AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Chemistry
Justify that the following reactions are
redox reactions:
\( \boldsymbol{C u O}(\boldsymbol{s})+\boldsymbol{H}_{2}(\boldsymbol{g}) \rightarrow \boldsymbol{C u}(\boldsymbol{s})+\boldsymbol{H}_{2} \boldsymbol{O}(\boldsymbol{g}) \)
Subject: Physics
A man is trying to start a fire by focusing sunlight on a piece of paper using an equiconvex lens of focal length 10 cm. The diameter of the sun is
\( 1.39 \times 10^{9} m \) and its mean distance
from the earth is \( 1.5 \times 10^{11} m \), the
diameter of the sun's image on the paper is
A. \( 3.1 \times 10^{-4} \mathrm{m} \)
B . \( 6.5 \times 10^{-5} m \)
c. \( 6.5 \times 10^{-4} m \)
D. \( 9.2 \times 10^{-4} m \)
Subject: Physics
In the circuit shown in fig., all wires
have equal resistance \( \mathrm{R}(=5 \Omega) \). The
equivalent resistance between \( A \) and \( B \) :
A \( \cdot 10 / 7 \Omega \)
B. 15/4 \( \Omega \)
\( c .7 \Omega \)
D. 3 \( \Omega \)
Subject: Physics
A long straight wire of radius \( a \) carries a
steady current i. The current is uniformly distributed across its cross section. The ratio of the magnetic field \( \operatorname{ata} / 2 \) and \( 2 a \) is:
A . \( 1 / 2 \)
в. \( 1 / 4 \)
\( c \cdot 4 \)
D.
Subject: Maths
Evaluate the following deteminants:
i) \( \left|\begin{array}{cc}\boldsymbol{x} & -\mathbf{7} \\ \boldsymbol{x} & \mathbf{5} \boldsymbol{x}+\mathbf{1}\end{array}\right| \)
ii) \( \mid \begin{array}{cc}\cos 15^{\circ} & \sin 15^{\circ} \\ \sin 75^{\circ} & \cos 75^{\circ}\end{array} \)
Subject: Chemistry
An organic compound contains a
functional group, multiple bonds, and a side chain then what will be the order of
preference?
A. Double bond \( > \) Triple bond \( > \) Side chain \( > \) Functional group
B. Functional group > Double bond > Triple bond > Side chain
c. Triple bond > side chain > Double bond > Functional group
D. Functional group > Triple bond > Double bond > Side chain
Subject: Chemistry
\( \boldsymbol{A} \boldsymbol{g}_{2} \boldsymbol{S}+\boldsymbol{N} \boldsymbol{a} \boldsymbol{C}+\boldsymbol{Z} \boldsymbol{n} \longrightarrow \boldsymbol{A} \boldsymbol{g}^{+} \)
This method of extraction of Ag by the complex formation and then its displacement is called:
A. Parke's method
B. Mac Arthur-Forest method
c. Serpek method
D. Hall's method
Subject: Maths
If \( A, B \) are two events with
\( \boldsymbol{P}(\boldsymbol{A} \cup \boldsymbol{B})=\mathbf{0 . 6 5}, \boldsymbol{P}(\boldsymbol{A} \cap \boldsymbol{B})=\mathbf{0 . 1 5} \)
then find the value of \( \boldsymbol{P}\left(\boldsymbol{A}^{c}\right)+\boldsymbol{P}\left(\boldsymbol{B}^{c}\right) \)
Subject: Maths
f \( \boldsymbol{y}=\tan ^{-1} \frac{\boldsymbol{x}}{\mathbf{1}+\sqrt{\mathbf{1}-\boldsymbol{x}^{2}}}+ \)
\( \sin \left(2 \tan ^{-1} \sqrt{\frac{1-x}{1+x}}\right), \) then find \( \frac{d y}{d x} \) for
\( \boldsymbol{x} \in(-1,1) \)
Subject: Physics
A man crosses a \( 320 \mathrm{m} \) wide river
perpendicular to the current in 4 min. If in still water he can swim with a speed
\( 5 / 3 \) times that of the current, then the
speed of the current, in \( m \) min\( ^{-1} \) is?
