AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Chemistry
Complete the given reaction. \( 2 M n^{2+}+5_{--}(i)_{--}+8 H_{2} O \rightarrow 2_{--} \)
\( (i i)_{--}+16 H^{+} \)
\( (i i)_{--}+10_{--} \)
A \( \cdot(i)-S O_{4}^{2-},(i i)-M n O_{4}^{-},(i i i)-S_{2} O_{8}^{2-} \)
B . \( (i)-S_{2} O_{8}^{2-},(i i)-M n O_{4}^{-},(i i i)-S_{2} O_{4}^{2} \)
C \( \cdot(i)-M n O_{4}^{-},(i i)-S_{2} O_{8}^{2-},(i i)-S O_{4}^{2} \)
D \( \cdot(i)-S_{2} O_{8}^{2-},(i i)-S O_{4}^{2-},(i i i)-M n O_{4} \)
Subject: Physics
If Ram takes 4 seconds by path 1 and Shyam takes 5 seconds by the path 2 to
go from \( P \) to \( Q \), find the average velocity
of Shyam?
\( A \cdot 25 \mathrm{m} / \mathrm{s} \)
B. 20 \( \mathrm{m} / \mathrm{s} \)
\( c \cdot 10 m / s \)
D. \( 40 \mathrm{m} / \mathrm{s} \)
Subject: Chemistry
The values of the limiting molar
conductivity \( \left(\wedge^{\circ}\right) \) for \( N a C l, H C l \) and NaOAc are 126.4,425.9 and
\( 91.0 S \mathrm{cm}^{2} \) mol \( ^{-1}, \) respectively. For
\( H O A c, \wedge^{\circ} \) in \( S c m^{2} m o l^{-1} \) is:
A. 390.5
B . 299.5
c. 208.5
D. 217.4
Subject: Chemistry
Which of the following increasing order is not correct as mentioned in the
property with it?
A \( \left.. H C l O<H C l O_{2}<H C l O_{3}<H C l O_{4} \text { (thermal stability }\right) \)
B. \( H C l O_{4}<H C l O_{3}<H C l O_{2}<H C l O \) (oxidising power)
C. \( F^{-}<C l^{-}<B r^{-}<I^{-} \) (reducing nature)
D. \( H I O_{4}<I C l<I_{2}<H I \) (oxidation number of iodine)
Subject: Physics
Consider two perfectly elastic spheres
having velocities \( u_{1} \) and \( u_{2} \) in the same
direction and masses \( m \) and \( m^{\prime} . \) When
these two spheres collide, the impulse of the blow on the spheres is
A \( \cdot \frac{2 m m^{1}}{m+m^{1}}\left(u_{1}-u_{2}\right) \)
в. \( \frac{2 m m^{1}}{m-m^{1}}\left(u_{1}-u_{2}\right) \)
c. \( \frac{2 m m^{1}}{m+m^{1}}\left(u_{1}+u_{2}\right) \)
D. \( \frac{2 m m^{1}}{m-m^{1}}\left(u_{1}+u_{2}\right) \)
Subject: Maths
Prove the following identities:
\[
\begin{array}{l}
\frac{\boldsymbol{a}^{3}(\boldsymbol{b}+\boldsymbol{c})}{(\boldsymbol{a}-\boldsymbol{b})(\boldsymbol{a}-\boldsymbol{c})}+\frac{\boldsymbol{b}^{3}(\boldsymbol{c}+\boldsymbol{a})}{(\boldsymbol{b}-\boldsymbol{c})(\boldsymbol{b}-\boldsymbol{a})}+ \\
\frac{\boldsymbol{a}^{3}(\boldsymbol{a}+\boldsymbol{b})}{(\boldsymbol{c}-\boldsymbol{a})(\boldsymbol{c}-\boldsymbol{b})}=\boldsymbol{b} \boldsymbol{c}+\boldsymbol{c} \boldsymbol{a}+\boldsymbol{a} \boldsymbol{b}
\end{array}
\]
Subject: Chemistry
The decomposition \( N H_{3} \) gas on a
heated tungsten surface gave the
following results:
Initial
pressure 65
105
\[
(\mathrm{mm})
\]
Half-life
\[
\begin{array}{lll}
\text { 290 } & \text { x } & \text { 670 }
\end{array}
\]
\( (\mathrm{sec}) \)
Calculate approximately the values of \( x \)
and \( y \)
A. \( x=410 \) sec, \( y=115 \) mm
B. \( x=467 \) sec, \( y=150 \mathrm{mm} \)
C \( . x=490 \) sec, \( y=120 \mathrm{mm} \)
D. \( x=430 \) sec \( , y=105 \mathrm{mm} \)
Subject: Physics
The sum of magnitudes of two forces
acting at a point is 16 N. If their resultant is normal to the
smaller force and has a magnitude of 8
N, the forces are:
A. \( 6 N, 10 N \)
в. \( 8 N, 8 N \)
c. \( 4 N, 12 N \)
D. \( 2 N, 14 N \)
Subject: Biology
Assertion
Cell division is necessary because it is a physiological process bound to occur as a rule of nature.
