AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Physics
Neutron ratio(r) (availability for fusion) of an atomic reactor and atom bomb are
A. \( r>1 \) in atomic reactor and \( r<1 \) in bomb
B. \( r=1 \) in atomic reactor and \( r>1 \) in bomb
c. \( r>1 \) in both atomic reactor and bomb
D. r \( <1 \) in both atomic reactor and bomb
Subject: Physics
A man can row a boat with \( 4 k m / h \) in
still water. If he is crossing a river where the current is \( 2 k m / h . \) Width of river is 4 k \( m \). In what direction should he head
the boat if he wants to cross the river in
shortest time and what is this
minimum time?
A. Parallel to river current, 2 hrs
B. Perpendicular to river current, 2 hrs
C. Parallel to river current, 1 hrs
D. Perpendicular to river current, 1 hrs
Subject: Physics
A car moving along a circular path of radius R with uniform speed covers an
angle \( \theta \) during a given time t. What is
its average velocity?
A \( \cdot \frac{2 R \sin (\theta / 2)}{t} \)
B. \( \frac{2 R \cos (\theta / 2)}{t} \)
c. \( \frac{2 R \sin (\theta)}{t} \)
D. \( \frac{R \sin (\theta / 2)}{t} \)
Subject: Physics
In the pulley system shown, if radii of the bigger and smaller pulley are \( 2 \mathrm{m} \) and \( 1 \mathrm{m} \), respectively and the
acceleration of block \( A \) is \( 5 m / s^{-2} \) in the downward direction, the
acceleration of block B will be :
A \( \cdot 0 \mathrm{ms}^{-2} \)
B. \( 5 \mathrm{ms}^{-2} \)
\( \mathrm{c} \cdot 10 \mathrm{ms}^{-2} \)
D. \( \frac{5}{2} m s^{-3} \)
Subject: Maths
\( \ln \) a shop \( X, 30 \) tin pure ghee and 40 tin adultered ghee are kept for sale while in
shop \( Y, 50 \) tin pure ghee and 60 tin adultered ghee are there. One tin of ghee is purchased from one of the shops randomly and it is found to be adultered. Find the probability that it is
purchased from shop B.
Subject: Chemistry
The organic compouds \( A \) and \( B \) react
with sodium metal and release \( \boldsymbol{H}_{2} \) gas.
A and B react with each other to given ethyl acetate. Then \( A \) and \( B \) are
A. \( C H_{3} \) COOHand \( C_{2} H_{5} \) OH
в. \( H C O O H a n d C_{2} H_{5} O H \)
c. \( C H_{3} \) COOHand \( C H_{3} \) OH
D. \( C H_{3} \) СООНапдНСООН
Subject: Maths
In an entrance test, there are multiple
choice questions. There are four possible options of which one is correct. The probability that a student knows
the answer to a question is \( 90 \% \). If he
gets the correct answer to a question, then the probability that he was guessing is
A \( \cdot \frac{1}{37} \)
B. \( \frac{36}{37} \)
\( c \cdot \frac{1}{4} \)
D. \( \frac{1}{49} \)
Subject: Physics
A block 'A' of mass \( 4 k g \) is kept on ground. The coefficient of friction
between the block and the ground is 0.8 The external force of magnitude \( 30 N \) is applied parallel to the ground. The resultant force exerted by the ground on the block is: \( \left(g=10 m s^{-2}\right) \)
A . \( 40 N \)
в. \( 30 N \)
c. zero
D. \( 50 N \)