A . 30
B . 40
c. 50
D. 60
Subject: Maths
If \( f(x)=\frac{\tan x}{\sqrt{1+\tan ^{2} x}}, \lim _{x \rightarrow(\pi / 2)^{-}} f(x)= \)
\( \boldsymbol{a} \) and \( \lim _{\boldsymbol{x} \rightarrow(\boldsymbol{\pi} / \mathbf{2})^{+}} \boldsymbol{f}(\boldsymbol{x})=\boldsymbol{b} \) then
\( \mathbf{A} \cdot a=b \)
B . \( a=1+b \)
\( \mathbf{c} \cdot a+b=0 \)
D. \( a+b=2 \)
Subject: Physics
A particle executes SHM with
amplitudes \( 25 \mathrm{cm} \) and period 3 seconds. The minimum time required
for it to move between two points 12.5 \( \mathrm{cm} \) on either side of the mean position
is
A. \( 0.25 \mathrm{sec} \)
B . 0.50 sec
c. \( 0.75 \mathrm{sec} \)
D. \( 1.00 \mathrm{sec} \)
Subject: Maths
Let \( \boldsymbol{f}: \boldsymbol{R} \rightarrow \boldsymbol{R} \) be a function such that \( \boldsymbol{f}\left(\frac{\boldsymbol{x}+\boldsymbol{y}}{\mathbf{2}}\right)=\frac{\boldsymbol{f}(\boldsymbol{x})+\boldsymbol{f}(\boldsymbol{y})}{2} \) for all \( \mathbf{x}, \mathbf{y} \)
and \( f(0)=3 \) and \( f^{\prime}(0)=3 . \) Then
A . \( f(x) / x \) is continuous on \( \mathbb{R} \)
B. \( f(x) \) is continuous on \( R \)
c. \( f(x) \) is bounded on \( R \)
D. none of these
Subject: Maths
Vectors \( \vec{a}, \vec{b} \) and \( \vec{c} \) are such that \( \vec{a}+\vec{b}+ \) \( \vec{c}=\overrightarrow{0} \) and \( |\vec{a}|=3, \mid \vec{b}=5 \) and \( |\vec{c}|=7 \)
Find the angle between \( \vec{a} \) and \( \vec{b} \)
Subject: Maths
In the given figure, ABCD is a trapezium
of area \( 24.5 c m^{2} . \) If \( A D \| \)
\( \boldsymbol{B C}, \angle \boldsymbol{D A B}=\mathbf{9 0}^{0}, \boldsymbol{A D}= \)
\( 10 c m, B C=4 c m \) and \( A B E \) is
quadrant of circle then find the area of
the shaded region.
Subject: Chemistry
Answer the following by appropriately matching the lists based on the
information given in the paragraph.
If the process on one mole of
monatomic ideal gas is as shown in the TV-diagram with \( P_{0} V_{0}=\frac{1}{3} R T_{0} \), the
correct match is,
A. \( I \rightarrow P, I I \rightarrow R, I I I \rightarrow T, I V \rightarrow S \)
в. \( I \rightarrow P, I I \rightarrow T, I I I \rightarrow Q, I V \rightarrow T \)
c \( . I \rightarrow S, I I \rightarrow T, I I I \rightarrow Q, I V \rightarrow U \)
D. \( I \rightarrow P, I I \rightarrow R, I I I \rightarrow T, I V \rightarrow P \)
Subject: Physics
Equal volume of two immiscible liquids
of densities \( \rho \) and \( 2 \rho \) are filled in a
vessels as shown in the figure. Two
small holes are punched at depths \( h / 2 \) and \( 3 h / 2 \) from the surface of lighter
liquid. if \( v_{1} \) and \( v_{2} \) are the velocities of
efflux at these two holes, then \( \frac{\mathrm{v}_{1}}{\mathrm{r}} \) is
\( A \cdot \frac{1}{2 \sqrt{2}} \)
B. \( \frac{1}{2} \)
\( c \cdot \frac{1}{4} \)
D. \( \frac{1}{\sqrt{2}} \)
Subject: Physics
A radioactive nucleus undergoes \( \alpha \)
emission to form a stable element.What
will be the recoil of the daughter
nucleus if \( v \) is the velocity of \( \alpha \) emission?
