AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Chemistry
Statement 1: The temperature of a substance always increases as heat energy is added to the system.
Statement 2: The average kinetic energy of the particles in the system
increases with an increase in
temperature.
A. Statement 1 and Statement 2 are correct and Statement 2 is the correct explanation of Statement 1
B. Both the Statement 1 and Statement 2 are correct and Statement 2 is NOT the correct explanation of Statement 1.
c. Statement 1 is correct but Statement 2 is not correct.
D. Statement 1 is not correct but Statement 2 is correct.
E. Both the Statement 1 and Statement 2 are not correct.
Subject: Maths
If \( f \) be the differentiable for \( \forall x \). If
\( \boldsymbol{f}(1)=-2 \) and \( \boldsymbol{f}^{\prime}(\boldsymbol{x}) \geq 2 \) for \( [\mathbf{1}, \boldsymbol{6}] \) then
A. \( f(6)<8 \)
В. \( f(6)=5 \)
\( \mathbf{c} \cdot f(6) \geq 8 \)
D. \( f(6)<5 \)
Subject: Chemistry
The difference between amylose and
amylopectin is
A. Amlyopetin have \( 1 \rightarrow 4 \alpha \) -linkage and \( 1 \rightarrow 6 \beta \) - linkage
B. Amlyopetin have \( 1 \rightarrow 4 \alpha \) -linkage and \( 1 \rightarrow 6 \alpha \) - linkage
C. Amylose is made up of glucose and galactose
D. Amylose have \( 1 \rightarrow 4 \alpha \) -linkage and \( 1 \rightarrow 6 \beta \) - linkage
Subject: Physics
An object is taken to height \( 2 \mathrm{R} \) above the surface of earth, the increase in potential energy is [R is radius of earth]
\( ^{\mathrm{A}} \cdot \frac{m g R}{2} \)
в. \( \frac{m g R}{3} \)
c. \( \frac{2 m g R}{3} \)
D. 2 mgR
Subject: Maths
\( A B C D \) is a trapezium in which \( A B \| \) \( C D ; B C \) and \( A D \) are non-parallel sides. It
is given that \( A B=75 c m, B C= \)
\( 42 c m, C D=30 c m \) and \( A D=39 c m \)
Find the area of the trapezium.
Subject: Maths
Assertion
STATEMENT-1:
\( \int \frac{\left\{\boldsymbol{f}(\boldsymbol{x}) \boldsymbol{\phi}^{\prime}(\boldsymbol{x})-\boldsymbol{f}^{\prime}(\boldsymbol{x}) \phi(\boldsymbol{x})\right\}}{\boldsymbol{f}(\boldsymbol{x}) \phi(\boldsymbol{x})}\{\log \phi(\boldsymbol{x}) \)
\( \frac{1}{2}\left\{\log \frac{\phi(x)}{f(x)}\right\}^{2}+c \)
Reason STATEMENT-2 : \( \int(\boldsymbol{h}(\boldsymbol{x}))^{\boldsymbol{n}} \boldsymbol{h}^{\prime}(\boldsymbol{x}) \boldsymbol{d} \boldsymbol{x}= \)
\( \frac{(h(x))^{n+1}}{n+1}+c \)
A. STATEMENT-1 is True, STATEMENT-2 is True:
STATEMENT-2 is a correct explanation for STATEMENT
B. STATEMENT-1 is True, STATEMENT-2 is True STATEMENT-2 is NOT a correct explanation for STATEMENT-
c. STATEMENT-1 is True, STATEMENT-2 is False
D. STATEMENT-1 is False, STATEMENT-2 is True
Subject: Physics
Which of the statements are correct?
