AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Maths
\( \mathbf{f} \boldsymbol{A}=\left[\begin{array}{ccc}\mathbf{0} & \boldsymbol{a}+\mathbf{1} & \boldsymbol{b}-\mathbf{2} \\ \mathbf{2} \boldsymbol{a}-\mathbf{1} & \mathbf{0} & \boldsymbol{c}-\mathbf{2} \\ \mathbf{2} \boldsymbol{b}+\mathbf{1} & \mathbf{2}+\boldsymbol{c} & \mathbf{0}\end{array}\right] \) is skew
symmetric then \( a+b+c= \)
\( A \cdot 3 \)
B. -3
\( c \cdot \frac{1}{3} \)
\( D \)
Subject: Maths
If \( f: R^{+} \rightarrow R^{+}, f(x)=x^{2}+2 \) and \( g: \)
\( \boldsymbol{R}^{+} \rightarrow \boldsymbol{R}^{+}, \boldsymbol{g}(\boldsymbol{x})=\sqrt{\boldsymbol{x}+\mathbf{1}} \)
then \( (\boldsymbol{f}+\boldsymbol{g})(\boldsymbol{x}) \) equals
A. \( \sqrt{x^{2}+3} \)
B. \( x+3 \)
c. \( \sqrt{x^{2}+2}+(x+1) \)
D. \( x^{2}+2+\sqrt{(x+1)} \)
Subject: Maths
If \( \boldsymbol{A}=\left[\begin{array}{ll}\mathbf{3} & \mathbf{7} \\ \mathbf{2} & \mathbf{5}\end{array}\right] \) and \( \boldsymbol{B}=\left[\begin{array}{cc}-\mathbf{3} & \mathbf{2} \\ \mathbf{4} & -\mathbf{1}\end{array}\right] \) find
the matrix \( C \) if \( 2 C=A+B \)
Subject: Maths
During the month of July, the number of units, \( y \), of a certain product sold per
day can be modeled by the function
\( y=-3.65 x+915, \) where \( x \) is the
average daily temperature in degrees Fahrenheit. Find the statement which
directly follows from the above
equation.
A. As the temperature increases, the number of units sold decreases.
B. As the temperature increases, the number of units sold remains constant
C. As the temperature increases, the number of units sold increases
D. There is no linear relationship between temperature and the number of units sold
Subject: Maths
A vector \( a \) can be written as
\( \mathbf{A} \cdot(a \cdot i) i+(a \cdot j) j+(a \cdot k) k \)
B. \( (a \cdot j) i+(a \cdot k) j+(a \cdot i) k \)
\( \mathbf{c} \cdot(a \cdot k) j+(a \cdot i) j+(a \cdot j) k \)
\( \mathbf{D} \cdot(a \cdot a) i+(i+j+k) k \)
Subject: Physics
When an elastic material with Young's
modulus \( ^{\prime} Y^{\prime} \) is subjected to a
stretching stress \( ^{\prime} S^{\prime}, \) then the elastic
energy stored per unit volume is:
\( ^{A} \cdot \frac{S^{2}}{2 Y} \)
B. \( \frac{Y S^{2}}{2} \)
c. \( \frac{s}{2 Y} \)
D. \( \frac{Y S}{2} \)
Subject: Physics
Two particles of masses m and \( 2 \mathrm{m} \)
on an object are connected by a spring,
then with respect to the object's frame
of reference
A. the two particles are considered as rigid body, if the object moves with uniform velocity
B. the two particles are considered as rigid body, if the object moves with uniform acceleration
C. the two particles are considered as rigid body, if the object moves with uniform speed
D. the two particles are cannot be a rigid body, since deformation in the spring can bring about a change in the positions of the particles
Subject: Maths
\( f(x)=\frac{1+e^{1 / x}}{1-e^{1 / x}}(x \neq 0), f(0)=1, \) then
\( f(x) \) is
A. left coninuous at \( x=0 \)
B. right continuous at \( x=0 \)
c. continuous at \( x=0 \)
D. none
Subject: Physics
Assertion
Speed of a particle moving in a circle varies with time as, \( \boldsymbol{v}=(\mathbf{4} \boldsymbol{t}-\mathbf{1 2}) . \) Such
type of circular motion is not possible.