Reason
Division of nucleus is followed by division of cytoplasm.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion.
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Assertion is incorrect but Reason is correct
Subject: Physics
A wire \( A B \) is carrying a steady current 12 A and is lying on the table. Another wire CD carrying 5 A is held directly above \( A B \) at a height of \( 1 \mathrm{mm} \). Find the mass per unit length of the wire CD so that it remains suspended at its position when left free. Give the directions of the
current flowing in \( \mathrm{CD} \) with respect to that in \( A B[\text { Take the value of } g= \)
\( \left.10 m s^{-2}\right] \)
Subject: Maths
Find the values of \( x \), if \( \left|\begin{array}{cc}\boldsymbol{x}+\mathbf{1} & \boldsymbol{x}-\mathbf{1} \\ \boldsymbol{x}-\mathbf{3} & \boldsymbol{x}+\mathbf{2}\end{array}\right|=\left|\begin{array}{cc}\mathbf{4} & \mathbf{- 1} \\ \mathbf{1} & \mathbf{3}\end{array}\right| \)
Subject: Chemistry
(t)-Sucrose has a specific rotation of \( +66.5, \) while \( D-(+) \) -glucose and \( D-(-) \) fructose have specific rotations of +52.5 and -92.4 respectively. After complete hydrolysis of (+)-sucrose by dilute acid, the specific rotation of the hydrolysis
product, called invert sugar [a 1: 1 mixture of \( \mathrm{D}-(+)-\mathrm{g} \) lucose and \( \mathrm{D}-(-) \) fructose] is \( -x \)
the nearest integer value of \( x \) is:
Subject: Physics
Carbon, Silicon and Germanium atoms
have limn valence electrons each. Their
valence and conduction bands
are separated by energy band gaps
represented by \( \left(\boldsymbol{E}_{\boldsymbol{g}}\right)_{\boldsymbol{c}},\left(\boldsymbol{E}_{\boldsymbol{g}}\right)_{\boldsymbol{s i}} \) and \( \left(\boldsymbol{E}_{\boldsymbol{g}}\right)_{\boldsymbol{G} \boldsymbol{e}} \)
respectively. Which one of the following relationship is true in their
case?
A \( \cdot\left(E_{g}\right)_{C}>\left(E_{g}\right)_{s i} \)
B. \( \left(E_{g}\right)_{C}<\left(E_{g}\right)_{s i} \)
\( \mathbf{c} \cdot\left(E_{g}\right)_{C}=\left(E_{g}\right)_{s i} \)
D \cdot \( \left(E_{g}\right)_{C}<\left(E_{g}\right)_{G e} \)
Subject: Maths
In a bolt factory, three machines \( A, B \)
and \( C \) manufacture \( 25 \%, 35 \% \) and \( 40 \% \)
of the total production respectively. Of
their respective outputs, \( 5 \%, 4 \% \) and \( 2 \% \) are defective. A bolt is drawn at random
from the total production and it is found to be defective. Find the probability that
it was manufactured by machine \( C \)
Subject: Maths
A student noted the number of cars
passing through a spot on a road for
100 periods each of 3 minutes and summarised it in the table given below.
