 2) \)
B. one point of maximum in the interval \( (0, \pi / 2) \)
C. no point of maximum,no point of minumum in the interval \( (0, \pi / 2) \)
D. two points of maximum in the interval \( (0, \pi / 2) \)
Subject: Physics
A capacitor of capacitance \( C \) is charged to a potential difference \( V \) from a cell and then disconnected from it. A charge
\( +\mathrm{Q} \) is now given to its positive plate. The potential difference across the capacitor is now:
A.
в. \( v+\frac{Q}{C} \)
c. \( v+\frac{Q}{2 C} \)
D. \( V-\frac{Q}{C} \), if \( Q<C V \)
Subject: Physics
Assertion
Magnetic field due to current carrying solenoid is independent of its length
and cross-sectional area.
Reason
The magnetic field inside the solenoid is uniform.
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
If \( \boldsymbol{A}=\left[\begin{array}{ll}\mathbf{3} & \mathbf{2} \\ \mathbf{1} & \mathbf{4}\end{array}\right], \) then \( \boldsymbol{A}(\boldsymbol{A} \boldsymbol{d} \boldsymbol{j} \cdot \boldsymbol{A}) \) equals-
A. \( \left[\begin{array}{cc}10 & 0 \\ 0 & 10\end{array}\right] \)
В. \( \left[\begin{array}{cc}0 & 10 \\ 10 & 0\end{array}\right] \)
c. \( \left[\begin{array}{ll}10 & 1 \\ 1 & 10\end{array}\right] \)
D. none of these
Subject: Physics
When a small uncharged conducting ball of radius \( a=1 c m \) and mass \( m=50 \) g
is dropped from a height h above the
center of another large conducting sphere of radius b \( (=1 \mathrm{m}) \) having charge
\( Q(=100 \mu C), \) it rises to a height \( h_{1} \in \)
\( 2 m \) ) after the collision. The value of h is
\( \mathbf{1 0} \)
Find \( x \)
Assume that during the impact there is no dissipation of energy.
Subject: Maths
Which of the following given statements
is/are not correct?
This question has multiple correct options
A \( \cdot \frac{d}{d x}(\operatorname{cosec} x)=\operatorname{cosec} x \cdot \cot x \)
B. \( \frac{d}{d x}(\sec x)=\sec x . \tan x \)
C \( \cdot \frac{d}{d x}(3 \cot x)=-3 \operatorname{cosec}^{2} x \)
D \( \cdot \frac{d}{d x}(2 \tan x)=-2 \sec ^{2} x \)
Subject: Maths
\( \mathrm{n} \triangle \boldsymbol{A B C}, \sum\left(\frac{\sin ^{2} \boldsymbol{A}+\sin \boldsymbol{A}+\mathbf{1}}{\sin \boldsymbol{A}}\right) \) is
always greater than
\( A \cdot 9 \)
B. 3
c. 27
D. None of these
Subject: Physics
In the figure given below, Find the
equivalent capacitance of the network between points \( A \) and \( B \)
Given \( : \boldsymbol{C}_{\mathbf{1}}=\boldsymbol{C}_{\mathbf{5}}=\mathbf{4} \boldsymbol{\mu} \boldsymbol{F}, \boldsymbol{C}_{\mathbf{2}}=\boldsymbol{C}_{\mathbf{3}}= \)
\( C_{4}=2 \mu F \)
Subject: Physics
A simple microscope consists of a concave lens of power \( 10 \mathrm{D} \) and a convex lens of power 15 D. Its magnification at
near point is (least distance of distinct vision, \( \mathrm{D}= \)
\( 25 \mathrm{cm} \)
A . 2.25
B. 5
\( c \cdot 10 \)
D. 20
Subject: Chemistry
Mixed ether will not be formed in the
reaction?