Reason

Speed cannot change linearly with time.
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 is incorrect and Reason is correct
Subject: Chemistry
Which of the these are
disproportionation reactions?
I. \( 2 \mathrm{C}_{6} \mathrm{H}_{5} \mathrm{CHO}-^{\mathrm{A}\left(\mathrm{CC}_{2} \mathrm{H}_{5}\right)_{3}} \mathrm{C}_{6} \mathrm{H}_{5} \mathrm{COOCH}_{2} \mathrm{C}_{6} \mathrm{H}_{5} \)
III. \( \mathrm{Cl}_{2}+2 \mathrm{OH}^{-} \longrightarrow \mathrm{Cl}^{-}+\mathrm{ClO}^{-}+\mathrm{H}_{2} \mathrm{O} \)
IV. \( 2 \mathrm{KClO}_{3} \longrightarrow 2 \mathrm{KCl}+3 \mathrm{O}_{2} \)
\( \mathbf{A} \cdot \) ।, ॥।, ॥ ॥
в. ॥, IV
c. ॥, ॥ा, । v
D. I, IV
Subject: Physics
Figure shows a network of three
resistances.When some potential
difference is applied across the network, thermal powers dissipated by
A, \( B, \) and \( C \) are in the ratio
\( A \cdot 2: 3: 4 \)
B. 2: 4: 3
\( c \cdot 4: 2: 3 \)
D. 3: 2: 4
Subject: Chemistry
The standard reduction potentials of
\( A g, C u, C o \) and \( Z n \) is 0.799,0.337
\( -0.277,-0.762 \mathrm{V} \) respectively. Which of the following cells will have maximum cell e.m.f.?
A \( \cdot Z n\left|Z n^{2+}(1 M) \| C u^{2+}(1 M)\right| C u \)
в. \( Z n\left|Z n^{2+}(1 M) \| A g^{+}(1 M)\right| A g \)
C . \( C u\left|C u^{2+}(1 M)\right|\left|A g^{+}(1 M)\right| A g \)
D. \( Z n\left|Z n^{2+}(1 M) \| C o^{2+}(1 M)\right| C o \)
Subject: Maths
\( \mathbf{1} . \mathbf{3}+\mathbf{3 . 5}+\mathbf{5 . 7}+\ldots+(\mathbf{2 n}-\mathbf{1})(\mathbf{2 n}+ \)
1) \( = \)
A \( \frac{n\left(4 n^{2}+6 n-1\right)}{3} \)
в. \( \frac{n\left(3 n^{2}+5 n+1\right)}{3} \)
\( \frac{n\left(5 n^{2}+7 n-1\right)}{3} \)
D. \( \frac{n\left(7 n^{2}-5 n+1\right)}{3} \)
Subject: Chemistry
(i) \( \boldsymbol{C a O}(\boldsymbol{s})+\boldsymbol{H}_{2} \boldsymbol{O}(l)=\boldsymbol{C a}(\boldsymbol{O H})_{2}(\boldsymbol{s}) \)
\( \Delta H_{180^{\circ} C}=-15.26 k c a l \)
(ii) \( \boldsymbol{H}_{2} \boldsymbol{O}(\boldsymbol{l})=\boldsymbol{H}_{2}(\boldsymbol{g})+\frac{1}{2} \boldsymbol{O}_{2}(\boldsymbol{g}) \)
\( \boldsymbol{\Delta} \boldsymbol{H}_{180^{\circ} C}=\mathbf{6 8 . 3 7} \boldsymbol{k c a l} \)
(iii) \( C a(s)+\frac{1}{2} O_{2}(g)=C a O(s) \)
\( \boldsymbol{\Delta} \boldsymbol{H}_{180^{\circ} C}=-151.80 k c a l \)
From the following data, the heat of
formation of \( \boldsymbol{C a}(\boldsymbol{O H})_{2}(\boldsymbol{s}) \) at \( \mathbf{1 8}^{\circ} \boldsymbol{C} \) is:
A . -98.69 kcal
B . -235.43 kcal
c. 194.91 kcal
D. 98.69 kcal
Subject: Chemistry
Name the reducing agent in the following:
\( \mathbf{3} M n O_{2}+4 A l \rightarrow 3 M n+2 A l_{2} O_{3} \)
\( \mathbf{A} \cdot M n \)
