AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Maths
Solution of the different equation,
\( y d x-x d y+x y^{2} d x=0 \) can be
A \( \cdot 2 x+x^{2} y=\lambda y \)
в. \( 2 y+y^{2} x=\lambda y \)
c. \( 2 y-y^{2} x=\lambda y \)
D. none of these
Subject: Maths
The area of the region bounded by the curves \( \boldsymbol{f}(\boldsymbol{x})=\operatorname{maximum}\left\{|\boldsymbol{x}|, \boldsymbol{x}^{2}, \sqrt{\boldsymbol{x}}\right\} \)
where \( \boldsymbol{x}>\mathbf{0}, \boldsymbol{g}(\boldsymbol{x})=|\boldsymbol{x}| \forall \boldsymbol{x} \leq \mathbf{0} \) and
\( h(x)=4 \) is-
\( A \cdot \frac{7}{3} \)
B. 9
c. 13
D. \( \frac{40}{3} \)
Subject: Physics
According to Newton, the viscous force
acting between liquid layers of area \( \boldsymbol{A} \)
and velocity gradient \( \frac{\Delta v}{\Delta z} \) is given by \( F=-\eta a \frac{d v}{d z}, \) where \( \eta \) is constant called
\( \mathbf{A} \cdot\left[M L^{-2} T^{-2}\right] \)
В \( \cdot\left[M^{0} L^{0} T^{0}\right] \)
\( \mathbf{c} \cdot\left[M L^{2} T^{-2}\right] \)
D. \( \left[M L^{-1} T^{-1}\right] \)
Subject: Physics
Two batteries of different emf and
internal resistances connected in series
with each other and with an external
load resistor. The current is 3.0 A. When
the polarity of one battery is reversed, the current becomes 1.0 A. The ratio of
the emf of the two batteries is :
A .2 .5: 1 \)
в. 2: 1
c. 3: 2
D. 1: 1
Subject: Physics
The angle \( \theta \) between the vector \( p=\hat{i}+ \) \( \hat{j}+\hat{k} \) and unit vector along \( x \) -axis is
\( ^{A} \cdot \cos ^{-1}\left(\frac{1}{\sqrt{3}}\right) \)
в. \( \cos ^{-1}\left(\frac{1}{\sqrt{2}}\right) \)
\( ^{\mathrm{c}} \cdot \cos ^{-1}\left(\frac{\sqrt{3}}{2}\right) \)
D. \( \cos ^{-1}\left(\frac{1}{2}\right) \)
Subject: Maths
Now, we construct rectangles with class-limits as bases and respective adjusted frequencies as heights. Draw a histogram for the marks of students given below:
\begin{tabular}{|l|c|c|c|c|c|}
\hline Marks: & \( 0-10 \) & \( 10-30 \) & \( 30-45 \) & \( 45-50 \) & \( 50-60 \) \\
\hline No. of students: & 8 & 32 & 18 & 10 & 6 \\
\hline
\end{tabular}
Subject: Maths
\( A \) has 3 tickets of a lottery containing 3 prizes and 9 blanks. \( B \) has two tickets
of another lottery containing 2 prizes and 6 blanks. The ratio of their chances
of success is
A \( \cdot \frac{32}{55}: \frac{15}{28} \)
в. \( \frac{32}{55}: \frac{13}{28} \)
c. \( \frac{34}{55}: \frac{13}{28} \)
D. \( \frac{34}{55}: \frac{15}{28} \)
Subject: Physics
An electron gun with its collector at a potential of \( 100 \mathrm{V} \) fires out electrons in a spherical bulb containing hydrogen gas at low pressure \( \left(\sim 10^{-2} \mathrm{mm} \text { of } \mathrm{Hg} \text { ). } \mathrm{A}\right. \)
magnetic field of \( 2.83 \times 10^{4} T \)
curves the path of the electrons in a
circular orbit of radius 12.0 cm.
(The path can be viewed because the
gas ions in the path focus the beam by attracting electrons, and emitting light by electron capture; this method is known as the fine beam tube method.) Determine e/m from the data.