This question has multiple correct options
A. Unit of work is \( \mathrm{kgm}^{2} \mathrm{s}^{-2} \)
B. Unit of force is \( k g m s^{-2} \)
C. Unit of work is \( k g m s^{-2} \)
D. Unit of force is \( k g m^{2} s^{-2} \)
Subject: Physics
The dimensional formula of wave
number is :
\( \mathbf{A} \cdot\left[M^{0} L^{0} T^{0}\right] \)
B . \( \left[M^{0} L^{-1} T^{0}\right] \)
C . \( \left[M^{0} L^{0} T^{-1}\right] \)
D. \( \left[M^{-1} L^{-1} T^{0}\right] \)
Subject: Maths
\( \left|\begin{array}{lll}a^{2}+\lambda^{2} & a b+c \lambda & c a-b \lambda \\ a b-c \lambda & b^{2}+\lambda^{2} & b c+a \lambda \\ c a+b \lambda & b c-a \lambda & c^{2}+\lambda^{2}\end{array}\right| \mid \begin{array}{cc}\lambda & c \\ -c & \lambda \\ b & -a\end{array} \)
\( \left(1+a^{2}+b^{2}+c^{2}\right)^{3}, \) then the value of \( \lambda \)
is
\( A \cdot 8 \)
в. 2
\( c \)
\( D \)
Subject: Maths
\( \int_{0}^{\pi / 2} \frac{x d x}{\sin x+\cos x}= \)
A \( \cdot \frac{\pi}{2 \sqrt{2}} \log (\sqrt{2}+1) \)
\( \frac{\pi^{2}}{2 \sqrt{2}} \log (\sqrt{2}+1) \)
\( \mathbf{c} \cdot \pi \log (\sqrt{2}+1) \)
\( \mathbf{D} \cdot \log (\sqrt{2}+1) \)
Subject: Chemistry
What coefficients are required to balance the following equation? \( \boldsymbol{C a}(\boldsymbol{O H})_{2}+\boldsymbol{H C l} \rightarrow \boldsymbol{C a C l}_{2}+\boldsymbol{H}_{2} \boldsymbol{O} \)
A .2,4,2,4
в. 1,2,2,2
\( \mathrm{c} .1,2,1,1 \)
D. 1,2,1,2
Subject: Chemistry
Dilute \( 20.8 \mathrm{mL} \) of \( 6.0 \mathrm{M} \mathrm{H}_{2} \mathrm{SO}_{4} \) to a
volume of 1 L. The concentration of the
resultant \( \boldsymbol{H}_{2} \boldsymbol{S} \boldsymbol{O}_{4} \) solution is \( \boldsymbol{2 5} \boldsymbol{y} \times \)
\( 10^{-3} M, \) then \( y \) is
Subject: Maths
The middle term in the expansion of
\( \left(x+\frac{1}{x}\right)^{10} \)
A \( \cdot \) io \( C_{4} \cdot \frac{1}{x} \)
в. \( ^{10} C_{5} \)
c. \( _{10} \mathrm{C}_{5} . \frac{1}{x} \)
D. \( ^{10} C_{6} . x \)
Subject: Chemistry
The reagent used in Wolff-Kishner
reduction is:
A. \( N H_{2}-N H_{2} \) and \( K O H \) in ethylene glycol
в. \( Z n-H g / \) сопс. \( H C l \)
c. \( N a B H_{4} \)
D. \( N a-H g / H_{2} O \)
Subject: Physics
Two plane mirrors are placed parallel to each other at a distance Lapart. A point
object 0 placed between them, at a distance L/3 from one mirror. Both
mirrors form multiple images. The distance between any two images
cannot be
A \( \cdot \frac{3 L}{2} \)
в. \( \frac{2 L}{3} \)
\( c \cdot 2 L \)
D. \( L \)
Subject: Physics
An \( \alpha \) - particle accelerated through volt is fired towards a nucleus. Its
distance of closest approach is \( r \). If a proton is accelerated through the same potential and fired towards the same nucleus, the distance of closest approach of proton will be:
\( A \)
B . \( 2 r \)
\( \mathrm{c} \cdot r / 2 \)
D. \( r / 4 \)
Subject: Chemistry
For the gas phase reaction,
\[
\mathbf{2} \boldsymbol{S} \boldsymbol{O}_{2}+\boldsymbol{O}_{2} \rightleftharpoons \mathbf{2} \boldsymbol{S} \boldsymbol{O}_{3} ; \quad \boldsymbol{\Delta} \boldsymbol{H}=
\]
\( -x \)
carried out in a vessel, the equilibrium
concentration of \( S O_{2} \) can be increased
by :
This question has multiple correct options
A. increasing the temperature.
B. decreasing the pressure.
c. removing some oxygen.
