AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Maths
Statement-1: The point \( \boldsymbol{A}(\mathbf{3}, \mathbf{1}, \boldsymbol{6}) \) is the mirror image of the point \( B(1,3,4) \) in
the plane \( \boldsymbol{x}-\boldsymbol{y}+\boldsymbol{z}=\mathbf{5} \)
Statement-2: The plane \( \boldsymbol{x}-\boldsymbol{y}+\boldsymbol{z}=\mathbf{5} \)
bisects the line segment joining
\( \boldsymbol{A}(\boldsymbol{3}, \mathbf{1}, \boldsymbol{6}) \) and \( \boldsymbol{B}(\mathbf{1}, \boldsymbol{3}, \boldsymbol{4}) \)
A. Statement-1 is true and Statement-2 is true:
Statement-2 is not the correct explanation for Statement-1
B. Statement-1 is true, Statement-2 is false
c. Statement-1 is false, Statement-2 is true
D. Statement-1 is true, Statement-2 is true; Statement-2 is the correct explanation for Statement-
Subject: Physics
What is the p.d. across the terminals
\( \left(V_{T}\right) \) of a cell with emf \( E \) for open circuit
\( ? \)
A \( \cdot V_{T}<E \)
в. \( V_{T}>E \)
c. \( V_{T}=0 \)
D. \( V_{T}=E \)
Subject: Physics
A jet plane is travelling towards west at a speed of \( 1800 \mathrm{km} / \mathrm{h} . \) What is the
voltage difference developed between the ends of the wing having a span of 25 \( \mathrm{m}, \) if the Earth's magnetic filed at the
location has a magnitude of \( 5 \times 10^{-4} T \)
and the dip angle is \( 30^{0} ? \)
Subject: Physics
Thin threads are tightly wound on the ends of a uniform solid cylinder of mass
m. The free ends of the threads are
attached to the ceiling of an elevator car. The car starts going up with an
acceleration \( \overrightarrow{\boldsymbol{w}}_{\mathbf{0}} \)
Find the acceleration \( \vec{w}^{\prime} \) of the cylinder
relative to the car:
A \( \cdot \vec{w}^{\prime}=\frac{2}{3}\left(g-\vec{w}_{0}\right) \)
B \( \cdot \vec{w}^{\prime}=\frac{3}{2}\left(g-\vec{w}_{0}\right) \)
c. \( \vec{w}^{\prime}=2 \frac{3}{2}\left(g-\vec{w}_{0}\right) \)
D・ \( \vec{w}^{\prime}=2 \frac{2}{3}\left(g-\vec{w}_{0}\right) \)
Subject: Maths
Write first four terms of the \( A P, \) when
the first term a and the common
difference d are given as follows:
\( (i) a=10 d=10 \)
(ii) \( a=-2, d=0-3 \)
(iii) \( a=4, d=-3 \)
(iv) \( a=-1, d=\frac{1}{2} \)
\( (v) a=-1, d=\frac{1}{2} \)
Subject: Physics
The ionospheric layer acts as a reflector for the frequency range
\( \mathbf{A} \cdot 1 \mathrm{kHz} \) to \( 10 \mathrm{kHz} \)
B. 3 to 30 МНz
\( c \cdot 3 \) to \( 30 \mathrm{kHz} \)
D. 100 kHz to 1 MHz
\( E . \) 3 GHz to 30 GHz
Subject: Physics
Assertion
The average mass of one Mg atom is
24.305 amu, which is not equal to the actual mass of one Mg atom.
Reason Three isotopes, \( ^{24} M g,^{25} M g \) and \( ^{26} M g \) of Mg can be found in nature.
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: Maths
The table shows the number of books on
each number of subjects. Find the
median.
Subject \( \quad 2 \quad 3 \quad 5 \quad 6 \) 3
50 \begin{tabular}{l|c|c|c|} 
number f books & 20 & 39 & 10 \\
\hline
\end{tabular} 20
\( A \cdot 2 \)
B. 3
c. 5
\( D \)
Subject: Physics
Assertion
Path of a particle in SHM is always a
straight line.
Reason
All straight line motions are not simple
harmonic.
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
Out of \( N i(C O)_{4}, N i(C N)_{4}^{2-} \) and
\( N i C l_{4}^{2-} \) select paramagnetic and diamagnetic.