Find the mode of the data
Number \( \begin{array}{ll}0- & 10 \\ 10 & 2\end{array} \) 30 of cars \( \begin{array}{ll}10- & 2 \\ 20 & 3\end{array} \) \( 20- \)
30 40
Frequency 14
Subject: Maths
Given that \( \boldsymbol{U}= \)
\( \{3,7,9,11,15,17,18\}, M= \)
\{3,7,9,11\} and \( N=\{7,11,15,17\} \)
Find
(i) \( \boldsymbol{M}-\boldsymbol{N} \)
(ii) \( \boldsymbol{N}-\boldsymbol{M} \)
(iii) \( N^{\prime}-M \)
(iv) \( M^{\prime}-N \)
\( (v) M \cap(M-N) \)
\( (v i) N \cup(N-M) \)
(vii) \( \boldsymbol{n}(\boldsymbol{M}-\boldsymbol{N}) \)
Subject: Chemistry
For the reaction \( \boldsymbol{C O}(\boldsymbol{g})+\boldsymbol{H}_{2} \boldsymbol{O}(\boldsymbol{g}) \rightleftharpoons \)
\( \boldsymbol{C O}_{2}(\boldsymbol{g})+\boldsymbol{H}_{2}(\boldsymbol{g}) \) at a given
temperature the equilibrium amount of
\( C O_{2}(g) \) can be increased by:
A. Adding a suitable catalyst
B. Adding an inertgas
c. Decreasing the volume of container
D. Increasing the amount of \( C O(g) \)
Subject: Chemistry
Three copper wires of lengths and cross sectional areas are \( (\ell, \boldsymbol{A}),(2 \ell, \boldsymbol{A} / 2) \)
and \( (\ell / 2,2 A) . \) Resistance is minimum in:
A. wire of cross-sectional area \( A / 2 \)
B. wire of cross-sectional area A
c. wire of cross-sectional area \( 2 A \)
D. same in all the three cases
Subject: Physics
What is the projection of \( \vec{P} \) on \( \vec{Q} ? \)
A \( . \vec{Q} . \vec{P} \)
в. \( \hat{P} . \hat{Q} \)
c. \( \vec{P} . \vec{Q} \)
D. \( \vec{P} . \hat{Q} \)
Subject: Maths
The angle of elevation of the top of a vertical tower from a point A due east of
it is \( 45^{\circ} . \) The angle of elevation of the top of the same tower from a point B due south of \( A \) is \( 30^{\circ} \) If the distance
between \( A \) and \( B \) is \( 54 \sqrt{2} m \),then the
height of the tower (in metres),is
A. \( 18 \sqrt{3} \)
is
B . 54
c. \( 27 \sqrt{2} \)
D. 108
Subject: Maths
Factorise the following: \( a^{6}-b^{6} \)
\( \mathbf{A} \cdot(a+b)(a-b)\left(a^{2}+b^{2}+a b\right)\left(a^{2}-b^{2}+a b\right) \)
B \( \cdot(a+b)(a-b)\left(a^{2}+b^{2}+a b\right)\left(a^{2}+b^{2}-a b\right) \)
\( \mathbf{c} \cdot(a+b)(a-b)\left(a^{2}-b^{2}-a b\right)\left(a^{2}+b^{2}-a b\right) \)
D. None of these
Subject: Maths
f \( \boldsymbol{A}=(\boldsymbol{6}, \boldsymbol{7}, \boldsymbol{8}, \boldsymbol{9}), \boldsymbol{B}=(\boldsymbol{4}, \boldsymbol{6}, \boldsymbol{8}, \boldsymbol{1} \boldsymbol{0}) \) and
\( C=\{x: x \in N: 2<x \leq 7\} ; \) find :
\( \boldsymbol{B}-(\boldsymbol{A} \cap \boldsymbol{C}) \)
The sum of the elements in the above
\( \operatorname{set} \) is?