D. none of the above
Subject: Chemistry
A saturated solution of \( A g_{2} S O_{4} \) is
\( \mathbf{2 . 5} \times \mathbf{1 0}^{-\mathbf{2}} \mathbf{M} . \) The value of its solubility
product is
\( \mathbf{A} \cdot 6.25 \times 10^{-6} \)
В. \( 6.25 \times 10^{-4} \)
c. \( 15.625 \times 10^{-6} \)
D. 3.125 \( \times 10^{-6} \)
Subject: Physics
Behind a thin converging lens having both the surfaces of the same radius
\( \mathbf{1} \boldsymbol{c m}, \) a plane mirror has been placed. The image of an object at a distance of
\( 40 \mathrm{cm} \) from the lens is formed at the
same position. What is the refractive
index of the lens?
A . 1.5
B. \( 5 / 3 \)
\( c \cdot 9 / 8 \)
D. None of these
Subject: Physics
A metal rod has the length of \( 50 \mathrm{cm} \) at
\( 20^{\circ} \mathrm{C} . \) When it is heated to \( 95^{\circ} \mathrm{C} \), its
length becomes \( 50.06 \mathrm{cm} . \) Find the
length of the rod at \( 0^{\circ} \mathrm{C} \)
Subject: Maths
A buys an old bicycle for Rs. 162 and
spends Rs. 18 on its repairs. He then
sells the bicycle for Rs. 207 ; find his gain or loss as percent.
A. Gain = 15\%
B. Gain = 20\%
\( c \cdot \cos s=12 \% \)
D. \( \operatorname{Loss}=19 \% \)
Subject: Physics
Torque acting on an electric dipole in a uniform electric field is maximum if the angle between \( \vec{P} ; \) and \( \vec{E} \) is:
A \( .180^{\circ} \)
B . \( 0^{\circ} \)
\( c \cdot 90^{\circ} \)
D. \( 45^{\circ} \)
Subject: Physics
Two uniformly large parallel thin plates
having charge densities \( +\sigma \) and \( -\sigma \) are
kept in the \( X Z \) -plane at distance \( d \) apart. Sketch an equipotential surface due to electric field between the plates.
If a particle of mass \( m \) and charge \( -q \) remains stationary between the plates. What is the magnitude and direction of this field?
Subject: Maths
The angle between the pair of lines whose equation is \( 4 x^{2}+10 x y+ \)
\( m y^{2}+5 x+10 y=0 \) is
A \( \cdot \tan ^{-1}\left(\frac{3}{8}\right) \)
B. \( \tan ^{-1} \frac{2 \sqrt{25-4 m}}{m+4} \)
\( ^{\mathbf{c}} \cdot \tan ^{-1}\left(\frac{3}{4}\right) \)
D. \( \tan ^{-1} \frac{\sqrt{25-4 m}}{m+4} \)
Subject: Maths
\[
\operatorname{Let}\left|\begin{array}{ccc}
\boldsymbol{x}^{2}+\boldsymbol{x} & \boldsymbol{2} \boldsymbol{x}-\mathbf{1} & \boldsymbol{x}+\boldsymbol{3} \\
\boldsymbol{3} \boldsymbol{x}+\mathbf{1} & \boldsymbol{2}+\boldsymbol{x}^{2} & \boldsymbol{x}^{\boldsymbol{3}} \\
\boldsymbol{x}-\boldsymbol{3} & \boldsymbol{x}^{\boldsymbol{2}}+\boldsymbol{4} & \boldsymbol{2} \boldsymbol{x}
\end{array}\right|=\boldsymbol{p} \boldsymbol{x}^{2}+
\]
\( \boldsymbol{q} \boldsymbol{x}^{\boldsymbol{6}}+\boldsymbol{r} \boldsymbol{x}^{\boldsymbol{5}}+\boldsymbol{s} \boldsymbol{x}^{4}+\boldsymbol{t} \boldsymbol{x}^{\boldsymbol{3}}+\boldsymbol{u} \boldsymbol{x}^{\boldsymbol{2}}+\boldsymbol{v} \boldsymbol{x}+\boldsymbol{w} \)
then which of the following is not true?