Subject: Maths
The equation of the plane through the
intersection of \( p_{1} \& p_{2} \) containing the
point (1,1,2) is
A. \( 5 x-6 y+4 z=4 \)
в. \( 5 x+6 y-4 z=3 \)
c. \( 3 x-2 y+4 z=9 \)
D. Nonoe of these
Subject: Maths
Assertion
The point \( \boldsymbol{A}(\mathbf{1}, \mathbf{0}, \mathbf{7}) \) is the mirror image of the point \( B(1,6,3) \) in the line \( : \frac{x}{1}= \) \( \frac{\boldsymbol{y}-\mathbf{1}}{\mathbf{2}}=\frac{\boldsymbol{z}-\mathbf{2}}{\mathbf{3}} \)
Reason
The line \( \frac{x}{1}=\frac{y-1}{2}=\frac{z-2}{3} \) bisects
the line segment joining \( \boldsymbol{A}(\mathbf{1}, \mathbf{0}, \mathbf{7}) \) and \( \boldsymbol{B}(\mathbf{1}, \mathbf{6}, \mathbf{3}) \)
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
If electric field in a region is radially
outward with magnitude \( \boldsymbol{E}=\boldsymbol{A} \boldsymbol{r}, \) the
charge contained in a sphere of radius \( r \) centred at the origin is :
\( ^{\mathbf{A}} \cdot \frac{1}{4 \pi \varepsilon_{0}} A r^{3} \)
В. \( 4 \pi \varepsilon_{0} A r^{3} \)
c. \( \frac{1}{4 \pi \varepsilon_{0}} \frac{A}{r^{3}} \)
D. \( \frac{4 \pi \varepsilon_{0} A}{r^{3}} \)
Subject: Maths
For the vectors \( \overline{\boldsymbol{x}}=(\mathbf{1}, \mathbf{2}, \mathbf{1}) ; \overline{\boldsymbol{y}}= \)
(2,-3,-1) Component of \( \bar{y} \) along \( \bar{x}= \)
A \( \frac{5}{\sqrt{14}} \)
в. \( -\frac{5}{14} \)
c. \( \frac{5}{14} \)
D. \( -\frac{5}{\sqrt{14}} \)
Subject: Maths
Identify the median class.
\( \begin{array}{lllll}\mathbf{x} & \mathbf{5}- & \mathbf{9}- & \mathbf{1 3}- & \mathbf{1 7}- \\ & \mathbf{9} & \mathbf{1 3} & \mathbf{1 7} & \mathbf{2 1}\end{array} \)
F \( \quad 3 \) 8 9
A. \( 5-9 \)
B. \( 9-13 \)
D. \( 17-21 \)
Subject: Chemistry
Names of some compounds are given.
Which one is not correct in IUPAC
system?
\( \mathbf{A} \)
\[
\begin{array}{c}
C H_{3}-C H-C H-C H_{3} \\
\mid \begin{array}{cc}
_{1} & \mid \\
O H & C H_{3}
\end{array}
\end{array}
\]
3-Methyl-2-butanol
B. \( C H_{3}-C H_{2} \equiv C-C H\left(C H_{3}\right)_{2} \)
\( \mathbf{c} \)
\[
\begin{array}{c}
C H_{3}-C H_{2}-C-C H-C H_{3} \\
\|_{C H_{2}} \stackrel{1}{C H_{3}}
\end{array}
\]
2-Ethyl-3-methyl-but-1-ene
D.
\[
C H_{3}-C H_{2}-C H_{2}-C_{\mid} C H_{3}^{C H_{3}}
\]
3-Methyl-4-ethyl heptane
Subject: Chemistry
The following compounds may exist as two or more stereoisomers. These may
be classified as enantiomer pairs or
meso compounds.
What are total number of
stereoisomers(A) of each of the given
compounds?
(b)
\( \mathrm{c}\left(\mathrm{CH}_{3} \mathrm{CHCl}_{4}\right. \)
\( (g) \)
\( (\mathbf{h}) \)
Subject: Physics
A parallel-plate capacitor is connected
to a cell. Its positive plate \( A \) and its
negative plate \( \boldsymbol{B} \) have charges \( +\boldsymbol{Q} \) and
\( -Q \) respectively. A third plate \( C \)
identical to \( A \) and \( B, \) with charge \( +Q \)
is now introduced midway between \( \boldsymbol{A} \)
and \( B, \) parallel to them. Which of the
following are correct?