A \( \cdot \frac{4 v}{A-4} \)
в. \( \frac{2 v}{A-4} \)
c. \( \frac{4 v}{A+4} \)
D. \( \frac{2 v}{A+4} \)
Subject: Physics
An accumulator of emf 2 Volt and
negligible internal resistance is connected across a uniform wire of
length \( 10 \mathrm{m} \) and resistance \( 30 \Omega \). The
appropriate terminals of a cell of emf
\( 1.5 V o l t \) and internal resistance \( 1 \Omega \) is
connected to one end of the wire, and
the other terminal of the cell is
connected through a sensitive galvanometer to a slider on the wire. If the balancing change when the cell of
1.5 volt is shunted with a resistance of \( 5 \Omega \) is \( \frac{x}{4} m . \) Find \( x \)
Subject: Maths
ff \( \boldsymbol{A}=\left[\begin{array}{cc}\boldsymbol{6} & \boldsymbol{2} \\ \boldsymbol{5} & \boldsymbol{-} \boldsymbol{4}\end{array}\right] \) and \( \boldsymbol{B}=\left[\begin{array}{cc}\mathbf{1} & \boldsymbol{2} \\ -\boldsymbol{5} & \boldsymbol{1}\end{array}\right], \) find
a matrix \( X \) such that \( 2 A+3 B- \)
\( \mathbf{5} \boldsymbol{X}=\mathbf{0} \)
Subject: Physics
The dimensional formula for
permittivity of free space \( \left(\epsilon_{0}\right) \) in the equation \( \boldsymbol{F}=\frac{\mathbf{1}}{\mathbf{4} \boldsymbol{\pi} \boldsymbol{\epsilon}_{0}} \frac{\boldsymbol{q}_{1} \boldsymbol{q}_{2}}{\boldsymbol{r}^{2}} \) where
symbols have their usual meaning is
\( \mathbf{A} \cdot\left[M^{1} L^{3} A^{-2} T^{-4}\right. \)
B \( \cdot\left[M^{-1} L^{-3} T^{4} A^{2}\right] \)
C \( \cdot\left[M^{-1} L^{-3} A^{-2} T^{-4}\right] \)
D・ \( \left[M^{1} L^{3} A^{2} T^{-4}\right] \)
Subject: Chemistry
An electron has \( u_{r m s} \) value at \( 27^{0} C \)
\( \left(\text { Given } \boldsymbol{m}_{e}=\mathbf{9 . 1 0 8} \times \mathbf{1 0}^{-\mathbf{3 1}} \mathbf{k g}\right) \)
This question has multiple correct options
A. \( 3.7 \times 10^{4} m / \) sec
B . \( 1.3 \times 10^{5} \mathrm{km} / \mathrm{hr} \)
c. \( 1.3 \times 10^{5} \mathrm{m} / \mathrm{sec} \)
D. \( 11.7 \times 10^{4} k m / h r \)
Subject: Chemistry
In a cubic structure of diamond which
is made from \( X \) and \( Y \), where \( X \) atoms
are at the corners of the cube and \( Y \) at
the face centres of the cube. The
molecular formula of the compound is:
A. \( X_{2} Y \)
\( Y \)
в. \( X_{3} Y \)
c. \( X Y_{2} \)
D. \( X Y_{3} \)
Subject: Physics
Find the maximum zener current for the
zener diode as shown in figure. Given,
\( \boldsymbol{V}_{Z}=\mathbf{6} \boldsymbol{V}, \boldsymbol{R}_{Z}=\mathbf{1 . 5 \Omega}, \boldsymbol{R}=\mathbf{4 0 0 \Omega} \)
A. \( 35.00 \mathrm{mA} \)
в. \( 30.87 m A \)
\( c .34 .87 m A \)
D. \( 34.87 A \)
Subject: Chemistry
The dissociation constant of \( N H_{4} O H \)
\( \operatorname{at} 25^{\circ} C \) is \( K_{b}=X \times 10^{-6}, \) if \( \Delta H^{o} \) and
\( \Delta S^{o} \) for the given changes are as follows: \( \boldsymbol{N} \boldsymbol{H}_{4}+\boldsymbol{H}^{+} \rightleftharpoons \)
\( \boldsymbol{N} \boldsymbol{H}_{4}^{+} ; \quad \boldsymbol{\Delta} \boldsymbol{H}^{o}= \)
\( -\mathbf{5 2 . 2} \quad k J m o l^{-1} ; \quad \Delta S^{o}= \)
\( +1.67 J K^{-1} m o l^{-1} H_{2} O \rightleftharpoons H^{+}+ \)
\( \boldsymbol{O} \boldsymbol{H}^{-} ; \quad \boldsymbol{\Delta} \boldsymbol{H}^{o}= \)
\( \mathbf{5 6 . 6} \quad \boldsymbol{k J m o l}^{-1} ; \quad \boldsymbol{\Delta} \boldsymbol{S}^{o}= \)
\( -78.2 J K^{-1} \) mol \( ^{-1} . \) Value of \( X \) is \( =5 Y+2 \)
What is the value of Y?
