AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Chemistry
Complete the reactions with
appropriate products.
(i) \( C H_{3} C H O+N H_{2} O H \rightarrow X \)
(ii) \( \boldsymbol{C H}_{2}=\boldsymbol{C H}_{2}+\boldsymbol{P d C l}_{2}+ \)
\( \boldsymbol{H}_{2} \boldsymbol{O} \stackrel{\boldsymbol{C u C l}_{2}}{\longrightarrow} \boldsymbol{Y} \)
(iii) \( \boldsymbol{C H}_{3} \boldsymbol{C H}_{2} \boldsymbol{C H}_{2} \boldsymbol{C H}_{2} \boldsymbol{O H} \frac{C r \boldsymbol{O}_{3}-\boldsymbol{H}_{2} \boldsymbol{S O}_{4}}{\boldsymbol{\lambda}} \boldsymbol{Z} \)
A. \( X=C H_{3} C H=N O H, Y=C H_{3} C H O, Z= \)
\( C H_{3} C H_{2} C H_{2} C O O H \)
B. \( X=C H_{3} C H_{2} N H_{2}, Y=C H_{3} C H_{2} C H O, Z= \)
\( C H_{3} C H_{2} C H_{2} C O O H \)
c. \( X=C H_{3} C O N H_{2}, Y=H C H O, Z=C H_{3} C O C H_{3} \)
Subject: Maths
The area of triangle formed by the lines
\( 18 x^{2}-9 x y+y^{2}=0 \) and the line \( y=9 \)
is
A. \( \frac{27}{4} \)
в. \( \frac{27}{2} \)
c. \( \frac{27}{8} \)
D. 27
Subject: Maths
The value of \( \cos ^{4}\left(\frac{\pi}{4}\right)-\cos ^{4}\left(\frac{\pi}{6}\right)+ \)
\( \sin ^{4}\left(\frac{\pi}{6}\right)+\sin ^{4}\left(\frac{\pi}{3}\right) \) is
A \( \cdot \frac{1}{16} \)
в. \( \frac{1}{8} \)
c. \( \frac{5}{16} \)
D. \( \frac{3}{16} \)
Subject: Chemistry
A \( 0.66 \mathrm{kg} \) ball is moving with a speed of \( 100 \mathrm{m} / \mathrm{s} . \) The associated wavelength will
be:
\( \left[h=6.6 \times 10^{-34} \mathrm{J.s}\right] \)
A \( \cdot 6.6 \times 10^{-32} \mathrm{m} \)
B \( \cdot 6.6 \times 10^{-34} \mathrm{m} \)
c. \( 1.0 \times 10^{-35} \mathrm{m} \)
D. \( 1.0 \times 10^{-32} \mathrm{m} \)
Subject: Physics
Find the angle that the vector \( \vec{A}=2 \hat{i}+ \) \( 3 \hat{j}-\hat{k} \) makes with y-axis.
A \( \cdot \theta=\cos ^{-1}\left(\frac{3}{\sqrt{14}}\right) \)
B. \( \theta=\cos ^{-1}\left(\frac{2}{\sqrt{14}}\right) \)
\( ^{\mathrm{c}} \cdot_{\theta}=\cos ^{-1}\left(\frac{3}{\sqrt{16}}\right) \)
D. \( \theta=\cos ^{-1}\left(\frac{3}{\sqrt{28}}\right) \)
Subject: Maths
If \( \alpha, \beta \) and \( \gamma \) are the roots of the
equation \( x^{3}+p x+q=0 \) then the value of the determinant \( \left|\begin{array}{lll}\boldsymbol{\alpha} & \boldsymbol{\beta} & \gamma \\ \boldsymbol{\beta} & \gamma & \boldsymbol{\alpha} \\ \boldsymbol{\gamma} & \boldsymbol{\alpha} & \boldsymbol{\beta}\end{array}\right| \) is
2
\( \mathbf{A} \cdot \underline{p} \)
B. \( q \)
c. \( p^{2}-2 q \)
\( D \)
Subject: Physics
An equation is given here \( \left(\boldsymbol{P}+\frac{\boldsymbol{a}}{\boldsymbol{V}^{2}}\right)= \)
\( b \frac{9}{V} \) where \( P= \) pressure, \( V= \) Volume
and \( \theta= \) Absolute temperature. if \( a \) and \( b \)
