AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Physics
Assertion
When the distance between two bodies
is doubled and also the mass of each
body is doubled, the gravitational force between them remains the same
Reason
According to Newton's law of gravitation, force is directly
proportional to mass of the bodies and
inversely proportional to square of the distance between them
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: Chemistry
Assertion
Isoelectric point is \( p H \) at which
colloidal can move towards either of
electrode.
Reason
At isoelectric point, colloidal solution
become electrically neutral.
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 incorrect but Reason is correct
D. Both Assertion and Reason are correct
Subject: Physics
A ball is thrown vertically up. If the ball reached at maximum height in \( 3 s \) Assume air resistance is negligible. The maximum height of the ball is most nearly :
A . \( 10 m \)
B. \( 15 \mathrm{m} \)
c. \( 30 m \)
D. \( 45 m \)
E . \( 60 m \)
Subject: Chemistry
A hydrocarbon \( C_{6} H_{10} \) absorbs only one
molecule of \( \boldsymbol{H}_{2} \) on catalytic hydrogenation. On ozonolysis, the
hydrocarbon yields \( C H O\left(C H_{2}\right)_{4} C H O \)
The hydrocarbon is:
A. cyclohexene
B. 1,5-hexadiene
c. 1,3 -cyclohexadiene
D. 1-methylcyclopentene
Subject: Maths
An auto charges Rs. 15 for first kilometer and Rs. 8 each for each
subsequent kilometer. For a total
distance of \( ^{\prime} x^{\prime} k m \) an amount of Rs. \( ^{\prime} y^{\prime} \)
is said.

Write the linear equation representing this information
A \( . y=8 x+7 \)
В. \( y=8 x-7 \)
c. \( y=8 x+15 \)
D. None of these
Subject: Chemistry
A mixture of 2 moles \( C O \) and 1 mole \( O_{2} \)
in a closed vessel is ignited to convert
CO into \( C O_{2} \). Then
\( \mathbf{A} \cdot \Delta H=\Delta E \)
в. \( \Delta H>\Delta E \)
c. \( \Delta H<\Delta E \)
D. none of the above
Subject: Maths
If \( \overline{\boldsymbol{a}}=\hat{\boldsymbol{i}}+\hat{\boldsymbol{j}}-\mathbf{2} \hat{\boldsymbol{k}}, \overline{\boldsymbol{b}}=\mathbf{2} \hat{\boldsymbol{i}}-\mathbf{0} \hat{\boldsymbol{j}}+\hat{\boldsymbol{k}}, \overline{\boldsymbol{c}}= \)
\( \mathbf{3} \hat{\mathbf{i}}-\hat{\boldsymbol{k}} \) and \( \overline{\boldsymbol{c}}=\boldsymbol{m} \overline{\boldsymbol{a}}+\boldsymbol{n} \overline{\boldsymbol{b}} \) then \( \boldsymbol{m}+\boldsymbol{n}= \)
\( \mathbf{A} \cdot \mathbf{0} \)
B.
\( c \cdot 2 \)
D. -
Subject: Maths
Ram mixes \( 15 \mathrm{kg} \) of sugar purchased with the rate of Rs. 8.00 per \( \mathrm{kg} \) with 25 kg of sugar purchased at the rate of Rs. 10.00 per kg. At what rate per kg should Ram sell the mixture to get a profit of 3 per kg?
