AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Physics
A ray of light is incident on glass slab making an angle of incidence \( \sin ^{-1}\left(\frac{\sqrt{3}}{2}\right) . \) What will be the angle of
refraction in glass of refractive index
1.5?
\( \mathbf{A} \cdot 40^{\circ} 18 \)
В \( \cdot 24^{\circ} 49^{\prime} \)
c. \( 25^{\circ} \) о \( 7^{\text {। }} \)
\( \mathbf{D} \cdot 35^{\circ} 16^{\prime} \)
Subject: Maths
If \( \boldsymbol{\alpha}=\cos \left(\frac{\boldsymbol{8} \boldsymbol{\pi}}{\mathbf{1 1}}\right)+\boldsymbol{i} \sin \left(\frac{\boldsymbol{8} \boldsymbol{\pi}}{11}\right), \) then
\( \boldsymbol{R} e\left(\boldsymbol{\alpha}+\boldsymbol{\alpha}^{2}+\boldsymbol{\alpha}^{3}+\boldsymbol{\alpha}^{4}+\boldsymbol{\alpha}^{5}\right) \) is
A \( \cdot \frac{1}{2} \)
B. \( -\frac{1}{2} \)
\( c \cdot 0 \)
D. None of the above
Subject: Chemistry
The values of Planck's constant is
\( 6.63 \times 10^{-34} J s . \) The velocity of light is
\( 3.0 \times 10^{8} m s^{-1} . \) Which value is closest
to the wavelength in nanometres of a quantum of light which frequency of
\( 8 \times 10^{15} s^{-1} ? \)
\( \mathbf{A} \cdot 5 \times 10^{-18} \)
B. \( 4 \times 10^{1} \)
\( c \cdot 3 \times 10^{7} \)
D. \( 2 \times 10^{-25} \)
Subject: Physics
Which of the following options is the
only correct representation of a process
in which \( \Delta U=\Delta Q-P \Delta V ? \)
A. \( (I I I)(i i i)(P) \)
B. \( (I I)(i i i)(P) \)
c. \( (I I)(i i i)(S) \)
D. \( (I I)((i v)(R) \)
Subject: Chemistry
At \( 300 K \), two pure liquids \( A \) and \( B \)
have vapour pressures \( 150 \mathrm{mm} \mathrm{Hg} \)
and 100 mm \( H g \) respectively. In an equimolar liquid mixture of \( \boldsymbol{A} \) and \( \boldsymbol{B} \) the mole fraction of \( B \) in the vapour
mixture at this temperature is:
A . 0.6
B. 0.5
c. 0.8
D. 0.4
Subject: Maths
The coordinates of a point in 3 -D space is \( (3,1,2) . \) Then the position vector of the point is:
A \( .3 \hat{i}+3 \hat{j}+3 \hat{k} \)
B. \( 3 \hat{i}+2 \hat{j}+\hat{k} \)
c. \( 3 \hat{i}+\hat{j}+2 \hat{k} \)
D. \( \hat{i}+2 \hat{j}+3 \hat{k} \)
Subject: Chemistry
Calculate the mass in mole of \( C O_{2} \) that
will dissolve in enough water to form
\( 900 m L \) of solution at \( 20^{\circ} \mathrm{C} \) if the
partial pressure of \( \boldsymbol{C O}_{2} \) is 1 atm. \( \boldsymbol{K}_{\boldsymbol{H}} \) for \( C O_{2} \) is \( 2.3 \times 10^{-2} \) mol \( / \) litre
\( a t m \)
A . 0.0401 mole
B. 0.0301 mole
c. 0.0217 mole
D. 0.0207 mole
Subject: Chemistry
The rate of the first order reaction is
\( 0.69 \times 10^{-2} \) mol \( L^{-1} \) min \( ^{-1} \) and the
initial concentration is \( 0.2 m o l L^{-1} \). The
half life period is:
A . \( 1205 s \)
в. 330
c. \( 600 s \)
D. \( 1 s \)
Subject: Chemistry
A sample of \( C a C O_{3} \) has \( C a-40 \%, C= \) \( 12 \% \) and \( 0=48 \% \). If the law of constant
proportions is true, then the mass of Ca
in 5 g of \( C a C O_{3} \) from another source
will be:
A. 2.0
B. \( 0.2 \mathrm{g} \)
c. \( 0.02 g \)
D. 20.0
Subject: Maths
If \( \operatorname{cosec} \theta=2 x \) and \( y \cot \theta=2, \) then the
value of \( 4\left(x^{2}-\frac{1}{y^{2}}\right) \) is :
\( A \)
B. \( \frac{1}{2} \)
\( c \cdot \frac{1}{3} \)
D.