are constants, the dimension of a will
be
\( \mathbf{A} \cdot\left[M L^{-5} T^{-1}\right] \)
B \( \cdot\left[M L^{5} T^{1}\right] \)
C \( \cdot\left[M L^{5} T^{-2}\right] \)
D \( \cdot\left[M L^{-1} L^{5} T^{2}\right] \)
Subject: Maths
A fair die is rolled. Consider the events
\( \boldsymbol{E}=\{1, \mathbf{3}, \mathbf{5}\} \) and \( \boldsymbol{F}=\{\mathbf{2}, \mathbf{3}\}, \) find
\( \boldsymbol{P}(\boldsymbol{E} \mid \boldsymbol{F}) \)
Subject: Physics
An infinitely long straight conductor is
bent into shape as shown in figure. It
carries a current I A. and the radius of
circular loop is r metre. Then the
magnetic induction at the centre of the
circular loop is:
\( A \)
B. \( \frac{\mu_{0}}{\pi r_{0}} \)
c. \( \frac{\mu_{0} i}{2 \pi r}(\pi+1) \)
D \( \cdot \frac{\mu_{0} i}{2 \pi r}(\pi-1) \)
Subject: Chemistry
The correct order of decreasing acidity
of nitrophenols will be:
A. \( m- \) nitrophenol \( >p- \) nitrophenol \( >o \) - nitrophenol
B. \( o \) - nitrophenol \( >m- \) nitrophenol \( >p- \) nitrophenol
c. \( p- \) nitrophenol \( >m- \) nitrophenol \( >o- \) nitrophenol
D. \( p- \) nitrophenol \( >o \) - nitrophenol \( >m- \) nitrophenol
Subject: Chemistry
Write the expression for the
equillibrium constant \( \left(\boldsymbol{K}_{c}\right) \) for the
following reactions.
(i) \( \boldsymbol{H}_{2}(\boldsymbol{g})+\boldsymbol{I}_{2}(\boldsymbol{g}) \leftrightharpoons \boldsymbol{2} \boldsymbol{H} \boldsymbol{I}(\boldsymbol{g}) \)
(ii) \( 4 N H_{3}(g)+5 O_{2}(g) \leftrightharpoons 4 N O(g)+ \)
\( \boldsymbol{6} \boldsymbol{H}_{2} \boldsymbol{O}(\boldsymbol{g}) \)
Subject: Maths
Let \( n(\cup)=700, n(A)=400, n(B)=300, n(A \cap \)
\( \mathrm{B})=300 . \) Then \( \left(\mathrm{A}^{\prime} \cap \mathrm{B}^{\prime}\right)= \)
A . 300
B. 400
\( c . \) 350
D. 250
Subject: Physics
What is the density of lead under a pressure of \( 2.0 \times 10^{8} N / m^{2}, \) if the bulk
modulus of lead is \( 8.0 \times 10^{9} N / m^{2} \)
Also, the initial density of lead is \( 11.4 g / c m^{3} \)
A \( \cdot 12.89 g / c m^{3} \)
в. \( 14 g / \mathrm{cm}^{3} \)
c. \( 11.69 g / c m^{3} \)
D. Zero
Subject: Physics
A particle is acted upon by a force whose component's variations with time are shown in diagrams. Then the magnitude of change in momentum
of the particle in 0.1 sec will be
\( ^{\mathbf{A}} \cdot 2 K g \frac{m}{S e c} \)
В. \( 10 \mathrm{Kg} \frac{\mathrm{m}}{\mathrm{Sec}} \)
\( \mathrm{c} \cdot_{12 \mathrm{Kg}} \frac{\mathrm{m}}{\mathrm{Sec}} \)
D. \( 5 \sqrt{2} \mathrm{Kg} \frac{\mathrm{m}}{\mathrm{sec}} \)
Subject: Chemistry
Q Type your question-
\( \bigcirc\rangle-\mathbf{C}=\mathbf{C H} \frac{\mathbf{H B r} / \mathbf{R}_{2} \mathbf{O}_{2}}{(\text { 1equivalent })} \)
\( A \)
B.
