AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Physics
Which of the following statement
regarding transformer is incorrect?
A. A transformer makes use of Faradays Law.
B. The ferromagnetic properties of an iron core is used by it to efficiently raise or lower AC voltage
C. It cannot increase power so that if the voltage is raised, the current is proportionally lowered and vice versa.
D. The current induced in primary circuit is of same nature as in secondary circuit with differences in amplitude only.
Subject: Physics
A particle of mass \( m \) is made to move
with uniform speed \( v \) along the perimeter of a regular hexagon. The magnitude of impulse applied at each
corner is:
A . \( m v \)
B. \( m v \sqrt{3} \)
c. \( \frac{m v}{2} \)
D. \( \frac{m v}{\sqrt{3}} \)
Subject: Physics
An insect sits on the end of a long board
of length 5 m. The board rests on a frictionless horizontal table. The insect
wants to jump to the opposite end of the board. What is the minimum take-off speed (in \( \mathrm{m} / \mathrm{s} \) ) of insect relative to
ground, that allows the insect to do the trick? The board and the insect have
equal masses. \( \left(\boldsymbol{g}=\mathbf{1 0} \boldsymbol{m} / \boldsymbol{s}^{2}\right) \)
Subject: Maths
The equation of the plane passing through the intersection of the planes \( \boldsymbol{x}+\boldsymbol{y}+\boldsymbol{z}=\boldsymbol{6} \) and \( \boldsymbol{2} \boldsymbol{x}+\boldsymbol{3} \boldsymbol{y}+\boldsymbol{4} \boldsymbol{z}+\boldsymbol{5}= \)
\( 0, \) and the point (1,1,1) is
A. \( 20 x+23 y+26 z-69=0 \)
B. \( 20 x+23 y+26 z+69=0 \)
c. \( 23 x+20 y+26 z-69=0 \)
D. None of these
Subject: Physics
Assertion
Newton's law of gravitation resembles Coulomb's law of electrical forces.
Reason
Coulomb's law has the product of two charges in place of the product of the masses, and the electrostatic constant
in place of the gravitational constant.
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
Fill in the blanks by choosing the appropriate word/words from those given in the brackets:
(square pyramidal, electrical, 74, 26 \( s p^{3} d^{2}, s p^{3} d, \) chemical, 68,32
tetrahedral, yellow, white, iodoform, Lucas)
Propan-2-ol on reaction with iodine and sodium hydroxide gives precipitate and the reaction is called
test.
Subject: Maths
Equation of the plane containing the \( \operatorname{lines} \overline{\boldsymbol{r}}=(\overline{\boldsymbol{i}}-\boldsymbol{2} \overline{\boldsymbol{j}}+\overline{\boldsymbol{k}})+\boldsymbol{t}(\overline{\boldsymbol{i}}+\mathbf{2} \overline{\boldsymbol{j}}-\overline{\boldsymbol{k}}) \)
\( \boldsymbol{\boldsymbol { r }}=(\overline{\boldsymbol{i}}+\mathbf{2} \overline{\boldsymbol{j}}-\overline{\boldsymbol{k}})+\boldsymbol{s}(\overline{\boldsymbol{i}}+\overline{\boldsymbol{j}}+\mathbf{3} \overline{\boldsymbol{k}}) \) is
A. \( \bar{r}(7 \bar{i}-4 \bar{j}-\bar{k})=14 \)
В. \( \bar{r}(\bar{i}+2 \bar{j}-\bar{k})=10 \)
c. \( \bar{r}(\bar{i}+\bar{j}+3 \bar{k})=20 \)
D. \( \bar{r}(\bar{i}-2 \bar{j}+\bar{k})=27 \)
Subject: Physics
If the maximum velocity of a particle in
SHM is \( v_{0}, \) then its velocity at half the amplitude from position of rest will be :
A \( \cdot v_{0} / 2 \)
B. \( v_{0} \)
c. \( v_{o} \sqrt{3} / 2 \)
D . \( v_{0} \sqrt{3} / 4 \)
Subject: Maths
If \( \frac{1}{a}+\frac{1}{b}+\frac{1}{c}=\frac{1}{a+b+c} \) where \( (a+ \)
\( b+c) \neq 0 \) and \( a b c \neq 0 . \) What is the
value of \( (\boldsymbol{a}+\boldsymbol{b})(\boldsymbol{b}+\boldsymbol{c})(\boldsymbol{c}+\boldsymbol{a}) ? \)
\( \mathbf{A} \cdot \mathbf{0} \)
B.