Subject: Physics
A body of mass \( m \) slides down a smooth inclined plane having an inclination of
\( 45^{\circ} \) with the horizontal. It takes 4 sec to
reach the bottom. If the body is placed on a similar plane having coefficient of friction \( 0.5 . \) What is the time taken for it
to reach bottom?
A \( .4 \sqrt{2} s e c \)
B. 4 sec
\( \mathrm{c} \cdot 3 \sqrt{2} \mathrm{sec} \)
D. \( 2 s e c \)
Subject: Maths
The shortest distance between the lines \( \frac{\boldsymbol{x}-\mathbf{5}}{\mathbf{4}}=\frac{\boldsymbol{y}-\mathbf{7}}{-\mathbf{5}}=\frac{\boldsymbol{z}+\mathbf{3}}{-\mathbf{5}} \) and \( \frac{\boldsymbol{x}-\mathbf{8}}{\mathbf{4}}= \)
\( \frac{y-7}{-5}=\frac{z-5}{-5} \) is
A . 45
B . 46
c. 47
D. 48
Subject: Physics
A step-down transformer converts
transmission line voltage from \( 11000 V \)
to \( 220 V \) The primary of the transformer has 6000 turns and the efficiency of the transformer is \( 60 \% \). If the output power
is \( 9 k W, \) then the input power will be
\( \mathbf{A} \cdot 11 k W \)
в. \( 12 k W \)
c. \( 14 k W \)
D. \( 15 k W \)
Subject: Physics
A concave shaving mirror has a radius of curvature of \( 35.0 \mathrm{cm} . \) It is positioned so that the (upright) image of a mans face is 2.50 times the size of the face.
How far is the mirror from the face?
A. \( 5.25 \mathrm{cm} \)
B. 21.0 \( \mathrm{cm} \)
\( c \cdot 10.5 \mathrm{cm} \)
D. \( 42 \mathrm{cm} \)
Subject: Maths
Solve:
\( \frac{\boldsymbol{d} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}}=\frac{(\boldsymbol{x}-\boldsymbol{y})+\boldsymbol{3}}{\boldsymbol{2}(\boldsymbol{x}-\boldsymbol{y})+\boldsymbol{5}} \)
Subject: Chemistry
The correct statement(s) about the
oxoacids, \( H C l O_{4} \) and \( H C l O, \) is (are):
This question has multiple correct options
A. the central atom in both \( H C l O_{4} \) and \( H C l O \) is \( s p^{3} \)
hybridized
B. the conjugate base of \( H C l O_{4} \) is weaker base than \( H_{2} O \)
C \( \cdot H C l O_{4} \) is formed in the reaction between \( C l_{2} \) and \( H_{2} O \)
D. \( H C l O_{4} \) is more acidic than \( H C l O \) because of the resonance stabilization of its anion
Subject: Chemistry
Choose the correct answer form the
alternatives given

Match column I with column II and
mark the appropriate choice.
\( \begin{array}{llll} & \text { Column I } & & \text { Column II } \\ \text { (A) } & \text { Li } & \text { (i) } & M_{2} O_{2} \\ \text { (B) } & \text { Na } & \text { (ii) } & M O_{2} \\ \text { (C) } & \text { Rb } & \text { (iii) } & M_{2} O\end{array} \)
\( A \)
\( (A) \rightarrow(i),(B) \rightarrow(i i),(C) \rightarrow(i i i) \)
в. \( (A) \rightarrow(i i i),(B) \rightarrow(i i),(C) \rightarrow(i) \)
\( c \)
\( (A) \rightarrow(i i i),(B) \rightarrow(i),(C) \rightarrow(i i) \)
\( D \)
\( (A) \rightarrow(i i),(B) \rightarrow(i i i),(C) \rightarrow(i) \)
Subject: Chemistry
Which of the following reactions does not occur in stratosphere?