\( c \)
\( D \)
Subject: Physics
A heater of power \( \boldsymbol{P} \boldsymbol{W} \) raises the
temperature of \( m k g \) of a liquid by
\( \Delta T K \) in time \( t s . \) Express the specific heat capacity of liquid in terms of above
data
A \( \cdot \frac{P t}{\Delta T} \)
B. \( \frac{P t(\Delta T+273)}{m(\Delta T)^{2}} \)
c. \( \frac{P}{m \Delta T} \)
D. \( \frac{P t}{m \Delta T} \)
Subject: Physics
Assertion
If objective and eye lenses of a microscope are interchanged then it
can work as telescope.
Reason
The objective lens of telescope has small focal length.
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
Which term of the sequence
\( \mathbf{3}, \mathbf{8}, \mathbf{1 3}, \mathbf{1 8}, \dots \dots . . \) is \( \mathbf{4 9 8} \)
A. 95 th
B. 100 th
c. \( 102 t h \)
D. \( 101 t h \)
Subject: Chemistry
At \( 80^{\circ} \mathrm{C}, \) the vapour pressure of pure
liquid \( A \) is 520 mmHg and that of pure liquid \( B \) is 1000 mmHg. If a mixture
solution of \( A \) and \( B \) boils at \( 80^{\circ} \) and 1
atm pressure, the amount of \( A \) (mole
percent) in the mixture is:
A . \( 50 \% \)
B. 54\%
c. \( 32 \% \)
D. 44\%
Subject: Physics
A uniform rod is resting freely over a
smooth horizontal plane. A particle
moving horizontally strikes at one end
of the rod normally and gets stuck. Then
This question has multiple correct options
A. the momentum of the particle is shared between the particle and the rod and remains conserved
B. the angular momentum about the mid-point of the rod before and after the collision is equal
C. the angular momentum about the centre of mass of the combination before and after the collision is equal
D. the centre of mass of the rod particle system starts to move translationally with the original momentum of the particle
Subject: Physics
A capacitor of capacitance \( 9 n F \) having
dielectric slab of \( \varepsilon_{r}=2.4 \) dielectric
strength \( 20 \mathrm{MV} / \mathrm{m} \) and \( \boldsymbol{P . D .}=20 \mathrm{V} \)
Calculate area of plates.
В . \( 4.2 \times 10^{-4} \mathrm{m}^{2} \)
c. \( 1.4 \times 10^{-4} m^{2} \)
D. 2.4 \( \times 10^{-4} m^{2} \)
Subject: Physics
A horizontal rod of length L and mass \( \mathrm{m} \) lying on the floor is fixed at one end and a force \( F \) is applied at an angle \( \theta \) with the horizontal. The torque experienced by the rod is
\( \mathbf{A} \cdot\left(m L^{2} \alpha\right) / 12 \)
В. \( \left(m L^{2} \alpha\right) / 3 \)
c. \( \left(m L^{2} \alpha\right) / 4 \)
D. \( \left(m L^{2} \alpha\right) / 2 \)
Subject: Maths
Evaluate \( \boldsymbol{P}(\boldsymbol{A} \cup \boldsymbol{B}), \) if \( \boldsymbol{2} \boldsymbol{P}(\boldsymbol{A})= \)
\( \boldsymbol{P}(B)=\frac{\boldsymbol{5}}{13} \) and \( \boldsymbol{P}(\boldsymbol{A} / B)=\frac{2}{5} \)
Subject: Physics
\( 5 \mathrm{Gm} \) of steam at \( 100^{\circ} \mathrm{C} \) is passed into