\( c \cdot-1 \)
\( D \)
Subject: Physics
The height \( h_{m} \) at which the hole should
be punched so that the liquid travels
the maximum distance is
A. \( \frac{2 H}{3} \)
в. \( \frac{3 H}{8} \)
c. \( \frac{4 H}{3} \)
\( D \cdot \frac{5 H}{3} \)
Subject: Physics
10 grams of steam at \( 100^{\circ} \mathrm{C} \) is mixed
with \( 50 g m \) of ice at \( 0^{\circ} C \) then final temperature is
A \( \cdot 20^{\circ} \mathrm{C} \)
В. \( 50^{\circ} \mathrm{C} \)
c. \( 40^{\circ} \mathrm{C} \)
D. \( 100^{\circ} \mathrm{C} \)
Subject: Maths
If the straight line \( a x+b y+p=0 \) and
\( x \cos \alpha+y \sin \alpha=p \) enclosed an angle
of \( \frac{\pi}{4} \) and the line \( x \sin \alpha-y \cos \alpha=0 \)
meets them at the same point, the
\( a^{2}+b^{2} \) is
A .4
B. 3
\( c \cdot 2 \)
D.
Subject: Chemistry
Electronic configuration \( [\boldsymbol{K} \boldsymbol{r}] \boldsymbol{4} \boldsymbol{d}^{10} \)
belongs to:
A. Period(4) Group(10) Block(d)
B. Period(5) Group(12) Block (d)
c. Period(5) Group(10) Block \( (d) \)
D. Period(4) Group(12) Block(d)
Subject: Physics
The potential energy of a conservative
system is given by \( V(x)=\left(x^{2}-3 x\right) \)
joule where \( x \) is measured in metre. Then its equilibrium position is at
A . \( 1.5 \mathrm{m} \)
B. 2 \( m \)
\( c \cdot 3 m \)
\( D \cdot 1 \mathrm{m} \)
E. 5 m
Subject: Maths
If the projection of a line segment on
\( x, y \) and \( z \) axes are respectively 3,4 and
\( 5, \) then the length of the line segment is
\begin{tabular}{l} 
A \( 3 \sqrt{2} \) \\
\hline
\end{tabular}
B. \( 5 \sqrt{2} \)
c. \( 6 \sqrt{2} \)
D. None of these
Subject: Chemistry
Given below are the two reactions of
\( H_{2} O_{2} . \) Mark the correct statement which follows:
\( (\mathrm{i}) 2 \mathrm{K} M n O_{4}+3 \mathrm{H}_{2} \mathrm{SO}_{4}+5 \mathrm{H}_{2} \mathrm{O}_{2} \rightarrow \)
\( \boldsymbol{K}_{2} \boldsymbol{S} \boldsymbol{O}_{4}+\boldsymbol{2} \boldsymbol{M} \boldsymbol{n} \boldsymbol{S} \boldsymbol{O}_{4}+\boldsymbol{8} \boldsymbol{H}_{2} \boldsymbol{O}+\boldsymbol{5} \boldsymbol{O}_{2} \)
(ii) \( 2 C r(O H)_{3}+4 N a O H+ \)
\( \mathbf{3} \boldsymbol{H}_{2} \boldsymbol{O}_{2} \rightarrow \boldsymbol{2} \boldsymbol{N} \boldsymbol{a}_{2} \boldsymbol{C r} \boldsymbol{O}_{4}+\boldsymbol{8} \boldsymbol{H}_{2} \boldsymbol{O} \)
A . (i) Shows oxidizing nature of \( H_{2} O_{2} \) and (ii) shows reducing nature of \( H_{2} O_{2} \)
B. \( \ln \left(\text { i) } H_{2} O_{2} \) acts as a reducing agent and in (ii) it acts \right. as an oxidizing agent
\( c \cdot \ln \operatorname{both}(i) \) and
(ii), \( H_{2} O_{2} \) acts as an oxidizing agent
D. In both (i) and
(i), \( H_{2} O_{2} \) acts as a reducing agent
Subject: Maths
Arrange in the descending order of the values:
A: If (9,12) is one end of a focal chord of
the parabola \( y^{2}=16 x \) then the slope of
it is
B: The parabola \( x^{2}=p y \) passes
through \( (12,16), \) the focal distance of the point is