A. \( O_{2}+U V \rightarrow O+O \)
в. \( O_{2}+O \rightarrow O_{3} \)
c. \( C l+O_{3} \rightarrow O_{2}+C l O \)
D. \( S O_{3}+H_{2} O \rightarrow H_{2} S O_{4} \)
Subject: Maths
Q Type your question
an apartment are groupea as roılows:
The mean length of the plants is 33.43
years using direct method. Find y in the
table
\( \begin{array}{ll}\text { Age(years) } & \text { Number of people } \\ 0-10 & 10 \\ 10-20 & 15 \\ 20-30 & 26 \\ 30-40 & \mathrm{Y} \\ 40-50 & 23 \\ 50-60 & 16 \\ 60-70 & 3 \\ 70-80 & 1\end{array} \)
A . 23
B . 28
c. 15
\( D \)
Subject: Chemistry
Mass of the one atom of the element \( X \)
is \( 1.66 \times 10^{-26} \) g. Number of atoms in 1
g of the element is:
A \( \cdot 1.66 \times 10^{-26} \)
B . \( 1.66 \times 10^{25} \)
c. \( 1.66 \times 10^{-24} x N o \)
D. \( 6.024 \times 10^{25} \)
Subject: Physics
When the values of inductance and
capacitance in an \( L-C \) circuit are
\( 0.5 H \) and \( 8 \mu F \) respectively then
current in the circuit is maximum. The
angular frequency of alternating e.m.f. applied in the circuit will be
A \( .5 \times 10^{3} \) Radian/sec
B. 50 Radian/sec
c. \( 5 \times 10^{2} \) Radian/sec
D. 5 Radian/sec
Subject: Physics
The flux linked with a coil of any instant
\( t \) is given by \( \phi=t^{2}-5 t+25 . \) The
induced emf \( \operatorname{at} t=4 s \) is?
A \( .2 v \)
B. \( -3 v \)
c. \( 4 v \)
D. - \( 4 v \)
Subject: Chemistry
The e.m.f. of the cell \begin{tabular}{l|c||c|c}
\( \boldsymbol{P t} \boldsymbol{H}_{2} \) & \( \boldsymbol{H O C N} \) & \( \boldsymbol{A} \boldsymbol{g}^{+} \) \\
\( \boldsymbol{1} \boldsymbol{a} \boldsymbol{t m} \) & \( \boldsymbol{1} . \boldsymbol{3} \times \mathbf{1 0}^{-\boldsymbol{3}} \boldsymbol{M} \) & \( \boldsymbol{0 . 8} \boldsymbol{M} \)
\end{tabular} \mid \( \boldsymbol{A} \boldsymbol{g}(s) \) is
\( 0.982 \mathrm{V} . \) The \( \mathrm{K}_{a} \) for HOCN is :
\( \boldsymbol{A} \boldsymbol{g}^{+}+\boldsymbol{e} \rightarrow \boldsymbol{A} \boldsymbol{g}(\boldsymbol{s}) ; \boldsymbol{E}^{o}=\mathbf{0 . 8 0} \boldsymbol{V} \)
A. \( 3.33 \times 10^{-4} \)
B . \( 2.22 \times 10^{-4} \)
c. \( 4.44 \times 10^{-4} \)
D. \( 1.6 \times 10^{-3} \)
Subject: Maths
In the following, the coordinates of the three vertices of a rectangle \( A B C D \) are given. By plotting the given points; find, the coordinates of the fourth vertex:
\( A(-4,-6), C(6,0) \) and \( D(-4,0) \)
Claim: The co-ordinates of the fourth
vertex are \( (x,-6) \)
Find \( \boldsymbol{x} \)
Subject: Physics
A body of mass \( 2 k g \) slides down a plane
inclined at an angle of \( 30^{\circ} \) with horizontal. The co-efficient of friction between the body and the plane is \( \sqrt{\frac{3}{2}} \) What force must be applied on the body so that it moves down without
acceleration?
