AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Maths
What fraction lies exactly halfway between \( \frac{2}{3} \) and \( \frac{3}{4} ? \)
A \( \cdot \frac{3}{5} \)
в. \( \frac{5}{6} \)
c. \( \frac{7}{12} \)
D. \( \frac{9}{16} \)
E \( \frac{17}{24} \)
Subject: Chemistry
\( \boldsymbol{C}_{6} \boldsymbol{H}_{5} \boldsymbol{C} \boldsymbol{H}_{3}-\frac{C r \boldsymbol{O}_{2} C l_{2}}{\longrightarrow} \boldsymbol{Z} \)
In the given sequence, \( Z \) is:
A. Benzaldehyde
B. Toluic acid
c. Phenul acetic acid
D. Benzoic acid
Subject: Maths
Area bounded by \( y=2 x-x^{2} \&(x- \)
1) \( ^{2}+y^{2}=1 \) in first quadrant, is:
A \( \cdot \frac{\pi}{2}-\frac{4}{3} \)
B \( \cdot \frac{\pi}{2}-\frac{2}{3} \)
c. \( \frac{\pi}{2}+\frac{4}{3} \)
D. \( \frac{\pi}{2}+\frac{2}{3} \)
Subject: Maths
In a three-dimensional coordinate
system, P, Q and R are images of a point \( \mathbf{A}(\boldsymbol{a}, \boldsymbol{b}, \boldsymbol{c}) \) in the \( \boldsymbol{x}-\boldsymbol{y}, \boldsymbol{y}-\boldsymbol{z} \) and \( \boldsymbol{z}-\boldsymbol{x} \)
planes, respectively. If G is the centroid of triangle PQR, then area of triangle AOG is (O is the origin)-
A .
B . \( a^{2}+b^{2}+c^{2} \)
C \( \cdot \frac{2}{3}\left(a^{2}+b^{2}+c^{2}\right) \)
D. None of these.
Subject: Maths
In a school, students thought of planting trees in and around the school to reduce air pollution. It was decided that the number of trees, that each
section of each class will plant, will be the same as the class, in which they are
studying, e.g., a section of class I will plant 1 tree, a section of class II will
plant 2 trees and so on till Class XII.
There are three sections in each class.
How many trees will be planted by the
students
Subject: Maths
Find the curve for which the sum of the
lengths of the tangent and subtangent at any of its point is proportional to the product of the coordinates of the point of tangency, the proportionality factor is equal to k.
A \( \cdot y=\frac{1}{k} \ln \left|c\left(k^{2} x^{2}-1\right)\right| \)
B. \( y=\frac{1}{k} \ln \mid c\left(k x^{2}-1\right) \)
c. \( y=\frac{1}{k} \ln \mid c\left(k x^{2}+1\right) \)
D. \( y=\frac{1}{k} \ln \mid c\left(k^{2} x^{2}+1\right) \)
Subject: Maths
If \( \left[\mathbf{3} \boldsymbol{x}^{2}+\mathbf{1 0 x y}+\mathbf{5 y}^{2}\right]=\left[\begin{array}{ll}\boldsymbol{x} & \boldsymbol{y}\end{array}\right] \boldsymbol{A}\left[\begin{array}{l}\boldsymbol{x} \\ \boldsymbol{y}\end{array}\right] \)
and \( A \) is a symmetric matrix then \( \mathbf{A}= \)
\( \mathbf{A} \cdot\left[\begin{array}{ll}3 & 10 \\ 10 & 5\end{array}\right] \)
B. \( \left[\begin{array}{ll}10 & 3 \\ 5 & 10\end{array}\right] \)
\( \mathbf{c} \cdot\left[\begin{array}{cc}+3 & -5 \\ -5 & +5\end{array}\right] \)
D. \( \left[\begin{array}{ll}3 & 5 \\ 5 & 5\end{array}\right] \)
Subject: Chemistry
When acetone and chloroform are
mixed together, hydrogen bonds are formed between them. Which of the
following statements is correct about the solution made by mixing acetone and chloroform ?