This question has multiple correct options
A \( \cdot \) The charge on the inner face of \( B \) is now \( -\frac{3 Q}{2} \)
B. There is no change in the potential difference between
\( A \) and \( B \)
C. The potential difference between \( A \) and \( C \) is one-third of the potential difference between \( B \) and \( C \)
D. The charge on the inner face of \( A \) is now \( Q / 2 \)
Subject: Physics
Two capacitors of caacity \( C_{1} \) and \( C_{2} \) are connected in series and potential difference V is applied across it. Then
the potential difference across \( C_{1} \) will
be
\( ^{\mathrm{A}} \cdot \frac{C_{2} V}{C_{1}+C_{2}} \)
в. \( \frac{C_{1} V}{C_{1}+C_{2}} \)
\( ^{c} \cdot\left(1+\frac{C_{2}}{C_{1}}\right) V \)
D. \( \left(1-\frac{C_{2}}{C_{1}}\right) v \)
Subject: Chemistry
Conc. \( \boldsymbol{H}_{2} \boldsymbol{S} \boldsymbol{O}_{4} \) displaces hydrogen chloride from chlorides because:
A . it is stronger acid
B. sulphates are less soluble than chlorides
c. sulphates are more soluble than chloride
D. \( H C l \) is a gas while \( H_{2} S O_{4} \) is a liauid
Subject: Physics
short steel rods each of cross-sectional
\( \operatorname{area} 5 c m^{2} . \) The lower ends of \( A \) and \( B \)
are welded to a fixed plate \( C D . \) The
upper end of \( A \) is welded to the \( L- \)
shaped piece \( \boldsymbol{E F G}, \) which can slide
without friction on upper end of \( \boldsymbol{B} . \mathbf{A} \)
horizontal pull of \( 1200 N \) is exerted at
\( G \) as shown. Neglect the weight of \( \boldsymbol{E F G} \)
Longitudinal stress in \( \boldsymbol{A} \) is
A. Tensile in nature and having magnitude \( 180 N / m^{2} \)
B. Tensile in nature and having magnitude \( 240 N / m^{2} \)
c. compressive in nature and having magnitude \( 180 N / c m^{2} \)
D. Compressive in nature and having magnitude \( 240 N / c m^{2} \)
Subject: Maths
A function \( f(x) \) is defined by \( f(x)= \)
\( \left\{\begin{array}{cl}\frac{\left[x^{2}-1\right]}{x^{2}-1} & \text { for } x^{2} \neq 1 \\ 0 & \text { for } x^{2}=1\end{array} \) Discuss the \right.
contiuuity of \( f(x) \) at \( x=1 \)
Subject: Chemistry
\( 1^{s t} \) excitation potential for the \( \mathrm{H}- \) like(hypothetical)sample is 24V. Choose the correct statement.
This question has multiple correct options
A \( \cdot 1^{s t} \) excitation potential for the \( \mathrm{H} \) like(hypothetical)sample is 24v
B. Ionisation energy of the sample is 32 ev
C. Binding energy of \( 3^{r d} \) excited state is 2 ev
D. \( 2^{\text {nd }} \) excitation potential of the sample is \( \frac{32 \times 8}{9} V \)
Subject: Chemistry
Two equilibria, \( A B \rightleftharpoons A^{+}+B^{-} . \) are
simultaneously maintained in a solution with equilibrium constants,
\( K_{1} \) and \( K_{2} \) respectively. The ratio of
\( \left[\boldsymbol{A}^{+}\right] \) to \( \left[\boldsymbol{A B}_{2}^{-}\right] \) in the solution is:
A. directly proportional to \( \left[B^{-}\right] \)
B . inversely proportional to [ \( B^{-} \)
C. directly proportional to the square of \( \left[B^{-}\right] \)
D. inversely proportional to the square of \( \left[B^{-}\right] \)
E. independent of \( \left[B^{-}\right] \)
Subject: Maths
The crossection of a canal is a
trapezium. The breadths of the top and
bottom of the canal are \( 8 m \) and \( 6 m \)
respectively. If the earth of volume \( 112 \times 10^{4} m^{3} \) is taken out to build the
canal of \( 50 \mathrm{km} \) long, then the depth of the canal will be
\( \mathbf{A} \cdot 3.2 m \)
B. \( 3.8 m \)
c. \( 4.0 m \)
D. 4.2 \( m \)
Subject: Maths
A door of length \( 2 m \) and breadth 1 m is fitted in a wall. The length of the wall is 4.5 and the breadth is 3.6 m. Find the
\( \operatorname{cost} \) of the wall washing the wall, if the
rate white washing the wall is \( R s .20 \) per
\( \boldsymbol{m}^{2} \)
Subject: Physics
The magnitude of the force (in Newton)
acting on a body varies with time \( t \) (in
microseconds) as shown in the figure. \( A B, B C \) and \( C D \) are straight line
segments. The magnitude of the total
impulse of the force in the body from
\( \boldsymbol{t}=\mathbf{4} \boldsymbol{\mu} \boldsymbol{s} \) to \( \boldsymbol{t}=\mathbf{1 6} \boldsymbol{\mu} \boldsymbol{s} \) is
Ns.