Subject: Physics
The vertical limbs of a \( U \) shaped tube
are filled with a liquid of density \( \boldsymbol{p} \) upto
a height \( h \) on each side. The horizontal
portion of the \( U \) tube having length \( 2 h \) contains a liquid of density \( 2 p . \) The \( U \) is moved horizontally with an accelerator
\( \boldsymbol{g} / 2 \) parallel to the horizontal arm. The
difference in heights in liquid levels in th two vertical limbs, at steady state
will be
A \( \cdot \frac{2 h}{7} \)
B. \( \frac{8 h}{7} \)
\( c \cdot \frac{4 h}{7} \)
D. None of these
Subject: Physics
Three thin prisms are combined as
shown in figure. The refractive indices of the crown glass for red, yellow and
violet rays are \( \mu_{r}, \mu_{y} \) and \( \mu_{v} \)
respectively and those for the flint glass \( \operatorname{are} \mu_{r}^{\prime}, \mu_{y}^{\prime} \) and \( \mu_{v}^{\prime} \) respectively. Find the
\( \frac{A^{\prime}}{\text { for which, there is no net angular }} \)
\( \boldsymbol{A} \)
dispersion.
A \( \cdot \frac{\mu_{y}-1}{\mu_{y}^{\prime}-1} \)
в. \( \frac{2 \mu_{y}-1}{\mu_{y}^{y}-1} \)
c. \( \frac{3 \mu_{y}-1}{\mu_{y}^{y}-1} \)
D. \( \frac{4 \mu_{y}-1}{\mu_{y}^{\prime}-1} \)
Subject: Physics
An alternating e.m.f. of \( \boldsymbol{E}= \) \( 100 \sin (100 \pi t) \) is connected to a choke of negligible resistance and current oscillations of amplitude 1 A
are produced. The inductance of the choke should be
\( \mathbf{A} \cdot 100 H \)
в. \( \frac{1}{\pi} H \)
c. \( 1 H \)
D. \( \pi H \)
Subject: Physics
On the surface of the earth, force of gravitational attraction between two masses kept at distance dapart is 6
Newtons. If these two masses are taken
to the surface of the moon and kept at
the same distance d, the force between
them will be
A . \( 1 \mathrm{N} \)
B. 36N
\( c \cdot \frac{1}{6} N \)
D. 6N
Subject: Physics
A car is moving along a straight line say OP in the figure. It moves from \( \boldsymbol{O} \) to \( \boldsymbol{P} \)
in 18 sec and returns from \( P \) and \( Q \) in
6 sec. What are average velocity of the
car in going from
(a) \( O \) to \( P ?(b) \) from \( O \) to \( P \) and back to
\( Q ? \)
A \( \cdot 10 m s^{-1}, 20 m s^{-1} \)
B . \( 20 \mathrm{ms}^{-1}, 10 \mathrm{ms}^{-1} \)
C \( .10 m s^{-1}, 10 m s^{-1} \)
D \( \cdot 20 m s^{-1}, 20 m s^{-1} \)
Subject: Maths
If \( \frac{(1+x)(1+2 x)(1+3 x)}{(1-x)(1-2 x)(1-3 x)}=K+ \)
\( \frac{\mathbf{A}}{\mathbf{1}-\mathbf{x}}+\frac{\mathbf{B}}{\mathbf{1}-\mathbf{2} \mathbf{x}}+\frac{\mathbf{C}}{\mathbf{1}-\mathbf{3} \mathbf{x}}, \) then which
of the following is correct
\( \mathbf{A} \cdot \mathbf{K}=6 \)
B. \( A=12 \)
c. \( \mathrm{B}=30 \)
\( \mathbf{D} \cdot \mathbf{C}=-20 \)
Subject: Maths
\( A \) and \( B \) are the points (2,0) and (0,2) respectively. The coordinates of the point \( P \) on the line \( 2+3 y+1=0 \) are
A. (7,-5) if |PA - PBl is maximum
B. \( \left(\frac{1}{5}, \frac{1}{5}\right) \) if \( |P A-P B| \) is maximun
c. (7,-5) if \( \mid P A-P B / \) is minimum
D. \( \left(\frac{1}{5}, \frac{1}{5}\right) \) if \( \mid \) PA - PB l is minimun
Subject: Physics
Three stars each of mass \( \mathrm{M} \) and radius
\( \mathrm{R} \) are initially at rest and the distance between centres of any two stars is d
and they form an equilateral triangle. They start moving towards the centroid
due to mutual force of attraction. What
are the velocities of the stars just before the collision?