A. \( 11 N \)
в. \( 14.7 \sqrt{2} N \)
c. zero
D. None of these
Subject: Physics
In Youngs double slit experiment, the
slits are \( 2 m m \) apart and are
¡IIluminated with a mixture of two
wavelengths \( \lambda=12000 A^{\circ} \) and \( \lambda= \)
\( 10000 A^{\circ} . \) At what minimum distance
from the common central bright fringe
on a screen \( 2 m \) from the slits will a
bright fringe from one interference
coincide with a bright fringe from the other?
A. \( 3.2 \mathrm{mm} \)
B. \( 6.0 \mathrm{mm} \)
c. \( 7.2 \mathrm{mm} \)
D. \( 9.2 \mathrm{mm} \)
Subject: Chemistry
The correct order of decreasing polarity
¡s:
\( \mathbf{A} \cdot H F>S O_{2}>H_{2} O>N H_{3} \)
B \( \cdot H F>H_{2} O>S O_{2}>N H_{3} \)
\( \mathbf{C} \cdot H F>N H_{3}>S O_{2}>H_{2} O>H F \)
D. none of the above
Subject: Maths
\( A=(2,3,0) \) and \( B=(2,1,2) \) are two
points. If the points \( P, Q \) are on the line
\( A B \) such that \( A P=P Q=Q B, \) then
\( \boldsymbol{P Q}= \)
\( A \cdot 2 \sqrt{2} \)
B. \( 6 \sqrt{2} \)
\( c \cdot \sqrt{\frac{8}{9}} \)
D. \( \sqrt{2} \)
Subject: Physics
The displacement \( (x) \) of a particle
starting from rest is given by \( \boldsymbol{x}=\mathbf{6} \boldsymbol{t}^{2}- \)
\( t^{3} . \) The time at which the particle will
attain zero velocity again is
A . 2
B. 4
\( c .6 \)
D.
Subject: Chemistry
The lowest value of paramagnetism is shown by?
\( \mathbf{A} \cdot\left[\operatorname{Co(CN)}_{6}\right]^{3} \)
B . \( \left[F e(C N)_{6}\right]^{3-} \)
c. \( \left[C r(C N)_{6}\right]^{3-} \)
D. \( \left[M n(C N)_{6}\right]^{3} \)
Subject: Physics
A tunnel is dug along a diameter of earth. The force on a particle of mass \( \boldsymbol{m} \)
and distance \( x \) from the centre in this
tunnel will be :
A \( \cdot \frac{G M_{e} m}{R^{3} x} \)
в. \( \frac{G M_{e} m R^{3}}{x} \)
c. \( \frac{G M_{e} m x}{R^{2}} \)
D. \( \frac{G M_{e} m x}{R^{3}} \)
Subject: Maths
\( \boldsymbol{S}=\boldsymbol{3}^{10}+\boldsymbol{3}^{9}+\frac{3^{9}}{4}+\frac{3^{7}}{2}+\frac{5.3^{6}}{16}+\frac{3^{2}}{16}+ \)
\( \frac{7.3^{4}}{64}+\ldots \ldots \ldots \) upto infinite terms, then
\( \left(\frac{25}{36}\right) S \) equal to
A \( \cdot 6^{\text {? }} \)
B. \( 3^{10} \)
\( c \cdot 3^{1} \)
D. \( 2.3^{10} \)
Subject: Chemistry
For the reaction between \( M n O_{4}^{-} \) and
\( C_{2} O_{4}^{-} \) in basic solution, the unbalanced
equation is \( M n O_{4}^{-}+C_{2} O_{4}^{2-} \longrightarrow M n O_{2}(s)+ \)
\( \boldsymbol{C O}_{3}^{2-} \)
In a balanced equation, the number of
\( O H^{-} \) ions is :
\( A \cdot 0 \)
B. 4 on the right
c. 4 on the left
D. 2 on the left
Subject: Maths
Find a vector in which two of the three
direction angles are \( \boldsymbol{\alpha}=\mathbf{7} \mathbf{5}^{\boldsymbol{o}} \) and \( \boldsymbol{\beta}= \)
\( \mathbf{5 5}^{\circ} \)
\( \mathbf{A} \cdot v=\cos 55^{o} \hat{i}+\cos 75^{\circ} \hat{j}+\cos 39^{o} \hat{k} \)
B . \( v=\cos 75^{\circ} \hat{i}+\cos 55^{\circ} \hat{j}+\cos 39^{\circ} \hat{k} \)
c. \( v=\cos 55^{\circ} \hat{\imath}+\cos 39^{\circ} \hat{\jmath}+\cos 75^{\circ} \hat{k} \)
D . \( v=\cos 75^{\circ} \hat{i}+\cos 39^{\circ} \hat{j}+\cos 55^{\circ} \hat{k} \)
Subject: Chemistry
Assertion
The extent to which a dissolved
substance can act as an acid or base
depends largely on the solvent.