A. on mixing acetone and chloroform will form an ideal solution
B. On mixing acetone and chloroform positive deviation is shown since the vapour pressure increases
c. on mixing acetone and chloroform negative deviation is shown since there is decrease in vapour pressure
D. At a specific composition, acetone and chloroform will form minimum boiling azeotrope
Subject: Physics
Calculate the velocity of an electron
having wavelength of \( 0.15 n m . \) Mass of an electron is: \( 9.109 \times 10^{-28} g \)
\( \left(h=6.626 \times 10^{-27} e r g-s\right) \)
A \( \cdot 2.062 \times 10^{-8} \mathrm{cms}^{-1} \)
B. \( 2.062 \times 10^{15} \mathrm{cms}^{-1} \)
c. \( 2.062 \times 10^{10} \mathrm{cms}^{-1} \)
D. \( 4.84 \times 10^{8} \mathrm{cms}^{-1} \)
Subject: Physics
A particle oscillates simple harmonically with a period of 16 s. Two second after crossing the equilibrium position its velocity becomes \( 1 \mathrm{m} / \mathrm{s} \). The amplitude is
A \( \cdot \frac{\pi}{4} \mathrm{m} \)
B. \( \frac{8 \sqrt{2}}{\pi} \mathrm{m} \)
c. \( \frac{8}{\pi} \mathrm{m} \)
D. \( \frac{4 \sqrt{2}}{\pi} \mathrm{m} \)
Subject: Chemistry
Anhydrous \( A l C l_{3} \) is covalent however
when it is dissolved in water hydrated ionic species are formed. This transformation is owing to:
A. the trivalent state of Al
B. the large hydration energy of \( A l^{3+} \)
C. the low hydration energy of \( A l^{3} \)
D. the polar nature of water
Subject: Physics
A positively charged particle of charge 1
C and mass 40 g, is revolving along a circle of radius \( 40 \mathrm{cm} \) with velocity
\( 5 \mathrm{m} / \mathrm{s} \) in a uniform magnetic field with centre at origin 0 in \( x \) -y plane \( . A t t=0 \) the particle was at \( (0,0.4 \mathrm{m}, 0) \) and velocity was directed along positive \( x \) direction.Another particle having charge \( 1 \mathrm{C} \) and mass \( 10 \mathrm{g} \) moving uniformly parallel to z-direction with velocity \( \frac{40}{\pi} m / s \) collides with revolving particle at \( t=0 \) and gets stuck with it. Neglecting gravitational force and coulombian force,calculate \( x, y \) and \( z \) coordinates of the combined particle at \( t=\frac{\pi}{40} \sec \)
Subject: Chemistry
\( \frac{3}{2} O_{2}(g) \longrightarrow O_{3}(g) K_{p} \) for this reaction
is \( 2.47 \times 10^{-29} . \) At \( 298 \mathrm{K}, \Delta_{r} G^{o} \) for
conversion of oxygen to ozone will be:
A \( \cdot \) 100 \( k \) J mol \( ^{-1} \) -
B . 150 kJ mol-
c. \( 163 \mathrm{kJ} \mathrm{mol}^{-1} \)
D. 2303 kJ mol-1
Subject: Physics
Given a uniform electric field \( \boldsymbol{E}=\mathbf{5} \times \) \( 10^{3} \hat{i} N / C . \) What would be the flux
through the same square if the plane
makes an angle of \( 30^{\circ} \) with the \( x \) -axis?
A. \( 5 N m^{2} / C \)
B. \( 25 N m^{2} / C \)
\( \mathbf{c} \cdot 50 N m^{2} / C \)
D. \( 500 \mathrm{Nm}^{2} / \mathrm{C} \)
Subject: Physics
Two uniform stretched strings \( A \) and \( B \), made of steel, are vibrating under the same tension. If the first overtone of \( A \) is
equal to the second overtone of B and if
the radius of \( A \) is twice that of \( B \), the
ratio of the lengths of the strings is:
A .2: 3
B. 1: 2
c. 1: 3
D. 1: 4
Subject: Maths
Draw a triangle \( A B C \) with side \( B C= \)
\( \mathbf{7} c \boldsymbol{m}, \angle \boldsymbol{B}=\mathbf{4 5}^{o}, \angle \boldsymbol{A}=\mathbf{1 0 5}^{\circ} . \) Then
construct a triangle whose side are \( \frac{4}{3} \)
times the corresponding sides of \( \triangle A B C . \) Write the construction.
