AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Physics
The equation of progressive wave is \( \boldsymbol{Y}=\mathbf{4} \sin \left\{\boldsymbol{\pi}\left(\frac{\boldsymbol{t}}{\mathbf{5}}-\frac{\boldsymbol{x}}{\mathbf{9}}\right)+\frac{\boldsymbol{\pi}}{\mathbf{6}}\right\} \) where \( \boldsymbol{x} \)
and \( y \) are in \( \mathrm{cm}, \) which of the following
statement is true?
\( \mathbf{A} \cdot \lambda=18 \mathrm{cm} \)
B. Amplitude = 0.04cm
c. velocity \( v=50 \mathrm{cm} / \mathrm{s} \)
D. frequency \( f=20 \mathrm{Hz} \)
Subject: Chemistry
\( N H_{3} \) has much higher boiling point
than \( P H_{3} \) because:
A. \( N H_{3} \) has much higher molecular mass
B. \( N H_{3} \) forms hydrogen bonds
c. \( N H_{3} \) contains ionic bonds while \( P H_{3} \) contains covalent bonds
D. \( N H_{3} \) undergoes umbrella inversion.
Subject: Chemistry
Which of the following species are correctly matched with their geometries according to the VSEPR theory? This question has multiple correct options
A. \( B r F_{6}^{+} \rightarrow \) octahedral
B . \( S n C l_{5}^{-} \rightarrow \) trigonal bipyramidal
c. \( C l F_{2}^{-} \rightarrow \) linear
D. \( I F_{4}^{+} \rightarrow \) see-saw
Subject: Maths
\( A: \) The area bounded by \( x=3, y^{2}=3 x \)
\( B: \) The area bounded by \( y=1-|x| \) and
X-axis
\( C: \) The area enclosed between the curve
\( y=x^{2} \) and the line \( y=\sqrt{3} x \)
The descending order of \( \boldsymbol{A}, \boldsymbol{B}, \boldsymbol{C} \) is
A. \( A, C, B \)
в. \( C, B, A \)
c. \( A, B, C \)
D. \( C, A, B \)
Subject: Chemistry
Complete the missing components/variables given as \( x \) and \( y \) in the following reactions.
\( P b\left(N O_{3}\right)_{2}(a q)+2 K I(a q) \rightarrow \)
\( \boldsymbol{P b I}_{2}(\boldsymbol{x})+\boldsymbol{2} \boldsymbol{K} \boldsymbol{O}_{3}(\boldsymbol{y}) \)
A \( . x \rightarrow s ; y \rightarrow g \)
в. \( x \rightarrow s ; y \rightarrow a q \)
c. \( x \rightarrow a q ; y \rightarrow g \)
D. None of these
Subject: Physics
Let \( V \) and \( E \) denote the gravitational potential and gravitational field at a point. It is possible to have This question has multiple correct options
A. \( V=0 \) and \( E=0 \)
B. \( V=0 \) and \( E \neq 0 \)
c. \( V \neq 0 \) and \( E=0 \)
D. \( V \neq 0 \) and \( E \neq 0 \)
Subject: Maths
The value of \( \int \frac{d t}{t^{2}+2 x t+1}\left(x^{2}>1\right) \) is...