A. \( w=21, v=75 \)
B . \( q=0, s=-4 \)
c. \( p=0, t=-8 \)
D. \( p=q=-1 \)
Subject: Physics
A calorimeter of water equivalent 5 g has water of mass 55 g upto a certain level. Another identical calorimeter has
a liquid of mass 38 g up to same level. As both of them cool in the same
surroundings from \( 50^{\circ} \mathrm{C} \) to \( 46^{\circ} \mathrm{C}, \) water takes 80 s whereas the liquid takes 32 s
to cool. If the specific heat of water is 1
cal/g-o \( C \), the specific heat of the liquid in cal/g-o \( C \) is :
A . 0.8
B. 0.4
\( c \cdot 0.5 \)
D. 0.2
Subject: Physics
Assertion
The excess pressure above atmospheric
pressure is usually called as gauge
pressure.
Reason
Gauge pressure = (Total pressure) (atmospheric pressure)
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: Physics
Two billiard balls of the same size and
mass are in contact on a billiard table.
third ball of the same size and mass
strikes them symmetrically and remains at rest after the impact. The coefficient of restitution between the
ball is:
A \( \cdot \frac{1}{2} \)
B. \( \frac{1}{3} \)
\( c \cdot 2 \)
\( \overline{3} \)
\( D \cdot 3 \)
\( \bar{A} \)
Subject: Maths
toppr
Q Type your question
following steps. Step 1: First of all we find the successive
difference (first difference, second
difference, third difference \( \ldots \text { so on }) \)
Step 2: If first successive difference is
in A.P, then general term can be taken \( \operatorname{as} t_{n}=a n^{2}+b n+c\left(\text { i.e.consider } t_{n} \) as \right.
quadratic polynomial in the decreasing power of \( n \text { with constants } a, b, c) \)
Step 3: If the second, third successive
differences are in \( \mathbf{A} . \mathbf{P}, \) then \( \boldsymbol{t}_{\boldsymbol{n}}=\boldsymbol{a} \boldsymbol{n}^{\boldsymbol{3}}+ \)
\( b n^{2}+c d+d \) for second successive
difference in A.P and so on where
\( a, b, c, d \) are constants whose order can be changed. Step 4: If the first difference in step 1 is
in G.P, then take \( t_{n}=a r^{n-1}+b n+c \)
Similarly if second, third difference are in \( G . P, \) then general terms are considered by \( t_{n}=a r^{n-1}+b n^{2}+ \)
\( \boldsymbol{c n}+\boldsymbol{d} \) and \( \boldsymbol{t}_{\boldsymbol{n}}=\boldsymbol{a} \boldsymbol{r}^{\boldsymbol{n}-\mathbf{1}}+\boldsymbol{b} \boldsymbol{n}^{\boldsymbol{3}}+\boldsymbol{c n}^{\boldsymbol{2}}+ \)
\( \boldsymbol{d} \boldsymbol{n}+\boldsymbol{e} \) respectively where \( \boldsymbol{a}, \boldsymbol{b}, \boldsymbol{c}, \boldsymbol{d}, \boldsymbol{e} \ldots \)
are constants whose orders can be
changed. Now consider the sequences
\( P: 9,16,29,54,103, \dots \)
\( Q: 4,14,30,52,80,114, \dots \)
\( R: 2,12,36,80,150,252, \dots \)
\( \boldsymbol{S}: \mathbf{2}, \mathbf{5}, \mathbf{1 2}, \mathbf{3 1}, \mathbf{8 6}, \dots \)
On the basis of above data
(information) answer the following questions:If \( t_{n}=A+B n+C n^{2} \) for
sequence \( Q \), then the value of \( A^{2}+ \)
\( B^{2}+C^{2} \) equals
A. 10
B. 8
\( c . \)
D. None of these
Subject: Chemistry
The correct order of radii is:
\( \mathbf{A} \cdot L i<B e<M g \)