A \( \cdot N i(C O)_{4} \) and \( N i(C N)_{4}^{2-} \) are diamagnetic
B . \( N i C l_{4}^{2-} \) is paramagnetic
c. Both (A) and
(B) Correct
D. None of these
Subject: Physics
A particle having charge \( q \) and mass \( m \) is projected with velocity \( \overrightarrow{\boldsymbol{v}}=2 \hat{\mathbf{i}}-\mathbf{3} \hat{\mathbf{j}} \)
in a uniform electric field \( \overrightarrow{\boldsymbol{E}}=\boldsymbol{E}_{0} \cdot \hat{\boldsymbol{j}} \)
Change in momentum \( |\Delta \bar{p}| \) during any
time interval \( t \) is given by:
A \( \cdot \sqrt{q E_{0} t} \)
в. \( q E_{0} \)
c. \( \frac{q E_{0} t}{m} \)
D. zero
Subject: Maths
If \( \boldsymbol{f}: \boldsymbol{R} \rightarrow \boldsymbol{R} \) and \( \boldsymbol{g}: \boldsymbol{R} \rightarrow \boldsymbol{R} \) are defined
by \( \boldsymbol{f}(\boldsymbol{x})=\boldsymbol{x}-[\boldsymbol{x}] \) and \( \boldsymbol{g}(\boldsymbol{x})=[\boldsymbol{x}] \) for
\( \boldsymbol{x} \in \boldsymbol{R}, \) where \( [\boldsymbol{x}] \) is the greatest integer
not exceeding \( x, \) then for every \( x \in \) \( \boldsymbol{R}, \boldsymbol{f}(\boldsymbol{g}(\boldsymbol{x}))= \)
A . \( x \)
в. 0
c. \( f(x) \)
D. \( g(x) \)
Subject: Physics
Assertion
The density of water remains constant as it is cooled from room temperature
until its temperature reaches \( 4^{\circ} C \)
Reason

Below \( 4^{\circ} C \),the density increases.
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
Let \( \boldsymbol{R}=\{(1, \mathbf{3}),(2,2),(3,2)\} \) and \( \boldsymbol{S}= \)
\{(2,1),(3,2),(2,3)\} be two relations on
\( \operatorname{set} A=\{1,2,3\} . \) Then \( R_{0} S \) is equal
A \( \cdot\{(2,3),(3,2),(2,2)\} \)
B . \{(1,3),(2,2),(3,2),(2,1),(2,3)\}
c. \{(3,2),(1,3)\}
D. \{(2,3),(3,2)\}
Subject: Maths
If \( \theta \) be the angle between the vectors \( i+ \) \( j \) and \( j+k, \) then \( \theta \) is
\( \mathbf{A} \cdot \mathbf{0} \)
в. \( \pi / 4 \)
c. \( \pi / 2 \)
D . \( \pi / 3 \)
Subject: Physics
A cell sends a current through a resistance \( R \) for time \( t ; \) next the same
cell sends current through another resistance \( r \) for the heat is developed in
both the resistance, then the internal
resistance of the cell is:
A. \( (R+r) / 2 \)
в. \( (R-r) / 2 \)
c. \( \sqrt{R r} \)
D. \( \sqrt{R r} / 2 \)
Subject: Chemistry
Some gaseous equilibrium are following:
\( \boldsymbol{C O}+\boldsymbol{H}_{2} \boldsymbol{O} \stackrel{\boldsymbol{K}}{\rightleftharpoons} \boldsymbol{C O}_{2}+\boldsymbol{H}_{2} \)
\( 2 C O+O_{2} \stackrel{K_{1}}{\rightleftharpoons} 2 C O_{2} \)
\( 2 H_{2}+O_{2} \stackrel{K_{2}}{\rightleftharpoons} 2 H_{2} O \)
then find out the relation between
equilibrium constants :-
A \( \cdot K=K_{1} K_{2} \)
B. \( K=\left(K_{1} K_{2}\right)^{2} \)
C . \( K=\left(K_{1} K_{2}\right)^{-1 / 2} \)
D. \( K=\left(K_{1} / K_{2}\right)^{1 / 2} \)
Subject: Physics
A uniform sphere of radius \( \boldsymbol{R} \) is placed on a smooth horizontal surface and a
horizontal force \( \boldsymbol{F} \) is applied on it at a
distance \( h \) above the centre. The
acceleration of the centre of mass of the
sphere is
A. maximum when \( h=0 \)
B. maximum when \( h= \) R
c. maximum when \( h=R / 2 \)
D. independent of \( h \)
Subject: Maths
Assertion
