AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Physics
Either a fuse or a circuit-breaker can be
used to protect electrical cables from
large currents that could cause
overheating.
When a fuse is used, where should it be
connected, and when a circuit-breaker
is used, where should it be connected?
A. Position of fuse \( -X \), Position of circuit-breaker \( -X \)
B. Position of fuse - \( X \), Position of circuit-breaker - \( Y \)
c. Position of fuse \( -Y \), Position of circuit-breaker \( -X \)
D. Position of fuse - \( Y \), Position of circuit-breaker - \( Y \)
Subject: Physics
The optical length of an astronomical telescope with magnifying power of 10 for normal vision is \( 44 \mathrm{cm} . \) What is focal
length of the objective?
A. \( 40 \mathrm{cm} \)
B. 22cm
\( c \cdot 10 c m \)
D. \( 4 \mathrm{cm} \)
Subject: Physics
A spot light \( S \) rotates in a horizontal
plane with a constant angular velocity of \( 0.1 \mathrm{rad} / \mathrm{s} \). The spot of light \( \boldsymbol{P} \) moves
along the wall at a distance \( 3 m \). What is
the velocity of the spot \( \boldsymbol{P} \) when \( \boldsymbol{\theta}=\mathbf{4 5}^{o} \) ?
A. \( 0.6 \mathrm{m} / \mathrm{s} \)
B. \( 0.5 \mathrm{m} / \mathrm{s} \)
\( c .0 .4 m / s \)
D. \( 0.3 \mathrm{m} / \mathrm{s} \)
Subject: Chemistry
For a given reaction: \( \boldsymbol{M}^{(\boldsymbol{x}+\boldsymbol{n})}+ \)
\( \boldsymbol{n} e^{-} \rightarrow \boldsymbol{M}^{x+}, \boldsymbol{E}_{r e d}^{\ominus} \) is known along with
\( M^{x+n} \) and \( M^{x+} \) ion concentration.
Then:
A. \( n \) can be evaluated
B. \( x \) can be evaluated
c. \( (x+n) \) can be evaluated
D. \( n, x,(x+n) \) can be evaluated
Subject: Maths
A die is thrown, a man \( C \) gets a prize of
Rs. 5 if the die turns up 1 and gets a prize of Rs. 3 if the die turns up \( 2, \) else
he gets nothing, A man \( A \) whose probability of speaking the truth is \( \frac{1}{2} \)
tells \( C \) that the die has turned up 1 and another man \( B \) whose probability of speaking the truth is \( \frac{2}{3} \) tells \( C \) that the
die has turned up 2. Find the
expectation value of \( \boldsymbol{C} \)
Subject: Chemistry
What is the process of leaching in case of low grade copper ores?
A . Leaching is carried out with \( N a O H \) and \( O_{2} \)
B. Leaching is carried out with \( N a C N \)
C. Leaching is carried out with acids in presence of \( O_{2} \)
D. Leaching is carried out by boiling the ore with water
Subject: Maths
Draw a parallelogram \( A B C D \) in which \( B C=5 \mathrm{cm}, A B=3 \mathrm{cm} \) and \( \angle A B C= \)
\( 60^{0} . \) divide it into triangles \( B C D \) and
\( A B D \) by the diagonal \( B D . \) Construct
the triangle \( B D^{\prime} C^{\prime} \) similar to \( B D C \) with scale factor \( \frac{4}{3} . \) Draw the line
\( \operatorname{segment} D^{\prime} A^{\prime} \) parallel to \( D A, \) where \( A^{\prime} \)
lies on extended side \( B A \). Is \( A^{\prime} B C^{\prime} D^{\prime} \) a
parallelogram?
A. Yes
B. No
c. Data insufficient
D. Ambiguous
Subject: Chemistry
Assertion
Sulphide ores are concentrated by froth flotation process.
Reason
Pine oil forms emulsions in water.