Subject: Maths
The value of the expression \( 2 \sec ^{-1} 2+ \) \( \sin ^{-1} \frac{1}{2} \) is
A \( \cdot \frac{\pi}{6} \)
в. \( \frac{5 \pi}{6} \)
c. \( \frac{7 \pi}{6} \)
D.
Subject: Physics
A particle experiences constant acceleration for \( 20 s \) after starting from
rest. If it travels a distance \( X_{1} \), in the
first \( 10 s \) and distance \( X_{2}, \) in the remaining \( 10 s, \) then which of the
following is true?
\( \mathbf{A} \cdot X_{1}=2 X_{2} \)
В. \( X_{1}=X_{2} \)
\( \mathbf{c} \cdot X_{1}=3 X_{2} \)
D. None of these
Subject: Chemistry
Statement - I: \( 1 \mathrm{M} \) solution of NaCl has a
higher osmotic pressure than 1 M solution of glucose at the same temperature. Statement - II: The number of particles present in 1 M NaCl solution are more
than those present in 1 M glucose solution and osmotic pressure depends upon number of particles present in the
solution.
A. Statement-lis True, Statement - II is True; Statement I is a correct explanation for Statement -
B. Statement-lis True, Statement - /I is True; Statement I is NOT a correct explanation for Statement- -
c. Statement - - is True, Statement - II is False
D. Statement-lis False, Statement - II is True
Subject: Maths
\( \int \sin ^{-1} \sqrt{\frac{x}{a+x}} d x=\dots \)
A \( \cdot(a+x) \tan ^{-1} \sqrt{x / a}+\sqrt{a x}+c \)
B. \( (a+x) \tan ^{-1} \sqrt{x / a}-\sqrt{a x}+c \)
C. \( (a+x) \cot ^{-1} \sqrt{x / a}+\sqrt{a x}+c \)
D. \( (a-x) \cot ^{-1} \sqrt{x / a}-\sqrt{a x}+c \)
Subject: Physics
For a coil having \( L=2 m H, \) current
flow through it is \( I=t^{2} e^{-t} \) then the
time at which emf becomes zero:
\( \mathbf{A} \cdot 2 \sec \)
B. 1 sec
\( \mathbf{c} \cdot 4 \sec \)
D. 3 sec
Subject: Biology
Assertion
All food chains will come to stand still if
bacteria disappear from earth.
Reason
Bacteria are only associated with the soil fertility and hardly have any role in food chains.
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 standard enthalpy of combustion of sucrose is-5645 kJ mol \( ^{-1} \).What is the
advantage (in kJ \( m o l^{-1} \) of energy released as heat) of complete aerobic oxidation compared to anaerobic hydrolysis of sucrose to lactic acid? \( \triangle H_{\int}^{\circ} \) for lactic acid,CO_ \{2\} and \( H_{2} O \) is
-694,-395 and -286.0 respectively
A . advantage=4356 k..mol \( ^{-1} \)
B. advantage=5396 k..mol-
c. advantage=4756 kJ.mol-
D. advantage=5657 kJ.mol-
Subject: Maths
Find the value of
\( [4+3 \sqrt{-20}]^{1 / 2}+[4-3 \sqrt{-20}]^{1 / 2} \)
\( \mathbf{A} \cdot \mathbf{6} \)
B \( \cdot 2(3+\sqrt{5}) \)
\( \mathbf{c} \cdot 2(3-\sqrt{5}) \)
D. \( 2 \sqrt{5} \)
Subject: Maths
A cuboid is such that its length is 2 times the width and the width is 2
times its height. The side of a square, whose area is equal to the total surface area of the cuboid, in terms of the height of the cuboid is
\( \mathbf{A} \cdot 4 h \)
в. \( 6 h \)
c. \( 2 \sqrt{7} h \)
D. \( 4 \sqrt{7} h \)
Subject: Chemistry
topp \( E \)
Q Type your question