\( \operatorname{Let} \boldsymbol{A}=\{1,2,3,4,5\} \rightarrow B= \)
\{1,2,3,4,5\} then number of one-one
mapping from \( \boldsymbol{A} \) to \( \boldsymbol{B} \) such that \( \boldsymbol{f}(\boldsymbol{i}) \neq \)
\( j \) is equal to \( 44(1 \leq i \leq 5,1 \leq j \leq 5) \)
Reason
The number of dearrengement of \( n \) object is given by
\( n !\left\{1-\frac{1}{1 !}+\frac{1}{2 !}-\frac{1}{3 !}+\ldots+\frac{(-1)^{n}}{1 !}\right\} \)
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
Find the distance of the point (2,12,5) from the point of intersection of the line \( \vec{r}=2 \hat{i}-4 \hat{j}+2 \hat{k}+\lambda(3 \hat{i}+4 \hat{j}+2 \hat{k}) \)
and the plane \( \vec{r}(\hat{i}-2 \hat{j}+\hat{k})=0 \)
Subject: Physics
A charged drop of radius \( 1.92 \mathrm{mm} \) is kept stationary by the application of an electric field of \( 1.65 \times 10^{6} \mathrm{N} / \mathrm{C} \) in
Millikans oil drop experiment. The charge, if the density of oil is 920 \( K g / m^{3}, \) is
A \( \cdot 1.72 \times 10^{-18} \)
В. \( 16.2 \times 10^{-19} \)
c. \( 1.82 \times 10^{-17} \)
D. \( 1.92 \times 10^{-17} \)
Subject: Maths
\( \boldsymbol{f}: \boldsymbol{R} \rightarrow \boldsymbol{R}, \boldsymbol{g}: \boldsymbol{R} \rightarrow \boldsymbol{R} \) and \( \boldsymbol{f}(\boldsymbol{x})=\sin \boldsymbol{x} \)
\( \boldsymbol{g}(\boldsymbol{x})=\boldsymbol{x}^{2} \) then \( \boldsymbol{f o g}(\boldsymbol{x})= \)
A \( \cdot x^{2}+\sin x \)
B. \( x^{2} \sin x \)
\( \mathbf{c} \cdot \sin ^{2} x \)
\( D \cdot \sin x^{2} \)
Subject: Physics
A particle is located at \( (3 m, 4 m) \) and moving with \( \overrightarrow{\boldsymbol{v}}=(4 \hat{\boldsymbol{i}}-\boldsymbol{3} \hat{\boldsymbol{j}}) \boldsymbol{m} / \boldsymbol{s} . \) Find
its magnitude of angular velocity about origin at this instant in rad/sec
Subject: Maths
\( \begin{array}{ccc}(\boldsymbol{b}+\boldsymbol{c})^{2} & \boldsymbol{a}^{2} & \boldsymbol{a}^{2} \\ \boldsymbol{b}^{2} & (\boldsymbol{c}+\boldsymbol{a})^{2} & \boldsymbol{b}^{2} \\ \boldsymbol{c}^{2} & \boldsymbol{c}^{2} & (\boldsymbol{a}+\boldsymbol{b})^{2}\end{array} \mid= \)
Subject: Chemistry
Assertion
Element can form different compound.
Reason

Any substance that contains only one
kind of an atom is known as an element.
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
Solve the following pair of linear equations by the substitution method.
(i) \( \boldsymbol{x}+\boldsymbol{y}=\mathbf{1 4} ; \boldsymbol{x}-\boldsymbol{y}=\mathbf{4} \)
(ii) \( s-\boldsymbol{t}=\mathbf{3} ; \frac{\boldsymbol{s}}{\mathbf{3}}+\frac{\boldsymbol{t}}{\mathbf{2}}=\mathbf{6} \)
(iii) \( 3 x-y=3 ; 9 x-3 y=9 \)
(iv) \( 0.2 x+0.3 y=1.3 ; 0.4 x+0.5 y= \)
\( \mathbf{2 . 3} \)
(v) \( \sqrt{\mathbf{2}} \boldsymbol{x}+\sqrt{\mathbf{3}} \boldsymbol{y}=\mathbf{0} ; \sqrt{\mathbf{3}} \boldsymbol{x}-\sqrt{\mathbf{8}} \boldsymbol{y}=\mathbf{0} \)
(vi) \( \frac{\mathbf{3} \boldsymbol{x}}{\mathbf{2}}-\frac{\mathbf{5} \boldsymbol{y}}{\mathbf{3}}=-\mathbf{2} ; \frac{\boldsymbol{x}}{\mathbf{3}}+\frac{\boldsymbol{y}}{\mathbf{2}}=\frac{\mathbf{1 3}}{\mathbf{6}} \)
Subject: Chemistry
Assertion
Adsorption is exothermic and spontaneous inspite of the fact that
adsorption is accompained with decrease in entropy.