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: Biology
The four elements called "big-four" which make up \( 95 \% \) of all elements found in a living system are
A. \( \mathrm{C}, \mathrm{H}, \mathrm{O}, \mathrm{N} \)
B. \( \mathrm{C}, \mathrm{H}, \mathrm{O}, \mathrm{P} \)
c. \( \mathrm{c}, \) н, \( 0, \mathrm{s} \)
D. \( \mathrm{C}, \mathrm{N}, \mathrm{O}, \mathrm{P} \)
Subject: Chemistry
The electronic configuration of elements \( A, B, C, D \) and \( E \) are as follows:
\( \begin{array}{llll}A(2,8,7) & B(2,8,1) & C(2) & D(2,\end{array} \)
6) \( \quad E(2,8) \)
The element which can donate electrons in a chemical reaction is:
\( A \cdot A \)
B. B
\( c \cdot D \)
D.
Subject: Maths
On every Friday, a veggie store owner offers a discount of \( 30 \% \) on potatoes,
which he sell for \( \$ 0.90 \) per pound on other days. The store also sells carrots for \( \$ 3.50 \) per pound. If a customer buys
2 pound of carrots and \( p \) pounds of
potatoes then the total cost, \( c \), customer
has to pay is
A \( c=0.63 p+7 \)
7
B. \( c=0.9 p+7 \)
c. \( c=0.3 p+3.5 \)
D. \( c=0.9 p+3.5 \)
Subject: Physics
What is the temperature of Fahrenheit
scale corresponding to \( -10^{\circ} \mathrm{C} \) ?
\( \mathbf{A} \cdot 14^{\circ} F \)
B. \( -14^{\circ} F \)
\( \mathbf{c} \cdot 22^{\circ} F \)
D . \( 24^{\circ} F \)
Subject: Chemistry
The IUPAC name of
\( \left[\boldsymbol{F e}\left(\boldsymbol{H}_{2} \boldsymbol{O}\right)_{5}(\boldsymbol{N O})\right] \boldsymbol{S} \boldsymbol{O}_{4} \) is penta
aquanitrosylium iron
(I) sulphate.
A. True
B. False
Subject: Physics
A particle of mass \( \mathrm{m} \) is revolving in a horizontal circle of radius r with
constant angular speed \( \omega . \) The areal
velocity of the particle is:
A \( \cdot r^{2} \omega \)
B . \( r^{2} \theta \)
\( ^{c \cdot \frac{r^{2} \omega}{2}} \)
D. \( \frac{r \omega^{2}}{2} \)
Subject: Maths
Factorise the following:
\( 3\left(x^{2}-5 x\right)^{2}-2\left(x^{2}-5 x+5\right)-6 \)
A \( \cdot\left(x^{2}-5 x+2\right)\left(3 x^{2}-5 x-8\right) \)
B. \( \left(x^{2}-5 x+2\right)\left(3 x^{2}-15 x-8\right) \)
C. \( \left(x^{2}-5 x-2\right)\left(3 x^{2}-15 x+8\right) \)
D. \( \left(x^{2}-5 x-2\right)\left(3 x^{2}-5 x+8\right) \)
Subject: Physics
The figure shows the elliptical orbit of a
planet \( P \) about the sun S. The shaded
area SCD is a twice shaded area SAB. if
\( t_{1} \) is the the time for the planet to move
from \( C \) to \( D \) and \( t_{2} \) is the time to move
from \( A \) to \( B \), then
A \( \cdot t_{1}=t_{2} \)
\( \mathbf{B} \cdot t_{1}=2 t_{2} \)
\( \mathbf{c} \cdot t_{1}=4 t_{2} \)
\( \mathbf{D} \cdot t_{1}>t_{2} \)
Subject: Physics
A particle moves with a uniform speed of \( 5 \mathrm{m} / \mathrm{s} \) in a circular path. If the speed increases to \( 8 \mathrm{m} / \mathrm{s} \) in the 20 th second
The motion of the particle in the 22 nd second will be
A. Uniform circular motion
B. Non uniform circular motion
c. Linear motion, since the particle flies off from the circular path
D. Non linear motion, since velocity has increased
Subject: Chemistry
For the reaction, \( N_{2} O_{4}(g) \underset{K_{2}}{\rightleftharpoons} K_{1} \)
\( 2 N O_{2}(g), \) the rate of disappearance of
\( N O_{2} \) will be :
A \( \cdot K_{1}\left[N_{2} O_{4}\right]-K_{2}\left[N O_{2}\right]^{2} \)
B . \( 2 K_{1}\left[N_{2} O_{4}\right]-2 K_{2}\left[N O_{2}\right]^{2} \)
c. \( K_{2}\left[N O_{2}\right]^{2}-K_{1}\left[N_{2} O_{4}\right] \)
D \( \cdot 2 K_{2}\left[N O_{2}\right]^{2}-2 K_{1}\left[N_{2} O_{4}\right] \)
Subject: Physics
When unpolarised light is incident on a plane glass plate at Brewster's angle, then which of the following statements
is correct?