Subject: Physics
Resistance of a resistor at temperature
\( t^{\circ} \boldsymbol{C} \) is \( \boldsymbol{R}_{t}=\boldsymbol{R}_{0}\left(\mathbf{1}+\boldsymbol{\alpha} \boldsymbol{t}+\boldsymbol{\beta} \boldsymbol{t}^{2}\right), \) where \( \boldsymbol{R}_{0} \)
is the resistance at \( 0^{\circ} \mathrm{C} \). The
temperature coefficient of resistance at
temperature \( t^{\circ} C \) is
A \( \cdot \frac{\left(1+\alpha t+\beta t^{2}\right)}{\alpha+2 \beta t} \)
B. \( (\alpha+2 \beta t) \)
c. \( \frac{\alpha+2 \beta t}{\left(1+\alpha t+\beta t^{2}\right)} \)
D. \( \frac{\alpha+2 \beta t}{2\left(1+\alpha t+\beta t^{2}\right)} \)
Subject: Chemistry
In a certain electronic transition in the
hydrogen atoms from an initial state (1) to a final state (2), the difference in the
orbital radius \( \left(r_{1}-r_{2}\right) \) is 24 times the
first Bohr radius.
Identify the transition.
\( A \cdot 5 \rightarrow 1 \)
B. 25 \( \rightarrow 1 \)
\( c \cdot 8 \rightarrow 3 \)
\( D \cdot 6 \rightarrow 5 \)
Subject: Maths
Evaluate \( \int \frac{(x+\sqrt{1+x^{2}})^{15}}{\sqrt{1+x^{2}}} d x \)
A. \( \frac{(x+\sqrt{1+x^{2}})^{14}}{14}+C \)
B. \( \frac{(x+\sqrt{1+x^{2}})^{15}}{15}+C \)
c. \( \frac{(x+\sqrt{1+x^{2}})^{16}}{16}+C \)
D. \( \frac{(x+\sqrt{1+x^{2}})^{17}}{17}+C \)
Subject: Chemistry
\( \boldsymbol{H}_{2} \boldsymbol{O}_{(g)} \rightarrow \boldsymbol{H}_{(g)}+\boldsymbol{O H}_{(g)}: \boldsymbol{\Delta} \boldsymbol{H}_{1}=\boldsymbol{x}_{1} \)
\( \boldsymbol{O H}_{(g)} \rightarrow \boldsymbol{H}_{(g)}+\boldsymbol{O}_{(g)}: \boldsymbol{\Delta} \boldsymbol{H}_{2}=\boldsymbol{x}_{2} \)
Based on the above given data, determine the bond energy (BE) of \( \boldsymbol{O}- \)
\( \boldsymbol{H} \) bond :
A \( \cdot \frac{x_{1}+x_{2}}{2} \)
в. \( x_{1}+x_{2} \)
c. \( \frac{x_{1}-x_{2}}{2} \)
D. \( x_{1}-x_{2} \)
Subject: Chemistry
Hydrocarbon containing minimum
mass \( \% \) of carbon will have which of the
following characteristics?
A. Has mass ratio \( \mathrm{C}: \mathrm{H}=1: 4 \)
B. Produces double moles of \( H_{2} O \) than \( C O_{2} \) upon complete combustion
c. Contains carbon in its maximum possible oxidation state
D. can be used as a reducing agent
Subject: Maths
The length of the perpendicular from the origin to the plane passing through the point \( a \) and containing the line \( r=\bar{b}+ \)
\( \lambda \bar{c} \) is
A \( \cdot \frac{[a b c]}{|a \times b+b \times c+c \times a|} \)
В. \( \frac{[a b c]}{|a \times b+b \times c|} \)
c. \( \frac{[a b c]}{|b \times c+c \times a|} \)
D. \( \frac{[a b c]}{|a \times b+c \times a|} \)
Subject: Chemistry
The decreasing order of energy for the electrons represented by the following sets of quantum numbers is :
1. \( n=4, l=0, m=0, s=\pm 1 / 2 \)
\( 2 . n=3,1=1, m=1, s=-1 / 2 \)
3. \( n=3,1=2, m=0, s=+1 / 2 \)
4. \( n=3, l=0, m=0, s=-1 / 2 \)
\( A \cdot 1>2>3>4 \)
B \( .2>1>3>4 \)
\( (-3>1>2>4 \)
D. \( 4>3>2>1 \)
Subject: Maths
If \( x=\sin ^{-1} t \) and \( y=\log \left(1-t^{2}\right), \) then
\( \frac{d^{2} y}{d x^{2}} \) at \( t=1 / 2 \) is
A \( \cdot \frac{-8}{3} \)
в. \( \frac{8}{3} \)
\( c \cdot \frac{3}{4} \)
D. \( \frac{-3}{4} \)
Subject: Physics
Assertion: Smaller drops of liquid resist deforming forces better than the larger
drops

Reason: Excess pressure inside a drop is directly proportional to its surface
area.