Subject: Physics
The current through the ammeter
shown in the figure is \( 1 A \). If each of the
4 resistor is replaced by 2 resistor, the
current in the circuit will become
\( A \cdot(a) \frac{10}{9} A \)
\( \mathbf{B} \cdot(\mathbf{b}) \frac{5}{4} A \)
\( \mathbf{c} \cdot(\mathrm{c}) \frac{9}{8} A \)
\( \mathbf{D} \cdot(\mathrm{d}) \frac{5}{8} A \)
Subject: Maths
If \( \log _{e}\left(\frac{1}{\left(1+x+x^{2}+x^{3}\right)}\right) \) be
expanded in a series of ascending
powers of \( \boldsymbol{x} \) the coefficient of \( x^{n} \) is \( -\frac{b}{n} \) if \( n \) be odd or of the form \( 4 m+2 \) and \( \frac{a}{n} \) if \( n \) be of the
form \( 4 m . \) Find the value of \( a+b^{2} \)
Subject: Chemistry
\( \triangle-C O O H \stackrel{H B r}{\rightarrow} ? \)
Which of the following is the major product?
\( \mathbf{A} \cdot H_{3} C-C H_{2}-\underset{B r}{C} H-C H_{3} \)
в. \( B r-C H_{2}-C H_{2}-C H_{2} C O O H \)
c. \( H_{3} C-C H-C H_{2}-B r \)
Coot
D. \( H_{3} C-C_{\text {। }} H-C H_{2} \) COCH
Subject: Physics
Column 1
a) A linear S.H.M
e) \( \frac{d^{2} \Theta}{d t^{2}}=\frac{c}{\Theta} \)
b) Angular S.H.M
f) \( \frac{d^{2} x}{d t^{2}}+ \)
\( \frac{\boldsymbol{R}}{\boldsymbol{m}} \frac{\boldsymbol{d} \boldsymbol{x}}{\boldsymbol{M} \boldsymbol{t}}+\boldsymbol{x} \boldsymbol{w}^{2}=\frac{\boldsymbol{F}}{\boldsymbol{m}} \cos \boldsymbol{\theta} \)
c) Damped harmonic
motion
g) \( \frac{d^{2} x}{d t^{2}}- \)
\( \frac{k}{m} x=0 \)
d) forced oscillation
h) \( m \frac{d^{2} x}{d t^{2}}+ \)
\( R \frac{d n}{d t}+m x \omega^{2}=0 \)
A. a-e, \( b-h, c-g, d-f \)
B. \( a-f, b-g, c-e, d-h \)
\( c \cdot a-g, b-e, c-h, d-f \)
D. a-g, b-h, c-e, d-f
Subject: Maths
\( \int \frac{x \sin ^{-1} x}{\sqrt{1-x^{2}}} d x \) is equal to
A. \( x-\sqrt{1-x^{2}} \sin ^{-1} x+c \)
B. \( x+\sqrt{1-x^{2}} \sin ^{-1} x+c \)
c. \( x+\sin ^{-1} x+c \)
D. \( x-\sin ^{-1} x+c \)
Subject: Chemistry
Assertion
HClO is stronger acid than HBro.
Reason
Greater is the electronegativity of the halogen, greater will be attraction of electron pair towards it and hence more
easily the \( \boldsymbol{H}^{+} \) ion will be released.