Reason
The factor \( T \Delta S \) is lesser than \( \Delta H \)
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
If \( \mathrm{K} \) for the reaction \( \boldsymbol{H}_{2}+\boldsymbol{I}_{2} \rightleftharpoons 2 \boldsymbol{H} \boldsymbol{I} \) is
equal to 45.9 at \( 450^{\circ} \mathrm{C} \) and 1 mole of
each \( \boldsymbol{H}_{2} \) and \( \boldsymbol{I}_{2} \) are introduced into a \( \mathbf{1} \)
liter box at same temperature, what will
be the expression for \( \mathrm{K} \) at equilibrium?
A \( \cdot \frac{\left[x^{2}\right]^{2}}{[1-x][1-x]} \)
В. \( \frac{\left[2 x^{2}\right]^{2}}{[1-x][1-x]} \)
c. \( \frac{\left[2 x^{2}\right]^{2}}{[x][x]} \)
D. \( \frac{[1-x][1-x]}{\left[2 x^{2}\right]} \)
E \( \cdot \frac{[1-x][1-x]}{\left[x^{2}\right]^{2}} \)
Subject: Maths
n tne Tlgure (IIVIAGE
(a) \( \operatorname{Is} \angle 1 \)
adjacent to \( \angle 2 ? \)
(b) \( \operatorname{ls} \angle A O C \)
adjacent to \( \angle A O E \) ?
(c) Do \( \angle C O E \) and \( \angle E O D \) from linear
pair?
(d) Are \( \angle B O D \) and \( \angle D O A \)
supplementary?
(e) is \( \angle 1 \) vertically opposite to \( \angle 4 ? \)
(f) What is the vertically opposite angle
of \( \angle 5 ? \)
Subject: Chemistry
Excess \( F_{2}(g) \) reacts at \( 150^{0} \mathrm{C} \) and 1.0
\( \operatorname{atm} \) pressure with \( B r_{2}(g) \) to give a
compound \( B r F_{n} . \) What is n? [Atomic mass \( \mathrm{Br}=80, \mathrm{F}=19] \)
Subject: Physics
Imagine an atom made up of proton and a a hypothetical particle of double the mass of the electron but having the same charge as the electron. Apply the Bohr atom model and consider all
possible transitions of this hypothetical
particle to the first excited level. The longest wavelength photon that will be
emitted has wavelength \( \lambda \) (give in term
of the Rydberg constant R for the hydrogen atom) equal to
\( A \cdot 9 / 5 R \)
B. 36/5 R
c. \( 18 / 5 \) R
D. 4/ R
Subject: Chemistry
\( \boldsymbol{C H}_{3}-\boldsymbol{C H}\left(\boldsymbol{C H}_{3}\right)-\boldsymbol{C H}\left(\boldsymbol{C}_{6} \boldsymbol{H}_{5}\right)- \)
\( N H_{2} \)
The IUPAC name of the compound is :
A. \( 1- \) Amino -1 - phenyl - 2 - methyl propane
B. 2- Methyl-1- phenyl propan-1 - amine
c. 2- Methyl-1- amino -1 - phenyl propane
D. 1- -Isopropyl -1 - phenyl methyl amine
Subject: Maths
The values of he equation afor which
both the roots of the equation \( (a- \)
6)\( x^{2}=a(x-3) \) are positive are given
by
в. \( \left(0, \frac{72}{11}\right) \)
c. \( \left(6, \frac{72}{11}\right) \)
D. \( \left(\frac{72}{13}, 6\right) \)
Subject: Maths
\( \operatorname{Let} \boldsymbol{f}(\boldsymbol{x})=\left\{\begin{array}{l}\mathbf{1}+|\boldsymbol{x}|, \quad \boldsymbol{x}<-\mathbf{1} \\ {[\boldsymbol{x}], \quad \boldsymbol{x} \geq-\mathbf{1}}\end{array} \) where \right.
denotes the greatest integer function,
Find \( \boldsymbol{f}\{\boldsymbol{f}(-\mathbf{2 . 3})\} \)
Subject: Chemistry
Rearrangement of carbon skeleton of substrate is possible in which of the following reactions?