C: If the parabola \( y^{2}=k x \) passes
through (9,6) then the value of \( k \) is
D: The Ordinate of the point on the
parabola \( \boldsymbol{y}^{2}=\mathbf{3 6 x} \) whose ordinate is
three times its abscissa is
Write the value of the above statements
in the descending order
A. \( \mathrm{B}, \mathrm{D}, \mathrm{C}, \mathrm{A} \)
B. \( \mathrm{B}, \mathrm{D}, \mathrm{A}, \mathrm{C} \)
c. \( D, B, C, A \)
D. A,B,C,D
Subject: Physics
When forces \( F_{1}, F_{2}, F_{3} \) are acting on a
particle of mass \( \mathrm{m} \) such that \( \boldsymbol{F}_{2} \) and \( \boldsymbol{F}_{3} \)
are mutually perpendicular, then the particle remains stationary. If the force
\( F_{1} \) is now removed then the acceleration
of particle the is
A. \( F_{1} / m \)
B . \( F_{2} F_{3} / m F_{1} \)
\( \mathbf{c} \cdot\left(F_{2}-F_{3}\right) / m \)
D. \( F_{2} / m \)
Subject: Physics
Three right angled prisms of refractive
indices \( \mu_{1}, \mu_{2} \) and \( \mu_{3} \) are joined
together ao that the faces of the middle
prism are each in contact with one of
the outside prisms. If the ray passes through the composite block undeviated, then
A \( \cdot 1+\mu_{2}^{2}=\mu_{1}^{2}+\mu_{3}^{2} \)
B \( \cdot \mu_{1}^{2}-\mu_{3}^{2}+\mu_{2}^{3}=1 \)
C. \( \mu_{1}^{2}-\mu_{3}^{2}-\mu_{2}^{3}=1 \)
D \( \cdot \mu_{2}^{2}+\mu_{3}^{3}-\mu_{2}^{1}=1 \)
Subject: Physics
A point dipole \( \overrightarrow{\boldsymbol{p}}=\boldsymbol{p}_{0} \hat{\boldsymbol{x}} \) is kept at the
origin. The potential and electrical field due to this dipole on the y-axis at a distance \( d \) are, respectively:
(Take \( V=0 \text { at infinity }) \)
A \( \cdot \frac{|\vec{p}|}{4 \pi \varepsilon_{d} d^{2}}, \frac{-\vec{p}}{4 \pi \varepsilon_{0} d^{3}} \)
В. \( 0, \frac{\vec{p}}{4 \pi \varepsilon_{0} d^{3}} \)
c. \( \frac{|\vec{p}|}{4 \pi \varepsilon_{0} d^{2}}, \frac{\vec{p}}{4 \pi \varepsilon_{0} d^{3}} \)
D. \( _{0,} \frac{-\vec{p}}{4 \pi \varepsilon_{0} d^{3}} \)
Subject: Maths
A double ordinate of the parabola \( y^{2}= \) \( 8 p x \) is of length \( 16 p . \) The angle
subtended by it at the vertex of the parabola is
A.
в. \( \frac{\pi}{2} \)
c. \( \frac{\pi}{3} \)
D. none of these
Subject: Maths
Three coins are tossed once. Let \( \boldsymbol{A} \)
denote the event 'three heads show", \( \boldsymbol{B} \)
denote the event "two heads and one tail
show" \( C \) denote the event "three tails
show" and \( D \) denote the event 'a head
shows on the first coin" Which events
are
(i) mutually exclusive?
(ii) simple?
(iii) compound?
Subject: Maths
Differentiate \( \frac{\tan ^{-1} x}{1+\tan ^{-1} x} \) w.r.t. \( \tan ^{-1} x . \)
A. \( \frac{1}{\left(1+\tan ^{-1} x\right)^{2}} \)
s. \( \frac{1}{\left(1-\tan ^{-1} x\right)^{4}} \)
c. \( \frac{1}{\left(1+\tan ^{-1} x\right)^{4}} \)
D. \( \frac{1}{\left(1-\tan ^{-1} x\right)^{2}} \)
Subject: Maths
The following table shows the scores of
a group of 20 football players. Identify
the modal class.