Radius of each star is \( \mathrm{R} \).
Subject: Maths
If \( \boldsymbol{\theta} \in\left(\mathbf{0}, \frac{\boldsymbol{\pi}}{\mathbf{2}}\right), \) then the value of
\( \cos \left(\theta-\frac{\pi}{4}\right) \) lies in the interval
\( ^{\mathbf{A}} \cdot\left(\frac{1}{2}, 1\right) \)
B \( \cdot\left(\frac{1}{\sqrt{2}}, 1\right) \)
\( ^{\mathbf{c}} \cdot\left(-\frac{1}{\sqrt{2}}, 1\right) \)
D. (0,1)
Subject: Chemistry
In the conversion of \( \boldsymbol{O}_{2} \longrightarrow \boldsymbol{O}_{2}^{-} \) the
incoming electron goes to the orbital:
A \( \cdot \pi^{*} 2 p x \)
B . \( \pi_{2 p x} \)
\( \mathbf{c} \cdot \sigma_{2 p z}^{*} \)
\( D \cdot \sigma_{2 p^{2}} \)
Subject: Biology
Consider the following four statements
(i)- (iv) and select the correct option
stating which ones are true (T) and which ones are false (F)
(i) In male cockroach, genital pouch or chamber lies at the hind end of
abdomen bounded dorsally by 9 th and 10th terga and ventrally by the 9 th sternum.
(ii) In cockroach, the haemolymph is composed of colourless plasma and haemocytes
(ii) In female cockroach each ovary is formed of a group of ten ovarian tubules or ovarioles, containing a chain developing ova
(iv) In cockroach the nymph grows by moulting about 13 times to reach the adult form.
A \( \cdot\left(\text { i) }-F_{i} \text { (ii) }-\text { T; (iii) }-F_{i} \text { (iv) }-T\right. \)
B. (i)- F; (ii)- F; (iii) - T; (iiv)- T
\( c \cdot(i)-T_{i}(\text { ii })-T ;\left(\text { (iii) }-F_{i}(\text { iv } \gamma)-T\right. \)
D. (i)- T; (ii)- F; (iii) - T; (iv) - f
Subject: Maths
Let \( \boldsymbol{f}(\boldsymbol{x})=[\boldsymbol{x}]+[-\boldsymbol{x}] . \) Then for any
integer \( n \) and \( k \in R-I \)
This question has multiple correct options
A \( \cdot \lim _{x \rightarrow n} f(x) \) exists
B. \( \lim _{x \rightarrow k} f(x) \) exists
c. f is continuous at \( x=n \)
D. f is continuous at \( x=k \)
Subject: Chemistry
Chlorine on reaction with hot and
concentrated sodium hydroxide gives:
\( \mathbf{A} \cdot C l^{-} \) and \( C l O_{2}^{-} \)
в. \( C l^{-} \) and \( C l O_{3}^{-} \)
c. \( C l^{-} \) and \( C l O^{-} \)