\( ^{\mathrm{A}} \cdot \frac{1}{2 \sqrt{\left(x^{2}-1\right)}} \log \frac{t+x-\sqrt{x^{2}-1}}{t+x+\sqrt{\left(x^{2}+1\right)}} \)
B. \( \frac{1}{2 \sqrt{\left(x^{2}-1\right)}} \log \frac{t+x-\sqrt{x^{2}-1}}{t+x+\sqrt{\left(x^{2}-1\right)}}+c \)
c. \( \frac{1}{2 \sqrt{\left(x^{2}+1\right)}} \log \frac{t+x-\sqrt{x^{2}+1}}{t+x+\sqrt{\left(x^{2}+1\right)}} \)
D. \( \frac{1}{2 \sqrt{\left(x^{2}+1\right)}} \log \frac{t+x-\sqrt{x^{2}+1}}{t+x+\sqrt{\left(x^{2}-1\right)}}+c \)
Subject: Maths
A shopkeeper buys an article at a discount of \( 30 \% \) from the wholesaler
(the printed price of the article being \( R s .2,000) \) and paid sales-tax at the
rate of \( 8 \% \). The shopkeeper sells the article to a buyer at the printed price
and charges tax at the same rate. Find the VAT (Value Added Tax) paid by the shopkeeper
Subject: Maths
\( \mathbf{f} \mathbf{\Delta}=\left|\begin{array}{ccc}\boldsymbol{x}+\mathbf{1} & \boldsymbol{x}+\mathbf{2} & \boldsymbol{x}+\boldsymbol{a} \\ \boldsymbol{x}+\mathbf{2} & \boldsymbol{x}+\mathbf{3} & \boldsymbol{x}+\boldsymbol{b} \\ \boldsymbol{x}+\mathbf{3} & \boldsymbol{x}+\boldsymbol{4} & \boldsymbol{x}+\boldsymbol{c}\end{array}\right|=\mathbf{0}, \) then
the family of lines \( a x+b y+c=0 \)
passes through
A. (1,-1)
B. (1,-2)
c. (2,-3)
D. (0,0)
Subject: Physics
A short solenoid of length \( 4 c m, \) radius
\( 2 c m \) and 100 turns is placed inside and
on the axis of a long solenoid of length
\( 80 c m \) and 1500 turns. A current of \( 3 A \)
flows through the short solenoid. The mutual inductance of two solenoids is
A. \( 0.012 H \)
H
в. \( 5.3 \times 10^{-5} H \)
\( \mathbf{c} \cdot 5.91 \times 10^{-3} \mathrm{H} \)
D. \( 8.3 \times 10^{-5} H \)
Subject: Chemistry
Assertion
\( N_{2} \) is adsorbed on iron surface at \( 83 \mathrm{K} \)
which decreases rapidly with increase
in temperature and at room temperature, practically no adsorption
of \( N_{2} \) occurs. The adsorption, however,
becomes significant at \( 773 \mathrm{K} \)
Reason
At lower temperature, adsorption of \( N_{2} \)
molecules on iron surface is
physisorption and at high
temperatures, \( N_{2} \) shows chemisorption
of \( N \) atoms on iron surface.
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
The angle at which the curve \( y=k e^{k x} \)
intersects the \( y \) - axis is This question has multiple correct options
A \( \cdot \tan ^{-1} k^{2} \)
B \( \cdot \cot ^{-1}\left(k^{2}\right) \)
\( \mathrm{c} \cdot_{\sin }^{-1}\left(\frac{1}{\sqrt{1+k^{4}}}\right) \)
D・sec- \( 1(\sqrt{1+k^{4}}) \)
Subject: Chemistry
Reaction of \( \boldsymbol{O}_{2} \) is faster with \( \boldsymbol{C} \boldsymbol{a} \) or \( \boldsymbol{M} \boldsymbol{g} \) ?
\( \mathbf{A} \cdot M g \)
в. \( C a \)
c. Equally react
D. Do not react
Subject: Maths
Examine the continuity of the function
\[
\boldsymbol{f}(\boldsymbol{x})=\left\{\begin{array}{ll}
\frac{\log \boldsymbol{x}-\log \mathbf{7}}{\boldsymbol{x}-\mathbf{7}} & \text { for } \boldsymbol{x} \neq \mathbf{7} \\
\mathbf{7}, & \text { for } \boldsymbol{x}=\mathbf{7}
\end{array}\right.
\]
at \( x=7 \)
Subject: Chemistry
The equilibrium of which of the following reactions will not be disturbed by the addition of an inert gas at
constant volume?

This question has multiple correct options
A \( \cdot H_{2}(g)+I_{2}(g) \rightleftharpoons 2 H I(g) \)
B. \( N_{2} O_{4}(g) \rightleftharpoons 2 N O_{2}(g) \)
\( \mathrm{c} \cdot \mathrm{CO}_{2}(g)+2 \mathrm{H}_{2}(g) \rightleftharpoons \mathrm{CH}_{3} \mathrm{OH}(g) \)
D. \( C(s)+H_{2} O(g) \rightleftharpoons C O(g)+H_{2}(g) \)
Subject: Chemistry
The equilibrium constant for the reaction, \( \boldsymbol{A} \boldsymbol{g} \boldsymbol{C l}_{(s)} \rightleftharpoons \boldsymbol{A} \boldsymbol{g}_{(a q)}^{+}+\boldsymbol{C l}_{(a q)}^{-} \) is:
(Given that \( : \Delta G_{f A g C l}^{0}=-109.7 k J \)
\( \Delta G_{f A g^{+}}^{0}=77.1 k J ; \Delta G_{f C l^{-}}^{0}= \)
\( -131.2 k J) \)
A \( \cdot 2 \times 10^{-10} \)
B . \( 6 \times 10^{-10} \)
c. \( 8 \times 10^{-10} \)
D. \( 2 \times 10^{-8} \)
Subject: Physics
A ray of light is incident on the plane mirror at rest. The mirror starts turning
at a uniform acceleration of \( 2 \pi r a d / s^{2} \) about an axis in plane of mirror. The reflected ray at the end of \( \frac{1}{4} \) s must have turned through:
A . 90
B. 45
c. 22.5
D. 11.25
Subject: Physics
A thinwalled, spherical conducting shel S of radius \( R \) is given charge \( Q \). The same amountof charge is also placed at its centre C. Which of the following
statements are correct?