\( \mathbf{A} \cdot 1.005 \)
B. 0.005
c. 2.005
D. 4.005
Subject: Physics
A dip circle shows an apparent dip of \( 60^{0} \) at a place where the true dip is \( 45^{0} \)
If the dip circle is rotated by \( 90^{0}, \) what will be the apparent dip?
\( ^{\mathbf{A}} \cdot \cos ^{-1} \sqrt{\frac{2}{3}} \)
B. \( \tan ^{-1} \sqrt{\frac{2}{3}} \)
\( c \cdot \sin ^{-1} \sqrt{\frac{2}{3}} \)
D. \( \cot ^{-1} \sqrt{\frac{2}{3}} \)
Subject: Chemistry
The equilibrium constant \( \boldsymbol{K}_{\boldsymbol{p}} \) for the
reaction \( 2 H_{2}(g)+O_{2}(g) \rightleftharpoons 2 H_{2} O(g) \)
at \( 2000 \mathrm{K} \) is \( 1.6 \times 10^{7} . \) The equilibrium
constant of the reaction \( \boldsymbol{H}_{2} \boldsymbol{O}(\boldsymbol{g}) \rightleftharpoons \)
\( \boldsymbol{H}_{2}(\boldsymbol{g})+\frac{1}{2} \boldsymbol{O}_{2}(\boldsymbol{g}) \) is
A. \( 6.25 \times 10^{-8} \)
B . \( 2.5 \times 10^{-4} \)
c. \( 7.5 \times 10^{-12} \)
D. \( 4 \times 10^{-6} \)
Subject: Physics
A box of weight \( 150 k g f \) has
gravitational potential energy stored in it equal to \( 14700 J \). Find the height of the box above the ground. (Take \( g= \)
\( 9.8 N k g^{-1} \)
\( \mathbf{A} \cdot 10 \mathrm{cm} \)
B. \( 10 k m \)
\( c .1 m \)
D. \( 10 m \)
Subject: Maths
\( \int_{0}^{\frac{\pi}{2}} \frac{\sqrt{\sin x}}{\sqrt{\sin x}+\sqrt{\cos x}} d x \) is equal to
\( \mathbf{A} \cdot \mathbf{0} \)
в. \( -\pi \)
c. \( \frac{3 \pi}{2} \)
D. \( \frac{\pi}{2} \)
E. \( \frac{\pi}{4} \)
Subject: Physics
Let \( \left[\varepsilon_{0}\right] \) denote the dimensional formula of the permittivity of vacuum. If \( \boldsymbol{M}= \) mass, \( \boldsymbol{L}= \) length, \( \boldsymbol{T}= \) time and \( \boldsymbol{A}= \)
electric current, then:
\( \mathbf{A} \cdot\left[\varepsilon_{0}\right]=\left[M^{-1} L^{-3} T^{4} A^{2}\right] \)
B . \( \left[\varepsilon_{0}\right]=\left[M^{-1} L^{2} T^{-1} A^{-2}\right] \)
\( \mathbf{c} \cdot\left[\varepsilon_{0}\right]=\left[M^{-1} L^{2} T^{-1} A\right] \)
\( \mathbf{D} \cdot\left[\varepsilon_{0}\right]=\left[M^{-1} L^{-3} T^{2} A\right] \)
Subject: Maths
Identify which of the following is/are
a quadratic polynomial function:
This question has multiple correct options
\( \mathbf{A} \cdot f(x)=(x+1)^{3}-(x+2)^{3} \)
\( g(x)=\left\{\begin{array}{cc}\frac{x^{4}}{x^{2}} & \text { if } x \neq 0 \\ 0 & \text { if } x=0\end{array}\right. \)
C \( \cdot h(x)=(x+1)^{2}-(x+2)^{2} \)
D. All of these
Subject: Maths
\( f_{n}(x)=e^{f_{n-1}(x)} \) for all \( n \epsilon N \) and
\( f_{0}(x)=x, \) then \( \frac{d}{d x}\left\{f_{n}(x)\right\} \) is