A. Rs. 12.25
B . Rs. 11.25
c. Rs. 13.25
D. Rs. 14.25
Subject: Maths
The conjugate of \( (2+i) /(3+i) \) in the
form of \( a+i b \) is
\( \mathbf{A} \cdot 13 / 2+i(15 / 2) \)
B . \( 7 / 10+i(-1 / 10) \)
c. \( 13 / 10+i(-15 / 2) \)
D. \( 13 / 10+i(9 / 10) \)
Subject: Physics
Calculate the charge on a body if \( 10^{5} \) electrons have been added to it
\( \mathbf{A} \cdot-1.6 \times 10^{-14} C \)
В. \( 1.6 \times 10^{-14} C \)
c. \( 1.6 \times 10^{14} C \)
D. \( -1.6 \times 10^{14} C \)
Subject: Chemistry
Statement 1: correct order of acidic
strength is \( \boldsymbol{C H}_{3} \boldsymbol{C H}_{3}>\boldsymbol{C H}_{2}= \)
\( \boldsymbol{C H}_{2}>\boldsymbol{H C}=\boldsymbol{C h} \)
Statement 2:- C-H bond energy in ethene is more than ethane but less than
ethyne
A. Statement 1 is true, Statement 2 is true and Statement 2 is correct explanation for Statement 1
B. Statement 1 is true, Statement 2 is true and Statement 2 is NOT the correct explanation for Statement 1.
c. statement 1 is true, Statement 2 is false
D. Statement 1 isfalse, Statement 2 is true
Subject: Maths
Construct a triangle \( A B C \), in which
\( A B=5.5 c m, A C=6.5 c m \) and
\( \angle B A C=70^{\circ} \)
Steps for its construction is given in a jumbled form.Identify its correct
sequence
1) At \( A, \) construct a line segment \( A E \)
sufficiently large, such that \( \angle B A C \) at
\( 70^{\circ}, \) use protractor to measure \( 70^{\circ} \)
2) Draw a line segment which is sufficiently long using ruler.
3) With \( A \) as centre and radius \( 6.5 \mathrm{cm} \)
draw the line cutting \( A E \) at \( C \), join \( B C \),
then \( A B C \) is the required triangle.
4) Locate points \( A \) and \( B \) on it such that
\( A B=5.5 c m \)
A. 2,4,1,3
B. 2,1,4,3
c. 1,2,4,3
D. 4,2,1,3
Subject: Maths
Use mathematical induction to prove:
\( \frac{1}{1 \cdot 3}+\frac{1}{3 \cdot 5}+\frac{1}{5 \cdot 7}+\dots+ \)
\( \frac{1}{(2 n-1)(2 n+1)}=\frac{n}{2 n+1} \)
Subject: Physics
A uniform rod of mass \( m \), length \( L \), area
of cross-section \( A \) is rotated about an
axis passing through one its ends and perpendicular to its length with constant angular velocity \( \omega \) in a
horizontal plane. If \( Y \) is the Young's modulus of the material of rod, the
increase in its length due to rotation of
rod is:
\( ^{A} \cdot \frac{m \omega^{2} L^{2}}{A Y} \)
в. \( \frac{m \omega^{2} L^{2}}{2 A Y} \)
\( ^{\mathbf{C}} \cdot \frac{m \omega^{2} L^{2}}{3 A Y} \)
D. \( \frac{2 m \omega^{2} L^{2}}{A Y} \)
Subject: Physics
A ball moving with velocity \( 2 m / s \) collides head on with another stationary
ball of double the mass. If the
coefficient of restitution is \( 0 \cdot 5, \) then
their velocities \( (\operatorname{in} m / s) \) after collision
will be
A . 0,1
в. 1,1
c. \( 1,0 \cdot 5 \)
D. 0,2
Subject: Maths
Find 'c' of the mean value theorem,if
\( f(x)=x(x-1)(x-2) \)
\( \boldsymbol{a}=\mathbf{0}, \boldsymbol{b}=\frac{\mathbf{1}}{\mathbf{2}} \)
\( ^{\mathrm{A}} \cdot_{C}=1-\frac{\sqrt{21}}{5} \)
в. \( \quad C=1-\frac{\sqrt{21}}{6} \)
\( ^{\mathrm{c}} \cdot_{C}=2-\frac{\sqrt{21}}{6} \)
D. \( c=1+\frac{\sqrt{21}}{6} \)
Subject: Physics
Q Type your question
a wall. The jeep has to take a sharp
perpendicular turn along the wall. A rocket flying at uniform speed of 100kmh \( ^{-1} \) starts from the wall towards
the jeep which is \( 30 k m \) away. The
rocket reaches the windscreen and
returns to wall. Total distance covered
by the rocket is
A . \( 100 k m \)
\( \mathbf{B} .50 k m \)
\( c .37 k m \)
D. \( 75 k \)
Subject: Maths
Let \( A \) and \( B \) be two symmetic matrices
of order 3
Statement \( -1: \boldsymbol{A}(\boldsymbol{B} \boldsymbol{A}) \) and \( (\boldsymbol{A B}) \boldsymbol{A} \) are
symmetric matrices.