\( 6 \mathrm{gm} \) of ice at \( 0^{\circ} \mathrm{C} \). If the latent heats of steam and ice n cal per \( \mathrm{gm} \) are 540 and 80 respectively, them the final temperature is:-
\( \mathbf{A} \cdot 0^{\circ} C \)
B. \( 100^{\circ} \mathrm{C} \)
\( \mathbf{c} \cdot 50^{\circ} C \)
D. \( 30^{\circ} \mathrm{C} \)
Subject: Maths
If \( \overrightarrow{\boldsymbol{a}}=\boldsymbol{x} \hat{\boldsymbol{i}}+\boldsymbol{2} \hat{\boldsymbol{j}}-\boldsymbol{z} \hat{\boldsymbol{k}} \) and \( \overrightarrow{\boldsymbol{b}}=\boldsymbol{3} \hat{\boldsymbol{i}}- \)
\( y \hat{j}+\hat{k} \) are two equal vectors, then write
the value of \( \boldsymbol{x}+\boldsymbol{y}+\boldsymbol{z} \)
Subject: Physics
If a piece of copper having internal cavity weighs 264 gms.in air and 221 gms. in water, then volume of the cavity is \( \ldots . . . . . . . . . . . . . . . . . \) Density of copper \( =8.8 \) \( \left.g / c m^{3}\right) \)
\( \mathbf{A} \cdot 10 \mathrm{cm}^{3} \)
В. \( 11 \mathrm{cm}^{3} \)
\( \mathbf{c} \cdot 13 c m^{3} \)
D. \( 15 \mathrm{cm}^{3} \)
Subject: Biology
Assertion
Gemmae formation in Funaria occurs in
favourable condition
Reason
The gemmed form on the stern and
leaves
A. If both the assertion and the reason are true and the
reason is a correct explanation of the assertion
B. If both the assertion and reason are true but the reason is not a correct explanation of the assertion
C. If the assertion is true but the reason is false
D. If both the assertion and reason are false
Subject: Chemistry
In equilibrium \( \boldsymbol{C H}_{3} \boldsymbol{C O O H}+\boldsymbol{H}_{2} \boldsymbol{O} \rightleftharpoons \)
\( \boldsymbol{C H}_{3} \boldsymbol{C O O}^{-}+\boldsymbol{H}^{+} \)
The equilibrium constant may not
change when:
\( \mathbf{A} \cdot C H_{3} C O O^{-} \) are added
B. \( C H_{3} C O O H \) is added
c. catalyst is added
D. mixture is heated
Subject: Maths
\( \boldsymbol{I} \boldsymbol{f} \quad \boldsymbol{x}^{\boldsymbol{y}}=\boldsymbol{e}^{\boldsymbol{x}-\boldsymbol{y}} \quad \) then
A. \( \frac{d y}{d x} \) doesn't exist at \( x=1 \)
B. \( \frac{d y}{d x}=0 \quad \) when \( \quad x=1 \)
c. \( \frac{d y}{d x}=\frac{1}{2} \quad \) when \( \quad x=e \)
D. None of these
Subject: Physics
The current flowing through the resistor
in a series LCR a.c. circuit, is \( \boldsymbol{I}=\varepsilon / \boldsymbol{R} \)
Now the inductor and capacitor are
connected in parallel and joined in series with the resistor as shown in
figure. The current in the circuit is now.
(Symbols have their usual meaning)
A . equal to I
B. more than I
c. less than 1
D. zero
Subject: Physics
\( n \) capacitors each of capacitance \( 2 \mu F \) are connected in parallel and a potential difference of \( 200 \mathrm{V} \) is applied to the
combination. The total charge on all the positive plates is 1 Coulomb then \( n \) is
equal to :
A . 3333
в. 3000
\( c .2500 \)
D. 25
Subject: Chemistry