A. If both assertion and reason are true but the reason is the correct explanation of assertion.
B. If both assertion and reason are true but the reason is not the correct explanation of assertion
c. If assertion is true but reason is false
D. If both the assertion and reason are false.
E . If reason is true but assertion is false
Subject: Physics
If \( \vec{a}=2 \hat{i}+6 n \hat{j}+m \hat{k} \) and \( \vec{b}=\hat{i}+ \)
\( 18 \hat{j}+3 \hat{k} \) are parallel to each other then
the values of \( \boldsymbol{m}, \boldsymbol{n} \) are:
A . 6,6
B. \( 6, \)
\( c \cdot-1,6 \)
D. - -1.- 6
Subject: Maths
Consider the following statements: The system of equations \( .2 x-y=4 \) and
\( \boldsymbol{p} \boldsymbol{x}-\boldsymbol{y}=\boldsymbol{q} \)
I. has a unique solution if \( y \neq 2 \)
Il. has infinitely many solutions if \( \boldsymbol{p}= \)
\( 2, q=4 \) Of these statements:
A. I alone is correct
B. II alone is correct
c. I and II are correct
D. I and II are false
Subject: Maths
\( P, Q, R \) are three collinear points. The coordinates of \( \mathrm{P} \) and \( \mathrm{R} \) are (3,4) and (11
10) respectively and PQ is equal to 2.5 units. Coordinates of \( Q \) are-
A \( \cdot(5,11 / 2) \)
B. (11,5/2)
c. \( (5,-11 / 2) \)
D. \( (-5,11 / 2) \)
Subject: Chemistry
When \( 20 g m \) of a compound
\( (A)\left(M . F .=C_{4} H_{10} O_{4}\right) \) reacts with
excess of \( C H_{3} M g B r, 14.6 L \) of \( C H_{4} \) is
obtained at STP. What is structural
formula of \( (\boldsymbol{A}) \) ?
\( A \)
B.
\( c \)
D. Both (a) \& (b)
Subject: Physics
A ball of mass m moves towards a
moving wall of infinite mass with a speed 'v' along the normal to the wall. The speed of the wall is 'u' toward the ball. The speed of the ball after elastic
collision with wall is
A. \( u+v \) away from the wall
B. \( 2 u+v \) away from the wall
c. \( |u-v| \) away from the wall
D. \( |v-2 u| \) away from the wall
Subject: Chemistry
The equilibrium constant for a reaction,
\( A+B \rightleftharpoons C+D \) is \( 1.0 \times 10^{-2} \) at 298
and is 2.0 at 373 K. The chemical
process resulting in the formation of \( C \)
and D is :
A. Exothemic
B. Endothermic
c. unpredictable
D. none
Subject: Chemistry
A sample of peanut oil weighing 2 added to \( 25 \mathrm{mL} \) of \( 0.40 \mathrm{M} \) KOH. After
saponification is complete, \( 8.5 \mathrm{mL} \) of
\( 0.28 \mathrm{M} H_{2} S O_{4} \) is needed to neutralize
excess of KOH. The saponification number of peanut oil is: (Saponification number is defined as the milligrams of
KOH consumed by 1 g of oil
A . 146.72
в. 223.44
c. 98.9
D. none of these
Subject: Chemistry
Which of the following is correct?