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
If \( \vec{A} \) and \( \vec{B} \) are two vectors, the value of \( (\vec{A}+\vec{B}) \times(\vec{A}-\vec{B}) \) is then
B . \( -2(\vec{B} \times \vec{A}) \)
C . \( (\vec{B} \times \vec{A}) \)
D. \( (\vec{A} \times \vec{B}) \)
Subject: Chemistry
The decreasing leaving group order of the following compounds is:
\( \boldsymbol{i} . \boldsymbol{F}_{3} \boldsymbol{C} \boldsymbol{S} \boldsymbol{O}_{3}^{\ominus} \quad \boldsymbol{i} \boldsymbol{i} . \boldsymbol{C l}_{3} \boldsymbol{C}-\boldsymbol{C O O}^{\ominus} \)
iii. Ph \( S O_{3}^{\ominus} \) iv. \( M e S O_{3}^{\ominus} \)
A \( \cdot(i)>(i i)>(i i i)>(i v) \)
B. \( (i v)>(i i i)>(i i)>(i) \)
c. \( (i i i)>(i)>(i i)>(i v) \)
D. \( (i)>(i i i)>(i v)>(i i) \)
Subject: Physics
Consider a uniform electric field \( \boldsymbol{E}= \)
\( 3 \times 10^{3} \hat{i} N C^{-1} \)
(a) What is the flux of
this field through a square of \( 10 \mathrm{cm} \) on a side whose plane is parallel to the yz plane?
(b) What is the flux through the same square if the normal to its plane
makes a \( 60^{\circ} \) angle with the \( x \) -axis?
Subject: Chemistry
Match the following.
SET-A SET-B
Type of hormone

Name of
hormone
1) Steroid hormone
a) Cytokinins
2) Non Steroid
b) Estrogens
3) Plant hormone
c) Auxins
4) Peptide hormone
d) Insulin
A. \( 1-b, 2-b, 3-c, 4-d \)
B. 1-b, 2-a, 3-d, 4-c
c. 1-b, 2-a,d 3-a,c, 4-d
D. 1-c, 2-a, 3-d, 4-b
Subject: Chemistry
Write the composition of aqua-regia:
\( \mathbf{A} \cdot 67 \% \) conc. \( H C l \) and \( 33 \% \) conc. \( H N O_{3} \)
B. \( 25 \% \) conc. \( H C l \) and \( 75 \% \) conc. \( H N O_{3} \)
C \( .75 \% \) conc. \( H C l \) and \( 25 \% \) conc. \( H N O_{3} \)
D. \( 50 \% \) conc. \( H C l \) and \( 50 \% \) conc. \( H N O_{3} \)
Subject: Maths
The solution of the equation \( \boldsymbol{x}+\frac{\mathbf{1}}{\boldsymbol{x}}=\mathbf{2} \)
will be
A .2,-1
в. \( _{0,-1,-\frac{1}{5}} \)
\( \mathrm{c} \cdot_{-1,-\frac{1}{5}} \)
D. None of these
Subject: Maths
n a right angled \( \triangle A B D, \angle B= \)
\( \mathbf{6 0}^{\circ}, \angle \boldsymbol{A}=\mathbf{3 0}^{\circ} \)
Then \( \sin 30^{\circ} \) is equal to
\( A \)
\( 3 \frac{1}{2} \)
\( c \)
\( D \cdot 1 \)
Subject: Maths
The value of \( \sin ^{-1} x+\cos ^{-1} x, \forall x \in \)
[-1,1] is
A \( \cdot \frac{\pi}{2} \)
в. \( \frac{-5 \pi}{3} \)
c. \( \frac{-3 \pi}{2} \)
D.