D. \( C l O_{3}^{-} \) and \( C l O_{2}^{-} \)
Subject: Chemistry
toppr
Q Type your question_
-
\( 2 I^{-}(a q)+S_{2} O_{8}^{2-}(a q) \rightarrow I_{2}(a q)+ \)
\( 2 S_{2} O_{4}^{-2}(a q)(s l o w) \)
\( \boldsymbol{I}_{2}(\boldsymbol{a} \boldsymbol{q})+\boldsymbol{2} \boldsymbol{S}_{2} \boldsymbol{O}_{3}^{2-}(\boldsymbol{a} \boldsymbol{q}) \rightarrow \boldsymbol{2} \boldsymbol{I}^{-}(\boldsymbol{a} \boldsymbol{q})+ \)
\( \boldsymbol{S}_{4} \boldsymbol{O}_{\boldsymbol{6}}^{\boldsymbol{2}-}(\boldsymbol{a} \boldsymbol{q})(\boldsymbol{f} \boldsymbol{a} \boldsymbol{s} \boldsymbol{t}) \)
A little of these sulphate ions along with starch are added in the first
reaction. The iodine formed in the first
reaction reacts with sulphate ions and
the blue colour of iodine starts
developing as soon as the whole \( S_{2} O_{3}^{2-} \)
are used up. The sulphur containing
atoms in the course of reactions are:
This question has multiple correct options
\( \mathbf{A} \)
\[
\left[\begin{array}{c}
o \\
o-S^{\prime}-O \\
_{o}
\end{array}\right]^{2}
\]
B.
\[
\left[\begin{array}{cc}
o & o \\
O-S^{\prime}-O-O-S^{\prime}-O \\
_{O} & _{O}^{\prime}
\end{array}\right]^{2-}
\]
\( c \)
\[
\left[\begin{array}{c}
o \\
O-\underset{S}{S}-S \\
o
\end{array}\right]^{2}
\]
D.
\[
\left[\begin{array}{cc}
o & o \\
O-S & -S-S-S^{\prime} \\
\rho & \vdots \\
o
\end{array}\right]^{2-}
\]
Subject: Maths
The surface area of a cube is \( 600 \mathrm{cm}^{2} \)
Find its volume
A \( \cdot 1000 \mathrm{cm}^{3} \)
в. \( 729 \mathrm{cm}^{3} \)
\( c \cdot 512 c m^{3} \)
D. None of these
Subject: Maths
Which congruence criterion do you use
in the following?
Given: \( \angle \mathrm{MLN}=\angle \mathrm{FGH}, \angle \mathrm{NML}=\angle \mathrm{HFG}, \mathrm{ML} \)
= FG. So \( \Delta \) LMN \( \equiv \Delta G F H \)
Subject: Maths
If Rolle's theorem holds for the function
\( \boldsymbol{f}(\boldsymbol{x})=\mathbf{2} \boldsymbol{x}^{\mathbf{3}}+\boldsymbol{b} \boldsymbol{x}^{2}+\boldsymbol{c} \boldsymbol{x}, \boldsymbol{x} \in[-\mathbf{1}, \mathbf{1}], \) at
the point \( x=\frac{1}{2}, \) then \( 2 b+c \) equals:
A . -1
B.
c. -3
D.