Statement - \( 2: A B \) is symmetric matrix if matrix multiplication of \( \boldsymbol{A} \) and \( \boldsymbol{B} \) is
commutative.
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-1 is True, Statement-2 is False
D. Statement-1 is False, Statement-2 is True
Subject: Chemistry
What would be the minimum
uncertainty in de-Broglie wavelength of a moving electron accelerated by potential difference of 6 volt and whose uncertainty in position is \( \frac{7}{22} n m ? \)
A \( .6 .25 \AA \)
в. 6 А
c. 0.625 ,
D. \( 0.3125 \dot{A} \)
Subject: Physics
Calculate the quantity of heat required to convert \( 1.5 \mathrm{kg} \) of ice at \( 100^{\circ} \mathrm{C} \) to water
\( \operatorname{at} 15^{\circ} C .\left(L_{i c e}=3.34 \times\right. \)
\( \mathbf{1 0}^{\mathbf{5}} \boldsymbol{J} \quad \boldsymbol{k} \boldsymbol{g}^{-\mathbf{1}}, \boldsymbol{C}_{\boldsymbol{w} a t e r}= \)
\( \begin{array}{llll}\mathbf{4 1 8 0} & \boldsymbol{J} & \boldsymbol{k g}^{-1} & ^{\circ} \boldsymbol{C}^{-1} \mathbf{)}\end{array} \)
\( \begin{array}{llll}\text { A } \cdot 5.85 & \times & 10^{5} & J\end{array} \)
\( \begin{array}{llll}\text { В. } 5.95 & \times & 10^{5} & J\end{array} \)
\( \begin{array}{llll}\text { C } \cdot 3.95 & \times & 10^{5} & J\end{array} \)
\( \begin{array}{llll}\text { D. } 4.95 & \times & 10^{5} & J\end{array} \)
Subject: Maths
\( \ln \triangle D E F, \) Line PQ \( \| \) side EF. Find DP.
\( \boldsymbol{D} \boldsymbol{Q}=\mathbf{1 . 8} \mathrm{cm}, \boldsymbol{Q} \boldsymbol{F}=\mathbf{5} . \boldsymbol{4} \mathrm{cm}, \boldsymbol{E} \boldsymbol{P}=\mathbf{7 . 2} \)
\( \mathrm{cm} \)
A \( .2 .4 \mathrm{cm} \)
B. \( 4.2 \mathrm{cm} \)
\( c .3 .5 \mathrm{cm} \)
D. \( 1.8 \mathrm{cm} \)
Subject: Physics
Three bars having length \( l, 2 l \) and \( 3 l \) and area of cross-section \( A, 2 A \) and \( 3 A \) are
joined rigidly and to end. Compound rod is subjected to a stretching force \( \boldsymbol{F} \). The increase in length of rod is (Young's modulles of material is \( Y \) and bars are
massless)
A \( \cdot \frac{13 F l}{2 A Y} \)
в. \( \frac{3 F l}{A Y} \)
c. \( \frac{9 F l}{A Y} \)
D. \( \frac{13 \mathrm{Fl}}{\mathrm{AY}} \)
Subject: Chemistry
One of the following is an incorrect
statement, point it out?