For \( 2 A+2 B \rightleftharpoons 2 C+2 D, K_{c}=1 / 6 \)
then \( \boldsymbol{K}_{\boldsymbol{c}} \) for \( \boldsymbol{C}+\boldsymbol{D} \rightleftharpoons \boldsymbol{A}+\boldsymbol{B} \)
is \( _{\text {十一一一一一一一一一 }} \) (write only integer part)
Subject: Physics
A train is approaching towards a platform with a speed of \( 10 m s^{-1} \) while blowing a whistle of frequency \( 340 \mathrm{Hz} \)
What is the frequency of whistle heard by a stationary observer on the platform? Given speed of sound \( =340 m s^{-1} \)
A. зЗО н 2
в. 350 нz
c. 340 н \( z \)
D. 360 нz
Subject: Maths
Maximum value of \( r \) where \( \frac{c^{2}}{r^{2}}= \) \( \frac{\mathbf{a}^{2}}{\sin ^{2} \theta}+\frac{b^{2}}{\cos ^{2} \theta} \) where \( c, a, b \)
are constants is
A. \( \frac{c}{a+b} \)
B. \( \frac{c}{a-b} \)
c. \( \frac{a^{2}+b^{2}}{c^{2}} \)
D. \( \frac{c^{2}}{a^{2}+b^{2}} \)
Subject: Maths
If the papers of 4 students can be
checked by any one of the seven teachers, then the probability that all the four papers are checked by exactly two teachers is
A \( \cdot \frac{6}{49} \)
B. \( \frac{2}{7} \)
c. \( \frac{32}{343} \)
D. \( \frac{2}{343} \)
Subject: Chemistry
\( C H_{3} C O O H \) dimerizes in benzene
when \( 1.65 g \) of \( C H_{3} C O O H \) dissolved in
\( 100 g \) of benzene the elevation of \( B p s \) of
the solution was found \( 0.36 K . \) If \( K_{b} \) for
benzene in 2.85 K.kgl mol. Then find
Vant Hoff factor and degree of
association of \( \boldsymbol{C} \boldsymbol{H}_{3} \boldsymbol{C O O H} \)
Subject: Physics
A tank, which is open at the top,
contains a liquid up to a height \( \boldsymbol{H} . \mathbf{A} \)
small hole is made in the side of a tank
at a distance y below the liquid surface.
The liquid emerging from the hole lands at a distance \( x \) from the tank.
his question has multiple correct options
A. If \( y \) is increased from zero to \( H, x \) will first increase and then decrease
B. x is maximum for \( y=H / 2 \).
c. The maximum value of \( x \) is \( H \)
D. The maximum value of \( x \) will depend on the density of the density of the liquid.
Subject: Maths
Evaluate \( \cos (A+B) \cdot \cos (A-B)= \)
\( A \cdot \sin ^{2} A-\cos ^{2} B \)
B. \( \cos ^{2} A+\sin ^{2} B \)
\( \mathbf{c} \cdot \cos ^{2} A-\sin ^{2} B \)
\( \mathbf{D} \cdot \cos ^{2} A+\cos ^{2} B \)
Subject: Maths
What is \( (\sin x \cos y+ \)
\( \cos x \sin y)(\sin x \cos y-\cos x \sin y) \)
equal to?
A \( \cdot \cos ^{2} x-\cos ^{2} y \)
B. \( \cos ^{2} x-\sin ^{2} y \)
\( c \cdot \sin ^{2} x-\cos ^{2} y \)
D. \( \sin ^{2} x-\sin ^{2} y \)
Subject: Physics
A clock pendulum having coefficient of linear expansion \( \boldsymbol{\alpha}=\mathbf{9} \times \mathbf{1 0}^{-\mathbf{7}} /^{\circ} \mathbf{C} \) has
a period of \( 0.5 s \) at \( 20^{\circ} \mathrm{C} . \) If the clock is
used in a climate where the
temperature is \( 30^{\circ} \mathrm{C} \), how much times
does the clock lose in each oscillation?