Subject: Maths
\( \triangle A B C \) is an isosceles triangle. If the
coordinates of the base are \( \boldsymbol{B} \equiv(\mathbf{1}, \mathbf{3}) \) and \( C \equiv(-2,7), \) the coordinates of vertex \( A \) can be This question has multiple correct options
A. (1,6)
(年) (1,66)
в. \( \left(-\frac{1}{2}, 5\right) \)
\( ^{c} \cdot\left(\frac{5}{6}, 6\right) \)
D. \( \left(-7, \frac{1}{8}\right) \)
Subject: Physics
In a two-slit experiment, with
monochromatic light, fringes are obtained on a screen placed at some distance from the slits. If the screen is
moved by \( 5 \times 10^{-2} \mathrm{m} \) towards the slits,
the change in fringe width is \( 10^{-3} \mathrm{m} \) The the wavelength of light used is
(given that distance between the slits is
\( 0.03 \mathrm{mm} \)
\( A \cdot 4500 \stackrel{\circ}{A} \)
B . 5000 ,
c. 5500 ,
D. 6000 ,
Subject: Physics
The length of a seconds hand in a watch
is \( 1 \mathrm{cm} . \) The change in its velocity in 15 s is
A. \( 0 \mathrm{cm} / \mathrm{s} \)
B. \( \frac{\pi}{30 \sqrt{2}} \mathrm{cm} / \mathrm{s} \)
c. \( \frac{\pi}{30} \mathrm{cm} / \mathrm{s} \)
D. \( \frac{\pi}{30} \sqrt{2} \mathrm{cm} / \mathrm{s} \)
Subject: Chemistry
\( \boldsymbol{O} \)
\( \boldsymbol{C} \boldsymbol{H}_{3}-\stackrel{\|}{\boldsymbol{C}}-\boldsymbol{C} \boldsymbol{H}-\boldsymbol{C} \boldsymbol{H}-\boldsymbol{C} \boldsymbol{H}-\boldsymbol{C} \boldsymbol{H}_{3} \)
\( \boldsymbol{C H}_{3} \quad \boldsymbol{C H O} \quad \boldsymbol{C H}_{3} \)
The IUPAC name of compound is:
A. 3,5-dimethyl-4-formylpentanone
B. 1-isopropy|-2-methy|-4-oxobutanal|
c. 2-isopropyl-3-methyl-4-oxopentanal
D. none of the above
Subject: Chemistry
What is \( X \) in the equation? \( \boldsymbol{C a O}+\boldsymbol{3 C} \rightarrow \boldsymbol{X}+\boldsymbol{C O} \)
A \( \cdot C a C O_{3} \)
в. \( C a C_{2} \)
\( c \cdot C O_{2} \)
D. None of these
Subject: Physics
A simple harmonic oscillator of angular
frequency 2 rad \( s^{-1} \) is acted upon by an
external force \( F=\sin t N . \) If the
oscillator is at rest in its equilibrium position at \( t=0, \) its position at later times is proportional to
A \( \cdot \sin t+\frac{1}{2} \cos 2 t \)
B \cdot \( \operatorname{cost}-\frac{1}{2} \sin 2 t \)
\( \mathrm{c} \cdot \operatorname{sint}-\frac{1}{2} \sin 2 t \)
D. \( \sin t+\frac{1}{2} \sin 2 t \)
Subject: Physics
Assertion
A planet moves faster, when it is closer
to the sun in its orbit and vice versa
Reason
Orbital velocity for an orbiting planet is
constant
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
A glass is filled with water up to its
brim and a thick hand card placed on
top of it. Now keeping the card tightly closed and pressed with palm, the glass full of water is inverted and placed
upside down. The palm is gently
removed from the card. It is observed
that the piece of card dose not fall off
the glass though the glass is full of water and its whole weight is exerting pressure on the card. Why does it happen?
Subject: Chemistry
\( H_{2} O_{2} \) can be obtained when following
reacts with \( \boldsymbol{H}_{2} \boldsymbol{S} \boldsymbol{O}_{4} \) except
with
A \( \cdot P b O_{2} \)
в. \( B a O_{2} \)
c. \( N a_{2} O_{2} \)
D. \( \operatorname{sr} O_{2} \)
Subject: Physics
Find the value of \( ^{\prime} a^{\prime} \) for which the vector
\( \boldsymbol{A}=\mathbf{3} \hat{\mathbf{i}}+\mathbf{3} \hat{\boldsymbol{j}}+\mathbf{9} \hat{\boldsymbol{k}} \) and \( \overline{\boldsymbol{B}}=\hat{\boldsymbol{i}}+\boldsymbol{a} \hat{\boldsymbol{j}}+\boldsymbol{3} \hat{\boldsymbol{k}} \)
are parallel
Subject: Chemistry
Arrange the following compounds in increasing order of boiling point.