A. Permanent hardness can be removed by boiling water.
B. Hardness of water effects soap consumption.
C. Temporary hardness is due to bicarbonates of \( C a \) and \( M g \)
D. Permanent hardness is due to the soluble \( S O_{4}^{2-}, C l^{-} \) of \( C a \) and \( M g \)
Subject: Physics
A particle moving, eastwards with a velocity of \( 5 m / s . \) In \( 10 s, \) its velocity changes to \( 5 m / s \) northwards. The average acceleration in this time is
A. zero
B. \( \frac{1}{\sqrt{2}} m / s^{2} \) towards north-west
c. \( \frac{1}{\sqrt{2}} m / s^{2} \) towards north-east
D \( \cdot \frac{1}{2} m / s^{2} \) towards north-west
Subject: Chemistry
How long (approximate) should water be electrolysed by passing through 100
amperes current so that the oxygen
released can completely burn \( 27.66 g \) of diborane?
(Atomic weight of \( \boldsymbol{B}=\mathbf{1 0 . 8 u} \) )
A. 3.2 hours
B. 1.6 hours
c. 6.4 hours
D. 0.8 hours
Subject: Chemistry
The density of a gas is found to be \( 1.56 g / L \) at \( 745 \mathrm{mm} \) pressure and \( 65^{\circ} \mathrm{C} \)
What is the molecular mass of the
gas?
\( \mathbf{A} \cdot 44.2 u \)
в. \( 4.42 u \)
c \( .2 .24 u \)
D. 22.4u
Subject: Chemistry
At \( 25^{\circ} C, \) the vapour pressure of pure benzene is 100 torr, while that of pure
ethyl alcohol is 44 torr. Assuming ideal behaviour, calculate the vapour
pressure at \( 25^{\circ} \mathrm{C} \) of a solution which
contains 10 g of each substance.
A. 33.775 torr
B. 54.775 torr
c. 64.775 torr
D. 60.775 torr
Subject: Chemistry
Which of the following is called a Wilkinson's catalyst?
\( \mathbf{A} \cdot\left[\left(P h_{3} P\right)_{3} R h C l\right] \)
в. \( \operatorname{TiCl}_{4}+\left(C_{2} \mathrm{H}_{5}\right)_{3} \) Аl
\( \mathbf{c} \cdot\left(C_{2} H_{5}\right)_{4} P b \)
D \( \cdot\left[P t C l_{2}\left(N H_{3}\right)_{2}\right] \)
Subject: Chemistry
Which of the following is correct representation of reaction of acidified permanganate solution with sulphur dioxide?
A \( \cdot 2 M n O_{4}+5 S O_{2}+2 H_{2} O \rightarrow 5 S O_{4}^{2-}+2 M n^{2+}+4 H^{+} \)
B. \( M n O+S O_{2}+2 H_{2} O \rightarrow S+M n^{2+} \)
c. \( 2 M n O_{4}+5 S O_{2}+2 H_{2} O \rightarrow 4 S O_{2}+S+2 M n^{2+}+4 H^{+} \)
D. \( 3 M n O_{4}+2 S O_{2}+2 H_{2} O \rightarrow 2 S+3 M n^{2+}+4 H^{+} \)
Subject: Physics
A mass of \( 5 \mathrm{kg} \) is suspended from a spring of stiffness \( 46 \mathrm{kN} / \mathrm{m} . \) A dashpot is fitted between the mass and the
support with a damping ratio of 0.3 Calculate the damped frequency.
A. \( 14.56 \mathrm{Hz} \)
B. 14.28 Hz
c. \( 14.42 \mathrm{Hz} \)
D. 14.14 нz
Subject: Maths
The area between the curves \( y=\sqrt{x} \)
and \( \boldsymbol{y}=\boldsymbol{x}^{3} \) is
A \( \cdot \frac{1}{12} \) sq. units
в. \( \frac{5}{12} \) sq. units
c. \( \frac{3}{5} \) sq. units
D. \( \frac{4}{5} \) sq. units
Subject: Maths
If \( f: R \rightarrow R \) be a differentiable function and \( f(0)=0 \) and \( f^{\prime}(0)=1 \) then
\( \lim _{x \rightarrow 0} \frac{1}{x}\left[f(x)+f\left(\frac{x}{2}\right)+\ldots+f\left(\frac{x}{100}\right)\right] \)
equals
A . 1
B \cdot \( 1+\frac{1}{2}+\frac{1}{3}+\ldots+\frac{1}{100} \)
D. Does not exist
Subject: Chemistry
In a compound, \( C, H \) and \( N \) atoms are
present in ratio of 9: 1: 3.5 by weight.