A. Reflected and refracted rays are completely polarised with their planes of polarisation parallel to each other
B. Reflected and refracted rays are completely polarised with their planes of polarisation perpendicular to each other
c. Reflected light is plane polarised but transmitted light is partially polarised
D. Reflected light is partially polarised but refracted light is plane polarised
Subject: Chemistry
At some temperature and under a
pressure of 4 atm, \( P C l_{5} \) is \( 10 \% \) dissociated. Calculate the pressure at
which \( P C l_{5} \) will be \( 20 \% \) dissociated,
temperature remaining same.
\( A \cdot 0.97 \) atm
B. 0.34 atm
C. 1.43 atm
D. 1.67 atm
Subject: Maths
The pairs \( \bar{a}, \bar{b} \) and \( \bar{c}, \bar{d} \) each determine a plane. Then the planes are parallel if \( (\overline{\boldsymbol{a}} \times \overline{\boldsymbol{c}}) \times(\overline{\boldsymbol{b}} \times \overline{\boldsymbol{d}})= \)
\( \mathbf{0} 2)(\overline{\boldsymbol{a}} \times \overline{\boldsymbol{c}}) \cdot(\overline{\boldsymbol{b}} \times \overline{\boldsymbol{d}})=\mathbf{0} \)
\( (\bar{a} \times \bar{b}) \times(\bar{c} \times \bar{d})= \)
\( \mathbf{0} 4)(\bar{a} \times \bar{b}) \cdot(\bar{c} \times \bar{d})=0 \)
Subject: Maths
The value of \( \int_{\frac{7 \pi}{4}}^{\frac{7 \pi}{3}} \sqrt{\tan ^{2} x} d x \) is equal to
A. \( 2 \log 2 \)
B. \( \log 2 \sqrt{2} \)
\( c \cdot \log 2 \)
D. \( \log \sqrt{2} \)
Subject: Chemistry
For which of the following parameters
the structural isomers \( \mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH} \) and
\( \mathbf{C H}_{3} \mathbf{O C H}_{3} \) would be expected to have
the same values?
A. Heat of vaporisation
B. Vapour pressure at the same temperature
c. Boiling points
D. Gaseous densities at the same temperature and pressure
Subject: Maths
Find a continuous function \( f, \) where
\( \left(x^{4}-4 x^{2}\right) \leq f(x) \leq\left(2 x^{2}-x^{3}\right) \) such
that the area bounded by \( \boldsymbol{y}=\boldsymbol{f}(\boldsymbol{x}), \boldsymbol{y}= \)
\( x^{4}-4 x^{2}, y \) -axis, and the line \( x=t \)
where \( (0 \leq t \leq 2) \) is \( k \) times the area
bounded by \( \boldsymbol{y}=\boldsymbol{f}(\boldsymbol{x}), \boldsymbol{y}=\mathbf{2} \boldsymbol{x}^{2}-\boldsymbol{x}^{3}, \mathbf{y} \)
axis, and line \( \boldsymbol{x}=\boldsymbol{t} \text { (where } \mathbf{0} \leq \boldsymbol{t} \leq \mathbf{2}) \)
Subject: Physics
A proton travels few distance in an
electric field, then it enters a crossed
magnetic field of \( 1 \mathrm{T} \) and radius \( 0.2 \mathrm{m} \) Find the velocity of proton.