B. \( A l \)
\( \mathrm{c} \cdot M n O_{2} \)
D. \( A l_{2} O_{3} \)
Subject: Physics
A gas bubble from an explosion under water oscillation with a period proportional to \( P^{a}, d^{b}, E^{c} \) where \( P \) is the
static pressure, \( d \) is the density of water
and \( \boldsymbol{E} \) is the energy of explosion. Then
\( a, b \) and \( c \) respectively are
A \( \cdot \quad-\frac{5}{6}, \frac{1}{2}, \frac{1}{3} \)
в. \( \frac{1}{2}, \frac{-5}{6}, \frac{1}{3} \)
c. \( \frac{1}{3}, \frac{1}{2}, \frac{-5}{6} \)
D. 1,1,1
Subject: Chemistry
Calculate the molarity of each of the following: (a) \( 30 g \) of \( C o\left(N O_{3}\right)_{2} .6 H_{2} O \)
in \( 4.3 L \) of solution
(b) \( 30 m L \) of 0.5
\( M H_{2} S O_{4} \) diluted to \( 500 m L \)
Subject: Chemistry
Which of the following do have \( \boldsymbol{p}_{\boldsymbol{\pi}}-\boldsymbol{d}_{\boldsymbol{\pi}} \)
bonding?
A \( . N O_{3}^{-} \)
B. \( S O_{3}^{-2} \)
\( \mathrm{c} \cdot B O_{3}^{-3} \)
D. \( C O_{3}^{-2} \)
Subject: Chemistry
A soluction contains \( 7 g \) of solute (molar \( \operatorname{mass} 210 g \operatorname{mol}^{-1} \) ) in \( 350 g \) of acetone
raised the boiling point of acetone from
\( 56^{\circ} C \) to \( 56.3^{\circ} C \)
The value of ebullioscopic constant of acetone in \( K . K g m o l^{-1} \) is:
A . 2.66
в. 3.15
c. 4.12
D. 2.86
Subject: Chemistry
Liquid benzene \( \left(C_{6} H_{6}\right) \) burns in oxygen
according to \( 2 C_{6} H_{6}(I)+15 O_{2}(g) \rightarrow \)
\( 12 C O_{2}(g)+6 H_{2} O(g) . \) How many litres
of \( O_{2} \) at STP are needed to complete the
combustion of 39 g of liquid benzene?
A . \( 74 L \)
B. \( 11.2 L \)
c. \( 22.4 \mathrm{L} \)
D. 84L
Subject: Physics
The \( \beta \) of a transistor is \( 74 . \) It is connected in common base configuration. If the emitter current is
\( 5 m A, \) the collector current is
(approximately)
A. \( 0.45 \mathrm{mA} \)
B. \( 4.93 \mathrm{mA} \)
\( \mathbf{c} .370 \mathrm{mA} \)
D. \( 5 m A \)
Subject: Physics
A thin horizontal uniform rod \( A B \) of
mass \( m \) and length \( l \) can rotate freely about a vertical axis passing through its end \( A . \) At a certain moment, the end
\( B \) starts experiencing a constant force
\( F \) which is always perpendicular to the original position of the stationary rod
and directed in a horizontal plane. Find the angular velocity of the rod as a function of its rotation angle \( \theta \) measured relative to the initial position
Subject: Physics
The amplitude and time period of a particle of mass \( 0.1 \mathrm{kg} \) executing simple harmonic motion are \( 1 \mathrm{m} \) and \( 6.28 \mathrm{s} \) respectively. Then its (i)angular frequency,