Subject: Maths
Let N denote the set of all natural
numbers. Define two binary relations on \( \mathrm{N} \) as \( \boldsymbol{R}_{1}=\{(\boldsymbol{x}, \boldsymbol{y}) \boldsymbol{\epsilon} \boldsymbol{N} \times \boldsymbol{N}: \boldsymbol{2} \boldsymbol{x}+\boldsymbol{y}= \)
\( \mathbf{1 0}\} \) and \( \boldsymbol{R}_{2}=\{(\boldsymbol{x}, \boldsymbol{y}) \boldsymbol{\epsilon} \boldsymbol{N} \times \boldsymbol{N}: \boldsymbol{x}+ \)
\( \mathbf{2} \boldsymbol{y}=\mathbf{1 0}\} . \) Then
\( A \cdot \) Both \( R_{1} \) and \( R_{2} \) are transitive relations
B. Both \( R_{1} \) and \( R_{2} \) are symmetric relations
C. Range of \( R_{2} \) is \{1,2,3,4\}
D. Range of \( R_{1} \) is \{2,4,8\}
Subject: Physics
The poisson's ratio for \( O_{2} \) is \( 1.4 . \) Which
of the following are correct for \( O_{2} ? \)
This question has multiple correct options
A. \( C_{V M}=5 c a l \)
В. \( C_{V}=0.156 \mathrm{cal} \)
\( \mathbf{c} \cdot C_{P}=\frac{R \Upsilon}{\Upsilon-1} \)
D. \( C_{V}=\frac{R}{(\Upsilon-1)} \)
Subject: Maths
Construct the matrix of order \( 3 \times 2 \)
whose elements are given by \( a_{i j}=2 i- \)
\( \boldsymbol{j} \)
A. \( \left[\begin{array}{ll}1 & 3 \\ 0 & 2 \\ -1 & 1\end{array}\right] \)
B. \( \left[\begin{array}{lll}1 & 3 & 5 \\ 0 & 2 & 4\end{array}\right] \)
\( \mathbf{c} \cdot\left[\begin{array}{ll}1 & 0 \\ 3 & 2 \\ 5 & 4\end{array}\right] \)
D. \( \left[\begin{array}{ccc}1 & 0 & -1 \\ 3 & 2 & 1\end{array}\right] \)
Subject: Maths
The order and power of differential
equation \( \frac{\boldsymbol{d}^{2} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}^{2}}+\boldsymbol{y} \frac{\boldsymbol{d} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}}+\int \boldsymbol{y} \boldsymbol{d} \boldsymbol{x}=\sin \boldsymbol{x} \) is
A . 1,3
в. 3,1
c. 1.2
D. 2,1
Subject: Chemistry
What products are formed during, the electrolysis of a concentrated aqueous solution of \( N a C l ? \)
(I) \( C l_{2} \)
(II) \( N a O H(a q) \)
\( (\| I) H_{2}(g) \)
A. I only
B. I and II only
C. \( I \) and \( I I I \) only
D. I, II and III
Subject: Physics
A metal wire of length I, area of crosssection A and Young's modulus Y behaves as a spring of spring constant k given by.
A \( \cdot k=\frac{Y A}{l} \)
B. \( k=\frac{2 Y A}{l} \)
c. \( _{k}=\frac{Y A}{2 l} \)
D. \( k=\frac{Y l}{A} \)
Subject: Maths
Find the cubic polynomial with three different variables.
A \( \cdot x^{3}+y^{3}+2^{3}-5^{3} \)
B \( \cdot a^{3}+b^{3}-c^{2}+1 \)
c. \( x^{3}+x^{2}+x \)
D. \( x y^{2}+x y^{3}-x y+6^{3} \)
Subject: Chemistry
Assertion
Treatment of 2 -methyl-2-pentene with
NBS in \( C C I_{4} \) gives 4 -bromo-2-methyl-2-
pentene as major product.
Reason
NBS brings about free radical abomination at acrylic position.
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
Five identical parallel conducting
plates each of area A have separation 'd between successive surface. The plates
are connected to the terminal of a
battery as shown in the figure. The effective capacitance of the circuit is
A \( \cdot \frac{A \varepsilon_{0}}{4 d} \)
в. \( \frac{4 A \varepsilon_{0}}{d} \)
c. \( \frac{A \varepsilon_{0}}{3 d} \)
D. \( \frac{3 A \varepsilon_{0}}{4 d} \)
Subject: Physics
op
Q Type your question
direction. The number of turns is \( n \) and
the cross sectional area of the coil is \( A \)
When the coil turns through \( 180^{\circ} \) about
its diameter, the charge flowing through the coil is \( Q \). The total
resistance of the circuit is \( R \). What is
the magnitude of the magnetic
induction?