A \( \cdot C H_{3} O C H_{2} C l+C_{2} H_{5} M g B r \)
в. \( C H_{2} N_{2}+C_{2} H_{5} O H \)
c. \( C_{2} H_{5} O N a+C H_{3} \)
D. \( C_{2} H_{5} O H+H_{2} S O_{4}\left(140^{0} C\right) \)
Subject: Chemistry
A complex is represented as \( \mathrm{CoCl}_{3} \cdot x N H_{3} \) its 0.1 molal solution in
aq. solution shows \( \Delta T_{f}=0.558^{0} C . K_{f} \)
for \( \boldsymbol{H}_{2} \boldsymbol{O} \) is \( 1.86 \boldsymbol{K} \boldsymbol{m o l}^{-1} \boldsymbol{k g} . \) Assuming
\( 100 \% \) ionisation of complex and
coordination no. of \( C o \) is six, calculate
formula of complex.
Subject: Physics
A particle moves in \( X Y \) plane according to the law \( x=a \sin (t) \) and \( y= \) \( \boldsymbol{a}(1-\cos (\boldsymbol{t})) \) where a is constant. The
particle traces:
A . a parabola
B. a straight line equallyinclined to x and y axes
c. a circle
D. a distance proportional to time
Subject: Maths
Find the value of \( a \) for which the ellipse \( \frac{x^{2}}{y^{2}}+\frac{y^{2}}{b^{2}}=1,(a>b), \) if the extremities
of the latus rectum of the ellipse having positive ordinates lie on the parabola \( x^{2}=-2(y-2) \)
Subject: Maths
Which of the following is not a linear polynomial?
A \( . p(y)=8 y+6 \)
В. \( p(x)=8 y+2 x \)
c. \( p(x)=4+\frac{5 x}{x}+8 x^{\circ} \)
D. \( p(x)=4+5 x \)
Subject: Maths
If \( C \) and \( D \) are two events such that
\( \mathbf{C} \subset \mathbf{D} \) and \( \mathbf{P}(\mathbf{D}) \neq \mathbf{0}, \) then the correct
statement among the following is
\( ^{\mathbf{A}} \cdot p\left(\frac{C}{D}\right)=\mathrm{P}(\mathrm{C}) \)
\( ^{\mathbf{B}} \cdot p\left(\frac{C}{D}\right) \geq \mathrm{P}(\mathrm{C}) \)
\( ^{c} \cdot p\left(\frac{C}{D}\right)<\mathrm{P}(\mathrm{C}) \)
\( P\left(\frac{C}{D}\right)=\frac{P(D)}{P(C)} \)
Subject: Physics
The number \( N_{X} \) of nuclei of \( X \) at time
\( \boldsymbol{t}=\boldsymbol{T}_{1 / 2} \) is
A \( \cdot \frac{K+\lambda N_{0}}{2 \lambda} \)
в. \( \left(2 \lambda N_{0} K\right) \frac{1}{\lambda} \)
\( ^{\mathbf{c}} \cdot\left[\lambda N_{0}+\frac{K}{2}\right] \frac{1}{\lambda} \)
D. Data insufficient
Subject: Chemistry
General electronic configuration of
lanthanides are:
\( \mathbf{A} \cdot(n-2) f^{1-14}(n-1) s^{2} p^{6} d^{0-1} n s^{2} \)
B \( \cdot(n-2) f^{10-14}(n-1) d^{0-1} n s^{2} \)
C \( \cdot(n-2) f^{0-14}(n-1) d^{10} n s^{2} \)
D. \( (n-2) f^{0-1}(n-1) f^{1-14} n s^{2} \)
Subject: Chemistry
Assertion
Helium will have fewer dispersion forces between its atoms than the other
noble gases
Reason
As the mass of nonpolar atoms and molecules increases, dispersion forces increase
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect
Subject: Chemistry
The reagent used for getting trans
alkene from alkyl substituted acetylene with hydrogen is :
\( \mathbf{A} \cdot N a \) in liq. \( N H_{3} \)
B. anhy. AlCla
c. \( Z n+H C l \)
D. \( H_{2} \) in presence of \( N i \) (or) \( P t \) (or) \( P d \)
Subject: Maths
The value of \( \int e^{\tan ^{-1} x}\left(\frac{1+x+x^{2}}{1+x^{2}}\right) d x \)
is equal to
A. \( x e^{\tan ^{-1} x}+C \)
B. \( x^{2} e^{\tan ^{-1} x}+C \)
c. \( \frac{1}{x} e^{\tan ^{-1} x}+C \)
D. \( x e^{\cot ^{-1} x}+C \)
Subject: Chemistry
Geometry of ammonia molecule and the
hybridisation of nitrogen involved in it
are:
A \( \cdot s p^{3} \) - hybridisation and tetrahedral geometry
B. \( s p^{3} \) - hybridisation and distorted tetrahedral geometry
C \( \cdot s p^{2} \) - hybridisation and trianguklar geometry
D. none of the above
Subject: Physics
Plot a graph showing the variation of current density (j) versus the electric field
(E) for two conductors of different
materials. What information from this
plot regarding the properties of the conducting material, can be obtained
which can be used to select suitable
materials for use in making (i) standard resistance and
(ii) connecting wires in electric circuits?