\( (g=\text { constant }) \)
A \( \cdot 2.5 \times 10^{-7} \mathrm{s} \)
B . \( 5 \times 10^{-7} \) s
D. \( 2.25 \times 10^{-6} \mathrm{s} \)
Subject: Maths
Let \( A=\{10,15,20,25,30,35,40,45\} 50 \)
\( B=\{1,5,10,15,20,30\} \) and \( C=\{1,5,15 \)
\( 20,35,45,3 . \) Verify \( A \backslash(B \cap C)=(A \backslash \)
\( \boldsymbol{B}) \cup(\boldsymbol{A} \backslash \boldsymbol{C}) \)
Subject: Physics
When a gold sheet is bombarded by a beam of \( \alpha \) -particles, only a few of them
get deflected whereas most go straight,
undeflected because:
This question has multiple correct options
A. the force of attraction exerted on the \( \alpha \) -particles by the oppositely charged electrons is not sufficient
B. a nucleus has a much smaller volume than that of an atom
c. the force of repulsion acting on the fast-moving \( \alpha \) particles is very small
D. the neutrons in the nucleus do not have any effect on the \( \alpha \) -particles
Subject: Physics
If wavelength of photon and electron is same then ratio of total energy of electron to total energy of photon would be:
A. \( \frac{\text { Velocity of electron }}{\text { Light's speed }} \)
B. \( \frac{\text { Light's speed }}{\text { Electon's speed }} \)
c. \( \frac{\text { Light's speed }}{\text { Velocity of electron }} \)
D. \( \frac{\text { Electron's speed }}{\text { Light's speed }} \)
Subject: Physics
A solid copper sphere (density \( \rho \) and specific capacity \( C \) ) of radius \( r \) at an initial temperature of \( 200 \mathrm{K} \) is supended inside a chamber whose walls are at almost 0 K. The time
required for the temperature of the sphere to drop to \( 100 \mathrm{K} \) is
A \( \cdot \frac{7 r \rho C}{72 \times 10^{6} \sigma} \)
в. \( \frac{r \rho C}{6 \sigma} \)
c. \( \frac{r \rho C}{\sigma} \)
D. none of the above
Subject: Maths
If \( A_{1}, A_{2} ; G_{1}, G_{2} ; H_{1}, H_{2} \) be two
A. \( M \cdot^{\prime} s, G . M .^{\prime} s \) and \( H . M .^{\prime} s \) between
two positive numbers then prove:
\( \frac{\boldsymbol{G}_{1} \boldsymbol{G}_{2}}{\boldsymbol{H}_{1} \boldsymbol{H}_{2}}=\frac{\boldsymbol{A}_{1}+\boldsymbol{A}_{2}}{\boldsymbol{H}_{1}+\boldsymbol{H}_{2}} \)
Subject: Maths
If \( y=\tan ^{-1} \sqrt{\frac{1-\cos x}{1+\cos x}}, \) then for \( 0< \)
\( \boldsymbol{x}<\frac{\boldsymbol{\pi}}{\mathbf{2}}, \frac{\boldsymbol{d} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}}= \)
\( \mathbf{A} \cdot 2 \sec ^{2}(x / 2) \)
B \( \cdot \frac{1}{2} \sec ^{2}(x / 2) \)
\( c \cdot \frac{1}{2} \)
D. \( -\frac{1}{2} \sec ^{2}(x / 2) \)
Subject: Physics
It takes 15 minutes for an electrical
kettle to heat a certain quantity of
water in grams from \( 0^{\circ} \mathrm{C} \) to boiling
point \( 100^{\circ} \mathrm{C} . \) If it takes 81 minutes to boil water into steam, the latent heat of steam is :
A. 80 cal \( l \),
в. 540 cal \( / g \)
c. 100 cal \( / g \)
D. 336 cal \( / g \)
Subject: Maths
The maximum value of the function
\( \boldsymbol{f}(\boldsymbol{x})=|\boldsymbol{x}-\boldsymbol{4}| \) exists at
\( \mathbf{A} \cdot x=0 \)
B. \( x=2 \)
c. \( x=4 \)
D. \( x=-4 \)
Subject: Chemistry
\( (X),(Y),(Z) \) are elements in the third period. Oxide of \( (X) \) is ionic, that of \( (Y) \) is amphoteric, and of \( (Z) \) a giant molecule.
\( (X),(Y) \) and \( (Z) \) will have atomic
numbers in the order:
\( A \cdot(x)<(y)<(z) \)
\( B \cdot(z)<(Y)<(X) \)
\( c \cdot(x)<(z)<(y) \)
\( D \cdot(Y)<(X)<(Z) \)
Subject: Physics
How is the acceleration due to gravity on earth surface related to the mass \( M \)
and radius \( R \) of earth?
A \( \cdot g=\frac{G}{M R^{2}} \)
в. \( g=\frac{M}{G R^{2}} \)
c. \( _{g}=\frac{G M}{R} \)
D. \( g=\frac{G M}{R^{2}} \)
Subject: Physics
A block of mass \( 10 \mathrm{kg} \) is kept on a fixed
rough \( (\mu=0.8) \) inclined plane of angle
of inclination \( 30 . \) The frictional
force acting on the block is
\( \mathbf{A} \cdot 50 \mathrm{N} \)
B. \( 50 \sqrt{3} \) N
\( \mathbf{c} \cdot 52 \mathrm{N} \)
\( \mathbf{D} \cdot 54 \mathrm{N} \)
Subject: Chemistry
The electronic configuration of neon is:
\( \mathbf{A} \cdot 1 \mathbf{s}^{2} 2 \mathbf{s}^{2} 2 \mathbf{p}^{6} \)
B. \( 1 \mathrm{s}^{2} \)
\( c \cdot 2 s^{2} \)
D. \( 1 s^{2} 2 s^{2} 2 p^{2} \)
Subject: Physics
A thin tube of uniform cross-section is
sealed at both ends. It lies horizontally.