B \( \cdot B e^{+2}<L i^{+}<H^{-} \)
\( \mathbf{C} \cdot M n^{3+}<M n^{2+}<M n^{+7} \)
D. \( K^{+}>C l^{-}>S^{2-} \)
Subject: Physics
The maximum deflection of the thread
with the vertical is
\( ^{\mathbf{A}} \cdot \cos ^{-1}\left(\frac{4}{5}\right) \)
B. \( \cos ^{-1}\left(\frac{3}{5}\right) \)
\( ^{\mathbf{c}} \cdot \cos ^{-1}\left(\frac{2}{3}\right) \)
D \( \cos ^{-1}\left(\frac{3}{4}\right) \)
Subject: Physics
Four point charges \( -Q,-q, 2 q \) and \( 2 Q \) are placed, one at each corner of the square. The relation between \( Q \) and \( q \) for
which the potential at the centre of the square is zero is
A. \( Q=-q \)
в. \( Q=-\frac{1}{q} \)
c. \( Q=q \)
\( \mathrm{D} \cdot Q=\frac{1}{q} \)
Subject: Physics
If the gas 'X' behaves ideally, then the
pressure \( P \) of \( \operatorname{gas} \) at \( 27^{\circ} C \) is :
\( \mathbf{A} \cdot 12.32 \mathrm{atm} \)
B. 24.63 atm
c. 1 atm
D. 6.15 atm
Subject: Physics
The number \( N_{Y} \) of nuclei of \( Y \) at \( t= \)
\( T_{1 / 2} \) is
A. \( K \frac{l n 2}{\lambda}+\frac{3}{2}\left(\frac{K-\lambda N_{0}}{\lambda}\right) \)
в. \( K \frac{l n 2}{\lambda}+\frac{1}{2}\left(\frac{K-\lambda N_{0}}{\lambda}\right) \)
c. \( \quad K \frac{l n 2}{\lambda}-\frac{1}{2}\left(\frac{K-\lambda N_{0}}{\lambda}\right) \)
D. \( K \frac{\ln 2}{\lambda}-2\left(\frac{K-\lambda N_{0}}{\lambda}\right) \)
Subject: Maths
If the straight line \( x \cos \alpha+y \sin \alpha= \)
\( p \) touches the curve \( \frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}=1, \) then
prove that \( \boldsymbol{a}^{2} \cos ^{2} \boldsymbol{\alpha}+\boldsymbol{b}^{2} \sin ^{2} \boldsymbol{\alpha}=\boldsymbol{p}^{2} \)
Subject: Chemistry
Which of the following is not an interstitial compound?
A . \( T i C \)
в. \( M o C \)
\( \mathrm{c} \cdot F e_{0.82} \mathrm{O} \)
\( \mathrm{D} \cdot \mathrm{Cr}_{2} \mathrm{O}_{3} \)
Subject: Physics
\( 3 V \) potentiometer used for the
determination of internal resistance of
a \( 2.4 \mathrm{V} \) cell. The balance point of the cell is open circuit is \( 75.8 \mathrm{cm} \). When a
resistor of \( 10.2 \Omega \) is used in the external
circuit of the cell the balance point
shifts to \( 68.3 \mathrm{cm} \) length of the potentiometer wire. The internal
resistance of the cell is?
A . \( 2.5 \Omega \)
B . \( 2.25 \Omega \)
c. \( 1.12 \Omega \)
D. 3.2\Omega
Subject: Physics
When a current carrying coil is placed in a uniform magnetic field of induction
\( B, \) then a torque \( \tau \) acts on it. If \( I \) is the current, \( n \) is the number of turns and \( A \)
is the face area of the coil and the
normal to the coil makes an angle \( \theta \)
with \( \boldsymbol{B}, \) Then
A \( \cdot \tau=B I n A \)
B. \( \tau=B \) In \( A \sin \theta \)
\( \mathbf{c} \cdot \tau=B \operatorname{In} A \cos \theta \)
\( \mathbf{D} \cdot \tau=B I n A \tan \theta \)
Subject: Chemistry
Assertion (A): The enthalpy of formation of gaseous oxygen molecules at \( 298 \mathrm{K} \) and under a pressure of 1 atm is zero. Reason (R): The entropy of formation of gaseous oxygen molecules under the same condition is zero.