A \( (\text { \curlyvee }) C H_{3} C H_{2} C H-C H_{2} O H \)
CHa
\( (X) \rightarrow \overbrace^{\mathrm{OH}} \mathrm{CH}_{2}^{-} \prod_{\mathrm{OH}}^{\mathrm{CH}-\mathrm{OCH}_{3}} \)
\( (X) \rightarrow \overbrace^{\mathrm{OH}} \mathrm{CH}_{2}-\underset{\mathrm{O}}{\|}^{\mathrm{C}-\mathrm{OCH}_{3}} \)
D \( \cdot(\curlyvee) C H_{3} C H_{2} C H_{2} C H_{2} C H_{2} O H \)
\( (X) \rightarrow \overbrace{[1]}^{\mathrm{O}} \mathrm{CH}_{2}-\underbrace{\mathrm{C}-\mathrm{O} \mathrm{CH}_{2} \mathrm{OH}} \)
Subject: Maths
The angle of elevation of the top of a
tower from a point on the ground \( 30 \mathrm{m} \)
away fro the foot of the tower is \( 30^{\circ} . \) The
height of the tower is
tower
\( \mathbf{A} \cdot 30 \mathrm{m} \)
B. \( 10 \sqrt{3} \mathrm{m} \)
\( \mathbf{c} \cdot 10 \mathrm{m} \)
D. \( 10 \sqrt{2} \mathrm{m} \)
Subject: Physics
The nucleus obtained after \( \alpha \) -emission
from the nucleus \( _{y} \mathbf{A}^{x} \) is
A・ \( _{y-2} \mathrm{B}^{x-2} \)
В. \( _{y+2} \mathrm{B}^{x+4} \)
\( \mathbf{c} \cdot_{y} \mathbf{B}^{x} \)
D. \( _{y-2} \mathrm{B}^{x-4} \)
Subject: Chemistry
In the electrolysis of aqueous \( N a C l \) solution, side reactions taking place
are :
(I) \( 2 O H^{-}+C l_{2} \rightarrow 2 O C l^{-}+H_{2} O \)
(II) \( 2 N a+2 H_{2} O \rightarrow 2 N a O H+H_{2} \)
(III) \( 4 O H^{-} \rightarrow O_{2}+2 H_{2}+4 e^{-} \)
Select the correct alternate :
A \( . \) (I) and (III)
B. (II) and (III)
c. (I) and (II)
D. (I), (II), and (III)
Subject: Maths
Transform the following expression
\( \frac{\tan \alpha+\tan \beta}{\cot \alpha+\cot \beta}+[\cos (\alpha- \)
\( \boldsymbol{\beta}) \boldsymbol{s e c}(\boldsymbol{\alpha}+\boldsymbol{\beta})+\mathbf{1}]^{-1} \)
Subject: Maths
If \( A \) and \( B \) are mutually exclusive events
with \( \boldsymbol{P}(\boldsymbol{B}) \neq 1, \) then \( \boldsymbol{P}(\boldsymbol{A} \mid \overline{\boldsymbol{B}})= \)
\( ^{A} \cdot \frac{1}{P(B)} \)
В. \( \frac{1}{1-P(B)} \)
c. \( \frac{P(A)}{P(B)} \)
D. \( \frac{P(A)}{1-P(B)} \)
Subject: Chemistry
Which is the correct combination
\begin{tabular}{ll|l|l|} 
& & \multicolumn{2}{l} { change } \\
& & in \\
Emission & Atomic number & mass number \\
\hline (a) & \( \alpha \) & -2 & -2 \\
(b) & \( \beta^{-} \) & +1 & 0 \\
(c) & \( \gamma \) & 0 & 0 \\
(d) & \( \beta^{+} \) & -1 & 0 \\
\hline
\end{tabular}
Subject: Maths
Represent the following mixed infinite decimal periodic fractions as common fractions:
\( \left(\frac{1}{a-\sqrt{2}}-\frac{a^{2}+4}{a^{3}-\sqrt{8}}\right) \)
\( \left(\frac{a}{\sqrt{2}}+1+\frac{\sqrt{2}}{a}\right)^{-1} \)
Subject: Physics
In the circuit shown in figure in
adjoining figure \( \boldsymbol{E}=\mathbf{1 0} \boldsymbol{V}, \boldsymbol{R}_{1}= \)
\( \mathbf{1} \mathbf{\Omega}, \boldsymbol{R}_{2}=\mathbf{2} \mathbf{\Omega}, \boldsymbol{R}_{3}=\mathbf{3} \mathbf{\Omega} \) and \( \boldsymbol{L}=\mathbf{2} \boldsymbol{H} \)
Calculate value of current \( i_{1}, i_{2} \) and \( i_{3} \)
immediately after key \( S \) is closed.