\( \begin{array}{ll}\text { Propan-1-ol } & \text { Butan-1-ol } \\ \text { I } & \text { II } \\ \text { Butan-2-ol } & \text { Pentan-1-ol } \\ \text { III } & \text { IV }\end{array} \)
A. \( I<I I I<I I<I V \)
В. \( I I<I I I<I V<I \)
c. \( I I<I V<I I I<V I \)
D. \( I I I<I<I I<I V \)
Subject: Maths
IF \( \theta \) is in the first quadrant and \( \cos \theta= \)
3. then value of
\( \overline{\mathbf{5}} \)
\( 5 \tan \theta-4 \operatorname{cosec} \theta \sec \theta-4 \cot \theta \) is
A \( \cdot \frac{-14}{3} \)
в. \( \frac{5}{16} \)
\( c \cdot \frac{5}{-34} \)
D. \( \frac{-5}{16} \)
Subject: Physics
A charge \( Q \) is distributed over two
concentric hollow spheres of radii \( a \) and \( b(a>b), \) so that the surface charge
densities are equal. The potential at the common centre is \( \frac{1}{4 \pi \epsilon_{0}} \) times
A \( \cdot k Q\left(\frac{a+b}{a^{2}+b^{2}}\right) \)
в. \( 2 Q\left(\frac{a+b}{a^{2}+b^{2}}\right) \)
\( c \cdot Q \)
D. \( \frac{Q}{2}\left(\frac{a+b}{a^{2}+b^{2}}\right) \)
E \( \cdot \frac{Q}{4}\left(\frac{a+b}{a^{2}+b^{2}}\right) \)
Subject: Physics
In a meter bridge, the wire of length \( 1 \mathrm{m} \)
has a non-uniform cross-section such
that, the variation \( \frac{d R}{d l} \) of its resistance \( R \) with length \( l \) is \( \frac{d R}{d l} \propto \frac{1}{\sqrt{l}} . \) Two equal
resistances are connected as shown in
the figure. The galvanometer has zero deflection when the jockey is at point \( P \) What is the length \( A P: \)
\( A \cdot 0.2 m \)
В. \( 0.3 m \)
c. \( 0.25 m \)
D. \( 0.35 m \)
Subject: Chemistry
The IUPAC name of \( \boldsymbol{C H}_{3} \boldsymbol{C O C H}\left(\boldsymbol{C H}_{3}\right)_{2} \)
is:
A. 4-methylisopropyl ketone
B. 3-Methyl-2-butanone
c. Isopropylmethyl ketone
D. 2-methyl-3-butanone
Subject: Physics
The binding energy per nucleon for \( C^{12} \) is \( 7.68 M e V \) and that for \( C^{13} \) is
7.5 \( M e V \). How much energy is required
to remove a neutron from \( C^{13} \) ?
A. \( 5.34 \mathrm{MeV} \)
B. \( 5.5 \mathrm{MeV} \)
c. \( 9.5 \mathrm{MeV} \)
D. \( 9.34 \mathrm{MeV} \)
Subject: Maths
Consider the points \( \boldsymbol{P}=(-\sin (\boldsymbol{\beta}- \)
\( \boldsymbol{\alpha}),-\cos \beta), \boldsymbol{Q}=(\cos (\beta-\boldsymbol{\alpha}), \sin \beta) \)
and \( \boldsymbol{R}=(\cos (\boldsymbol{\beta}-\boldsymbol{\alpha}+\boldsymbol{\theta}), \sin (\boldsymbol{\beta}-\boldsymbol{\theta})) \)
where \( 0<\alpha, \beta<\frac{\pi}{4} \) then
A. \( P \) lies on the line segment \( R Q \)
B. \( Q \) lies on the line segment \( P R \)
c. \( R \) lies on the line segment \( Q P \)
D. \( P, Q, R \) are non-collinear
Subject: Chemistry
Cerium (atomic number \( =58 \) ) is an
important member of the lanthanoids Which of the following statements about cerium is incorrect?