Molecular weight of compound is 108 Molecular formula of compound is:
A \( \cdot C_{2} H_{6} N_{2} \)
в. \( C_{2} H_{6} N \)
c. \( C_{6} H_{8} N_{2} \)
D. \( C_{9} H_{12} N_{3} \)
Subject: Chemistry
In Haber's process \( 50.0 g \) of \( N_{2}(g) \) and
\( 10.0 g \) of \( H_{2}(g) \) are mixed to produced \( N H_{3}(g) . \) What are the number of moles
of \( \boldsymbol{N} \boldsymbol{H}_{3}(\boldsymbol{g}) \) formed?
A . 3.33
в. 2.36
c. 2.01
D. 5.36
Subject: Maths
In right triangle \( E D F \) is figure, the
length of \( \overline{D F} \) is \( 2 \mathrm{cm}, \) and the length of EF is \( 7 \mathrm{cm} \). Calculate the measure of
\( \angle E F D, \) to the nearest hundredth of a
degree. (Use \( \left.\sin 73.4^{0}=0.9583\right) \)
\( \mathbf{A} \cdot 15.95^{\circ} \)
в. \( 16.6^{\circ} \)
\( c \cdot 73.40^{\circ} \)
D. \( 90^{\circ} \)
E . 99.9
Subject: Biology
In one polynucleotide strand of a DNA molecule, the ratio of \( \boldsymbol{A}+\boldsymbol{T} / \boldsymbol{G}+\boldsymbol{C} \) is
0.3. What is the \( \boldsymbol{A}+\boldsymbol{G} / \boldsymbol{T}+\boldsymbol{C} \) ratio of
the entire DNA molecule?
A . 0.3
B. 0.6
c. 1.2
D.
Subject: Physics
A concave lens of refractive index \( \mu_{1} \) is placed in a medium of refractive index
\( \mu_{2} . \) A parallel beam of light strikes the surface of the lens on one side. Draw the
ray diagram for the refracted rays if
¡) \( \mu_{1}>\mu_{2} \)
ii) \( \mu_{1}<\mu_{2} \)
iii) \( \mu_{1}=\mu_{2} \)
Subject: Chemistry
The volume of \( \boldsymbol{H}_{2} \boldsymbol{S} \boldsymbol{O}_{4} \) acid \( (\boldsymbol{9} \boldsymbol{8} \% \) by
mass, \( d=1.80 \mathrm{g} / \mathrm{mL} \) ) required to prepare
1 litre of \( 0.1 M H_{2} S O_{4} \) solution is:
A \( .16 .65 \mathrm{mL} \)
B . \( 22.20 \mathrm{mL} \)
\( c .5 .55 \mathrm{mL} \)
D. \( 11.10 \mathrm{mL} \)
Subject: Maths
The Cartesian equation of the plane \( \overrightarrow{\boldsymbol{r}}=(1+\boldsymbol{\lambda}-\boldsymbol{\mu}) \hat{\boldsymbol{i}}+(\boldsymbol{2}-\boldsymbol{\lambda}) \hat{\boldsymbol{j}}+(\boldsymbol{3}- \)
\( 2 \lambda+2 \mu) \hat{k} \) is-
\( \mathbf{A} \cdot 2 x+y=5 \)
В . \( 2 x-y=5 \)
c. \( 2 x+z=5 \)
D. \( 2 x-z=5 \)
Subject: Maths
The projection of the line \( x+y=0 \)
\( z=0 \) on the plane \( x-y+z=1 \) is
\begin{tabular}{l} 
A \( \cdot \frac{3 x-1}{3}=\frac{3 y+1}{-3}=\frac{3 z-1}{-2} \) \\
\hline
\end{tabular}