\( A .3 .3 \) amp \( , 3.3 \) amp \( , 3.3 \) amp
B. 3.3 amp, 3.3 amp, 0 amp
c. 3.3 amp, 0 amp, 0 amp
D. 3.3 amp, 3.3 amp, 1.1 amp
Subject: Chemistry
The order of basic character of given
oxides is :
A. \( N a_{2} O>M g O>A l_{2} O_{3}>C u O \)
в. \( M g O>A l_{2} O_{3}>C u O>N a_{2} O \)
c. \( A l_{2} O_{3}>M g O>C u O>N a_{2} O \)
D. \( C u O>N a_{2} O>M g O>A l_{2} O_{3} \)
Subject: Maths
Consider the following statements:
i) If three sides of a triangle are equal to three sides of another triangle, then the triangles are congruent.
ii) If the three angles of a triangle are equal to three angles of another triangle
respectively, then the two triangles are
congruent.
A . (i) is correct and (ii) is false
B. Both (i) and (ii) are false
c. Both (i) and (ii) are correct
D. (i) is false and (ii) is correct
Subject: Physics
Two long parallel wires are a distance 2 a apart, as shown. Point P is in the plane of the wires and a distance a from wire
X. When there is a current lin wire \( X \)
and no current in wire \( Y \), the magnitude
of the magnetic field at \( P \) is \( B_{0} . \) When
there are equal currents lin the same direction in both wires, the magnitude of the magnetic field at P is?
A. \( \frac{2 B_{0}}{3} \)
в. \( B_{0} \)
c. \( \frac{10 B_{0}}{9} \)
D. \( \frac{4 B}{3} \)
Subject: Chemistry
A neutral atom (Ar) is converted to
\( \left(A r^{+3}\right) \) by the following process;
\( \boldsymbol{A r} \frac{\boldsymbol{E}_{1}}{-\boldsymbol{e}} \boldsymbol{A r}^{+} \frac{\boldsymbol{E}_{2}}{-\boldsymbol{e}} \boldsymbol{A r}^{+2} \frac{\boldsymbol{E}_{3}}{-\boldsymbol{e}} \boldsymbol{A r}^{+3} \)
The correct order of \( E_{1}, E_{2}, E_{3} \) energies
is:
A. \( E_{1}<E_{2}<E_{3} \)
в. \( E_{1}>E_{2}>E_{3} \)
c. \( E_{1}=E_{2}=E_{3} \)
D. \( E_{1}>E_{2}<E_{3} \)
Subject: Chemistry
\( \boldsymbol{K}_{a 1}, \boldsymbol{K}_{a 2} \) and \( \boldsymbol{K}_{a 3} \) values for \( \boldsymbol{H}_{3} \boldsymbol{P} \boldsymbol{O}_{4} \) are
\( 10^{-3}, 10^{-8} \) and \( 10^{-12} \) respectively. If
\( \boldsymbol{K}_{\boldsymbol{w}}\left(\boldsymbol{H}_{2} \boldsymbol{O}\right)=\mathbf{1 0}^{-14}, \) then which is
correct?