This question has multiple correct options
A \( \cdot f_{n}(x) \frac{d}{d x}\left\{f_{n-1}(x)\right\} \)
В \( \cdot f_{n}(x) f_{n-1}(x) \)
\( \mathbf{c} \cdot f_{n}(x) f_{n-1}(x) \cdots f_{2}(x) \cdot f_{1}(x) \)
D. none of these
Subject: Physics
The length of potentiometer wire is \( 10 \mathrm{m} \) and is connected in series with an
accumulator. The e.m.f. of a cell
balances against \( 250 \mathrm{cm} \) length of wire. If the length of potentiometer wire is increased by \( 1 \mathrm{m} \), calculate the new balancing length of wire.
Subject: Physics
A solenoid of length \( 0.4 \mathrm{m}, \) having 500 turns and 3 A current flows through it. A coil of radius \( 0.01 \mathrm{m} \) and have 10 turns
and carries current of 0.4 A has to
placed such that its axis is perpendicular to the axis of solenoid then torque on coil will be
A \( \cdot 5.92 \times 10^{-7} N \cdot m \)
В. \( 5.92 \times 10^{-5} \mathrm{N} . \mathrm{m} \)
c. \( 5.92 \times 10^{-4} N . m \)
D. \( 5.92 \times 10^{-3} N . m \)
Subject: Chemistry
Which will produce the least heat on
complete hydrogenation?
\( A \)
\( H_{2} C=C H-C=C H_{2} \)
в. \( \begin{array}{ll}c H_{3} & c h\end{array} \)
\( H_{2} C=C-C=C H_{2} \)
\( c \)
\( D \)
Subject: Maths
If \( A \) is an \( m \times n \) matrix such that \( A B \)
and \( B A \) are both defined, then order of
\( B \) is
\( \mathbf{A} \cdot m \times n \)
в. \( n \times m \)
c. \( n \times n \)
D. \( m \times m \)
Subject: Maths
Two complex numbers are represented
by ordered pairs \( z_{1}:(a, 0) \& z_{2}:(c, d) \)
which of the following is correct
simplification for \( z_{1} \times z_{2}=? \)
\( \mathbf{A} \cdot(a c,-a d) \)
B. \( (a d, a c) \)
\( \mathbf{c} \cdot(a c, a d) \)
D. None of these
Subject: Maths
IIf \( \mathbf{A}=\left[\begin{array}{ll}\boldsymbol{a} & \mathbf{0} \\ \boldsymbol{a} & \mathbf{0}\end{array}\right], \mathbf{B}=\left[\begin{array}{ll}\mathbf{0} & \mathbf{0} \\ \boldsymbol{b} & \boldsymbol{b}\end{array}\right], \) then
\( \mathbf{A B}= \)
\( \mathbf{A} \cdot \mathbf{0} \)
в. ВА
c. АВ
D. ABAB
Subject: Physics
If \( \mu_{r} \) be the relative permeability and \( \varepsilon_{r} \) be the relative dielectric constant of a
medium, its refractive index is:
\( ^{A} \cdot \frac{1}{\sqrt{\mu_{r} \epsilon_{r}}} \)
в. \( \frac{1}{\mu_{t} \epsilon_{r}} \)
c. \( \sqrt{\mu_{r} \epsilon_{r}} \)
D. \( \mu_{r} \epsilon_{r} \)
Subject: Physics
A thin rod length L is bent to form a circle. Its mass is M. What force will act
on the mass \( \mathrm{m} \) placed at the center of the circle?