B. \( \frac{4 x-1}{3}=\frac{2 y+1}{-3}=\frac{4 z+1}{-6} \)
\begin{tabular}{l} 
C. \( \frac{3 x-1}{-3}=\frac{3 y+1}{3}=\frac{3 z-1}{6} \) \\
\hline
\end{tabular}
D. \( \frac{4 x-1}{2}=\frac{2 y+1}{1}=\frac{4 z+1}{-2} \)
Subject: Biology
The typical floral formula of disc florets
is
\( \mathbf{A} \cdot K_{\text {pappus}} C_{5} A_{0} \underline{G}_{(2)} \)
B . \( K_{\text {рарриз}} C_{(5)} A_{(5)} \bar{G}_{(2)} \)
\( \mathbf{c} \cdot K_{5} C_{5} A_{(9)+1} \underline{G}_{(2)} \)
D. \( K_{0} C_{5} A_{5} G_{(2)} \)
Subject: Chemistry
The redox potential of \( \boldsymbol{F e}^{\mathbf{3}+} \mid \boldsymbol{F e}^{\mathbf{2}+} \)
electrode at \( \mathrm{pH}=4 \) is:
A. \( 0.8 \mathrm{v} \)
B. 0.5
c. \( 0.2 v \)
D. 0.1
Subject: Chemistry
If \( K_{a} \) for an acid, \( H A \) is \( 1 \times 10^{-6} \), then
\( K_{b} \) for \( A^{-} \) would be:
A \( \cdot 10^{-9} \)
B . \( 10^{-5} \)
\( c \cdot 10^{-8} \)
D. \( 10^{-3} \)
Subject: Physics
A car of mass \( 600 k g \) is moving with a
speed of \( 10 m s^{-1} \) while a scooter of
mass \( 80 k g \) is moving with a speed of
\( 50 m s^{-1} . \) Compare their momentum.
A .2: 3
B. 1: 2
c. 3: 1
D. 3: 2
Subject: Maths
The equation of line passing through (1,-2,3) and having \( \operatorname{drs}(2,3,1) \) is
\( ^{\text {A }} \cdot \frac{x-1}{2}=\frac{y+2}{3}=\frac{z-3}{1} \)
B. \( \frac{x+1}{2}=\frac{y+2}{3}=\frac{z-3}{1} \)
c. \( \frac{x-1}{2}=\frac{y-2}{3}=\frac{z-3}{1} \)
D. none of these
Subject: Physics
Q Type your question
custom-built capacitor. The magnitude
of charge on each plate for each separate voltage is recorded. The graph shows charge in micro-coulombs
plotted against potential difference. Use the graph to answer the following two questions. What is the approximate capacitance,
\( C, \) of this capacitor?
And what is the electric potential operating range during which this device properly acts like a capacitor?
A. \( C=60 \) micro-farads; Operating Range: \( 0-100 v \)
B. \( C=60 \) micro-farads; Operating Range: \( 0-40 v \)
c. \( C=2700 \) micro-farads; operating Range: \( 60-100 v \)
D. \( C=40 \) micro-farads; Operating Range: \( 0-40 v \)
E. \( C=0.017 \) micro-farads; operating Range: \( 0-40 \)
Subject: Maths
A man starts his job with a certain monthly salary and a fixed increment
every year. If his salary will be Rs. 11000
after 2 years and Rs. 14000 after 4 years of his service. What is his starting salary and what is the annual increment?