(ii) acceleration at
a displacement of \( 0.5 \mathrm{m} \) are respectively
A \( \cdot 1 \mathrm{rad} / \mathrm{s}, 0.5 \mathrm{m} / \mathrm{s}^{2} \)
B. 2 rad/s, 1 m/s'
c. \( 0.5 \mathrm{rad} / \mathrm{s}, 0.5 \mathrm{m} / \mathrm{s}^{2} \)
D. 1 rad/s, \( 1 \mathrm{m} / \mathrm{s}^{2} \)
Subject: Physics
The electric field \( E \) is uniform in the
shaded area and makes an angle \( \theta \)
with the normal. The conductivity of the
material in which the area \( \$ \) lies is \( \sigma \)
The electric current flowing out of the shaded area is
A. \( \sigma E S \cos \theta \)
B . \( \sigma E S \cos ^{2} \theta \)
c. \( \sigma E S \sin \theta \)
D. \( \sigma E S \sin ^{2} \theta \)
Subject: Maths
\begin{tabular}{lllll} 
Mark & \( 25- \) & \( 35- \) & \( 45- \) & \( 55- \) \\
obtained & 35 & 45 & 55 & 65 \\
Number of students & 7 & 31 & 33 & 17 \\
\hline
\end{tabular} Find mean
Subject: Maths
If \( A \) and \( B \) are two matrices of order
\( 3 \times m \) and \( 3 \times n \) respectively and \( m= \)
\( \boldsymbol{n}, \) then the order of \( \mathbf{5} \boldsymbol{A}-\mathbf{2} \boldsymbol{B} \) is
\( \mathbf{A} \cdot m \times 3 \)
B. \( 3 \times 3 \)
\( \mathrm{c} \cdot m \times n \)
D. \( 3 \times n \)
Subject: Maths
\( \boldsymbol{A}(\mathbf{5}, \mathbf{7}), \boldsymbol{B}(\mathbf{4}, \mathbf{1 2}), \boldsymbol{C}(\mathbf{9}, \mathbf{1 1}) \) and \( \boldsymbol{D}(\mathbf{1 0}, \mathbf{6} \)
are four points. Show that \( A B C D \) is a
rhombus
Subject: Maths
f \( a, b, c \) are in A.P then \( a\left(\frac{1}{b}+\frac{1}{c}\right), b\left(\frac{1}{c}+\frac{1}{a}\right), c\left(\frac{1}{a}+\frac{1}{b}\right) \)
are in
A. \( A . P . \)
в. G.P.
c . \( H . P \)
D. A.G.P
Subject: Maths
Identify the non-diagonal matrix from
the given options.
\( \mathbf{A} \cdot\left[\begin{array}{lll}1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{array}\right] \)
\( \mathbf{B} \cdot\left[\begin{array}{lll}1 & 0 & 0 \\ 0 & 2 & 0 \\ 1 & 9 & 0\end{array}\right] \)
\( \mathbf{C} \cdot\left[\begin{array}{lll}1 & 0 & 0 \\ 0 & 4 & 0 \\ 0 & 0 & 1\end{array}\right] \)
D. \( \left[\begin{array}{ccc}1 & 0 & 0 \\ 0 & 4 & 0 \\ 0 & 0 & -1\end{array}\right] \)
Subject: Physics
Parto of the uranium decay series is shown
\( 92^{2}-90 T h^{234} \rightarrow 91 P a^{234} \rightarrow \)
\( 92 U^{234} \rightarrow_{90} T h^{230} \rightarrow_{88} R a^{226} \)
How many pairs of isotopes are there in the above series:
A \( . \)
B. 2
\( c \cdot 3 \)
D.
Subject: Chemistry
Consider the following reactions. In which case the formation of product is favoured by decrease in pressure?