This question has multiple correct options
A \( \cdot \) on the outer surface of \( \mathrm{S} \), the charge density is \( \frac{Q}{2 \pi R^{2}} \)
B. The electric field is zero at all points inside
c. At a point just outside \( S \), the electric field is double the field at a point just inside
D. At any point inside S, the electric field is inversely proportional to the square of its distance from
Subject: Maths
In the figure above, \( A C=6 \) and \( B C= \)
3. Point \( P(\text { not shown }) \) lies on \( A B \)
between \( A \) and \( B \) such that \( C P \perp A B \)
Which of the following could be the
length of \( C P ? \)
\( A \cdot 2 \)
B. 4
\( c .5 \)
D.
\( E \)
Subject: Chemistry
The equilibrium constant for the reaction
\( \boldsymbol{H}_{2}(\boldsymbol{g})+\boldsymbol{S}(s) \rightleftharpoons \boldsymbol{H}_{2} \boldsymbol{S}(\boldsymbol{g}) \)
is 18.5 at \( 925 K \) and 9.25 at \( 1000 K \)
respectively. Calculate the enthalpy of
the reaction.
Subject: Physics
\( \mathbf{X} \) and \( \mathrm{Y} \) are large, parallel conducting plates close to each other. Each face
has an area A. X is given a charge Q.Y is without any charge. Point \( A, B \) and \( C \) are as shown in the figure. Which statement is wrong.
A . The field at B is \( \frac{Q}{2 \frac{6}{80 A}} \)
B. The field at B is \( \frac{Q}{6 \mathrm{c} A} \)
C. The fields at \( A, B \) and \( C \) are of the same magnitude.
D. The fields at A and C are of the same magnitude, but in opposite directions
Subject: Physics
A hypothetical radioactive nucleus decays according to the following series \( \mathrm{z}_{2} \boldsymbol{A}^{180} \underline{\boldsymbol{\alpha}} \boldsymbol{A}_{1} \stackrel{\boldsymbol{\beta}^{-}}{\longrightarrow} \boldsymbol{A}_{2} \underline{\boldsymbol{\alpha}} \boldsymbol{A}_{3} \underline{\boldsymbol{\Upsilon}} \boldsymbol{A}_{4} \)
If the mass number and atomic number
of A are respectively 180 and 72 . then the atomic number and mass number
of A will respectively be:
\( \mathbf{A} \cdot 69,171 \)
B. 70,172
c. 68,172
D. 69,172
Subject: Physics
Figure shows the strain-stress curve for
a given material. The Young's modulus
of the material is
\( \mathbf{A} \cdot 5 \times 10^{9} N \quad m^{-2} \)
B . \( 5 \times 10^{10} N \quad m^{-2} \)
\( \begin{array}{lll}\text { С. } 7.5 \times 10^{9} N & m^{-2}\end{array} \)
D. \( 7.5 \times 10^{10} N \quad m^{-2} \)
Subject: Physics
In the given figure, what is the force on
the charge \( Q \) kept at \( O \) which is at
the mid point of the line \( A B ? \)
A \( \cdot \frac{2 q Q}{\pi \varepsilon_{0} r^{2}} \) along \( B A \)
B. \( \frac{2 q Q}{\pi \varepsilon_{0} r^{2}} \) along \( A B \)
c. zero
D. \( \frac{q Q}{4 \pi \varepsilon_{0} r^{2}} \)
Subject: Maths
The two complex numbers satisfying
the equation \( z \bar{z}-(1+i) z- \)
\( (3+2 i) \bar{z}+(1+5 i)=0 \) are
A \( .1+i, 3+2 i \)
B. \( 1+i, 3-2 i \)
c. \( 1-i, 3+2 i \)
D. \( 1-i, 3-2 i \)
Subject: Chemistry
A group 13 element \( X \) reacts with
chlorine gas to produce a compound
\( X C l_{3} . X C l_{3} \) is electron deficient and
easily reacts with \( N H_{3} \) to form
\( \boldsymbol{C l}_{3} \boldsymbol{X} \rightarrow \boldsymbol{N} \boldsymbol{H}_{3} \) adduct; however, \( \boldsymbol{X} \boldsymbol{C l}_{3} \)
does not dimerize \( \boldsymbol{X} \) is:
A. \( B \)
в. \( A l \)
\( c . G a \)
D. In
Subject: Biology
Match List I with List II and select the
correct answer using the codes given:
List-I List-II
A. I langerhans
1. Calcitonin
в. Pituitary
2. Epinephrine rygland
c. Growth
hormone Thyroidgland 3. medere dgland s.