Reason
The solute only shows acidicproperties if its proton donating ability exceed that of the solvent
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: Maths
\( \int \frac{x}{1+\cos x} d x= \)
\( \mathbf{A} \cdot x \tan \frac{x}{2}-2 \log |\sec x / 2|+c \)
B. \( -x \tan x / 2-\frac{1}{2} \log |\sec x / 2|+c \)
c. \( _{x \tan x / 2+\frac{1}{2} \log |\sec x / 2|+c} \)
D. \( x \cot x / 2-\frac{1}{2} \log |\csc x / 2|+c \)
Subject: Physics
A material has Poisson's ratio \( 0.2 . \) If a
uniform rod of its suffers longitudinal
strain \( 4.0 \times 10^{-3}, \) calculate the
percentage change in its volume.
A . \( 0.15 \% \)
B . \( 0.02 \% \)
c. \( 0.24 \% \)
D. 0.48\%
Subject: Physics
Let \( n_{p} \) and \( n_{e} \) be the number of holes
and conduction electrons in an
extrinsic semiconductor. Then
A \( \cdot n_{p}>n_{e} \)
в. \( n_{p}=n_{e} \)
c. \( n_{p}<n_{e} \)
D \( \cdot n_{p} \neq n_{e} \)
Subject: Maths
If \( \boldsymbol{A}=\{\mathbf{1}, \mathbf{2}, \mathbf{3}\}, \boldsymbol{B}=\{\mathbf{1}, \mathbf{4}, \mathbf{6}, \mathbf{9}\} \) and \( \mathbf{R} \) is
a relation from \( A \) to \( B \) defined by \( ' x \) is
greater than \( y \) '. The range of R is
A \( \cdot\{1,4,6,9\} \)
в. \{4,6,9\}
c. \{1\}
D. \{4,6\}
Subject: Physics
Infinite long wire having linear charge density \( 0.2 \mathrm{C} / \mathrm{m} \). find electric intensity at a distance \( 2 \mathrm{m} \) from wire?
A \( \cdot 1.8 \times 10^{9} \mathrm{V} / \mathrm{m} \)
B. \( 0.9 \times 10^{9} \mathrm{V} / \mathrm{m} \)
c. \( 2.7 \times 10^{9} \vee / \) m
D. 0.3x10^ \( v / m \)
Subject: Physics
An automobile, travelling at \( 40 \mathrm{km} / \mathrm{h} \) Can be stopped at a distance of \( 40 \mathrm{m} \) by applying brakes. If the same automobile is travelling at \( 120 \mathrm{km} / \mathrm{h} \), the minimum stopping distance in meter, is(assume no skidding)
\( \mathbf{A} \cdot 270 \mathrm{m} \)
B. \( 160 \mathrm{m} \)
c. \( 100 \mathrm{m} \)
D. 360m
Subject: Chemistry
The diagram below shows a part of the
skelecton of the periodic table in which
elements are indicated by letters which
are not their usual symbols.

Which one of the following statement is
correct?