(1) \( \boldsymbol{C O}_{2}(\boldsymbol{g})+\boldsymbol{C}(\boldsymbol{s}) \rightarrow \boldsymbol{2} \boldsymbol{C O}(\boldsymbol{g}) ; \boldsymbol{\Delta} \boldsymbol{H}= \)
\( +172.5 \mathrm{kJ} \)
(2) \( N_{2}(g)+3 H_{2}(g) \rightarrow 2 N H_{3}(g) \)
\( \Delta \boldsymbol{H}=-\mathbf{9 1 . 8} \mathbf{k} \mathbf{J} \)
(3) \( N_{2}(g)+O_{2}(g) \rightarrow 2 N O(g) ; \Delta H= \)
\( +181 k J \)
\( (4) 2 H_{2} O(g) \rightarrow 2 H_{2}(g)+ \)
\( \boldsymbol{O}_{2}(\boldsymbol{g}) ; \boldsymbol{\Delta} \boldsymbol{H}=\mathbf{4 8 4 . 6} \mathbf{k J} \)
A . 2,3
B. 3,4
\( c \cdot 2,4 \)
D. 1.4
Subject: Maths
Let \( f \) and \( g \) be real-valued functions
such that
\( \boldsymbol{f}(\boldsymbol{x}+\boldsymbol{y})+\boldsymbol{f}(\boldsymbol{x}-\boldsymbol{y})=2 \boldsymbol{f}(\boldsymbol{x}) \)
\( \boldsymbol{g}(\boldsymbol{y}) \forall \boldsymbol{x}, \boldsymbol{y} \boldsymbol{\epsilon} \boldsymbol{R} \)
if \( f \) is not identically zero and \( f|(x)| \leq \)
\( \mathbf{1}, \forall \boldsymbol{x} \epsilon \boldsymbol{R}, \) then \( |\boldsymbol{g}(\boldsymbol{y})| \leq \mathbf{1}, \forall \boldsymbol{y} \boldsymbol{\epsilon} \boldsymbol{R} \)
If true enter 1 else enter 0
A. True
B. False
Subject: Maths
The statement pattern \( (\boldsymbol{p} \wedge \boldsymbol{q}) \wedge[\sim \boldsymbol{r} \vee \)
\( (p \wedge q)] \vee(\sim p \wedge q) \) is equivalent to
\( A \)
B. 9
\( c \cdot p \wedge q \)
D.
Subject: Maths
If \( \mathbf{A}-\mathbf{2 B}=\left[\begin{array}{cc}\mathbf{1} & -\mathbf{2} \\ \mathbf{3} & \mathbf{0}\end{array}\right] \) and \( \mathbf{2} \mathbf{A}-\mathbf{3} \mathbf{B}= \)
\( \left[\begin{array}{cc}-\mathbf{3} & \mathbf{3} \\ \mathbf{1} & \mathbf{- 1}\end{array}\right], \) then \( \mathbf{B}= \)
A \( \cdot\left[\begin{array}{cc}-5 & 7 \\ 5 & 1\end{array}\right] \)
B. \( \left[\begin{array}{cc}-5 & 7 \\ -5 & -1\end{array}\right] \)
c. \( \left[\begin{array}{cc}-5 & 7 \\ 5 & -1\end{array}\right] \)
D. \( \left[\begin{array}{cc}-5 & -7 \\ -5 & -1\end{array}\right] \)
Subject: Physics
In an energy emitting nuclear reaction the binding energies of reactants and
products are \( e_{1}, e_{2} \) respectively.Then which is correct of the following?
\( \mathbf{A} \cdot e_{1}<e_{2} \)
B . \( e_{1}=e_{2} \)
\( \mathbf{c} \cdot e_{1}>e_{2} \)
D. \( e_{1} \geq e_{2} \)
Subject: Physics
An electric bulb is rated at \( 220 \mathrm{V}, 100 \mathrm{W} \)
What safe current can be passed through it ?
\( \mathbf{A} \cdot 2 \cdot 20 A \)
B . \( 3.50 A \)
c. \( 0.45 A \)
D. \( 0.50 A \)
Subject: Maths
A Cylindrical vassel of volume \( 25 \frac{1}{7} \) cubic metres, which is open at the top
is to be manufactured from a sheet of
metal. Find the dimensions of the vessel
so that the amount of sheet used in
manufacturing it is the least possible.
\( \mathbf{A} \cdot r=h=2 \)
В. \( r=1, h=8 \)
c. \( r=2 \sqrt{2}, h=1 \)
D. \( r=2, h=1 \)
Subject: Maths
The total salary drawn by 3 watchmen, A, B and C is Rs. 1720. They spend 70\%, \( 60 \% \) and \( 50 \% \) respectively from their salaries. If the balance with them are
into Ratio \( 1: 2: 3, \) what is the salary of
each?
A. A Rs. 300; B Rs. 500; C- Rs. 700
B. A Rs. 200; B Rs. 300; C-Rs. 650
c. A Rs. 100; B Rs. 300; C-Rs. 600
D. A Rs. 400; B Rs. 600; C- Rs. 720
Subject: Maths
If \( \boldsymbol{f}: \boldsymbol{R} \rightarrow \boldsymbol{R} \) is defined by \( \boldsymbol{f}(\boldsymbol{x})=\boldsymbol{2} \boldsymbol{x}- \)
2, then \( (f \circ f)(x)+2= \)
A. \( f(x) \)
B. \( 2 f(x) \)
c. \( 3 f(x) \)
D. \( -f(x) \)
Subject: Biology
Select the incorrect statement.