\( \begin{array}{lllll}\text { Scores } & 7- & 14- & 21- & 28- \\ & 14 & 21 & 28 & 35\end{array} \)
Football 30 \( 40 \quad 20 \) players
A. \( 28-35 \)
B. \( 21-28 \)
c. \( 7-14 \)
D. \( 35-42 \)
Subject: Chemistry
The values of coefficients to balance the
following reaction are:
\( \boldsymbol{C r}(\boldsymbol{O H})_{3}+\boldsymbol{C l O}^{-}+\boldsymbol{O H}^{-} \rightarrow \)
\( \boldsymbol{C r} \boldsymbol{O}_{4}^{2-}+\boldsymbol{C l}^{-}+\boldsymbol{H}_{2} \boldsymbol{O} ? \)
A \( \cdot \operatorname{Cr}(O H)_{3}-(2), C l O^{-}-(3), C r O_{4}^{2-}-(3), C l^{-}-(3) \)
B. \( \operatorname{Cr}(O H)_{3}-(2), C l O^{-}-(4), C r O_{4}^{2-}-(3), C l^{-}-(2) \)
c. \( \operatorname{Cr}(O H)_{3}-(2), \operatorname{ClO}^{-}-(4), \operatorname{Cr} O_{4}^{2-}-(4), C l^{-}-(2) \)
D. \( \operatorname{Cr}(O H)_{3}-(2), C l O^{-}-(3), C r O_{4}^{2-}-(2), C l^{-}-(3) \)
Subject: Maths
Find the slope and \( y \) -intercept of the
line \( \boldsymbol{x}-\boldsymbol{y}=\mathbf{3} \)
A. slope \( =2, y \) -intercept \( =-3 \)
B. slope \( =0, y \) -intercept \( =-3 \)
c. slope \( =1, y \) -intercept \( =-3 \)
D. slope \( =1, y \) -intercept \( =3 \)
Subject: Chemistry
Ordinary hydrogen at room temperature is a mixture of
\( \mathbf{A} \cdot 75 \% o-\mathrm{Hydrogen}+25 \% p \) -Hydrogen
B. \( 25 \% \) o-Hydrogen \( +75 \% \) p-Hydrogen
\( \mathbf{c} .50 \% o \) -Hydrogen \( +50 \% p \) -Hydrogen
D. \( 1 \% \) o-Hydrogen \( +99 \% \) p-Hydrogen
Subject: Chemistry
\( \boldsymbol{C H}_{3} \boldsymbol{O H} \frac{(i) \boldsymbol{X}}{(i i) R \boldsymbol{h}, \boldsymbol{\Delta}} \boldsymbol{C H}_{3} \boldsymbol{C O O H} \)
In the above reaction, \( \boldsymbol{X} \) is :
A \( . C O_{2} \)
в. \( C O \)
с. \( M g O \)
D. \( C \)
Subject: Chemistry
If \( E_{1}^{o}, E_{2}^{o} \) and \( E_{3}^{o} \) are standard oxidation potentials for \( \boldsymbol{F e}\left|\boldsymbol{F} \boldsymbol{e}^{2+}, \boldsymbol{F} \boldsymbol{e}^{2+}\right| \boldsymbol{F} \boldsymbol{e}^{3+} \) and
\( \boldsymbol{F} e \mid \boldsymbol{F} e^{3+}, \) then \( \boldsymbol{E}_{3}^{o}=\frac{\boldsymbol{E}_{2}^{o}+\boldsymbol{2} \boldsymbol{E}_{1}^{o}}{\boldsymbol{n}} . \) The
value of \( n \) is:
Subject: Physics
A body is projected horizontally from a height of \( 78.4 m \) with a velocity \( 10 m s^{-1} \) Its velocity after 3 seconds is (
\( \boldsymbol{g}=\mathbf{1 0 m s}^{-1} \) ). (Take direction of
projection on \( \hat{i} \) and vertically upward direction on \( \hat{j} \) ):
\( \mathbf{A} \cdot 10 \hat{i}-30 \hat{j} \)
B. \( 10 \hat{i}+30 \hat{j} \)
c. \( 20 \hat{i}-30 \hat{j} \)
D. \( 10 \hat{i}+10 \sqrt{30} \hat{j} \)
Subject: Physics
A car is moving on a straight road. The
velocity of the car varies with time as shown in figure. Initially \( (a t t=0), \) the
car was at \( x=0, \) where, \( x \) is the
position of the car at any time \( t \)
Average speed from \( t=0 \) to \( t=70 s \) wil
be:
A \( \cdot \frac{16}{7} m / \)
в. \( \frac{24}{7} m / \)
c. \( \frac{20}{7} m / \)
\( D \)
Subject: Physics