A. The +4 oxidation state of cerium is not known in solutions
B. The +3 oxidation state of cerium is more stable than the +4 oxidation state
c. The common oxidation states of cerium are +3 and +4
D. Cerium (IV) acts as an oxidising agentt
Subject: Maths
Assertion
Degree of a zero polynomial is not
defined.
Reason
Degree of a non-zero constant
polynomial is 0
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
A plane polarized light passed through successive polarizers which are rotated
by \( 30^{\circ} \) with respect to each other in the
clockwise direction. Neglecting absorption by the polarizers and given that the first polarizer's axis is parallel to the plane of polarization of the incident light, the intensity of light at the exit of the fifth polarizer is closest
to.
A. Same as that of the incident light
B. 17.5\% of the incident light
c. \( 30 \% \) of the incident light
D. zero
Subject: Maths
If \( a=2 \hat{i}-\hat{j}-m \hat{k} \) and \( b=\frac{4}{7} \hat{i}-\frac{2}{7} \hat{j}+ \)
\( 2 \hat{k} \) are collinear, then the value of \( m \) is
equal to
A . -7
в. - -
\( c \cdot 2 \)
D.
E. -2
Subject: Maths
Assertion
\( \boldsymbol{x}=\mathbf{0} \) is point of minima of \( \boldsymbol{f} \)
Reason
\( f^{\prime}(0)=0 \)
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
Statement 1: The scalar product of two
vector can be zero.
Statement 2:If two vector are
perpendicular to each other, their scalar product will be zero.
A \( \cdot \) a) Statement- -1 is false, statement- 2 is true
B. b) Statement-1 is true, Statement-2 is true, Statement
2 is a correct explanation for statement-
c. c) Statement- - is true, Statement-2 is true; Statement
2 is not a correct explanation for statement-
D. d) Statement-1 is true, Statement-2 is false
Subject: Physics
A fringe width of a certain interference
pattern is \( \beta=0.002 \mathrm{cm} . \) What is the
distance of \( 5^{t h} \) dark fringe from centre?
\( \mathbf{A} \cdot 1 \times 10^{-2} \mathrm{cm} \)
B. \( 11 \times 10^{-2} \mathrm{cm} \)
\( \mathrm{c} \cdot 1.1 \times 10^{-2} \mathrm{cm} \)
D. \( 3.28 \times 10^{6} \mathrm{cm} \)
Subject: Maths
\( \boldsymbol{x}^{2}-(\boldsymbol{m}-\boldsymbol{3}) \boldsymbol{x}+\boldsymbol{m}=\mathbf{0}(\boldsymbol{m} \in \boldsymbol{R}) \) be a
quadratic equation. Find the value of \( m \)
for which, both roots are smaller than 2
\( ^{\mathrm{A}} \cdot\left(-\frac{3}{2}, 3\right) \)
в. \( (-\infty, 1] \)
c. (0,4]
D. \( (1, \infty) \)
Subject: Chemistry
Which of the following oxo-acids of sulphur has maximum number of \( \mathrm{p} \pi-\mathrm{d} \)
\( \pi \) bonds in it?
A \( \cdot H_{2} S_{2} O_{2} \)
в. \( H_{2} S_{2} O_{3} \)
c. \( H_{2} S_{2} O_{5} \)
D. \( H_{2} S_{2} O_{8} \)
Subject: Physics
A \( 150 m \) long train is moving north at a speed of \( 20 m / s . A \) bird flying south at a
speed of \( 5 m / s \) crosses the train. What
is the time taken by the bird to cross the train?
A . \( 30 s \)
в. \( 15 s \)
\( c \cdot 6 s \)
D. \( 3 s \)
Subject: Maths
If the latus-rectum of an ellipse is one half of its minor axis, then its
eccentricity is
A \( \cdot \frac{1}{2} \)
B. \( \frac{1}{\sqrt{2}} \)
c. \( \frac{\sqrt{3}}{2} \)
D. \( \frac{\sqrt{3}}{4} \)
Subject: Chemistry
Which of the following complexes exists as pair of enantiomers?