A. Both assertion and reason are correct, reason is the correct explanation of the assertion
B. Both assertion and reason are correct, reason is the not correct explanation of the assertion
c. Assertion is correct, reason is incorrect
D. Assertion is incorrect, reason is correct
Subject: Chemistry
Identify the wrong statement for long
form of periodic table.
A. It reflects the sequence of filling the electrons in the order of energy levels \( \mathrm{K}, \mathrm{L}, \mathrm{M}, \mathrm{N} \)
B. It helps to predict the stable valence states of the elements
C. It reflects trends in physical and chemical properties of the elements
D. It helps to predict the relative ionicity of the bond between any two elements
Subject: Physics
A frame thread is tied slightly loose to a wire frame as in figure and the frame is dipped into a soap solution and taken out. The frame is completely covered with the film.When the portion \( A \) is punctured with a pin, the thread:
A. becomes concave towards A
B. becomes convex towards A
c. either (a) or (b) depending on the size of A with respect to
D. remains in the initial position
Subject: Chemistry
Which of the following pairs of complexes whose aqueous solutions gives pale yellow and white precipitates
respectively with \( 0.1 M A g N O_{3} ? \)
\( ^{\mathbf{A}} \cdot\left[P t\left(N H_{3}\right)_{4} B r_{2}\right] C l_{2} \) and \( \left[P t\left(N H_{3}\right)_{4} C l_{2}\right] B r_{2} \)
B. \( \left[C o\left(N H_{3}\right)_{5} N O_{3}\right] B r \) and \( \left[C o\left(N H_{3}\right)_{5} B r\right] N O_{3} \)
\( \mathbf{c} \cdot\left[P t\left(N H_{3}\right)_{4} C l_{2}\right] B r_{2} \) and \( \left[P t\left(N H_{3}\right)_{4} B r_{2}\right] C l_{2} \)
D \( \cdot\left[\mathrm{Co}\left(\mathrm{NH}_{3}\right)_{5} \mathrm{NO}_{3}\right] \mathrm{Cl} \) and \( \left[\mathrm{Co}\left(\mathrm{NH}_{3}\right)_{5} \mathrm{Cl}\right] \mathrm{NO}_{3} \)
Subject: Chemistry
Balance the following redox reactions:
\[
\boldsymbol{I}_{2}(\boldsymbol{s})+\boldsymbol{O} \boldsymbol{C l}^{-}(\boldsymbol{a} \boldsymbol{q}) \longrightarrow \boldsymbol{I} \boldsymbol{O}_{3}^{-}(\boldsymbol{a} \boldsymbol{q})+
\]
\( \boldsymbol{C l}^{-}(\boldsymbol{a} \boldsymbol{q}) \)
\( \mathbf{A} \cdot I_{2}(s)+5 O C l^{-}(a q)+H_{2} O(l) \longrightarrow 2 I O_{3}^{-}(a q)+ \)
\[
5 C l^{-}(a q)+2 H^{+}(a q)
\]
B \( \cdot I_{2}(s)+5 O C l^{-}(a q)+2 H_{2} O(l) \longrightarrow I O_{3}^{-}(a q)+ \)
\[
4 C l^{-}(a q)+2 H^{+}(a q)
\]
\( \mathbf{c} \cdot I_{2}(s)+3 O C l^{-}(a q)+4 H_{2} O(l) \longrightarrow I O_{3}^{-}(a q)+ \)