Figure shows an Amperian path
\( A B C D A \). Part \( A B C \) is in verical plane
PSTU while part \( C D A \) is in horizontal
plane \( P Q R S \). Direction of circulation along the path is shown by an arrow
near point \( B \) and \( D \) \( \oint \vec{B} \cdot d \vec{l} \) for this path according to
Ampere's law will be:
\( \mathbf{A} \cdot\left(I_{1}-I_{2}+I_{3}\right) \mu_{0} \)
B・ \( \left(-I_{1}+I_{2}\right) \mu_{0} \)
\( \mathrm{c} \cdot I_{3} \mu_{0} \)
\( \mathbf{D} \cdot\left(I_{1}+I_{2}\right) \mu_{0} \)
Subject: Physics
Explain why :
(a) A body with large reflectivity is a poor emitter
(b) A brass tumbler feels much colder
than a wooden tray on a chilly day
(c) An optical pyrometer (for measuring high temperatures ) calibrated for an ideal black body radiation gives too low a value for the temperature of a red hot iron piece in the open but gives a correct value for the temperature when the same piece is in the furnace
(d) The earth without its atmosphere would be inhospitably cold
(e) Heating systems based on circulation of steam are more efficient
in warming a building than those based on circulation of hot water
Subject: Chemistry
Which of the statements are true about
the law of chemical combination?
This question has multiple correct options
A. Potassium combines with two isotopes of chlorine \( \left.^{35} C l \text { and }^{37} C l\right) \) to form two samples of \( K C l . \) Their
formation follows the law of definite composition.
B. Different proportions of oxygen in the various oxides of sulphur proves the law of multiple proportions.
\( \mathrm{C} \cdot H_{2} \mathrm{O} \) and \( \mathrm{H}_{2} S \) contain \( 11.11 \% \) hydrogen and \( 5.88 \% \) hydrogen respectively whereas \( S O_{2} \) contains \( 50 \% \) sulphur. The above data prove the law of reciprocal proportions.
D. In the decomposition of \( N H_{3}\left(2 N H_{3} \stackrel{\Delta}{\longrightarrow} N_{2}+3 H_{2}\right) \)
the ratio of volumes of \( N H_{3}, N_{2} \) and \( H_{2} \) is \( 2: 1: 3 . \) The above data proves the Gay Lussac's law.
Subject: Chemistry
The plot shows the variation of \( -\ln \boldsymbol{K}_{\boldsymbol{p}} \)
versus temperature for the two
reactions.
\( M(s)+\frac{1}{2} O_{2}(g) \rightarrow M O(s) \) and
\( C(s)+\frac{1}{2} O_{2}(g) \rightarrow C O(s) \)
Identify the correct statement?
A. \( A t T>1200 K, \) carbon will reduce \( M O(s) \) to \( M(s) \)
B. At \( T<1200 \mathrm{K} \), oxidation of carbon is unfavourable.
C. At \( T<1200 \) K, the reaction \( M O(s)+C(s) \rightarrow M(s)+ \)
\( C O(g) \) is spontaneous
D. Oxidation of carbon is favourable at all temperatures
Subject: Chemistry
\( \mathbf{2} \boldsymbol{C} \boldsymbol{a}_{3}\left(\boldsymbol{P} \boldsymbol{O}_{4}\right)_{2}+\boldsymbol{6} \boldsymbol{S} \boldsymbol{i} \boldsymbol{O}_{2}+\mathbf{1 0} \boldsymbol{C} \rightarrow \boldsymbol{P}_{4}+ \)
\( \boldsymbol{C a} \boldsymbol{S i O}_{3}+\mathbf{1 0 C O} \)
Which coefficient balances the reaction
given above?