A \( \cdot \frac{4 \pi^{2} G M m}{L^{2}} \)
B. \( \frac{G M m}{4 \pi^{2} L^{2}} \)
c. \( \frac{2 \pi G M m}{L^{2}} \)
D. zero
Subject: Chemistry
Which is the set of amphiprotic
species?
A \( \cdot H_{3} O^{+}, H P O_{4}^{2-}, H C O_{3} \)
B. \( H_{2} O, H P O_{3}^{2-}, H_{2} P O_{2}^{-} \)
\( \mathrm{c} \cdot \mathrm{H}_{2} \mathrm{PO}_{4}^{-}, \mathrm{H}_{2} \mathrm{PO}_{3}^{-}, \mathrm{H}_{2} \mathrm{O} \)
D. All of these
Subject: Physics
A circular disc of radius R and
thickness R/6 has moment of inertia I
about an axis passing through its center and perpendicular to its plane. It is melt and recast into a solid sphere.
The moment of inertia of the sphere
about its diameter as axis of rotation is:
A \( \cdot \frac{1}{5} \)
в. \( \frac{2 I}{5} \)
c. \( \frac{4 I}{5} \)
D. \( \frac{I}{10} \)
Subject: Maths
\( A \) and \( B \) are events such that \( p(A \cup \)
\( \boldsymbol{B})=\mathbf{3} / \mathbf{4}, \boldsymbol{P}(\boldsymbol{A} \cap \boldsymbol{B})=\frac{\mathbf{1}}{\mathbf{4}}, \boldsymbol{P}(\overline{\boldsymbol{A}})=\frac{\mathbf{2}}{\mathbf{3}} \)
\( \operatorname{then} P((\bar{A} \cap B) \) equals
A \( \cdot \frac{5}{12} \)
B. \( \frac{3}{8} \)
\( c \cdot \frac{4}{5} \)
\( D \cdot \frac{5}{4} \)
Subject: Maths
The solution set of the equation
\( \sin ^{-1} x=2 \tan ^{-1} x \)
\( \mathbf{A} \cdot\{1,2\} \)
B \( \cdot\{-1,2\} \)
\( \mathbf{c} \cdot\{-1,1,0\} \)
D. \( \left\{1, \frac{1}{2}, 0\right\} \)
Subject: Chemistry
A \( 5 \% \) solution of glucose is isotonic
with \( 1.1 \% \) solution of \( \mathrm{KCl} \) at \( 30^{\circ} \mathrm{C} \)
Calculate the degree of ionisation of KCI.
A . \( 90 \% \)
в. \( 88 \% \)
c. \( 78 \% \)
D. \( 80 \% \)
Subject: Chemistry
Statement-1: In the fermentation
process of molasses, along with yeast,
\( \left(N H_{4}\right)_{2} S O_{4} \) and \( \left(N H_{4}\right)_{3} P O_{4} \) are
added.
Statement-2: Both \( \left(N H_{4}\right)_{3} P O_{4} \) and
\( \left(N H_{4}\right)_{2} S O_{4} \) act as food and help in the
growth of yeast.
A. Statement-1 is True, statement-2 is True; statementis a correct explanation for statement-
B. Statement-1 is True, statement-2 is True; statementis NOT a correct explanation for statement-
c. Statement- - is True, statement-2 is False
D. Statement- 1 is False, statement- 2 is True
Subject: Physics
The diagram below shows the path of a light ray in three different materials.
The index of refraction for each material
is shown in the upper right portion of
the material.