\( 4 C l^{-}(a q)+2 H^{+}(a q) \)
\( \mathbf{D} \cdot I_{2}(s)+5 O C l^{-}(a q)+7 H_{2} O(l) \longrightarrow I O_{3}^{-}(a q)+ \)
\( 5 C l^{-}(a q)+2 H^{+}(a q) \)
Subject: Chemistry
\( \begin{array}{ll}\text { Item 'I' } & \text { Item 'II' } \\ \text { (compound) } & \text { (reagent) } \\ \text { (A) Lysine } & \text { (P)I-naphthol } \\ \text { (B)Furfural } & \text { (Q)ninhydrin } \\ \text { (C) Benzyl alcohol } & \text { (R) } K M n O_{4} \\ \text { (D)Styrene } & \text { (S)ceric ammonium }\end{array} \)
\( A \)
\( (A) \rightarrow(Q),(B) \rightarrow(P),(C) \rightarrow(S),(D) \rightarrow(R) \)
B. \( (A) \rightarrow(Q),(B) \rightarrow(R),(C) \rightarrow(S),(D) \rightarrow(P) \)
C \( .(A) \rightarrow(Q),(B) \rightarrow(P),(C) \rightarrow(R),(D) \rightarrow(S) \)
D. \( (A) \rightarrow(R),(B) \rightarrow(P),(C) \rightarrow(Q),(D) \rightarrow(S) \)
Subject: Chemistry
Anhydrous \( A l C l_{3} \) is covalent. from the
data given below Lattice Energy \( =5137 \mathrm{KJ} \) mol\( ^{-1} \)
\( \triangle \boldsymbol{H} \) hydration \( \boldsymbol{A l}^{3+}= \)
\( -4665 K J / m o l^{-1} \)
\( \triangle \boldsymbol{H} \) hydration \( \boldsymbol{C l}^{-}= \)
\( -381 K J / m o l^{-1} \)
Identify the correct statement-
A. It will remain covalent in aqueous solution
B. The solution will consists of \( A I^{3+} \) and \( C I^{-} \)
c. The solution will consists of hydrate \( A I^{3+} \) and \( C I^{-} \)
D. None of these
Subject: Physics
A condenser of \( 250 \mu F \) is connected in
parallel to a cell of inductance \( 0.16 \mathrm{mH} \) while its effective resistance is while
its. Determine the resonant frequency.
A \( \cdot 9 \times 10^{4} \mathrm{Hz} \)
B . \( 16 \times 10^{7} \) Н \( _{2} \)
c. \( 8 \times 10^{5} \) Н \( z \)
\( \mathbf{D} \cdot 9 \times 10^{3} \mathrm{Hz} \)
Subject: Physics
If \( \overrightarrow{\boldsymbol{A}}=\mathbf{2} \hat{\boldsymbol{i}}+\hat{\boldsymbol{j}}-\hat{\boldsymbol{k}} \) and \( \overrightarrow{\boldsymbol{B}}=\sqrt{\mathbf{2}}(\hat{\boldsymbol{i}}+\hat{\boldsymbol{j}}) \)
Find \( \vec{A} . \vec{B} \). Hence find the angle between \( \vec{A} \) and \( \vec{B} \). Also find the component of \( \overrightarrow{\boldsymbol{A}} \) along \( \overrightarrow{\boldsymbol{B}} \)
Subject: Chemistry
Assertion
Assertion: Higher order ionization constants \( \left(\boldsymbol{K}_{a_{2}}, \boldsymbol{K}_{a_{3}}\right) \) are smaller than
the lower order ionization constant \( \boldsymbol{K}_{\boldsymbol{a}_{\mathbf{1}}} \) of polyprotic acid.
Reason
Reason: Polyprotic acid solutions contain a mixture of acids.