\( \boldsymbol{S} \boldsymbol{O}_{3}+\boldsymbol{H} \boldsymbol{B} \boldsymbol{r} \rightarrow \boldsymbol{A}+\boldsymbol{B}+\boldsymbol{C} \)
Reddish Acidic Neutral
Brown Oxide compound
Coloured
Substance
A. B can act as bleaching agent
B. A can be starch iodide test
c. \( B \) can oxidise \( C l \)
D. A oxidises Hypo to \( S_{4} O_{6}^{2} \)
Subject: Maths
Area of the region bounded by the
\( \operatorname{curves} \boldsymbol{y}|\boldsymbol{y}| \pm \boldsymbol{x}|\boldsymbol{x}|=\mathbf{1} \) and \( \boldsymbol{y}=|\boldsymbol{x}| \) is:
A \( \cdot \frac{\pi}{8} \) sq.unit
B . \( \frac{\pi}{4} \) sq.unit
c. \( \frac{\pi}{2} \) sq.unit
D. \( \pi \) sq.unit
Subject: Biology
Which of the following is not a characteristic feature of Fabaceae
A. Descendingly. imbricate, ten stamens, diadelphous,
ovary superior
B. Sepals five, gamoseepalous, imbricate aestivation,
placentation marginal
c. Monocarpellary, ovary superior, style long, slightly bent
at the apex
D. zygomorphic flowers, diadelphous stamens, many
ovules
E. Corolla five petals, polypetalous, anterior one large and
outermost
Subject: Physics
A glass sphere, refractive index 1.5 and
radius \( 10 \mathrm{cm}, \) has a spherical cavity of
radius 5 cm concentric with it. A narrow
beam of parallel light is directed into the sphere. Find the final image and its
nature.
A \( .25 \mathrm{cm} \) left of \( S_{4} \), virtual
B. \( 25 \mathrm{cm} \) right of \( S_{4} \), virtual
C . \( 15 \mathrm{cm} \) left of \( S_{4} \), virtual
D. \( 20 \mathrm{cm} \) right of \( S_{4} \), virtual
Subject: Chemistry
Order of decreasing basic strength of halides is:
A \( \cdot F^{-}>C l^{-}>I^{-}>B r^{-} \)
B . \( F^{-}>C l^{-}>B r^{-}>I^{-} \)
c. \( I^{-}>B r^{-}>C I^{-}>F^{-} \)
D. \( I^{-}>C l^{-}>B r^{-}>F^{-} \)
Subject: Physics
There are four concentric shells \( \boldsymbol{A}, \boldsymbol{B}, \boldsymbol{C} \)
and \( D \) of radii \( a, 2 a, 3 a \) and \( 4 a \)
respectively. Shells \( B \) and \( D \) are given
charges \( +q \) and \( -q \) respectively. Shell \( C \) is now earthed. The potential difference \( V_{A}-V_{C} \) is \( \left(k=\frac{1}{4 \pi \varepsilon_{0}}\right) \)
\( \mathbf{A} \cdot \frac{k q}{2 a} \)
в. \( \frac{k q}{3 a} \)
\( \mathbf{c} \cdot \frac{k q}{4 a} \)
D. \( \frac{k q}{6 a} \)
Subject: Maths
Solve \( \int 2 x^{3} e^{x^{2}} \)
A \( \cdot\left(x^{2} e^{x^{2}}-e^{x^{2}}\right)+C \)
B. \( \frac{1}{2}\left(x^{2} e^{x^{2}}-e^{x^{2}}\right)+C \)
C \( \cdot \frac{1}{2}\left(x^{2} e^{x^{2}}+e^{x^{2}}\right)+C \)
D \( \cdot \frac{1}{4}\left(x^{2} e^{x^{2}}+e^{x^{2}}\right)+C \)
Subject: Physics
A radioactive nucleus undergoes a series of decays according to the
sequence \( \boldsymbol{A} \stackrel{\boldsymbol{\beta}}{\rightarrow} \boldsymbol{A}_{\mathbf{1}} \stackrel{\boldsymbol{\alpha}}{\rightarrow} \boldsymbol{A}_{2} \stackrel{\boldsymbol{\alpha}}{\rightarrow} \boldsymbol{A}_{\mathbf{3}} \)
If the mass number and atomic number
of \( A_{3} \) are 172 and 69 respectively, then
the mass number and atomic number
of A is
A. 56,23
B. 180,72
c. 120,52
D. 84,38
Subject: Physics
f \( \boldsymbol{n}(\boldsymbol{A})=\mathbf{4}, \boldsymbol{n}(\boldsymbol{B})=\boldsymbol{3}, \boldsymbol{n}(\boldsymbol{A} \times \boldsymbol{B} \times \)
\( C)=24, \) then \( n(C)=? \)
\( A \cdot 2 \)
B.