Electron drift speed is estimated to be
of the order of \( \mathrm{mm} s^{-1} \). Yet large current
of the order of few amperes can be set up in the wire. Explain briefly.
Subject: Maths
\( \operatorname{Let} \mathbf{L}=\lim _{\mathbf{x} \rightarrow 0}= \)
\( \frac{\boldsymbol{a}-\sqrt{\boldsymbol{a}^{2}-\boldsymbol{x}^{2}}-\frac{\boldsymbol{x}^{2}}{\boldsymbol{4}}}{\boldsymbol{x}^{4}}, \boldsymbol{a}>0 \) If \( \boldsymbol{L} \) is finite
then
This question has multiple correct options
\( \mathbf{A} \cdot a=2 \)
B. \( a=1 \)
\( c \cdot_{L}=\frac{1}{64} \)
D. \( L=\frac{1}{32} \)
Subject: Maths
The radius of a circle is given as \( 15 \mathrm{cm} \)
and chord AB subtends an angle of \( 131^{\circ} \)
at the centre \( C \) of the circle.Using trigonometry ,calculate:
(i) the length of \( A B \)
(ii) the distance of \( A B \) from the centre \( C \)
Subject: Chemistry
Specific heat of substance at m.pt. (or
b.pt. or for isothermal process) and specific heat of a substance during adiabatic change respectively are
\( A \cdot 0,0 \)
B. \( 0, \infty \)
\( c \cdot \infty, 0 \)
\( D \cdot \infty, \infty \)
Subject: Physics
A bar of mass \( M \) and length \( L \) is in pure
translatory motion and its centre of
mass has velocity \( V \). It collides and sticks to a second identical bar which
is initially at rest. (Assume that it becomes one composite bar of length
\( 2 L \) ). The angular velocity of the
composite bar after collision will be :
This question has multiple correct options
A \( \cdot \frac{3}{4} \frac{V}{L} \)
в. \( \frac{4}{3} \frac{V}{L} \)
c. counterclockwise
D. Clockwise
Subject: Chemistry
Choose the correct statements -
This question has multiple correct options
\( \mathbf{A} \cdot C_{2} H_{6}+O_{2} \rightarrow C O_{2}+H_{2} O \) is an unbalanced
combustion reaction.
B. \( 2 H_{2} O_{2} \rightarrow 2 H_{2} O+O_{2} \) is a balanced combustion
reaction.
C \( . A+B C \rightarrow A C+B \) represents a single replacement
reactions.
D. \( H N O_{3}+C a(O H)_{2} \rightarrow C a\left(N O_{3}\right)_{2}+2 H_{2} O \) is an
unbalanced neutralization reaction.
Subject: Chemistry
Assertion
Sulphur on reaction with HCl produces
sulphur monochloride.
Reason
Sulphur undeigoes displacement reaction with acid.
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