The middle \( 5 c m \) contains \( \mathrm{Hg} \) and two equal ends contain air at the same
pressure \( P_{0} . \) When the tube is held at an
angle of \( 60^{\circ} \) with the vertical, the length of the air column above and below the
Hg are \( 46 \mathrm{cm} \) and \( 44.5 \mathrm{cm} \). Calculate
pressure \( P_{0} \) in cm of Hg. Assume
temperature of the system to be
constant.
A. \( 55 \mathrm{cm} \) of \( \mathrm{Hg} \)
B. \( 65 \mathrm{cm} \) of \( \mathrm{Hg} \)
c. \( 70.4 \mathrm{cm} \) of \( \mathrm{Hg} \)
D. \( 75.4 \mathrm{cm} \) of \( \mathrm{Hg} \)
Subject: Chemistry
Among the following, the species that is both tetrahedral and diamagnetic is:
A \( \cdot\left[N i C l_{4}\right]^{2+} \)
B. \( N i(C O)_{4} \)
c. \( \left[N i(C N)_{4}\right]^{2+} \)
D. \( \left[N i\left(H_{2} O\right)_{6}\right]^{2+} \)
Subject: Chemistry
No. of 5 membered ring in \( \left[(\boldsymbol{C a}(\boldsymbol{E} \boldsymbol{D} \boldsymbol{T} \boldsymbol{A})]^{-2} \boldsymbol{i s}\right. \)
A . 5
B. 6
\( c \cdot 7 \)
D. 8
Subject: Maths
Statement I: The equation
\( \left(\sin ^{-1} x\right)^{3}+\left(\cos ^{-1} x\right)^{3}-a \pi^{3}=0 \) has
solution for all \( a \geqslant \frac{1}{32} \)
Statement II : For any \( \boldsymbol{x} \boldsymbol{\epsilon} \boldsymbol{R}, \boldsymbol{s} \boldsymbol{i n}^{-1} \boldsymbol{x}+ \)
\( \cos ^{-1} x=\frac{\pi}{2} \) and \( 0 \leq\left(\sin ^{-1} x-\frac{\pi}{4}\right)^{2} \leq \)
\( \frac{9 \pi^{2}}{16} \)
A. Both statements I and II are true.
B. Both statements I and II are true but I is not an explanation of I
c. statement l is true and statement II is false
D. Statement I is false and statement II is true.
Subject: Maths
The order and degree of \( \left(\frac{d^{2} y}{d x^{2}}\right)^{1 / 3}= \) \( \mathbf{1 0}+\mathbf{9} \boldsymbol{x} \frac{\boldsymbol{d} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}} \) is:
A . 2,3
B. 2,
\( c \cdot 1,3 \)
D. 1
Subject: Biology
Match the following with correct
answers.