A \( \cdot 0.2 \times 10^{8} \mathrm{ms}^{-1} \)
В. \( 0.2 \times 10^{7} \mathrm{ms}^{-1} \)
\( c \cdot 0.2 \times 10^{6} m s^{-1} \)
\( - \)
D. \( 2 \times 10^{8} \mathrm{ms}^{-1} \)
Subject: Maths
Figure is a graph of which of the
following?
A \( \cdot x^{2}+y^{2}=9 \)
в. \( |x|=3 \) and \( |y|=3 \)
c. \( |x+y|=3 \)
D. \( |x|+|y|=3 \)
E . \( x-y=3 \)
Subject: Maths
The plane \( X O Z \) divides the join of (1,-1,5) and (2,3,4) in the ratio \( \lambda: 1 \)
then \( \lambda \) is
A . -3
B. \( -1 / 3 \)
\( c \cdot 3 \)
D. \( 1 / 3 \)
Subject: Chemistry
Which of the following is correctly matched?
A. Momentum of H-atom when electrons return from
\( n=2 \) to \( n=1: \frac{3 R h}{4} \)
B. Momentum of proton: Independent of wavelength of light
c. e/m ratio of anode rays : Independent of gas in the discharge tube
D. Radius of nucleus :: (Mass no.) \( ^{1 / 2} \)
Subject: Chemistry
\( Z n \mid Z n^{2+}(a=0.1 M) \| F e^{2+}(a= \)
\( \mathbf{0 . 0 1} \boldsymbol{M}) \mid \boldsymbol{F} e \)
The EMF of the above cell is \( 0.2905 . \) The
equilibrium constant for the cell reaction is:
B . \( 10^{0.32 / 0.0295} \)
D. \( e^{0.32 / 0.0295} \)
Subject: Physics
A radioactive nuclide is produced at the constant rate of \( ^{\prime} \boldsymbol{n}^{\prime} \) per second (say, by bombarding a target with neutrons)
The expected number' \( N^{\prime} \) of nuclei in
existence \( t \) s after the number is \( N_{0} \) is
given by
A. \( N=N_{0} e^{-\lambda t} \)
B. \( N=\frac{n}{\lambda} N_{0} e^{-\lambda} \)
c. \( N=\frac{n}{\lambda}+\left(N_{0}-\frac{n}{\lambda}\right) e^{-\lambda t} \)
D. \( N=\frac{n}{\lambda}+\left(N_{0}+\frac{n}{\lambda}\right) e^{-\lambda t} \)
Subject: Maths
In \( \Delta A B C, A B=A C . D, E \) and \( F \) are
mid-points of the sides \( B C, C A \) and
\( A B \) respectively. then, \( : A D \) is
perpendicular to \( \boldsymbol{F C} \) If the above statement is true then
mention answer as 1 , else mention 0 if false
Subject: Chemistry
\( \boldsymbol{B}(\boldsymbol{O} \boldsymbol{H})_{3}+\boldsymbol{N} \boldsymbol{a} \boldsymbol{O} \boldsymbol{H} \rightarrow \)
\( \boldsymbol{N} \boldsymbol{a}\left[\boldsymbol{B}(\boldsymbol{O} \boldsymbol{H})_{4}\right]_{(a q)} \)
Then addition of which of the following proceeds the reaction in the forward direction:
A. cis-1, 2 dio
B. trans 1, 2 diol
c. borax
D. \( N a_{2} H P O_{4} \)
Subject: Chemistry
During burning of candle, different zones of combustion in the flame are listed below:
a) Outermost zone
b) Innermost zone
c) Middle zone
The correct order of temperature of zones is :
\( \mathbf{A} \cdot A>B>C \)
в. \( C>B>A \)
c. \( B>C>A \)
D. \( A>C>B \)
Subject: Physics
Young's modulus of a metal is \( 15 \times 10^{11} \)
Pa. If its poisson's ratio is \( 0.4 . \) The bulk modulus of the metal in \( P a \) is :
A \( \cdot 25 \times 10^{11} \)
В . \( 2.5 \times 10^{11} \)
c. \( 250 \times 10^{11} \)
D. \( 0.25 \times 10^{11} \)
Subject: Maths
\( f(1,2,3,4,5\}, Y=\{1,3,5,7,9\} \)
determine which of the following relations from \( X \) to \( Y \) are functions?