\( \boldsymbol{S}_{N} \mathbf{1}, \boldsymbol{S}_{N} \mathbf{2}, \boldsymbol{E} \mathbf{1}, \boldsymbol{E} \mathbf{2}, \boldsymbol{E} \mathbf{1} \mathbf{c} \mathbf{B}, \boldsymbol{S}_{N} \mathbf{2} \operatorname{Th}, \boldsymbol{S}_{N} \mathbf{2} \)
Ar, EAS(Electrophilic aromatic substitution), electrophilic addition on alkenes, free radical substitution of
alkanes.
Subject: Chemistry
In the given reaction, \( \boldsymbol{K}_{2} \boldsymbol{C r}_{2} \boldsymbol{O}_{7}+ \)
\( \boldsymbol{X} \boldsymbol{H}_{2} \boldsymbol{S} \boldsymbol{O}_{4}+\boldsymbol{Y} \boldsymbol{S} \boldsymbol{O}_{2} \rightarrow \boldsymbol{K}_{2} \boldsymbol{S} \boldsymbol{O}_{4}+ \)
\( \boldsymbol{C r}_{2}\left(\boldsymbol{S O}_{4}\right)_{3}+\boldsymbol{Z H}_{2} \boldsymbol{O} . \) Find \( \mathbf{X}, \mathbf{Y} \) and \( \mathbf{Z} \)
Subject: Chemistry
A student takes 2 mL acetic acid in a
dry test tube and adds a pinch of sodium hydrogen carbonate to it. He makes the following observations:
I. A colourless and odourless gas evolves with a brisk effervescence.
II. The gas turns lime water milky when
passed through it.
III. The gas burns with an explosion when a burning splinter is brought near ¡t
IV. The gas extinguishes the burning splinter that is brought near it. The correct observations are:
A. ।, , I, and III
B. II, III and IV
c. ॥ा, Iv and ।
D. IV, I and II
Subject: Physics
A midpoint of a thin uniform rod \( A B \) of
mass \( m \) and length \( l \) is rigidly fixed to a
rotation axle \( O O^{\prime} \) as shown in figure
above. The rod is set into rotation with a
constant angular velocity \( \omega . \) If the
resultant moment of the centrifugal
forces of inertia relative to the point \( \boldsymbol{C} \)
in the reference frame fixed to the axle
OO' and to the rod is given by \( N= \) \( \frac{1}{x} m \omega^{2} l^{2} \sin 2 \theta, \) then the value of \( x / 4 \) is :
Subject: Physics
Assertion
A body on an inclined plane just tends to slide down if the angle of inclination is equal to angle of friction.
Reason
When the angle of inclination is equal
to the angle of friction, the component of weight parallel to the plane is just sufficient to overcome the frictional
force.
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
\( \left(1+x^{2}\right)\left(1+y^{2}\right)\left(1+z^{2}\right) \) can be
expressed as \( \left(1-\sum x y\right)^{2}+ \)
\( \left(\sum x-x y z\right)^{2} . \) If this is true enter 1
else enter 0
Subject: Chemistry
0.1 mole of \( H_{2} \) and 0.2 mole of \( I_{2} \) are
made to react in order to attain
equilibrium \( \boldsymbol{H}_{2}+\boldsymbol{I}_{2} \rightleftharpoons \mathbf{2} \boldsymbol{H} \boldsymbol{I} . \mathrm{At} \)
equilirbrium \( 20 \% H_{2} \) is converted into
\( H I, \) calculate amount of \( H I \) formed
Subject: Chemistry
Which of the following monomers gives the polymer neoprene on polymerisation
?