A. Microelements involve \( \mathrm{N}, \mathrm{P}, \mathrm{Mn}, \mathrm{Cu}, \mathrm{Mo} \)
B. The concentration of microelements is \( 10 \mathrm{m} \) mole/kg
C. If the concentration is more than \( 10 \mathrm{m} \) mole/kg, they become toxic
D. The deficiency of microelements causes symptoms of disease
Subject: Physics
The velocity of a particle is given as
\( \boldsymbol{v}=\boldsymbol{a}+\boldsymbol{b} \boldsymbol{t}+\boldsymbol{c} \boldsymbol{t}^{2} \). the velocity is
measured in \( \mathrm{ms}^{-1} \), then units of a and
\( c \) are
\( \mathbf{A} \cdot m s^{-1} \) and \( m s^{-3} \)
B. \( m s^{-2} \) and \( m s \)
\( \mathbf{c} \cdot m^{2} s \) and \( m s^{2} \)
D. \( m s \) and \( m s^{-1} \)
Subject: Maths
\( \ln a \Delta A B C, \) if \( \cos A \cos B \cos C=\frac{\sqrt{3}-1}{8} \)
and \( \sin A \sin B \sin C=\frac{3+\sqrt{3}}{8}, \) then
The value of \( \tan A \tan B+\tan B \tan C+ \)
\( \tan C \tan A \) is
Subject: Biology
Match the name of the scientists with
their important contributions given under. Choose the answer which gives
correct combination.
\( A \cdot A-4, B-1, C-3, D-2 \)
B. \( A-1, B-4, C-2, D-3 \)
c. \( A-2, B-1, C-3, D-4 \)
D. \( A-4, B-3, C-2, D-1 \)
E . \( A-3, B-2, C-1, D \)
Subject: Maths
Let \( z_{1}, z_{2} \in C \) and \( x=\left|z_{1} z_{2}\right|- \)
\( \boldsymbol{\operatorname { R e }}\left(\boldsymbol{z}_{1} \boldsymbol{z}_{2}\right)-\frac{\mathbf{1}}{\mathbf{2}}\left|\overline{z_{2}}-\boldsymbol{z}_{1}\right|^{2}+\frac{\mathbf{1}}{\mathbf{2}}\left(\left|\boldsymbol{z}_{2}\right|-\right. \)
\( \left.\left|z_{1}\right|\right)^{2} \) then
\( \mathbf{A} \cdot x<0 \)
B. \( x=0 \)
c. \( x \geq 1 \)
D. \( 0<x<1 \)
Subject: Physics
A long straight conductor, carrying a
current \( I, \) is bent to form an almost
complete circular loop of radius \( r \) on it.
The magnetic field at the center of the
loop:
A. is directed into the paper
B. is directed out of the paper
C . has magnitude \( \frac{\mu_{0} I}{2 r}\left(1-\frac{1}{\pi}\right) \)
D. has magnitude \( \frac{\mu_{0} I}{2 r}\left(1+\frac{1}{\pi}\right) \)
Subject: Maths
The radius of the circle with centre at
the origin is 10 units. Write the
coordinates of the point where the circle intersects the axes. Find the distances
between any two of such points.
A \( . \) Co-ordinates \( =(10,0)(-10,0)(0,10)(0,-10) \) Distance \( =20,10 \sqrt{2} \) units
B. \( C o- \) ordinates \( =(10,0)(-10,0)(0,10)(0,-10) \) Distance \( =10,10 \sqrt{2} \) units
c. \( C o- \) ordinates \( =(10,0)(-10,0)(0,10)(0,-10), 0 \) Distance \( =20 \sqrt{2} \) or \( 10 \sqrt{2} \) units
D. none
Subject: Maths
\( A, B, C \) are three points on the axes of
\( x, y \) and \( z \) respectively at distance \( a, b, c \)
from the origin \( O ; \) then the co ordinates of the point which is
equidistant from \( A, B, C \) and \( O \) is
A \( \cdot(a, b, c) \)
B. \( \left(\frac{a}{2}, \frac{b}{2}, \frac{c}{2}\right) \)
\( ^{\mathbf{C}} \cdot\left(\frac{a}{3}, \frac{b}{3}, \frac{c}{3}\right) \)
D. None of these
Subject: Physics
A boy is standing in front of a plane mirror at a distance of \( 3 \mathrm{m} \) from it, if the
boy moves \( 1 \mathrm{m} \) backward, the distance between the image and the boy is
\( A \cdot 2 m \)
B. \( 4 \mathrm{m} \)
\( c \cdot 8 m \)
D. none of these
Subject: Physics
Assertion
A hollow metallic closed container
maintained at a uniform temperature can act as a source of a black body radiation.