Give reason for your answer. If it is a function, state its type.
(i) \( R_{1}=\{(x, y) \mid y=x+2, x \in X, y \in Y\} \)
(ii) \( R_{2}=\{(1,1),(2,1),(3,3),(4,3),(5,5)\} \)
(iii) \( R_{3}=\{(1,1),(1,3),(3,5),(3,7),(5,7)\} \)
(iv) \( R_{4}=\{(1,3),(2,5),(4,7),(5,9),(3,1)\} \)
Subject: Maths
If \( f(x) \) is continuous at \( x=c \) and \( g(x) \)
is continuous at \( x=f(c) \) then which of
the following is/are continuous at \( x=c \)
\( ? \)
A \( \cdot(f(x)-g(x)) * f(x) \)
в. \( f(g(x)) \)
c. \( f(f(x)) \)
D. None
Subject: Chemistry
Choose the correct options -
This question has multiple correct options
A. The metal added to gold to harden it is iron
B. The molten metal that catches fire in chlorine gas and gives off white fumes is sodium.
C. The metal that forms two types of its oxide and rust in moisture is iron. The formulas of its oxides are :
\( \mathrm{FeO} ; \mathrm{Fe}_{2} \mathrm{O}_{3} \)
D. The metal used in hot water systems is copper, because it is a good conductor of heat and electricity
Subject: Maths
If \( A \) and \( B \) are mutually exclusive such
that \( \boldsymbol{P}(\boldsymbol{A})=\mathbf{0 . 3 5} \) and \( \boldsymbol{P}(\boldsymbol{B})=\mathbf{0 . 4 5} \)
find
\( \boldsymbol{P}(\boldsymbol{A} \cup \boldsymbol{B}) \)
Subject: Maths
\( \boldsymbol{f}(\boldsymbol{x})=\mathbf{1}+\frac{\mathbf{1}}{\boldsymbol{x}} ; \boldsymbol{g}(\boldsymbol{x})=\frac{\mathbf{1}}{\mathbf{1}+\boldsymbol{f}(\boldsymbol{x})} \Rightarrow \)
\( \boldsymbol{g}^{\prime}(\mathbf{2})= \)
\( A \cdot \frac{1}{5} \)
в. \( \frac{1}{25} \)
c. 5
D. \( \frac{1}{16} \)
Subject: Chemistry
Assertion
Aquatic species are more comfortable in warm waters than cold waters.
Reason
\( \boldsymbol{K}_{\boldsymbol{H}} \) values for both \( \boldsymbol{N}_{2} \) and \( \boldsymbol{O}_{2} \)
decrease with increase of temperature.
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
\( f(x)=\frac{4}{\pi} \sin \left(\frac{\pi}{2} x\right)+B \) and
\( \int_{1}^{0} f(x) d x=\frac{4}{\pi} \int \sin \left(\frac{\pi}{2} x\right)+B d x, \) Find
\( \boldsymbol{B} \)
Subject: Chemistry
Match List-I with List-II.
List-I Chemical reaction List-II Name of
process
(1) \( 4 N H_{3}+5 O_{2} \stackrel{800^{\circ} C / P t}{\rightarrow} \)
(a) Contact
\[
4 N O+6 H_{2} O
\]
process
(2) \( 4 H C l+O_{2} \frac{3230^{\circ} C / C u C l_{2}}{450-500^{\circ} / V_{2} O_{5}} \)
(b) Ostwald's
\[
2 C l_{2}+2 H_{2} O
\]
process
(c) Deacon's
(3) \( 2 S O_{2}+O_{2} \rightarrow 2 S O 3 \quad \) process
(d) Haber's
(4) \( 2 N_{2}+3 H_{2} \stackrel{F e+M b}{\rightarrow} 2 N H_{3} \quad \) process
\( \mathbf{A} \cdot 1-a, 2-b, 3-d, 4-c \)
B. \( 1-b, 2-c, 3-a, 4-d \)
C \( .1-a, 2-d, 3-c, 4-b \)
D. \( 1-a, 2-c, 3-b, 4-d \)
Subject: Maths
The objective function \( z=x_{1}+x_{2} \)
subject to \( \boldsymbol{x}_{1}+\boldsymbol{x}_{2} \leq \mathbf{1 0},-\mathbf{2} \boldsymbol{x}_{\mathbf{1}}+\mathbf{3} \boldsymbol{x}_{2} \leq \)
\( \mathbf{1 5}, \boldsymbol{x}_{1} \leq \mathbf{6}, \boldsymbol{x}_{1}, \boldsymbol{x}_{2} \geq \mathbf{0} \) has maximum
value \( \ldots \ldots . . . . . . . . . \) of the feasible region.