A. Dissociation constant of \( H P O_{4}^{2-} \) is \( 10^{-12} \)
B. \( K_{b} \) of \( H P O_{4}^{2-} 10^{-6} \)
C. \( K_{b} \) of \( H_{2} P O_{4}^{-} 10^{-1} \)
D. All are correct
Subject: Maths
In \( \triangle A B C \) the mid points of the sides
\( A B, B C \) and \( C A \) are respectively
\( (l, 0,0),(0, m, 0) \) and \( (0,0, n) . \) Then
\( \frac{A B^{2}+B C^{2}+C A^{2}}{l^{2}+m^{2}+n^{2}} \) is equal to
\( A \cdot 2 \)
B. 4
c. 8
D. 16
Subject: Maths
Find the area of the region
\( \left\{(\boldsymbol{x}, \boldsymbol{y}): \boldsymbol{x}^{2}+\boldsymbol{y}^{2} \leq \mathbf{4}, \boldsymbol{x}+\boldsymbol{y} \geq \mathbf{2}\right\} \)
Subject: Chemistry
Calculate the heat of formation of
methane, given that heat of formation of water \( = \)
\( -286 k J \quad m o l^{-1} \)
heat of combustion of methane \( = \)
\( -890 k J \quad m o l^{-1} \)
heat of combustion of carbon \( = \)
\( -393.5 k J \quad m o l^{-1} \)
A \( .75 .5 ~ k J ~ m o l- \)
-
В. \( -75.5 \mathrm{kJ} \mathrm{mol}^{-1} \)
c. \( -55.5 ~ k J \) mol \( ^{-1} \)
D. \( 55.5 ~ k J \) mol \( ^{-1} \)
Subject: Chemistry
On heating a mixture of \( N H_{4} C l \) and
\( \boldsymbol{K} \boldsymbol{N} \boldsymbol{O}_{2}, \) we get:
A \( . N H_{4} N O_{3} \)
в. \( K N H_{4}\left(N O_{3}\right)_{2} \)
c. \( N_{2} \)
D. \( N O \)
Subject: Physics
A cord is used to lower vertically a block
of mass \( M \) by a distance \( d \) with constant downword acceleration \( \frac{g}{2} \) work done by the cord on the block is
\( ^{\mathbf{A}} \cdot \frac{-M g d}{2} \)
B. \( \frac{M g d}{4} \)
c. \( \frac{-3 M g d}{4} \)
D. \( M g d \)
Subject: Maths
\( P \) is a point on the common chord \( R S \) produced by two intersecting circles.
\( A B \) and \( C D \) are the chords of the
circles,they meet at \( P \) produced.Prove that \( \boldsymbol{P A} \times \boldsymbol{P B}=\boldsymbol{P C} \times \boldsymbol{P D} \)
Subject: Chemistry
Lalita has taken sulphur powder \( (P) \) in a deflagrating spoon, burnt it and put it
in a gas jar. Then she removed the spoon and added water. In another
experiment, she has taken water in one
beaker and added a small piece of
sodium (Q). After some time, she took
both the solutions and checked them
with litmus paper. What result would
she expect?
A. In case \( P \); blue to red, in case \( Q: \) red to blue
B. In both cases, \( P \) and \( Q \) : blue to red
c. In case \( P: \) red to blue, in case \( Q: \) blue to red
D. In both cases, \( P \) and \( Q: \) red to blue
Subject: Maths
State following are True or False
If \( m=n=p \) and the groups have identical qualitative characterstic then the number of groups \( =\frac{(3 n) !}{n ! n ! n ! 3 !} \)
Note : If 3n different things are to be
distributed equally three people then the number of ways \( =\frac{(3 n) !}{(n !)^{3}} \)
A . True
B. False
Subject: Chemistry
In the below shown reaction
sequence, the compound B formed is :
\( \boldsymbol{C H}_{3} \boldsymbol{C H}_{2} \boldsymbol{C H}_{2} \boldsymbol{O H} \stackrel{\boldsymbol{P C l}_{3}}{\longrightarrow} \boldsymbol{A} \stackrel{\text {alc. } \boldsymbol{K O H}}{\boldsymbol{N}} \boldsymbol{B} \)
A. propane
B. propanol
c. propene
D. propyne
Subject: Physics
The particle \( X \) in the following nuclear
reaction is \( \frac{13}{7} \mathrm{N} \longrightarrow_{6}^{13} \mathrm{C}+_{1}^{0} \mathrm{e}+X \)
A. \( P \)
B.
\( \mathbf{c} \cdot e^{-} \)
\( D \)
Subject: Physics
A particle \( P \) is fixed at certain point in
horizontal plane and another particle \( Q \)
is moving around \( \mathrm{P} \) in circular path (with centre 0 ) of radius 'r' with