(a) Toucan bird I Modified teeth
(b) Siberian bird II Silver white
mane
(c) Macaque \( \quad \) II Long beak
(d) Macaque \( \quad \) IV Migrate to India during winter
A . a- -II, b- -I, c- II, d- -IV
B. a- III, b- -IV, c-1, d- -I
c. a-।, b- II, c- -II, d-IV
D. a- -V, b- |II, c- ||, d- | -
Subject: Maths
Given \( \boldsymbol{f}: \boldsymbol{x} \rightarrow \mathbf{2} \boldsymbol{x}+\boldsymbol{p} \) and \( \boldsymbol{f}^{-1}: \boldsymbol{x} \rightarrow \)
\( \boldsymbol{m}(\boldsymbol{4} \boldsymbol{x}+\boldsymbol{3}), \) where \( \boldsymbol{p} \) and \( \boldsymbol{m} \) are
constants. Find the value of \( p \) and value
of \( \boldsymbol{m} \)
Subject: Physics
A particle starts with initial speed \( u \) and retardation a to come to rest in
time \( T . \) The time taken to cover the first
half of the total path travelled is
A \( \cdot \frac{T}{\sqrt{2}} \)
в. \( T\left(1-\frac{1}{\sqrt{2}}\right) \)
c. \( \frac{T}{2} \)
D. \( \frac{3 T}{4} \)
Subject: Maths
A circle of radius 7 is tangent to the
lines of an angle \( 60^{\circ} . \) is larger circle of
radius \( r \) is tangent to same lines as
well as given circle, then value of \( r \) is:
\begin{tabular}{l} 
A \( .7 \sqrt{3} \) \\
\hline
\end{tabular}
B. \( \frac{28}{\sqrt{3}} \)
\( c \cdot 21 \)
D. 14
Subject: Maths
Mid point \( \boldsymbol{A}(\mathbf{0}, \mathbf{0}) \) and \( \boldsymbol{B}(\mathbf{1 0 2 4}, \mathbf{2 0 4 8}) \) is
\( A_{1} \) and mid point of \( A_{1} \) and \( B \) is \( A_{2} \) and
so on. Coordinates of \( \boldsymbol{A}_{\mathbf{1 0}} \) are:
A. (1022,2044)
) (1022,2444)
B. (1025,2050)
c. (1023,2046)
D. (1,2)
Subject: Maths
\( \mathbf{f} \boldsymbol{A}=\left[\begin{array}{lll}\mathbf{1} & \mathbf{2} & \mathbf{3} \\ \mathbf{0} & \mathbf{5} & \mathbf{7} \\ \mathbf{6} & \mathbf{8} & \mathbf{9}\end{array}\right] \) and \( \boldsymbol{B}=\left[\begin{array}{lll}\mathbf{2} & \mathbf{0} & \mathbf{3} \\ \mathbf{3} & \mathbf{0} & \mathbf{5} \\ \mathbf{5} & \mathbf{7} & \mathbf{0}\end{array}\right] \)
then find the value of \( 3 A-2 B \)
Subject: Physics
A liquid P of specific heat capacity \( 1800 J k g^{-1} K^{-1} \) and at \( 80^{\circ} \mathrm{C} \) is mixed
with liquid \( R \) of specific heat capacity \( 1200 J k g^{-1} K^{-1} \) and at \( 30^{\circ} \mathrm{C} . \) After
mixing, the final temperature of
mixture is \( 50^{\circ} \mathrm{C} . \) In what proportion by weight are the liquids mixed?
Subject: Chemistry
Which among the following plots are liner (a-x) is the concentration of the
reactant remaining after time, t?
(1):- (a-x) vs t, for a first order reaction
(2)\( :-(a-x) \) vs \( t, \) for a zero order reaction
(3):- (a-x) vs t, for a second order
reaction
(4):-1/ (a-x) vs t, for a second order
reaction
A. 1 and 2
B. 1 and 3
\( c \cdot 2 \) and 3
D. 2 and 4
Subject: Maths
There are two A.P.s whose common
differences differ by unity, but sum of the three consecutive terms in each is
15. If \( P \) and \( P_{1} \) be the products of these terms such that \( \frac{\boldsymbol{P}}{\boldsymbol{P}_{1}}=\frac{\mathbf{7}}{\mathbf{8}}, \) then find the
two A.P.'s.
Subject: Maths
A man gives \( 40 \% \) of his money to his children and \( 20 \% \) of the remaining to a trust. If he is still left with \( \mathrm{Rs} .9,600 \) then what did he originally have?
A. Rs.14, 000
B . Rs.19, 845
c. Rs.20, 000
D. Rs.25, 409
Subject: Maths
If \( \frac{\boldsymbol{d}}{\boldsymbol{d} \boldsymbol{x}}\left(\frac{1+\boldsymbol{x}^{2}+\boldsymbol{x}^{4}}{1+\boldsymbol{x}+\boldsymbol{x}^{2}}\right)=\boldsymbol{a} \boldsymbol{x}+ \)
\( b, \) then \( (a, b)= \)
A. (-1,2)
B. (-2,1)
c. (2,-1)
D. (1,2)