A. at only one point
B. at only two points
c. at every point of the segment joining two points
D. at every point of the line joining two points
Subject: Chemistry
Dissolving 120 gm of a compound of (mol.wt. 60 ) in 1000 g of water gave a solution of density \( 1.5 \mathrm{g} / \mathrm{mL} \). The molarity of the solution is:
A \( .1 .00 M \)
в. \( 1.78 M \)
\( c .2 .50 M \)
D. \( 4.00 M \)
Subject: Physics
The magnifying power of a compound microscope is 20 and the distance between its two lenses is \( 30 \mathrm{cm} \) when
the final image is at the near point of the eye. If the focal length of eyepiece is \( 6.25 \mathrm{cm}, \) the focal length of objective is :
A. \( 2.5 \mathrm{cm} \)
B. 3.5 \( \mathrm{cm} \)
\( c .4 .5 \mathrm{cm} \)
D. 5.0 \( \mathrm{cm} \)
Subject: Maths
If the vectors \( 2 x \hat{i}-y \hat{j}-4 \hat{k} \) and \( 10 \hat{i}+ \) \( \hat{\boldsymbol{y}}+5 \hat{k} \) are perpendicular, then the locus of \( (x, y) \) is
A. A Parabola with vertex at (1,0) and latus rectum 10
B. A Parabola with vertex at (0,1) and latus rectum 20
c. A Parabola with vertex at (1,0) and latus rectum 20
D. A Parabola with vertex at (0,1) and latus rectum 10
Subject: Maths
If \( \boldsymbol{A}=\left[\begin{array}{cc}\mathbf{1} & \log _{\boldsymbol{b}} \boldsymbol{a} \\ \log _{\boldsymbol{a}} \boldsymbol{b} & \mathbf{1}\end{array}\right] \) then \( |\boldsymbol{A}| \) is equal
to
A. 0
B \( \cdot \log _{a} b \)
\( c \cdot-1 \)
\( \mathbf{D} \cdot \log _{b} a \)
Subject: Chemistry
Match the interhalogen compounds of
column I with the geometry in column II
and assign the correct code.