constant speed 'u'.' 'P' observes the
motion of 'Q'. Pick out correct statement
A. Velocity of approach between \( \mathrm{P} \) and \( \mathrm{Q} \) will be variable.
B. Velocity of approach between \( P \) and \( Q \) will be always negative.
C. Velocity of approach between \( \mathrm{P} \) and \( \mathrm{Q} \) will be always constant.
D. None of these
Subject: Maths
Show that \( \left|\begin{array}{lll}\boldsymbol{x} & \boldsymbol{x}^{2} & \boldsymbol{y} \boldsymbol{z} \\ \boldsymbol{y} & \boldsymbol{y}^{2} & \boldsymbol{z} \boldsymbol{x} \\ \boldsymbol{z} & \boldsymbol{z}^{2} & \boldsymbol{x} \boldsymbol{y}\end{array}\right|=(\boldsymbol{x}-\boldsymbol{y})(\boldsymbol{y}- \)
\( z(z-x)(x y+y z+z x) \)
Subject: Physics
A ball of mass m moving with a velocity u collides head on with a second ball of
mass \( m \) at rest. Coefficient of
restitution is e.

The ratio of the final and initial
velocities of the first ball is
A \( \cdot \frac{1-e}{1+e} \)
B. \( \frac{1+e}{1-e} \)
c. \( \frac{1+e}{2} \)
D. \( \frac{1-e}{2} \)
Subject: Chemistry
If \( E_{C H_{3} C O O O H \mid C_{2} H_{5} O H}^{\ominus}=0.06 V, \) Then \( E_{c e l l}^{\ominus} \)
of the reaction taking place in alcohol meter is :
\( \mathbf{A} \cdot 1.39 V \)
B. \( 1.27 V \)
c. \( 1.60 V \)
D. \( 1.51 V \)
Subject: Chemistry
Which one of the following electrolytes has the same value of van't Hoff's factor
(i) as that of \( A l_{2}\left(S O_{4}\right)_{3} \) (if all are \( 100 \% \) ionised)?
\( \mathbf{A} \cdot A l\left(N O_{3}\right)_{3} \)
B . \( K_{4}\left[F e(C N)_{6}\right] \)
\( \mathrm{c} \cdot \mathrm{K}_{2} \mathrm{SO}_{4} \)
D. \( K_{3}\left[F e(C N)_{6}\right] \)
Subject: Biology
Q Type your question
\( A \cdot A \cdot \) Cross arm
B. Actin binding site
C. Head
D. ATP binding site
B. A. Head
B. Cross arm
C. Actin binding site
D. ATP binding site
C . A. Actin binding site
B. Head
C. ATP binding site
D. Cross arm
D. A. ATP binding site
B. Actin binding site
C. Head
D. Cross arm
Subject: Chemistry
Which one of the following pairs of molecules will have a permanent dipole moments for both members?
A \( \cdot N O_{2} \) and \( O_{3} \)
B. \( \operatorname{SiF}_{4} \) and \( C O_{2} \)
c. \( \operatorname{SiF}_{4} \) and \( N O_{2} \)
D. \( N O_{2} \) and \( C O_{2} \)
Subject: Maths
Three cubes of sides \( 3 \mathrm{cm}, 4 \mathrm{cm}, \) and 5
\( \mathrm{cm} \) respectively are melted and recasted into a larger cube What is the
side of the cube so formed?
A . \( 12 \mathrm{cm} \)
B. \( 9 \mathrm{cm} \)
\( c .8 \mathrm{cm} \)
D. \( 6 \mathrm{cm} \)
Subject: Maths
Let \( A \) be a \( 3 \times 3 \) matrix such that \( A^{2}- \)
\( \mathbf{5 A}+\mathbf{7 I}=\mathbf{O} \)
Statement I: \( \boldsymbol{A}^{-1}=\frac{\mathbf{1}}{\mathbf{7}}(\mathbf{5} \boldsymbol{I}-\boldsymbol{A}) \)
Statement II: The polynomial \( \boldsymbol{A}^{\mathbf{3}}- \)
\( 2 A^{2}-3 A+I \) can be reduced to \( 5(A- \)
\( 4 I) \) Then:
A. Both the statements are true
B. Both the statements are false
c. Statement - - lis true, but Statement - -I is false
D. Statement-lis false, but Statement- -II is true
Subject: Chemistry
Which one is more stable in the
following pairs of complexes? Give
reasons.