Rank the index of refraction values,
greatest first
\( \mathbf{A} \cdot n_{1}, n_{2}, n_{3} \)
В. \( n_{1}, n_{3}, n_{2} \)
\( \mathbf{c} \cdot n_{2}, n_{1}, n_{3} \)
\( \mathbf{D} \cdot n_{2}, n_{3}, n_{1} \)
E \( . n_{3}, n_{1}, n_{2} \)
Subject: Maths
For any vector \( \vec{a}, \) the value of \( (\vec{a} \times \hat{i})^{2}+ \)
\( (\vec{a} \times \hat{j})^{2}+(\vec{a} \times \hat{k})^{2} \) is equal to
A \( \cdot 3 \vec{a}^{2} \)
в. \( \vec{a}^{2} \)
c. \( 2 \vec{a}^{2} \)
D. \( 4 \vec{a}^{2} \)
Subject: Biology
Match the column-I and column-I
\( \begin{array}{llll} & \text { Column-I } & & \text { Column-II } \\ \text { (i) } & \text { Chrysophyta } & \text { (a) } & \text { Fungi } \\ \text { (ii) } & \text { Gonyaulax } & \text { (b) } & \text { Diatom } \\ \text { (iii) } & \text { Penicillium } & \text { (c) } & \text { Plasmodium } \\ \text { (iv) } & \text { Slime mould } & \text { (d) } & \text { Dinoflagellate }\end{array} \)
\( A \)
(i) - a, (ii) - b, (iii) - c, (iv) - d
B. (i) \( -b, \) (ii) \( -c, \) (iii) \( -a, \) (iv) \( -d \)
\( c \cdot(i)-b,(\text { ii) }-c,(\text { iii) }-d,(\text { iv })-a \)
D. (i) - b, (ii) - d, (iii) - a, (iv) -
Subject: Physics
A long solenoid of radius 2 cm has 100
turns/cm and is surrounded by a 100
turn coil of radius \( 4 \mathrm{cm} \) having a total
resistance \( 20 \Omega \). If the current changes from \( 5 A \) to \( -5 A \), find the charge through the galvanometer.
A . zero
в. \( 800 \mu \) с
c. \( 400 \mu \) с
D. \( 600 \mu \) C
Subject: Physics
The total mechanical energy E
possessed by a body of mass 'm', moving with a velocity 'v' at a height 'h' is given by \( : E=\frac{1}{2} m v^{2}+m g h . \) Make
\( \mathrm{m}^{\prime} \) the subject of formula.
A \( \cdot m=\frac{2 E}{v^{2}+g h} \)
B. \( m=\frac{2 E}{v^{2}+2 g h} \)
c. \( _{m}=\frac{3 E}{v^{2}+2 g h} \)
D. \( _{m}=\frac{E}{v^{2}+2 g h} \)
Subject: Physics
At what distance from a long straight
wire carrying a current of \( 12 A \) will the
magnetic field be equal to \( 3 \times \) \( \mathbf{1 0}^{-\mathbf{5}} \boldsymbol{W b} / \boldsymbol{m}^{2} ? \)
A. \( 8 \times 10^{-2} \mathrm{m} \)
В. \( 12 \times 10^{-2} \mathrm{m} \)
c. \( 18 \times 10^{-2} \mathrm{m} \)
D. \( 24 \times 10^{-2} \mathrm{m} \)
Subject: Physics
The solar constant for the earth is \( S \). The
surface temperature of the sun is \( \boldsymbol{T} \boldsymbol{K} \)
The sun subtends an angle \( \theta \) at the
earth.
This question has multiple correct options
\( A \cdot S \propto T^{4} \)
в. \( S \propto T^{2} \)
c. \( S \propto \theta^{2} \)
\( \mathbf{D} \cdot S \propto \theta \)
Subject: Maths
The order of differential equation \( \left(\frac{d y}{d x}\right)^{3}+\left(\frac{d y}{d x}\right)^{2}+y^{4}=0 \) are
\( \mathbf{A} \cdot \mathbf{4} \)
B. 3
\( c \cdot 1 \)
\( D \)
Subject: Chemistry
correctmatch withA B C D is
List - I List - II
A) \( \mathrm{SO}_{3} \)
1) \( 119.5^{\circ} \), Angular
B) \( \mathrm{SO}_{2} \)
2) \( 109^{\circ} .28^{1}, \) tetrahedron
\( \mathrm{C}) \mathrm{H}_{2} \mathrm{O} \)
3) \( 120^{\circ}, \) Trigonal planar
\( \mathrm{D}) \mathrm{O}_{3} \)
4) \( 104^{\circ} .30^{\prime} \) angular
5) \( 116.5^{\circ} \) Angular
A. 2145
B. 5213
C. 3145
D. 1324
Subject: Maths
The period of the function \( f(x)= \) \( \sin 3 x \cos [3 x]-\cos 3 x \sin [3 x], \) where \( \square \)
denotes the greatest integer function is
\( \mathbf{A} \cdot \mathbf{6} \)
B. 3
c. \( 1 / 3 \)
D. 1/6
Subject: Maths
Consider the triangle OAB in the xyplane where \( 0=(0,0) A=(6,0), B= \)
\( (\sqrt{2}, 3) . \) A sqare PQRS is inscribed in
the square with \( P, Q \) on \( O A, R \) on \( A B \) and Son BO. Then the side of the square
equals
A. \( 3 / \sqrt{2} \)
B. \( \frac{9}{4} \)
c. \( \frac{3}{2} \sqrt{\frac{5}{2}} \)
D.