Column I
\( \begin{array}{ll}\text { (a) } & X X^{\prime}\end{array} \)
(i) \( \quad \) T-shape
Pentagona
\( \begin{array}{ccccc}(b) & X X_{3}^{\prime} & ( \text { ii) } & \text { bipyramida }\end{array} \)
\begin{tabular}{ll} 
(с) & \( X X_{5}^{\prime} \) \\
\\
\hline
\end{tabular}
(iii) \( \quad \) Linear
Square -
\( \begin{array}{llll}\text { (d) } & X X_{7}^{\prime} & \text { (iv) } & \text { pyramidal }\end{array} \)
\( (v) \)
Tetrahedral
A \( \cdot(a)-(i v),(b)-(i i i),(c)-(i i),(d)-(i) \)
B. \( (a)-(i i i),(b)-(i v),(c)-(i),(d)-(i i) \)
C \( .(a)-(i i i),(b)-(i),(c)-(i v),(d)-(i i) \)
D. \( (a)-(v),(b)-(i v),(c)-(i i i),(d)-(i i) \)
Subject: Physics
A concave mirror is made from a hollow
sphere of radius of curvature \( 30 \mathrm{cm} . \) If an object of height \( 2 \mathrm{cm} \) is placed at 10 \( \mathrm{cm} \) from the pole of the mirror, determine the size of the image:
\( A \cdot 3 \mathrm{cm} \)
B. 6 \( \mathrm{cm} \)
c. \( 12 \mathrm{cm} \)
D. \( 24 \mathrm{cm} \)
Subject: Physics
When two bodies move uniformly towards each other, the distance
decreases by \( 6 m / s . \) If both bodies
move in the same directions with the
same speeds (as above), the distance
between them increases by \( 4 m / s \). Then
the speeds of the two bodies are
A. \( 3 m / s \) and \( 3 m / s \)
B. \( 4 \mathrm{m} / \mathrm{s} \) and \( 2 \mathrm{m} / \mathrm{s} \)
\( \mathbf{c} .5 \mathrm{m} / \mathrm{s} \) and \( 1 \mathrm{m} / \mathrm{s} \)
D. \( 7 \mathrm{m} / \mathrm{s} \) and \( 3 \mathrm{m} / \mathrm{s} \)
Subject: Chemistry
For which of these redox pairs, the reduction potential vary with pH This question has multiple correct options
\( \mathbf{A} \cdot A m O_{2}^{2+} / A m O_{2}^{+} \)
B. \( A m O_{2}^{2+} / A m^{4} \)
c. \( M n O_{4}^{-} / M n^{2+} \)
D. \( Z n^{2+} / Z n \)
Subject: Physics
The coil \( X \) and \( Y \) have the same number
of turns and length. Each has a flux
density \( B \) in the middle and a flux
density \( 0.5 B \) at the ends when carrying the same current. When the coils are
joined to form a long coil of twice the
length of \( X \) or \( Y \) and the current \( I \) is sent through the coil, the flux density in the middle is given by:
A. 0
в. \( 0.5 B \)
c. \( 2 B \)
D. \( B \)
Subject: Physics
The four tyres of an automobile are inflated to a pressure of \( 2.0 \times 10^{5} \mathrm{Pa} \)
Each Tyre has an area of \( 0.024 m^{2} \) in
contact with the ground. Determine the weight of the automobile.
A \( \cdot 1.92 \times 10^{4} \mathrm{N} \)
B . \( 1.92 \times 10^{5} \mathrm{N} \)
c. \( 1.92 \times 10^{6} \mathrm{N} \)
D. \( 2.92 \times 10^{4} \mathrm{N} \)
Subject: Maths
The vector form of the equation of the
line passing through points (3,4,7) and (5,1,6) is
\( \mathbf{A} \cdot \vec{r}=(3 \hat{i}+4 \hat{j}-7 \hat{k})+\lambda(2 \hat{i}-3 \hat{j}+13 \hat{k}) \)
B \( \cdot \vec{r}=(3 \hat{i}+4 \hat{j}-7 \hat{k})+\lambda(8 \hat{i}+5 \hat{j}-\hat{k}) \)
C \( . \vec{r}=(3 \hat{i}+4 \hat{j}+7 \hat{k})+\lambda(2 \hat{i}-3 \hat{j}-\hat{k}) \)
D \( \cdot \vec{r}=(3 \hat{i}+4 \hat{j}-7 \hat{k})+\lambda(2 \hat{i}-3 \hat{j}-13 \hat{k}) \)
Subject: Physics
A charge \( +10^{-9} C \) is located at the origin in free space and another charge
\( Q \) at \( (2,0,0) . \) If the \( X \) -component of the electric field at (3,1,1) is zero, calculate the value of \( Q . \) Is \( Y- \) component zero at (3,1,1)\( ? \)
Subject: Chemistry
\( \ln H_{2} O, \) the bond angle \( \mathrm{HOH} \) is \( 104^{\circ} 28^{\prime} \)
but in \( H_{2} S, H_{2} S e \) and \( H_{2} T e \) the bond
angles are pretty close to \( 90^{\circ} . \) This
suggests that:
A . oxygen uses \( s p^{2} \) -hybrid orbitals while \( S, \) Se and Te use \( s p^{3} \) -hybrid orbitals for bonding with the hydrogen atoms
B. oxygen uses \( s p^{3} \) -hybrid orbitals to bond with the two hydrogen atoms while \( S, \) Se and Te use almost pure \( \mathrm{p} \) orbitals
c. oxygen uses \( s p^{3} \) -hybrid orbitals while \( S, \) Se and \( T e \) utilize d orbitals for bonding with the hydrogen atoms
D. all the atoms use pure p orbitals to bond with the hydrogen atoms
Subject: Physics
A mass \( M \) is broken in two parts : \( m \)
and (M- m). What would be the relation
between \( m \) and \( M \) so that the force of
gravitation between the two parts is maximum?