\( \mathbf{A} \cdot\left[\operatorname{Co}\left(N H_{3}\right)_{4} C l_{2}\right]^{+} \)
B. \( \left[C r(e n)_{3}\right]^{3+} \)
c. \( \left[\operatorname{Co}\left(P\left(C_{2} H_{5}\right)_{3}\right)_{2} C l B r\right. \)
D. \( \operatorname{trans}-\left[\operatorname{Co}(e n)_{2} C l_{2}\right]^{+} \)
Subject: Maths
If three positive numbers \( a, b \) and \( c \) are
in \( A . P . \) such that \( a b c=8 \), then the
minimum possible value of \( b \) is
\( A \cdot 2 \)
B. \( 4^{\frac{1}{5}} \)
\( \mathbf{c} \cdot 4^{\frac{2}{5}} \)
D.
Subject: Physics
A spherical convex surface of radius of
curvature \( R \) separates \( \operatorname{air}\left(\mu_{a}=1\right) \) from
\( \operatorname{glass}\left(a \mu_{g}=1.5\right) . \) The centre of
curvature is in the glass. A point object P placed in air is found to have a real image \( Q \) in the glass. The line PQ cuts the surface at a point 0 and \( P 0=0 Q \) The distance PO is equal to
A. 5R
B. 3R
\( c \cdot 2 R \)
D. 1.5 R
Subject: Maths
\( f(x)=\frac{a \sin x+b \cos x}{c \sin x+d \cos x} \) is an
increasing funtion if
A \( . a d-b c=0 \)
B. \( a d-b c<0 \)
c. \( a d-b c>0 \)
\( \mathbf{D} \cdot a b+c d=0 \)
Subject: Maths
IF \( A, B, C \) are non-singular \( n \times n \)
matrices, then \( (A B C)^{-1}= \)
\( \mathbf{A} \cdot A^{-1} C^{-1} B^{-1} \)
B. \( C^{-1} B^{-1} A^{-1} \)
c. \( C^{-1} A^{-1} B^{-1} \)
D. \( B^{-1} C^{-1} A^{-1} \)
Subject: Maths
Let \( \overrightarrow{\boldsymbol{\alpha}}=\mathbf{3} \hat{\boldsymbol{i}}+\hat{\boldsymbol{j}} \) and \( \overrightarrow{\boldsymbol{\beta}}=\mathbf{2} \hat{\boldsymbol{i}}-\hat{\boldsymbol{j}}+\boldsymbol{3} \hat{\boldsymbol{k}} . \) If
\( \overrightarrow{\boldsymbol{\beta}}=\overrightarrow{\boldsymbol{\beta}}_{1}-\boldsymbol{\beta}_{2}, \) where \( \overrightarrow{\boldsymbol{\beta}}_{1} \) is parallel to \( \overrightarrow{\boldsymbol{\alpha}} \)
and \( \vec{\beta}_{2} \) is perpendicular to \( \vec{\alpha}, \) then \( \vec{\beta}_{1} \times \)
\( \vec{\beta}_{2} \) is equal to?
\( \mathbf{A} \cdot-3 \hat{i}+9 \hat{j}+5 \hat{k} \)
B . \( 3 \hat{i}-9 \hat{j}-5 \hat{k} \)
c. \( \frac{1}{2}(-3 \hat{i}+9 \hat{j}+5 \hat{k}) \)
D・ \( \frac{1}{2}(3 \hat{i}-9 \hat{j}+5 \hat{k}) \)
Subject: Physics
A ball is thrown vertically upwards with
a velocity of \( 10 m s^{-1} . \).IT returns to the
ground with a velocity of9 \( m s^{-1} \) 1. If \( g= \)
\( 9.8 m s^{-} 2, \) then the maximum height
attained by the ball is nearly ( assume a resistance to be uniform)
A . \( 5.1 \mathrm{m} \)
B. 4.1 \( m \)
c. \( 4.61 \mathrm{m} \)
D. \( 5 \mathrm{m} \)