\( ^{A} \cdot \frac{Q R}{n A} \)
в. \( \frac{2 Q R}{n A} \)
c. \( \frac{Q n}{2 R A} \)
D. \( \frac{Q R}{2 n A} \)
Subject: Chemistry
Le-chatlier principle is not applicable
for:
A \( \cdot H_{2}(g)+I_{2}(g) \rightleftharpoons 2 H I(g) \)
В. \( F e(s)+S(s) \rightleftharpoons F e S(s) \)
C. \( N_{2}(g)+3 H_{2}(g) \rightleftharpoons 2 N H_{3}(g) \)
D. \( N_{2}(g)+O_{2}(g) \rightleftharpoons 2 N O(g) \)
Subject: Physics
Consider a young's doluble slit experiment as shown in figure. What
should be the slit seperation din term
of wavelength \( \lambda \) such that the first
minima occurs directly in front of the
slit \( \left(\boldsymbol{S}_{1}\right) ? \)
\( A \)
B.
c. \( \frac{\lambda}{(\sqrt{5}-2)} \)
D. \( \frac{\lambda}{2(\sqrt{5}-2)} \)
Subject: Chemistry
If \( M \) is the element of the actinoid
series, the degree of complex formation
decrease in the order:
A \( \cdot M^{4+}>M^{3+}>M O_{2}^{2+}>M O_{2}^{+} \)
B . \( M O_{2}^{+}>M O_{2}^{2+}>M^{3+}>M^{4} \)
c. \( M^{4+}>M O_{2}^{2+}>M^{3+}>M O_{2}^{\text {th }} \)
D. \( M O_{2}^{2+}<M O_{2}^{+}<M^{4+}>M^{3+} \)
Subject: Chemistry
Aluminum (Al) atom has ground-state
electron configuration as:
\( \mathbf{A} \cdot 1 s^{2} 2 s^{2} 2 p^{1} \)
B \( \cdot 1 s^{2} 2 s^{2} 2 p^{6} 3 s^{1} \)
\( \mathbf{C} \cdot 1 s^{2} 2 s^{2} 2 p^{6} 3 s^{2} 3 p^{1} \)
D. \( 1 s^{2} 2 s^{2} 2 p^{6} 3 s^{2} 3 p^{1} 3 p^{12} \)
E \( \cdot 1 s^{2} 2 s^{2} 2 p^{6} 3 s^{2} 3 p^{1} 3 p^{12} 4 p^{6} \)
Subject: Physics
A rectangle has sides of lengths \( 6 \mathrm{cm} \)
and \( 8 c m . \) Two magnetic poles each of
pole strength ' \( m \) ' are placed at the ends of one side of smaller length and magnetic force acting between them is
\( F^{\prime} . \) If they are moved to new positions of same rectangle so that they are diagonally opposite. Find the final force acting on each pole.
Subject: Chemistry
One mole of an ideal monoatomic gas is
heated at a constant pressure from 0 to
100. Then the change in the internal energy of the gas is:
\( \left(\text { Given }, \boldsymbol{R}=\mathbf{8 . 3 2} \boldsymbol{J} \boldsymbol{m o l}^{-1} \boldsymbol{K}^{-1}\right) \)
A \( \cdot 0.83 \times 10^{3} J \)
в. \( 4.6 \times 10^{3} J \)
c. \( 2.08 \times 10^{3} J \)
D. \( 1.25 \times 10^{3} J \)
Subject: Biology
Match the following.
\( \begin{array}{llll}\text { Sr.no } & \text { Column -I } & \text { Sr.no } & \text { Column -II } \\ \text { A. } & \text { Testosterone } & 1 . & \begin{array}{l}\text { Sexual } \\ \text { contraction } \\ \text { in male }\end{array} \\ \text { B. } & \begin{array}{l}\text { Atrial } \\ \text { natriuretic } \\ \text { factor }\end{array} & \text { 2. } & \begin{array}{l}\text { Decrease in } \\ \text { blood } \\ \text { pressure }\end{array} & \begin{array}{l}\text { Decrease in } \\ \text { liver } \\ \text { glycogen } \\ \text { content }\end{array} & \begin{array}{l}\text { Increases } \\ \text { in } \\ \text { heartbeat }\end{array} & \text { 3. } \\ \text { C. } & \text { Glucagon } & & & \\ \text { D. } & \text { Epinephrine } & \text { 4. } & & \\ & & & \end{array} \)
\( A \cdot A-1, B-2, C-3, D-4 \)
B. A-1, B-3, C-2, D-4
C. \( A-3, B-4, C-1, D-2 \)
D. A-3, B-4, C-2, D-1