A. \( m M=2 \)
в. \( m=\frac{M}{2} \)
\( \mathbf{c} \cdot M=m^{2} \)
D. none of these
Subject: Maths
If \( \boldsymbol{x} \sqrt{\mathbf{1}+\boldsymbol{y}}+\boldsymbol{y} \sqrt{\mathbf{1}+\boldsymbol{x}}=\mathbf{0} \) and \( \boldsymbol{x} \neq \boldsymbol{y} \)
then \( \frac{\boldsymbol{d} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}}= \)
A. \( \frac{1}{1+x} \)
B. \( \frac{1}{(1+x)^{2}} \)
c. \( \frac{-1}{(1+x)^{2}} \)
D. \( \frac{-1}{1+x} \)
Subject: Chemistry
Which are the correct statements for
\( N O_{2} ? \)
This question has multiple correct options
A. It is paramagnetic and dimerizes to \( N_{2} O_{4} \)
B. \( N_{2} O_{4} \) is planar and diamagnetic.
\( \mathrm{C} \cdot \mathrm{N} \mathrm{O}_{2} \) is linear containing an odd number of electrons.
D. N-O bonds in \( N O_{2} \) are different lengths.
Subject: Maths
Evaluate \( \int e^{x}\left(\log x+\frac{1}{x^{2}}\right) d x \)
A \( \cdot e^{x} \log x+c \)
B. \( e^{x}\left(\log x-\frac{1}{x}\right)+c \)
c. \( e^{x}\left(\log x+\frac{1}{x}\right)+c \)
D. \( \frac{e^{x}}{x^{2}}+c \)
Subject: Chemistry
How many grams of concentrated nitric acid solution should be used to prepare
\( 250 \mathrm{mL} \) of \( 2.0 \mathrm{M} H N O_{3} ? \)
The concentrated acid is \( 70 \% H N O_{3} \)
A \( \cdot 45.0 \mathrm{g} \) conc. \( \mathrm{H} \mathrm{NO}_{3} \)
B. 90.0 g conc. H NO
c. \( 70.0 \mathrm{g} \) conc. \( \mathrm{H} \mathrm{NO}_{3} \)
D. 54.0 g conc. \( H N O_{3} \)
Subject: Physics
Calculate the momentum of particle
whose de Broglie wavelength is \( 2^{\circ} A \)
A \( \cdot 3.313 \times 10^{-24} g m s^{-1} \)
В. \( 3.313 \times 10^{-24} k g m s^{-1} \)
c. \( 33.13 \times 10^{-20} k g m s^{-1} \)
D. none of these
Subject: Physics
\( M, M_{n} \) and \( M_{p} \) denotes the masses of
a nucleus of \( z X^{A}, \) a neutron, and a
proton respectively. If the nucleus is separated into its individual protons and neutrons then,
A \( \cdot M=(A-Z) M_{n}+Z M_{p} \)
B. \( M=Z M_{n}+(A-Z) M_{p} \)
C. \( M>(A-Z) M_{n}+Z M_{p} \)
D. \( M<(A-Z) M_{n}+Z M_{p} \)
Subject: Physics
A rocket is launched upward from the
Earth's surface whose velocity-time
graph is shown in figure.

The maximum height attained by
the rocket is:
\( \mathbf{A} \cdot 1 k m \)
B. \( 10 \mathrm{km} \)
\( \mathbf{c} \cdot 100 \mathrm{km} \)
D. \( 60 \mathrm{km} \)