A. The greatest ionic character of compounds formed by reaction of pairs of the listed elements would be
exhibited by the compounds with the formula \( M_{2} \)
B. The \( J^{2+} \) ion is colored and has an electronic
configuration of \( 1 s^{2}, 2 s^{2}, 2 p^{6}, 3 s^{2}, 3 p^{6}, 3 d^{7} \)
C. Element \( R \) is a gas at room temperature
D. Element T is an inert gas with an electronic configuration \( 1 s^{2}, 2 s^{2}, 2 p^{6}, 3 s^{2}, 3 p^{6}, 3 d^{10}, 4 s^{2}, 4 p^{6} \)
Subject: Physics
A beam of light consisting of red, green and blue colors is incident on a rightangled prism. The refractive indices of the material of the prism for the above red, green, and blue wavelengths are \( 1.39,1.44, \) and \( 1.47, \) respectively. The prism will
A. separate part of the red color from the green and blue color
B. separate part of the blue color from the red and green color
c. separate all the three colors from one another
D. not separate even partially any color from the other two colors
Subject: Physics
Calculate the neutron separation energy from the following data. \( \boldsymbol{m}\left(_{20}^{40} \boldsymbol{C a}\right)=\mathbf{3 9 . 9 6 2 5 9 1} \boldsymbol{u} \)
\( \boldsymbol{m}\left(_{20}^{41} \boldsymbol{C a}\right)=\mathbf{4 0 . 9 6 2 2 7 8} \boldsymbol{u} \)
\( \boldsymbol{m}_{n}=\mathbf{1 . 0 0 8 6 5} \)
\( \mathbf{1} \boldsymbol{u}=\mathbf{9 3 1 . 5} \boldsymbol{M} e \boldsymbol{V} / \boldsymbol{C}^{2} \)
\( \mathbf{A} \cdot 7.57 M e V \)
В. \( 8.36 \mathrm{MeV} \)
c. 9.12 MeV
D. 9.56 MeV
Subject: Maths
If one root of \( x^{2}-x-k=0 \) is square of
the other, then \( k= \)
A \( .2 \pm \sqrt{5} \)
B . \( 2 \pm \sqrt{3} \)
\( c \cdot 3 \pm \sqrt{2} \)
D. \( 5 \pm \sqrt{2} \)
Subject: Physics
A boy throws a ball of mass \( 0.5 \mathrm{kg} \) upwards with an initial speed of \( 14 \mathrm{m} / \mathrm{s} \) The ball reaches a maximum height of
8m. The amount of energy dissipated by air drag acting on the ball during the ascent is
A . 4.9
B. 9.8
c. 0 J
D. 13.8 J
Subject: Chemistry
The volume of gases evolved at \( S T P \) by
passing \( 0.1 A \) of current for \( 965 g \) through an aqueous solution of
potassium acetate:
A . \( 22.4 m L \)
в. \( 11.2 m L \)
\( c .89 .6 m L \)
D. \( 44.8 \mathrm{mL} \)
Subject: Maths
If a polynomial \( f(x)=4 x^{4}-a x^{3}+ \)
\( b x^{2}-c x+5,(a, b, c \in R) \) has four
positive real zeros \( r_{1}, r_{2}, r_{3}, r_{4} \) such that \( \frac{r_{1}}{2}+\frac{r_{2}}{4}+\frac{r_{3}}{5}+\frac{r_{4}}{8}=1, \) then value of \( a \)
is
A . 20
B. 21
c. 19
D. 22
Subject: Chemistry
The significance of leaching in the extraction of aluminium is:
A . it helps to remove the impurities like \( \operatorname{Si} \mathrm{O}_{2}, \mathrm{Fe}_{2} \mathrm{O}_{3} \), etco from the bauxite ore
B. it converts the ore into oxide
c. it reduces melting point of the ore
D. it eliminates water from bauxite
Subject: Physics
What should a piano tuner do to correct the sound of a string that is flat, that is, it plays at a lower pitch than it should?