A \( \cdot C C l_{2}=C C I_{2} \)
B . \( C H_{2}=C H C l \)
c. \( C H_{2}=C(C l)-C H=C H_{2} \)
\( \mathbf{D} \cdot C F_{2}=C F_{2} \)
Subject: Chemistry
Maximum change in \( p H \) is observed
when 50 of \( 1 M K O H \) solution is
added to
A . 25 ml. of \( 2.5 N \) HCl
B. \( 50 \mathrm{ml} \) of \( 1 \mathrm{N} \) HCl
c. \( 30 \mathrm{ml} \) of \( 2 \mathrm{N} \) HCl
D. \( 50 \mathrm{ml} \) distilled water
Subject: Chemistry
Which of the following represent \( s p- \)
\( s p-s p^{2}-s p-s p^{2}-s p^{3} \)
hybridization from left to right order?
\( A \)
\( C H_{2}=C H-C=C-C \equiv N \)
B. \( C H \equiv C-C H=C=C H-C H_{3} \)
c.
\( N \equiv C-C-C-C H-C H_{3} \)
\( D \)
Subject: Maths
In the following figure, \( \square A B C D \) is a
parallelogram. \( D L \perp A B \) and \( A B=13 \)
\( \mathrm{cm}=A D . \) If the area of parallelogram
is \( 156 \mathrm{cm}^{2} \). Find \( A L \)
\( A \cdot 5 \mathrm{cm} \)
B. \( 6 \mathrm{cm} \)
\( c \cdot 7 \mathrm{cm} \)
\( 0.8 \mathrm{cm} \)
Subject: Maths
Solve: \( \int \frac{x^{2}-1}{x^{3} \sqrt{2 x^{4}-2 x^{2}+1}} d x \) is equal
to
A \( \cdot \frac{\sqrt{2 x^{4}-2 x^{2}+1}}{x^{2}}+C \)
B. \( \frac{\sqrt{2 x^{4}-2 x^{2}+1}}{x^{3}}+C \)
c. \( \frac{\sqrt{2 x^{4}-2 x^{2}+1}}{x}+C \)
D. \( \frac{\sqrt{2 x^{4}-2 x^{2}+1}}{2 x^{2}}+C \)
Subject: Maths
If \( \boldsymbol{X}=\left\{4^{n}-3 n-1: n \in N\right\} \) and
\( \boldsymbol{Y}=\{\mathbf{9}(\boldsymbol{n}-\mathbf{1}): \boldsymbol{n} \in \boldsymbol{N}\}, \) where \( \mathrm{N} \) is
the set of natural numbers, then \( \boldsymbol{X} \cup \boldsymbol{Y} \)
is equal to:
A. \( Y \)
B. \( N \)
c. \( Y-x \)
D. \( x \)
Subject: Maths
The dimensions of a room are \( 10 \mathrm{m} \times 7 \)
\( \mathrm{m} \times 5 \mathrm{m} . \) There are 2 doors and 3
windows in the room. The dimensions of
the doors are \( 1 \mathrm{m} \times 3 \mathrm{m} \). One window is
of the size \( 2 \mathrm{m} \times 1.5 \mathrm{m} \) and other two
windows are size \( 1 \mathrm{m} \times 1.5 \mathrm{m} \). The cost
of painting the walls at Rs. 3 per \( m^{2} \) is
A. Rs. 474.00
B. Rs. 578.00
c. Rs. 648.00
D. Rs. 849.00
Subject: Physics
Find the projection of \( \vec{A}=2 \hat{i}-\hat{j}+ \)
\( \hat{\boldsymbol{k}} \quad \boldsymbol{o} \boldsymbol{n} \quad \overrightarrow{\boldsymbol{B}}=\hat{\boldsymbol{i}}-\boldsymbol{2} \hat{\boldsymbol{j}}+\hat{\boldsymbol{k}} \)
\( A \cdot \frac{5}{\sqrt{6}} \)
B. \( \frac{7}{10} \)
\( c \cdot \frac{6}{\sqrt{5}} \)
D. \( \$ \$ \) frac \( \{5 \text { ) ( } \mid \text { sqre }\{3\}\} \)
Subject: Physics
A block of metal weighing \( 2 k g \) is resting
on a frictionless plane. It is struck by a jet releasing water at a rate of \( 1 k g / s \)
and at a speed of \( 5 m / s \).The initia acceleration of the block will be
A \( .2 .5 m / s^{2} \)
B. \( 0.5 m / s^{2} \)
c. \( 10 m / s^{2} \)
D. \( 20 m / s^{2} \)
Subject: Maths
The area (in sq. units) of the region described by
\( \left\{(x, y) ; y^{2} \leq 2 x \text { and } y \geq 4 x-1\right\} \) is
\( A \cdot \frac{7}{32} \)
в. \( \frac{5}{64} \)
c. \( \frac{15}{64} \)
D. \( \frac{9}{32} \)
Subject: Maths
A diet of a sick person must contains at
least 48 units of vitamin \( A \) and 64 units
of vitamin \( B \). Two foods \( F_{1} \) and \( F_{2} \) are
available. Food \( F_{1} \) costs Rs. 6 per unit
and Food \( F_{2} \) costs Rs. 10 per unit. One
unit of food \( F_{1} \) contains 6 units of vitamin \( A \) and 7 units of vitamin \( B \). One
unit of food \( F_{2} \) contains 8 units of
vitamin \( A \) and 12 units of vitamin \( B \).