\( c \cdot 12 \)
D. None of these
Subject: Maths
The value of \( \lim _{n \rightarrow \infty} e^{\frac{3 i}{n}} \cdot \frac{3}{n}=? \)
A \( \cdot e^{4}-1 \)
B. \( e^{3}-1 \)
c. \( e^{5}-1 \)
D. \( e^{3}-2 \)
Subject: Physics
The north poles of pole strengths \( \mathrm{m}, 9 \mathrm{m} \) are kept apart by a certain distance. Find the distance of full point from
larger pole.
A \( \cdot \frac{3 d}{4} \)
в. \( \frac{3 d}{8} \)
c. \( \frac{3 d}{16} \)
D. \( \frac{3 d}{2} \)
Subject: Biology
How many molecules of ATP and NADPH
are require in formation of two molecules of glucose? How many Calvin cycles are required?
A. 36 ATP, 24 NADPH, 12 Calvin cycles
B. 18 ATP, 12 NADPH, 6 Calvin cycles
c. 36 ATP, 24 NADPH, 6 Calvin cycles
D. 24 ATP, 36 NADPH, 12 Calvin cycles
Subject: Physics
If the angle of a prism is \( 60^{\circ} \) and angle
of minimum deviation is \( 40^{\circ}, \) then the
angle of refraction will be
A \( .30^{\circ} \)
B . \( 4^{\circ} \)
\( c \cdot 3^{\circ} \)
D. \( 1.5^{\circ} \)
Subject: Physics
A semiconductor \( X \) is made by doping a germanium crystal with arsenic \( (\mathrm{Z}= \)
33). A second semiconductor Y is made
by doping germanium with indium \( (z= \)
49). The two are joined end to end and
connected to a battery as shown. Which
of the following statements is correct?
A. \( x \) is \( p \) -type, \( Y \) is \( n \) -type and the junction is forward biased
B. \( x \) is \( n \) -type, \( Y \) is \( p \) -type and the junction is forward biased
c. \( x \) is \( p \) -type, \( Y \) is \( n \) -type and the junction is reverse biased
D. \( x \) is \( n \) -type, \( Y \) is \( p \) -type and the junction is reverse biased
Subject: Physics
The total magnetic induction at point 0
due to curved portions and straight portion in the following figure, will be
A \( \cdot \frac{\mu_{0} i}{2 \pi r}[\pi-\phi+\tan \phi \)
в. \( \frac{\mu_{0} i}{2 \pi r} \)
c. \( \frac{\mu_{0} i}{\pi r}[\pi-\phi+\tan \phi \)
D.
Subject: Maths
Without expanding, show that the value
of the following determinant is zero:
\( \left|\begin{array}{ccc}\mathbf{0} & \boldsymbol{x} & \boldsymbol{y} \\ -\boldsymbol{x} & \boldsymbol{0} & \boldsymbol{z} \\ -\boldsymbol{y} & -\boldsymbol{z} & \boldsymbol{0}\end{array}\right| \)
Subject: Maths
\( \boldsymbol{f}:(\mathbf{0}, \infty) \rightarrow\left(-\frac{\boldsymbol{\pi}}{2}, \frac{\boldsymbol{\pi}}{2}\right) \) be defined as
\( f(x)=\arctan (x) \)
The above function can be classified as
A. injective but not surjective
B. surjective but not injective
c. neither injective nor surjective
D. both injective as well as surjective
Subject: Maths
If \( \mathbf{A}=\left\{x \mid \frac{\pi}{6} \leq x \leq \frac{\pi}{3}\right\} \) and \( f(x)= \)
\( \cos x-x(1+x), \) then \( f(A) \) is equal to
\( \mathbf{A} \cdot\left[\frac{\pi}{6}, \frac{\pi}{3}\right] \)
\( \mathbf{B} \cdot\left[-\frac{\pi}{3},-\frac{\pi}{6}\right] \)
\( \mathbf{C} \cdot\left[\frac{1}{2}-\frac{\pi}{3}\left(1+\frac{\pi}{3}\right), \frac{\sqrt{3}}{2}-\frac{\pi}{6}\left(1+\frac{\pi}{6}\right)\right] \)
\( \mathrm{D} \cdot\left[\frac{1}{2}+\frac{\pi}{3}\left(1-\frac{\pi}{3}\right), \frac{\sqrt{3}}{2}+\frac{\pi}{6}\left(1-\frac{\pi}{6}\right)\right] \)
Subject: Chemistry
If the element \( A \) has three electrons in
an outer shell and \( B \) has six electrons
in an outer shell, then the formula of the compound formed by these element will be:
A. \( A_{3} B_{2} \)
в. \( A_{2} B_{3} \)
\( \mathrm{c} \cdot A B_{3} \)
D. \( A_{6} B_{3} \)
Subject: Physics
A beam of light of wavelength 600 nm from a distant source falls on a single
slit \( 1.00 m m \) wide and the resulting
diffraction pattern is observed on a
screen 2 m away. The distance between
the first dark fringe on either side of the central maxima is :
A \( .1 .2 \mathrm{cm} \)
B. \( 1.2 \mathrm{mm} \)
\( c .2 .4 m m \)
D. \( 4.8 \mathrm{mm} \)
Subject: Physics
What is the electronic potential at the centre of square of side 1 m? The
charges \( 1 \times 10^{-8} C,-2 \times 10^{-8} C, 3 \times \)
\( 10^{-8} \) Cand \( 2 \times 10^{-8} C \) are placed at the
corners of the square.