Reason
All metals act as a black body.
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. If Assertion is incorrect but Reason is correct
Subject: Physics
A uniform electric field 'E' is directed
towards positive X-axis. If at \( X=0, \) the electric potential is zero, then the
potential at \( \boldsymbol{X}=+\boldsymbol{X}_{0}, \) would be
A \( \cdot \frac{E}{X_{0}} \)
в. \( \frac{-E}{X_{0}} \)
c. \( -E X_{0} \)
D. \( E X_{0} \)
Subject: Maths
If (4,3) and (-4,3) are two vertices of an equilateral triangle, find the coordinates of the third vertex, given that the origin lies in the interior of the triangle.
A \( \cdot(0,-3-4 \sqrt{3}) \)
В. \( (0,3+4 \sqrt{3}) \)
c. \( (0,3-4 \sqrt{3}) \)
D. \( (0,-3+4 \sqrt{3}) \)
Subject: Chemistry
The main reason for deviation of gases
from ideal behaviour is few
assumptions of kinetic theory. These
are
(i) there is no force of attraction
between the molecules of a gas
(ii) volume of the molecules of a gas is negligibly small in comparison to the volume of the gas
(iii) Particles of a gas are always in constant random motion.
A. (i) and (ii)
B. (ii) and (iii)
C . (i), (ii) and (iii)
D. (iii) only
Subject: Maths
If \( \boldsymbol{\alpha}, \boldsymbol{\beta} \in \boldsymbol{C} \) are the distinct roots, of the
equation \( x^{2}-x+1=0, \) then \( \alpha^{101}+ \)
\( \beta^{107} \) is equal to
A .
B. 2
\( c \cdot-1 \)
D.
Subject: Chemistry
Two hydrogen atoms collide head-on
and end up with zero kinetic energy. Each then emits a photon with a wavelength \( 121.6 n m . \) Which transition
leads to this wavelength? How fast were
the hydrogen atoms travelling before
the collision?
(Given, \( \boldsymbol{R}_{\boldsymbol{H}}=\mathbf{1 . 0 9 7} \times \mathbf{1 0}^{\mathbf{7}} \boldsymbol{m}^{-\mathbf{1}} \) and
\( \boldsymbol{m}_{\boldsymbol{H}}=\mathbf{1 . 6 7} \times \mathbf{1 0}^{-\mathbf{2 7}} \boldsymbol{k g} \boldsymbol{\jmath} \)
Subject: Maths
The differential equation of a free falling body is governed by the DE \( v \frac{d v}{d x}= \) \( -c x-b v^{2} \).where \( v \) and \( x \) are velocity
and displacement respectively. The velocity of the body is given by the equation \( v^{2}=\frac{c}{2 b^{2}}\left(1-e^{-2 b x}\right)-\frac{c x}{b} \)
A. True
B. False
Subject: Maths
One side of a parallelogram is \( 8 \mathrm{cm} \) If the corresponding altitude is \( 6 \mathrm{cm} \) then its area is given by
A \( .24 \mathrm{cm}^{2} \)
B. 36 \( c m^{2} \)
\( c \cdot 40 \mathrm{cm}^{2} \)
D. \( 48 \mathrm{cm}^{2} \)
Subject: Chemistry
The formula of the complex tris (ethylene diamine) cobalt (III) sulphate is:
A \( \cdot\left[\operatorname{Co}(e n)_{2} S O_{4}\right] \)
в. \( \left[\operatorname{Co}(e n)_{3} S O_{4}\right] \)
\( ^{\mathbf{c}}:\left[C o(e n)_{3}\right]_{2} S O_{4} \)
D \( \cdot\left[C o(e n)_{3}\right]_{2}\left(S O_{4}\right)_{3} \)
Subject: Physics
A current I ampere flows along an infinitely long straight thin walled hollow metallic cylinder of radius \( r . \) The magnetic field at any point inside the cylinder at a distance \( x \) from the axis of the cylinders is:
A \( \cdot \frac{\mu_{0} I}{4 \pi r} \)
В. \( \frac{\mu_{0} I}{2 \pi r} \)
c. \( \frac{\mu_{0} I}{2 \pi x} \)
D. zero
Subject: Chemistry
The volumes of two vessels at same
temperature are in theratio of \( 2: 3 . \) One
vessel contains \( H_{2} \) and other \( N_{2} \) at 600
\( \mathrm{mm} \) and \( 900 \mathrm{mm} \) respectively. The final pressure when they are connected
together is : (Assume that \( N_{2} \) and \( H_{2} \)
react to form \( N H_{3} \)
\( A \cdot 680 \mathrm{mm} \)
B. 760 mm
c. \( 780 \mathrm{mm} \)
D. 800 mm
Subject: Chemistry
The nuclei of which one of the following
pairs of nuclei are isotones:
\( A \cdot_{34} \mathrm{Se}^{74},_{31} \mathrm{Ga}^{71} \)
B \( \cdot_{38} \mathrm{Sr}^{84},_{38} \mathrm{Sr}^{86} \)
C \( \cdot_{42} \mathrm{Mo}^{92},_{40} \mathrm{Zr}^{9} \)
D. \( _{20} \mathrm{Ca}_{2}^{40},_{16} \mathrm{S}^{32} \)
Subject: Maths
Let the function \( f(x) \) be defined as
follows: \( f(x)= \)
\( \left\{\begin{array}{cc}x^{3}+x^{2}-10 x & -1 \leq x<0 \\ \cos x & 0 \leq x<\frac{\pi}{2} \\ 1+\sin x & \frac{\pi}{2} \leq x \leq \pi\end{array}, \) then \right.
which of the following statement(s) is/are correct
This question has multiple correct options
A. Local maximum at \( x=0 \)
B . Local maximum at \( x=\frac{\pi}{2} \)
c. Absolute maxima at \( x=-1 \)
D. Absolute minima at \( x=\pi \)
Subject: Physics
In hydrogen spectrum, the wavelength of the line is \( 656 \mathrm{nm} \), where as in the
spectrum of a distant galaxy, the line wavelength is \( 706 \mathrm{nm} \). Estimated speed of galaxy with respect to the earth is :
A \( \cdot 2 \times 10^{8} m / s \)
В. \( 2 \times 10^{7} m / s \)
c. \( 2 \times 10^{6} \mathrm{m} / \mathrm{s} \)
D. \( 2 \times 10^{5} \mathrm{m} / \mathrm{s} \)
Subject: Maths
If \( \boldsymbol{f}(\boldsymbol{x})=[\boldsymbol{x}], \) where \( [.] \) is the greatest
integer function, and \( \boldsymbol{g}(\boldsymbol{x})= \)
\( x\left(1-x^{2}\right)\left(4-x^{2}\right), \) then \( g[f(x)] \) is
A. discontinuous at all integer
B. continuous at all integer
c. continuous at \( x=0,\pm 1,\pm 2 \)
D. discontinuous at \( x=0,\pm 1,\pm 2 \)
Subject: Maths
Construct a right angled \( \triangle A B C \) with
\( \angle B=90^{\circ}, B C=5 c m \) and \( A C= \)
\( 10 \mathrm{cm} \) and find the the length of side
\( A B \)
\( \mathbf{A} \cdot 6.2 \mathrm{cm} \)
B. \( 5 \mathrm{cm} \)
\( c .8 .7 \mathrm{cm} \)
D. \( 7.2 \mathrm{cm} \)
Subject: Physics
Assertion:With increase in temperature
the pressure of given gas increases
Reason:Increase in temperature causes
decrease in no. of collision of molecules
with walls of container.
A. Both assertion (A) and reason
(R) are correct and gives the correct explanation
B. Both assertion (A) and reason
(R) are correct but \( R \) doesnt give the correct explanation
c. \( A \) is true but \( R \) is false
D. A is false but R is true