A. Starting salary is Rs. 7500 and increment is Rs. 2500
B. Starting salary is Rs.5000 and increment is Rs. 1800
C. Starting salary is Rs. 8000 and increment is Rs. 1500
D. Starting salary is Rs. 7000 and increment is Rs. 1300
Subject: Physics
The ends \( Q \) and \( R \) of two thin wires, \( P Q \) and \( R S, \) are soldered (joined) together Initially each of the wires has a length of
\( 1 \mathrm{m} \) at \( 10^{\circ} \mathrm{C} \). Now the end \( \mathrm{P} \) is
maintained at \( 10^{\circ} \mathrm{C} \), while the end \( \mathrm{S} \) is
heated and maintained at \( 400^{\circ} \mathrm{C} \). The
system is thermally insulated from its surroundings. If the thermal conductivity of wire \( \mathrm{PQ} \) is twice that of
the wire \( \mathrm{RS} \) and the coefficient of linear
thermal expansion of PQ is \( 1.2 \times \)
\( 10^{-5} K^{-1}, \) the change in length of the
wire PQ is?
\( \mathbf{A} \cdot 0.78 \mathrm{mm} \)
в. \( 0.90 \mathrm{mm} \)
c. \( 1.56 \mathrm{mm} \)
D. \( 2.34 \mathrm{mm} \)
Subject: Maths
The mean of the cubes of the first \( n \)
natural numbers is :
A \( \cdot \frac{n(n+1)^{2}}{4} \)
B \( \cdot n^{2} \)
c. \( \frac{n(n+1)(n+2)}{8} \)
D. \( \left(n^{2}+n+1\right) \)
Subject: Maths
Let \( 0(0,0), P(3,4), Q(6,0) \) be the vertices of the triangle OPQ. The point R inside the triangle OPQ is such that the triangles OPR,PQR, OQR are of equal area. The coordinates of \( \mathrm{R} \) are
\( ^{\mathrm{A}} \cdot\left(\frac{4}{3}, 3\right) \)
в. \( \left(3, \frac{2}{3}\right) \)
c. \( \left(3, \frac{4}{3}\right) \)
D \( \cdot\left(\frac{4}{3}, \frac{2}{3}\right) \)
Subject: Physics
The refractive index of glass is 1.520 for
red light and 1.525 for blue light. Let \( D_{1} \)
and \( D_{2} \) be angles of minimum deviation for red and blue
lights respectively in a prism of this glass. Then
A. \( D_{1}<D_{2} \)
В. \( D_{1}>D_{2} \)
\( \mathbf{c} \cdot D_{1}=D_{2} \)
D. \( D_{1} \) can be less than or greater than \( D_{2} \) depending upon the angle of prism
Subject: Physics
If energy( \( E \) ), velocity \( (V) \) and force \( (F) \) be taken as fundamental quantity, then what are the dimension of mass?
A \( . E V^{2} \)
B. \( E V^{-2} \)
\( \mathbf{c} \cdot F V^{-1} \)
D. \( F V^{-2} \)
Subject: Chemistry
Substance having maximum number of molecules is:
A \( \cdot 44.8 \mathrm{L} \) of \( \mathrm{H}_{2} \) at \( \mathrm{S.T.P.} \)
B. 2 g of \( H e \)
c. \( 16 \mathrm{g} \) of \( C H_{4} \)
D. 33 g of \( C O_{2} \)
Subject: Maths
The projection of \( \bar{a}=3 \hat{i}-\hat{j}+5 \hat{k} \) on \( \overline{\boldsymbol{b}}=\mathbf{2} \hat{\mathbf{i}}+\mathbf{3} \hat{\boldsymbol{j}}+\hat{\boldsymbol{k}} \) is
A \( \cdot 8 / \sqrt{(35)} \)
B . \( 8 / \sqrt{(39)} \)
c. \( 8 / \sqrt{(14)} \)
D. \( \sqrt{(14)} \)
Subject: Physics
Assertion
At some given instant \( I_{1} \) and \( I_{2} \) both are
\( \mathbf{2} \boldsymbol{A} \) each. Then \( \boldsymbol{I} \) at this instant should
be zero.