Subject: Maths
The shadow of the tower standing on a
level ground is found to be 60 meters
longer when the suns altitude is \( 30^{\circ} \)
than when it is \( 45^{\circ} . \) The height of the
tower is
\( A \cdot 60 m \)
в. \( 30 m \)
\( c \cdot 60 \sqrt{3} m \)
D. \( 20(\sqrt{3}+1) m \)
Subject: Maths
The resultant of two forces acting at an
angle of \( 150^{\circ} \) is \( 10 \mathrm{N} \) and its
perpendicular to one of the forces.The
two other force is:
A \( \cdot \frac{20}{\sqrt{3}} N \)
в. \( \frac{10}{\sqrt{3}} N \)
c. \( 20 N \)
D. \( \frac{20}{3} N \)
Subject: Physics
A box is put on a scale which is
adjusted to read zero,when the box is
empty. A stream of pebbles is then
poured into the box from a height \( h \)
above its bottom at a rate of n pebbles
collide with the box such that they
immediately come to rest after collision, the scale reading at time \( t \) after the pebbles begin to fill the box is:
\( \mathbf{A} \cdot m n\{\sqrt{(2 g h)}+g t\} \)
B. \( \{\sqrt{(2 g h)+g t}\} \)
c. \( \{\sqrt{(2 g h)-g t}\} \)
D \( \cdot \operatorname{mn}\{(2 g h)-g t\} \)
Subject: Chemistry
The change in the entropy of a mole of ideal gas which went through an isothermal process from an initial state
\( \left(P_{1}, V_{1}, T\right) \) to the final state \( \left(P_{2}, V_{2}, T\right) \)
is equal to
A . zero
в. \( R \ln T \)
\( ^{c} \cdot \ln \frac{V_{1}}{V_{2}} \)
D. \( \ln \frac{V_{2}}{V_{1}} \)
Subject: Chemistry
The pair whose both species are used in antacid medicinal preparation is
в. \( N a_{2} C O_{3} \) and \( C a\left(H C O_{3}\right) \)
c. \( C a\left(H C O_{3}\right)_{2} \) and \( M g(O H)_{2} \)
D. \( C a(O H)_{2} \) and \( N a H C O_{3} \)
Subject: Physics
In the circuit shown in fig., the potential
difference between the points \( C \) and \( D \) is balanced against \( 40 \mathrm{cm} \) length of
potentiometer wire of total length 100 \( \mathrm{cm} . \) In order to balance the potential
difference between the points D and \( E \) the jockey should be pressed on
potentiometer wire at a distance of
A . \( 16 \mathrm{cm} \)
B. 32 \( \mathrm{cm} \)
\( c .56 \mathrm{cm} \)
D. \( 80 \mathrm{cm} \)
Subject: Chemistry
Calcium hydroxide, \( C a(O H)_{2} \) has a
lower solubility in water than some of
the other Group II hydroxides \( \left(\boldsymbol{K}_{s p}=\right. \) \( 4.0 \times 10^{-6} \) at \( 25^{\circ} \mathrm{C} \) ). At this
temperature in a saturated solution of calcium hydroxide, determine the concentration of calcium ions?
A \( \cdot 2.0 \times 10^{-6} \)
B . \( 2.0 \times 10^{-3} \)
c. \( 1.0 \times 10^{-2} \)
D. \( 1.3 \times 10^{-2} \)
E \( .1 .6 \times 10^{-2} \)