A. Tighten the string to make the fundamental frequency higher
B. Tighten the string to make the fundamental frequency lower
c. Loosen the string to make the fundamental frequency higher
D. Loosen the string to make the fundamental frequency lower
E. Find a harmonic closer to the desired pitch
Subject: Physics
Equal masses of \( \mathrm{N}_{2} \) and \( \mathrm{O}_{2} \) gases are filled in vessels \( A \) and \( B \). The volume of
vessel B is double of A. The ratio of
pressure in vessel \( A \) and \( B \) will be
A . 16: 7
B. 16: 14
c. 32: 7
D. 32 : 28
Subject: Chemistry
A solution containing 0.2563 g of naphthalene (molecular mass = 128) in \( 50 \mathrm{g} \) of carbon tetrachloride yields a boiling point elevation of \( 0.201^{\circ} \mathrm{C} \) while a solution of 0.6216 g of an unknown solute in the same mass of the solvent
gives a boiling point elevation of
\( 0.647^{\circ} \mathrm{C} . \) Find the molecular mass of
the unknown solute.
Subject: Chemistry
The best reagent for converting, 2 phenylpropanamide into 1 phenylethanamine is:
A \( \cdot \operatorname{excess} H_{2} / P t \)
в. \( N a O H / B r_{2} \)
c. \( N a B H_{4} / \) methanol
D. \( L i A l H_{4} / \) ether
Subject: Maths
\( \left\{\mathbf{x} \in \mathbb{R}: \cos 2 x+2 \cos ^{2} x-2=0\right\}= \)
A \( \cdot\left\{2 n \pi+\frac{\pi}{3}, n \in Z\right\} \)
в \( \cdot\left\{n \pi \pm \frac{\pi}{6}, n \in Z\right\} \)
с \( \cdot\left\{n \pi+\frac{\pi}{3}, n \in Z\right\} \)
D \( \cdot\left\{2 n \pi-\frac{\pi}{3}, n \in Z\right\} \)
Subject: Biology
Eye colour in fruitfly is a sex linked trait and the cross of white eyed female with red eyed male gives red eyed females and white eyed males. Rarely this cross may give all white eyed females and red eyed males. This was found to be due to non-disjunction of
A. Two Y chromosomes in female fly
B. Two X chromosomes in female fly
c. Four Y chromosomes in male fly
D. Four \( x \) chromosomes in male fly
Subject: Physics
A block of wood mass \( 5 k g \) is placed on a
plane making an angle \( 30^{\circ} \) with the horizontal. If the coefficient of friction
between the surface of contact of the
body and the plane is \( 0.5 . \) What force is required to keep the body sliding down with uniform velocity?
A. \( 1.6 N \)
B. \( 4.8 N \)
\( c \cdot 6.4 N \)
D. \( 3.35 N \)
Subject: Maths
Find distance of point \( \boldsymbol{A}(2,3) \) measured
parallel to the line \( x-y=5 \) from the
line \( 2 x+y+6=0 \)
\( ^{\mathrm{A}} \cdot \frac{13 \sqrt{2}}{3} \) units
B. \( \frac{13}{3} \) units
\( ^{\mathrm{C}} \cdot \frac{13 \sqrt{2}}{6} \) units
D. None of these
Subject: Maths
How many of the following letters have rotational symmetry of order more than
1?