Reason
There is a phase difference of \( \pi \) between
\( I_{1} \) and \( I_{2} \) functions
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
The correct expression for Ampere's law
is :
A \( . \int B . d l=\Sigma i \)
в. \( \int B . d l=\frac{1}{\sum i} \)
c. \( \int B . d l=\mu_{0} \sum i \)
' - \( \int B . d l=\frac{\sum i}{\mu_{0}} \)
Subject: Physics
The amplitudes \( E_{0} \) and \( B_{0} \) of electric
and the magnetic component of an electromagnetic wave respectively are
related to the velocity \( c \) in vacuum as
A \( \cdot E_{0} B_{0}=\frac{1}{c} \)
B \( \cdot E_{0}=\frac{c}{B_{0}} \)
c. \( B_{0}=c E_{0} \)
D. \( E_{0}=c B_{0} \)
E \( . E_{0}=c^{3} B_{0} \)
Subject: Maths
\( f \sin \left(60^{\circ}+30^{\circ}\right)=\sin 60^{\circ} \cos 30^{\circ}+ \)
\( \sin 30^{\circ} \cos 60^{\circ} \) then what is the value of
\( \sin \left(60^{\circ}+30^{\circ}\right) .=? \)
Subject: Chemistry
Which of the following statements
is/are correct?
This question has multiple correct options
\( \mathbf{A} \cdot \) The common name of \( \left(H O O C-C H_{2}-C O O H\right) \) is
malonic acid
B. The common name of is succinic acid is butanedioic acid
C. The IUPAC name of \( \left(C H_{2}=C H-O C O C H_{3}\right) \) is vinyl
acetate
D. The IUPAC name of acrylonitrile is pror-2-enenitrile.
Subject: Physics
Assertion
Basic difference between an electric
line of force and magnetic lines of force is that former is discontinuous and the
latter is continuous or endless.
Reason
No electric lines of force exist inside a
charged body but magnetic lines do
exist inside a magnet.
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
Assertion
\( \overrightarrow{\boldsymbol{E}}=\boldsymbol{E}_{\boldsymbol{x}} \hat{\boldsymbol{i}}+\boldsymbol{E}_{\boldsymbol{y}} \hat{\boldsymbol{j}}+\boldsymbol{E}_{z} \hat{\boldsymbol{k}}, \vec{\nabla} \times \overrightarrow{\boldsymbol{E}}=\mathbf{0} \)
Reason
\( E_{x}, E_{y}, E_{z} \) is independent.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is
not the correct explanation for Assertion
C. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect
Subject: Maths
Let \( \boldsymbol{f}(\boldsymbol{x})=\cos \left[\boldsymbol{\pi}^{2}\right] \boldsymbol{x}+\cos \left[-\boldsymbol{\pi}^{2}\right] \boldsymbol{x} \)
where \( [x] \) is the greatest integer
function, then find \( f\left(\frac{\pi}{2}\right) \) and \( f(\pi) \)
Subject: Maths
Let \( X \) be the set of all citizens of India.
Elements \( x, y \) in \( X \) are said to be related if the difference of their age is 5 years.
Which one of the following is correct?
A. The relation is an equivalence relation on \( x \).
B. The relation is symmetric but neither reflexive nor transitive
c. The relation is reflexive but neither symmetric nor transitive
D. None of the above
Subject: Maths
\( \lim _{x \rightarrow \infty}\left(\frac{3 x^{2}+2 x+1}{x^{2}+x+2}\right)^{\frac{6 x+1}{3 x+2}} \) is equal to
\( A \cdot 3 \)
B. 9
\( c \)
D. none of these
Subject: Chemistry
Which of the following reactions is not
balanced?
\( \mathbf{A} \cdot 2 N a H C O_{3} \longrightarrow N a_{2} C O_{3}+H_{2} O+C O_{2} \)
B \( \cdot 2 C_{4} H_{10}+12 O_{2} \longrightarrow 8 C O_{2}+10 H_{2} O \)
\( \mathbf{c} \cdot 2 A l+6 H_{2} O \longrightarrow 2 A l(O H)_{3}+3 H_{2} \)
D. \( 4 N H_{3}+5 O_{2} \longrightarrow 4 N O+6 H_{2} O \)