A . 2
B. 4
c. 5
D. 6
Subject: Chemistry
If \( K_{a 1} \) and \( K_{a 2} \) are the ionization constants of \( \boldsymbol{H}_{3} \stackrel{+}{\boldsymbol{N}} \boldsymbol{C} \boldsymbol{H} \boldsymbol{R} \boldsymbol{C O O} \boldsymbol{H} \) and
\( \boldsymbol{H}_{3}^{+} \boldsymbol{N} \boldsymbol{C} \boldsymbol{H} \boldsymbol{R} \boldsymbol{C O O}^{-}, \) respectively, the \( \boldsymbol{p} \boldsymbol{H} \)
of the solution at the isoelectric point
is:
A \( \cdot p H=p K_{a 1}^{\circ}+p K_{a 2}^{\circ} \)
в.
\[
p H=\left(p K_{a 1}^{\circ} p K_{a 2}^{\circ}\right)^{\frac{1}{2}}
\]
c.
\[
p H=\left(p K_{a_{1}}^{\circ}+p K_{a 2}^{\circ}\right)^{\frac{1}{2}}
\]
D. \( _{p H}=\frac{\left(p K_{a 1}^{\circ}+p K_{a 2}^{\circ}\right)}{2} \)
Subject: Chemistry
Diborane \( \left(B_{2} H_{6}\right) \) reacts independently
with \( O_{2} \) and \( H_{2} O \) to produce :
A. \( H B O_{2} \) and \( H_{3} B O_{3} \)
B. \( H_{3} B O_{3} \) and \( B_{2} O_{3} \)
c. \( B_{2} O_{3} \) and \( H_{3} B O_{3} \)
D. \( B_{2} O_{3} \) and \( \left[B H_{4}\right]^{-} \)
Subject: Maths
If the function \( \boldsymbol{f}(\boldsymbol{x})= \)
\( \left\{\begin{array}{l}\frac{\sin ^{2} a x}{x^{2}}, w h e n x \neq 0 \text { is continuous at } \\ k, w h e n x=0\end{array}\right. \)
\( \boldsymbol{x}=\mathbf{0} \) then \( \boldsymbol{k}=? \)
\( A \cdot a \)
в. \( a^{2} \)
\( c .-2 \)
D. -
Subject: Maths
If \( (x-1)\left(x^{2}+1\right)>0, \) then find the
value of \( \sin \left(\frac{1}{2} \tan ^{-1} \frac{2 x}{1-x^{2}}-\tan ^{-1} x\right) \)
A . \( -1 / 2 \)
B. -
\( c \cdot 1 / 2 \)
D.
Subject: Physics
Two identical capacitors having plate
separation \( d_{0} \) are connected parallel to
each other across the points \( A \) and \( B \)
as shown in figure. A charge \( Q \) is imparted to the system by connecting
battery across \( A \) and \( B \) and the battery is removed. Now the first plate of the
first capacitor and the second plate of the second capacitor start moving with
constant velocity \( u_{o} \) toward left. The magnitude of the current flowing in the loop during this process is given as
\( \frac{Q u_{0}}{x d_{0}} . \) Find \( x \)
Subject: Physics
An electric dipole of moment \( \overrightarrow{\boldsymbol{p}} \) is placed at the origin along the \( x \) -axis. The angle made by electric field with \( x \) axis at a point \( P, \) whose position vector makes an angle \( \theta \) with \( x \) -axis, is (where \( \left.\tan \alpha=\frac{1}{2} \tan \theta\right) \)
\( A \cdot \alpha \)
B. \( \theta \)
\( c \cdot \theta+\alpha \)
D. \( \theta+2 \alpha \)
Subject: Chemistry
Which one of the following cyano complexes would exhibit the lowest value of paramagnetic behaviour? (Atomic Numbers: \( C r=24 ; M n= \)
\( 25 ; F e=26 ; C o=27) \)
\( \mathbf{A} \cdot\left[F e(C N)_{6}\right]^{3-} \)