\( \mathrm{R}, \mathrm{B}, \mathrm{F}, \mathrm{H}, \mathrm{O}, \mathrm{P}, \mathrm{S}, \mathrm{W}, \mathrm{X}, \mathrm{Z}, \mathrm{N} \)
A .4
B. 9
\( c .5 \)
\( D \)
Subject: Maths
The domain of \( \boldsymbol{f}(\boldsymbol{x})= \)
\( \sqrt{x-2-2 \sqrt{x-3}}- \)
\( \sqrt{x-2+2 \sqrt{x-3}}, \) is
A \( .[3,5] \)
в. (3,5)
\( c \cdot[5, \infty) \)
\( D \cdot[3, \infty) \)
Subject: Maths
The value of the integral \( \int_{-\pi / 4}^{\pi / 4} \frac{d x}{a^{2} \cos ^{2} x+b^{2} \sin ^{2} x} \)
This question has multiple correct options
A \( \cdot \frac{2}{a b} \tan ^{-1} \frac{b}{a}(a>0, b>0) \)
B \( \cdot \frac{2}{a b} \tan ^{-1} \frac{b}{a}(a<0, b<0) \)
C \( \cdot \frac{\pi}{2}(a=1, b=1) \)
D. \( \frac{2}{a b} \tan ^{-1} \frac{a}{b}+\frac{1}{a b} \)
Subject: Physics
The unit of inductance is equivalent to
A. \( \frac{\text { volt } \times \text { ampere }}{\text { second }} \)
в. \( \frac{\text { ampere }}{\text {volt } \times \text { second }} \)
c. \( \frac{v o l t}{\text { Ampere } \times \text { second }} \)
D. \( \frac{\text {volt } \times \text { second }}{\text { ampere }} \)
Subject: Chemistry
Which of the following statement is incorrect about the reaction?
A. The degree of decomposition is \( N_{2} O_{5}, \alpha=1-e^{-K_{1} \cdot t} \)
B. The forward reaction is endothermic
C. The forward reaction is exothermic
D. The half-life of reaction is \( \frac{l n 2}{K_{1}} \)
Subject: Physics
A straight segment \( O C \) (of length \( L \) ) of
a circuit carrying a current \( I \) is placed along the \( x \) -axis. Two infinitely long straight wires \( A \) and \( B \), each extending
from \( z=-\infty \) to \( +\infty, \) are fixed at \( y= \)
\( -a \) and \( y=+a \) respectively, as shown
in the figure. If the wires \( A \) and \( B \) each
carry a current \( I \) into the plane of the
paper, obtain the expression for the force acting ont he segment \( O C . \) What
will be the force on \( O C \) if the current in
the wire \( B \) is reversed?
Subject: Chemistry
Which of the following statement is
correct?
A \( \cdot D_{2} O, \) is more viscous than \( H_{2} O \)
B. \( D_{2} O, \) is less viscous than \( H_{2} O \)
\( \mathrm{C} \cdot D_{2} \mathrm{O}, \) is as viscous as \( \mathrm{H}_{2} \mathrm{O} \)
D. Viscosity of heavy water depends on temperature
Subject: Maths
If \( \lim _{x \rightarrow 0} \frac{x^{a} \sin ^{b} x}{\sin x^{c}} \) where \( a, b, c \epsilon R-\{0\} \)
exists and has non-zero value. Then
A \( \cdot a+c=b \)
B . \( a+b=c \)
\( \mathbf{c} \cdot a=b+c \)
D. \( a+b+c=0 \)
Subject: Chemistry
In aqueous solution, the following mixture acts as buffer:
A. \( H N O_{3}+K N O_{3} \)
в. \( H_{2} S O_{4}+K_{2} S O_{4} \)
c. \( N H_{4} O H+N H_{4} C l \)
D. \( C H_{3} C O O H+N a C l \)
Subject: Physics
The \( x \) -t plot shown in the figure below
describes the motion of the particle,
along \( x \) -axis, between two positions \( A \)
and B. The particle passes through two
intermediate points \( P_{1} \) and \( P_{2} \) as shown
in the figure.
A. The instantaneous velocity is positive as \( P_{1} \) and
negative at \( P_{2} \)
B. The instantaneous velocity is negative at both \( P_{1} \) and
\( P_{2} \)
C. The instantaneous velocity is negative at \( P_{1} \) and
positive at \( P_{2} \)
D. The instantaneous velocity is positive at both \( P_{1} \) and
\( P_{2} \)
E. The instantaneous velocity is always positive
Subject: Maths
The two sides of a right-angled triangle are \( \boldsymbol{x}, \boldsymbol{x}+\mathbf{1} \) and hypotenuse, the longest
side is \( \sqrt{1} 3 . \) Find the area of the
triangle.
A \( \cdot 1 \mathrm{m}^{2} \)
B. \( 2 \mathrm{m}^{2} \)
\( c \cdot 3 m^{2} \)
D. \( 4 \mathrm{m}^{2} \)