\( \left[\boldsymbol{C o}\left(\boldsymbol{N} \boldsymbol{O}_{2}\right)_{6}\right]^{4-} \) and \( \left[\boldsymbol{C o}\left(\boldsymbol{N} \boldsymbol{O}_{2}\right)_{\boldsymbol{6}}\right]^{3-} \)
ii) \( \boldsymbol{K}_{4}\left[\boldsymbol{F} e(\boldsymbol{C} \boldsymbol{N})_{6}\right] \) and \( \boldsymbol{K}_{3}\left[\boldsymbol{F} \boldsymbol{e}(\boldsymbol{C} \boldsymbol{N})_{6}\right] \)
\( \left(\text { iii) }\left[\boldsymbol{C O}\left(\boldsymbol{H}_{2} \boldsymbol{O}\right)_{6}\right]^{2+} \) and \right.
\( \left[\boldsymbol{C O}\left(\boldsymbol{N} \boldsymbol{H}_{3}\right)_{6}\right]^{2+} \)
Subject: Maths
\( \operatorname{Let} z=\frac{(1+i)^{2}}{a-i},(a>0) \) and \( |z|=\sqrt{\frac{2}{5}} \)
then \( \bar{z} \) is equal to
A. \( -\frac{1}{5}-\frac{3 i}{5} \)
в. \( \frac{1}{5}+\frac{3 i}{5} \)
\( c \cdot \frac{3}{5}-\frac{1 i}{5} \)
D. \( -\frac{3}{5}+\frac{1 i}{5} \)
Subject: Physics
In a radioactive decay, an element \( _{Z} X^{A} \) emits four \( \alpha \) -particles, three \( \beta \) -particles and eight gamma photons. The atomic number and mass number of the
resulting final nucleus are
A. \( Z-11, A-16 \)
в. \( Z-5, A-13 \)
c. \( Z-5, A-16 \)
D. \( Z-8, A-13 \)
Subject: Maths
If \( e^{x}=y+\sqrt{1+y^{2}}, \) then the value of \( y \)
is
A \( \cdot \frac{1}{2}\left(e^{x}+e^{-x}\right) \)
в. \( \frac{1}{2}\left(e^{x}-e^{-x}\right) \)
c. \( \quad \frac{-x}{2} \)
D. \( _{e^{x}}+e^{\frac{-x}{2}} \)
Subject: Physics
\( \ln \) a circuit \( L, C, R \) are connected in
series with an alternating voltage source of frequency \( f \). The current lags
the voltage by \( 45^{0} . \) The value of \( C \) is:
A \( \cdot \frac{1}{\pi f(2 \pi f L+R)} \)
B・ \( \frac{1}{2 \pi f(2 \pi f L-R)} \)
c. \( \frac{1}{2 \pi f(2 \pi f L+R)} \)
D. \( \frac{1}{\pi f(2 \pi f L-R)} \)
Subject: Physics
The incorrect statement for L-R-C series
circuit is
A. The potential difference across the resistance and the appleid e.m.f. are always in same phase
B. The phase difference across inductive coil is \( 90^{\circ} \)
C. The phase difference between the potential difference across capacitor and potential difference across inductance is \( 90^{\circ} \)
D. The phase difference between potential difference across capacitor and potential difference across resistance is \( 90^{\circ} \)
Subject: Chemistry
Assertion
Reduction potential of \( M n(+3 t o+2) \) is more positive than \( \boldsymbol{F e}(+\boldsymbol{3} \text { to }+\mathbf{2} \) ).
Reason
lonisation potential of \( M n \) is more than
that of \( F e \)
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
Polarizability of halide ions increases in
the order:
A \( \cdot F^{-}<I^{-}<B r^{-}<C l \)
B. \( C l^{-}<B r^{-}<I^{-}<F^{-} \)
c. \( I^{-}<B r^{-}<C l^{-}<F^{-} \)
D. \( F^{-}<C l^{-}<B r^{-}<I^{-} \)
Subject: Physics
A conducting hollow sphere of radius
\( 0.1 \mathrm{m} \) is given a charge of \( 10 \mu C . \) The
electric potential on the surface of
sphere will be :
A . zero
B . \( 3 \times 10^{5} V \)
\( \mathbf{c} \cdot 9 \times 10^{5} V \)
\( \mathbf{D} \cdot 9 \times 10^{9} V \)
Subject: Chemistry
Which compound to use for treatment
of tumor?