B . \( \left[\operatorname{Co}(C N)_{6}\right]^{3} \)
c. \( \left[\operatorname{Cr}(C N)_{6}\right]^{3-} \)
D. \( \left[M n(C N)_{6}\right]^{3} \)
Subject: Physics
If for a gas \( \frac{\boldsymbol{R}}{\boldsymbol{C}_{\boldsymbol{v}}}=\mathbf{0 . 6 7}, \) then the gas is
made up of molecules which are :
A. Diatomic
B. Monoatomic
c. Polyatomic
D. Mixture of Diatomic \& Polyatomic
Subject: Maths
The domain of the function \( \boldsymbol{f}(\boldsymbol{x})= \)
\( \log _{x}(\cos x) \) is
A \( \cdot\left(-\frac{\pi}{2}, \frac{\pi}{2}\right)-\{1\} \)
в. \( \left(\frac{\pi}{2}, \frac{\pi}{2}\right)-\{1\} \)
c. \( \left(-\frac{\pi}{2}, \frac{\pi}{2}\right) \)
D. \( \left(0, \frac{\pi}{2}\right)-\{1\} \)
Subject: Physics
In SHM the net force towards mean
position is related to its displacement
(x) from mean position by the relation
\( \mathbf{A} \cdot F \propto x \)
B . \( F \propto \frac{1}{x} \)
c. \( F \propto x^{2} \)
D. \( F \propto \frac{1}{x^{2}} \)
Subject: Maths
If \( \boldsymbol{A}=\left[\begin{array}{rrr}3 & -3 & 4 \\ 2 & -3 & 4 \\ 0 & -1 & 1\end{array}\right] \) then find
\( \boldsymbol{A} \boldsymbol{d} \boldsymbol{j}(\boldsymbol{A} \boldsymbol{d} \boldsymbol{j} \boldsymbol{A}) \)
A. \( \left[\begin{array}{lll}3 & -3 & 4 \\ 2 & -3 & 4 \\ 0 & -1 & 1\end{array}\right] \)
В. \( \left[\begin{array}{ccc}3 & 3 & 4 \\ 2 & -3 & -4 \\ 0 & -1 & 1\end{array}\right] \)
\( \begin{array}{llll}\text { C. } & {\left[\begin{array}{ccc}3 & 3 & 4 \\ 2 & -3 & 4 \\ 0 & 1 & 1\end{array}\right]}\end{array} \)
D. \( \left[\begin{array}{ccc}3 & -3 & 4 \\ 2 & -3 & -4 \\ 0 & 1 & 1\end{array}\right] \)
Subject: Physics
Three resistances are joined together to
form a letter \( Y \) as shown in the figure.If
the potentials of the terminals \( \mathbf{A}, \mathbf{B} \) and
\( \mathrm{C} \) are \( \mathrm{V}_{1}, \mathrm{V}_{2} \) and \( \mathrm{V}_{3} \) respectively, then
determine the potential of the node \( \boldsymbol{O} \)
\( ^{\mathbf{A}} \cdot\left[\frac{V_{1}}{R_{1}^{\frac{1}{1}}}+\frac{V_{2}}{R_{2}^{2}}+\frac{V_{3}}{R_{3}^{3}}\right]\left[\frac{1}{R_{1}}+\frac{1}{R_{2}}+\frac{1}{R_{3}}\right]^{-2} \)
\( ^{\mathbf{B}} \cdot\left[\frac{V_{1}}{R_{1}}+\frac{V_{2}}{R_{2}}+\frac{V_{3}}{R_{3}}\right]\left[\frac{1}{R_{1}}+\frac{1}{R_{2}}+\frac{1}{R_{3}}\right]^{-1} \)
\( \mathbf{C} \cdot\left[\frac{V_{1}}{R_{1}}+\frac{V_{2}}{R_{2}}+\frac{V_{3}}{R_{3}}\right]\left[R_{1}+R_{2}+R_{3}\right] \)
D. \( \left[\frac{V_{1}}{R_{2}^{2}}+\frac{V_{2}}{R_{2}^{2}}+\frac{V_{3}}{R_{2}}\right]\left[R_{1}^{2}+R_{2}^{2}+R_{3}^{2}\right] \)
Subject: Physics
In hydrogen atom, an electron is revolving in the orbit of radius \( 0.53 \dot{A} \)
with \( 6.6 \times 10^{15} \) radiation/s. Magnetic
field produced at the centre of the orbit is
A. \( 0.125 W b / m^{2} \)
B. \( 1.25 W b / m^{2} \)