Find the minimum cost for the diet that
consists of mixture of these two foods
and also meeting the minimum nutritional requirements.
Subject: Maths
\( \left\{\begin{array}{ccc}\text { Find } \lim _{x \rightarrow 0} f(x) & \text { where } f(x)= \\ x-1 & \text { if } & x<0 \\ 0 & \text { if } & x=0 \\ x+1 & \text { if } & x>0\end{array}\right. \)
Subject: Chemistry
\( A+B \rightleftharpoons C+D, K_{c} \) for this reaction is
10. If 1,2,3,4 mole/litre of \( A, B, C \) and
\( D \) respectively are present in a
container at \( 25^{\circ} C, \) the direction of
reaction will be:
A. from left to right
B. from right to left
c. reaction is at equilibrium
D. unpredictable
Subject: Physics
If the electric flux entering and leaving
a closed surface are \( 6 \times 10^{6} \) and \( 9 \times \)
\( 10^{6} S I \) units respectively, then the
charge inside the surface of
permittivity of free space \( \omega_{0} \) is
A. \( \omega_{0} \times 10^{6} \)
В . \( -\omega_{0} \times 10^{6} \)
c. \( -2 \omega_{0} \times 10^{6} \)
D. \( 3 \omega_{0} \times 10^{6} \)
E \( .2 \omega_{0} \times 10^{6} \)
Subject: Chemistry
Assertion
Micelles are formed by surfactant molecules above the critical micellar
concentration (CMC).
Reason
The conductivity of solution having surfactant molecules decreases sharply at the CMC.
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
An alternating voltage given as \( \boldsymbol{V}= \) \( \mathbf{1 0 0} \sqrt{\mathbf{2}} \sin 100 t \quad \) is applied to a
capacitor of \( 1 \mu F \). The current reading of
the ammeter will be equal to \( \mathrm{mA} \)
A . 10
B . 20
c. 40
D. 80
Subject: Chemistry
An organic compound \( \boldsymbol{A}\left(\boldsymbol{C}_{\mathbf{9}} \boldsymbol{H}_{8} \boldsymbol{O}_{3}\right) \) does
not react with an aqueous solution of
\( N a H C O_{3} \) and does not change the
color of litmus paper. A on acid
hydrolysis gives \( B\left(C_{9} H_{8} O_{4}\right) \) whereas \( A \) on treatment with methanol in acid
medium gives \( C\left(C_{10} H_{14} O_{4}\right) \) as the major alcoholysis product. B on heating with excess of soda-lime produces toluene. Deduce structures of \( A \) to \( C \)
Subject: Maths
If \( \lim _{x \rightarrow a}\left\{\frac{f(x)}{g(x)}\right\} \) exists, then
\( \mathbf{A} \cdot \operatorname{both} \lim _{x \rightarrow a} f(x) \) and \( \lim _{x \rightarrow a} g(x) \) must exist
B. \( \lim _{x \rightarrow a} f(x) \) need not exist but \( \lim _{x \rightarrow a} g(x) \) exists
C. neither \( \lim _{x \rightarrow a} f(x) \) nor \( \lim _{x \rightarrow a} g(x) \) may exist
D. \( \lim _{x \rightarrow a} f(x) \) exists but \( \lim _{x \rightarrow a} g(x) \) need not exist
Subject: Physics
A field of strength \( 5 \times 10^{4} / \pi \) ampere
turns / meter acts at right angles to the
coil of 50 turns of area \( 10^{-2} m^{2} . \) The coil
is removed from the field in 0.1 second.
Then the induced e.m.f. in the coil is :
A . \( 0.1 V \)
B. \( 0.2 V \)
c. \( 1.96 V \)
\( \mathbf{D} \cdot 0.98 V \)