A \( \cdot \operatorname{Cis}\left[P d C l_{2}\left(N H_{3}\right)_{2}\right] \)
B . \( \operatorname{Trans}\left[P d C l_{2}\left(N H_{3}\right)_{2}\right] \)
c. \( \operatorname{cis}\left[\operatorname{PtCl}_{2}\left(N H_{3}\right)_{2}\right. \)
D. \( \operatorname{Trans}\left[\operatorname{PtCl}_{2}\left(\mathrm{NH}_{3}\right)_{2}\right] \)
Subject: Physics
A small pin fixed on a table top is
viewed from above from a distance of
\( 50 \mathrm{cm} . \) By what distance would the pin
appear to be raised if it is viewed from
the same point through a \( 15 \mathrm{cm} \) thick glass slab held parallel to the table?
Refractive index of glass \( =1.5 . \) Does the answer depend on the location of the
slab?
Subject: Chemistry
Extraction of aluminium from
aluminium oxide \( \left(A l_{2} O_{3}\right) \) is best done
by:
A. Electrolytic reduction of \( A l_{2} O_{3} \)
B. Reduction of \( A l_{2} O_{3} \) with carbon
c. Reduction of \( A l_{2} O_{3} \) with sodium
D. Reduction of \( A l_{2} O_{3} \) with \( c o \)
Subject: Chemistry
Which of the following correctly represents the heat of formation of
methane?
A \( \cdot \mathrm{c} \) (diamond) \( +2 \mathrm{H}_{2(g)} \rightarrow \mathrm{CH}_{4(9)} \)
B. \( c \) (diamond) \( +2 H_{2(g)} \rightarrow C H_{4(l)} \)
c. c (graphite) \( +2 H_{2(g)} \rightarrow C H_{4(g)} \)
D. c (graphite) \( +4 H_{(g)} \rightarrow C H_{4(g)} \)
Subject: Maths
The line \( A x+B y+C=0 \) cuts the
circle \( \boldsymbol{x}^{2}+\boldsymbol{y}^{2}+\boldsymbol{a} \boldsymbol{x}+\boldsymbol{b} \boldsymbol{y}+\boldsymbol{c}=\boldsymbol{0} \) in \( \boldsymbol{P} \)
and \( Q \)
The line \( \boldsymbol{A}^{\prime} \boldsymbol{x}+\boldsymbol{B}^{\prime} \boldsymbol{y}+\boldsymbol{C}^{\prime}=\mathbf{0} \) cuts the
circle \( \boldsymbol{x}^{2}+\boldsymbol{y}^{2}+\boldsymbol{a}^{\prime} \boldsymbol{x}+\boldsymbol{b}^{\prime} \boldsymbol{y}+\boldsymbol{c}^{\prime}=\mathbf{0} \) in \( \boldsymbol{R} \)
and \( S \).
If \( P, Q, R, S \) are concyclic, then show
that
\( \left|\begin{array}{ccc}\boldsymbol{a}-\boldsymbol{a}^{\prime} & \boldsymbol{b}-\boldsymbol{b}^{\prime} & \boldsymbol{c}-\boldsymbol{c}^{\prime} \\ \boldsymbol{A} & \boldsymbol{B} & \boldsymbol{C} \\ \boldsymbol{A}^{\prime} & \boldsymbol{B}^{\prime} & \boldsymbol{C}^{\prime}\end{array}\right|=\mathbf{0} \)
Subject: Physics
An object thrown upwards with a
velocity \( u \) from the top of a tower of
height \( \boldsymbol{H} \) reaches the ground in \( \boldsymbol{t}_{\mathbf{1}} \) seconds. When thrown downwards with
the same speed it reaches the ground in
\( t_{2} \) seconds. When dropped from the top
of tower it reaches in \( t_{3} \) seconds. Then \( t_{3} \)
is equal to (in terms of \( t_{1} \) and \( t_{2} \) )
\( \mathbf{A} \cdot t_{1}+t_{2} \)
B. \( \sqrt{t_{1} t_{2}} \)
c. \( t_{1}-t_{2} \)
D. \( t_{1} / t_{2} \)