c. \( 12.5 W b / m^{2} \)
D. \( 125 W b / m^{2} \)
Subject: Maths
Prove that:
\[
\begin{array}{l}
{\left[\begin{array}{lll}
\mathbf{x} \mathbf{y} & \mathbf{z}
\end{array}\right]\left[\begin{array}{lll}
\boldsymbol{a} & \boldsymbol{h} & \boldsymbol{g} \\
\boldsymbol{h} & \boldsymbol{b} & \boldsymbol{f} \\
\boldsymbol{g} & \boldsymbol{f} & \boldsymbol{c}
\end{array}\right]\left[\begin{array}{l}
\boldsymbol{x} \\
\boldsymbol{y} \\
\boldsymbol{z}
\end{array}\right]} \\
= & {\left[\boldsymbol{a x}^{2}+\boldsymbol{b} \boldsymbol{y}^{2}+\boldsymbol{c} \boldsymbol{z}^{2}+\boldsymbol{c f} \boldsymbol{z}+\boldsymbol{2 g} \boldsymbol{z} \boldsymbol{x}+\boldsymbol{t}\right.}
\end{array}
\]
\( 2 h x y \)
Subject: Maths
The normal at any point \( \boldsymbol{P}(\boldsymbol{x}, \boldsymbol{y}) \) of \( \mathbf{a} \)
curve meets the \( x \) -axis at \( Q \) and \( N \) is
the foot of the ordinate at \( P \)

If \( N Q=\frac{x\left(1+y^{2}\right)}{1+x^{2}}, \) then equation of such curve, given that it passes through the point (3,1) is:
A. \( x^{2}-y^{2}=8 \)
B . \( x^{2}+2 y^{2}=11 \)
c. \( x^{2}-5 y^{2}=4 \)
D. \( x^{2}+3 y^{2}=7 \)
Subject: Physics
ends so that it lies horizontally and
without tension. A weight \( W \) is
suspended from the middle point of the wire. The vertical depression is
(Young's modulus is \( Y \).)
A \( \cdot \sqrt{\frac{2 T l^{2}}{4 A Y}+\frac{T^{2} l^{2}}{4 A^{2} Y^{2}}} \)
B. \( \sqrt{\frac{2 T l^{2}}{4 A Y}-\frac{T^{2} l^{2}}{4 A^{2} Y^{2}}} \)
c. \( \sqrt{\frac{2 T l^{2}}{4 A Y}} \)
D. \( \frac{T l}{2 A Y} \)
Subject: Chemistry
A beaker contains a saturated solution
of copper(l) chloride. Copper(l) chloride is slightly soluble salt with a solubility product of \( 1.2 \times 10^{-6} \)
Which of the following salts when added to the solution would precipitate
copper(l) chloride?
A. Sodium chloride
B. Potassium bromide
c. Silver(I) nitrate
D. Lead(II) acetate
E. Magnesium iodide
Subject: Chemistry
\( \boldsymbol{A} \rightleftharpoons \boldsymbol{B}+\boldsymbol{C} \)
Time \( t \)
Total pressure of \( (\boldsymbol{B}+\boldsymbol{C}) \quad \boldsymbol{P}_{2} \)
Find equilibrium constant \( k \)
A \( \cdot k=\frac{1}{t} \ln \frac{P_{3}}{2\left(P_{3}-P_{2}\right)} \)
в. \( _{k=\frac{1}{t} l n \frac{P_{2}}{2\left(P_{3}-P_{2}\right)}} \)
c. \( k=\frac{1}{t} \ln \frac{P_{3}}{2\left(P_{3}+P_{2}\right)} \)
D. None of these
Subject: Physics
As shown in the experimental setup,
two cells with the same \( e m f E \) and
different internal. resistance \( r_{1} \) and \( r_{2} \)
are connected in series to an external
resistance \( \boldsymbol{R} \). Value of \( \boldsymbol{R} \) so that the
potential difference across the cell be
zero, is :
\( \mathbf{A} \cdot r_{1}+r_{2} \)
в. \( \frac{r_{1}}{r_{2}} \)
\( c \cdot r_{1}-r_{2} \)
\( D \cdot r_{1} r_{2} \)