Subject: Physics
The ratio of the diameters of wires of
circular and straight parts is
\( ^{A} \cdot \frac{1}{\sqrt{2}} \)
B. \( \frac{2 \sqrt{3}}{\pi} \)
\( c \cdot \frac{3 \sqrt{3}}{2 \pi} \)
\( D \cdot \sqrt{2} \)
Subject: Physics
A biconvex lens of focal length \( f \) and
radii of culvature of both the surfaces \( \boldsymbol{R} \)
is made of a material of refractive index
\( \boldsymbol{n}_{1} . \) This lens is placed in a liquid of
refractive index \( n_{2} \). Now this lens will
behave like This question has multiple correct options
A. Either as a convex or as a concave lens depending solely on R
B. A convex lens depending on \( n_{1} \) and \( n_{2} \)
C. A concave lens depending on \( n_{1} \) and \( n_{2} \)
D. A convex lens of same focal length irrespective of R, \( n_{1} \) and \( n_{2} \)
Subject: Maths
In above fig. \( 2, \) if \( D \) is mid-point of \( B C \) the value of \( \frac{\cot y^{\circ}}{\cot x^{\circ}} \) is:
\( A \)
B. \( \frac{1}{4} \)
\( c \cdot \frac{1}{3} \)
D. 1
Subject: Maths
In the diagram, \( P \) is the centre of the
circle with radius \( 4 \mathrm{cm} \) and \( Q \) is the
centre of the circle with radius \( 3 \mathrm{cm} \)
Of the points marked \( W, X, Y \) and \( Z \)
which point is \( 4 \mathrm{cm} \) from \( P \) and more
than \( 3 \mathrm{cm} \) from \( Q ? \)
\( A \cdot W \)
в. \( x \)
\( c . Y \)
D.
Subject: Physics
A spherically symmetric charge distribution is characterised by a
charge density having the following variation:
\( \boldsymbol{p}(\boldsymbol{r})=\boldsymbol{p}_{o}\left(\mathbf{1}-\frac{r}{R}\right) \) for \( \boldsymbol{r}<\boldsymbol{R} \)
\( \boldsymbol{p}(\boldsymbol{r})=\mathbf{0} \) for \( \boldsymbol{r} \geqslant \boldsymbol{R} \)
Where \( r \) is the distance from the centre
of the charge distribution and \( p_{o} \) is a
constant. The electric field at an
internal point
\( ^{\text {A }} \cdot \frac{p_{o}}{4 \epsilon_{o}}\left(\frac{r}{3}-\frac{r^{2}}{4 R}\right) \)
в. \( \frac{p_{o}}{\epsilon_{o}}\left(\frac{r}{3}-\frac{r^{2}}{4 R}\right) \)
c. \( \frac{p_{o}}{3 \epsilon_{o}}\left(\frac{r}{3}-\frac{r^{2}}{4 R}\right) \)
D. \( \frac{p_{o}}{12 \epsilon_{o}}\left(\frac{r}{3}-\frac{r^{2}}{4 R}\right) \)