A. If both the assertion and reason are true and reason is the correct explanation of assertion
B. If both the assertion and reason are true but reason is not the correct explanation of assertion.
c. If assertion is true but reason is false
D. If both assertion and reason are false
Subject: Maths
\( \left(\frac{2 a x}{a^{2}+x^{2}}\right)+\frac{1}{3}\left(\frac{2 a x}{a^{2}+x^{2}}\right)^{3}+ \)
\( \frac{1}{5}\left(\frac{2 a x}{a^{2}+x^{2}}\right)^{5}+\dots= \)
\( A \cdot \log (a+x) \)
B. \( \log (a-x) \)
\( ^{\mathbf{C}} \cdot \log \left(\frac{a+x}{a-x}\right) \)
\( D \)
Subject: Chemistry
Which of the following statements is true for a solution containing
components \( A \) and \( B \) and following
Raoult's law:
A. \( A-B \) attraction force is greater than \( A-A \) and \( B- \) \( B \)
B. \( A-B \) attraction force is less than \( A-A \) and \( B-B \)
c. \( A-B \) attraction force remains same as \( A-A \) and \( B-B \)
D. Volume of solution is different from sum of volume of solute and solvent
Subject: Physics
A transformer with primary to secondary turns ratio of \( 1: 2, \) is connected to an alternator of voltage \( 200 \mathrm{V} . \) A current of \( 4 \mathrm{A} \) is flowing through the primary coil. Assuming that the transformer has no losses, the
secondary voltage and current are respectively:
\( A \cdot 100 \vee, 8 A \)
B. \( 400 \vee, 8 A \)
c. \( 400 \vee, 2 \mathrm{A} \)
D. \( 100 \vee, 2 A \)
Subject: Physics
A source of electrons or neutrons can be
located at \( S \). The beam is defined by
slits \( S_{1} \) and \( S_{2} . \) The particles pass
through two plates \( P_{1} \) and \( P_{2} \) such that
the first plate is at zero potential and
the second plate can be given any high potential. For using matter waves in a microscope of high resolution which of
the following combination must be chosen?
A. Electron beam with high accelerating potential
B. Electron beam with low accelerating potential
c. Neutron beam with high accelerating potential
D. Neutron beam with low accelerating potential
Subject: Physics
An object moving with kinetic energy \( K E=100 J \) and momentum \( p= \)
\( 50 k g m / s . \) Find out the mass of the
moving object?
A \( .2 k g \)
в. \( 4 k g \)
c. \( 6.25 k g \)
D. \( 12.5 k g \)
E . \( 25 k g \)
Subject: Chemistry
The increase in boiling point of a solution containing \( 0.6 g \) urea in \( 200 g \)
water is \( 0.50^{\circ} \mathrm{C} \). Find the molal
elevation constant.
A \( \cdot 10 K \) kg mol\( ^{-1} \)
в. \( 10 \mathrm{K} \) g \( \mathrm{mol}^{-1} \)
c. \( 10 K \) kg moll \( l \)
D. \( 1.0 K \) kg mol\( ^{-1} \)
Subject: Chemistry
Balance the following equation by ion electron method.
\( \boldsymbol{C}_{2} \boldsymbol{H}_{5} \boldsymbol{O} \boldsymbol{H}+\boldsymbol{I}_{2}+\boldsymbol{O} \boldsymbol{H}^{-} \rightarrow \boldsymbol{C} \boldsymbol{H} \boldsymbol{I}_{3}+ \)
\( \boldsymbol{H} \boldsymbol{C O}_{2}^{-}+\boldsymbol{I}^{-}+\boldsymbol{H}_{2} \boldsymbol{O} \)
Subject: Physics
A neutron, with kinetic energy KE and moving with velocity \( v, \) collides head on
with a nucleus of mass number \( \boldsymbol{A} \)
perfectly elastically. The fraction of total
energy possessed by the neutron transferred to nucleus is
A \( \cdot \frac{4 A}{(A+1)^{2}} \)
\( ^{\mathrm{B}}\left(\frac{A-1}{A+1}\right)^{2} \)
\( \left(\frac{A+1}{2 A}\right)^{2} \)
\( \left(\frac{A-1}{2 A}\right)^{2} \)
Subject: Maths
\( \frac{4}{9^{\frac{1}{3}}-3^{\frac{1}{3}}+1} \) is equal to
\( A \cdot 3^{\frac{1}{5}}+1 \)
B. \( 3^{\frac{1}{5}}-1 \)
c. \( 3^{\frac{1}{5}}+2 \)
D. \( 3^{\frac{1}{5}}-2 \)
Subject: Maths
If \( A \) is a symmetric and \( B \) skew
symmetric matrix and \( (\boldsymbol{A}+\boldsymbol{B}) \) is non-
singular and \( C=(A+B)^{-1}(A-B) \)
\( \operatorname{then} C^{T}(A+B) C=A+B \)
A. True
B. False