D. Adrenal gland 4. Insulin
\( A \cdot A-3, B-4, C-1, D-2 \)
B. \( A-4, B-3, C-1, D-2 \)
C. \( A-4, B-3, C-2, D-1 \)
D. A - 3, B - 2, C - 4, D-
Subject: Maths
The area (in square units) bounded by
\( \boldsymbol{y}=\boldsymbol{x} e^{|x|} \) and lines \( |\boldsymbol{x}|=\mathbf{1}, \boldsymbol{y}=\mathbf{0}, \) is
A .4
B. 6
\( c .1 \)
D. 2
Subject: Maths
A rational number is such that when
you multiply it with \( \frac{5}{2} \) and add \( \frac{2}{3} \) to the
product, you get \( -\frac{7}{12} . \) What is the
number?
A \( \cdot-\frac{4}{3} \)
в. \( -\frac{1}{2} \)
\( c \cdot \frac{4}{3} \)
D. \( -\frac{5}{3} \)
Subject: Maths
The area (in sq. units) of the region
bounded by the curves \( y=2^{x} \) and \( y= \)
\( |x+1|, \) in the first quadrant is:
\( ^{\mathbf{A}} \cdot \frac{3}{2}-\frac{1}{\log _{e} 2} \)
в. \( \frac{1}{2} \)
\( ^{\mathrm{C}} \cdot \log _{e} 2+\frac{3}{2} \)
D.
Subject: Maths
\( z_{1} z_{2} \in C, z_{1}^{2}+z_{2}^{2} \in \)
\( \boldsymbol{R}, \boldsymbol{z}_{1}\left(\boldsymbol{z}_{1}^{2}-\boldsymbol{3} \boldsymbol{z}_{2}^{2}\right)=\boldsymbol{2} \) and
\( z_{2}\left(3 z_{1}^{2}-z_{2}^{2}\right)=11, \) then the value of
\( z_{1}^{2}+z_{2}^{2} \) is
A . 2
B. 3
\( c \cdot 4 \)
D. 5
Subject: Chemistry
If a \( 360 m L \) sample of helium contains
0.25 moles, how many molecules of chlorine gas would occupy the same volume at the same pressure and temperature?
A. \( 1.2 \times 10^{24} \)
В. \( 6.022 \times 10^{23} \)
с. \( 3.01 \times 10^{23} \)
3
D. \( 1.51 \times 10^{23} \)
E \( .7 .55 \times 10^{22} \)
Subject: Maths
The area of a rhombus, one of whose
diagonals measures \( 8 \mathrm{cm} \) and the side
is \( 5 \mathrm{cm}, \) is
A \( .25 \mathrm{cm}^{2} \)
B. \( 24 \mathrm{cm}^{2} \)
c. \( 24.5 \mathrm{cm}^{2} \)
D. \( 26 \mathrm{cm}^{2} \)
Subject: Chemistry
The molecular mass of organic acid was determined by the study of its barium salt \( 4.290 \mathrm{g} \) of salt was quantitatively converted to the free acid by the
reaction with \( 21.64 \mathrm{ml} \) of 0.477
\( M H_{2} S O_{4} . \) The barium salt was found to
have two moles of water of hydration per \( B a^{2+} \) ion and acid is monobasic. What
is the molecular weight of anhydrous acid?
A . 130
B . 142
\( c \cdot 100 \)
D. 110
Subject: Chemistry
Assertion
Work and internal energy are not state functions.
Reason
The sum of \( \boldsymbol{q}+\boldsymbol{w} \) is state function
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
Oxidation number of \( \mathrm{P} \) in \( \boldsymbol{P}_{2} \boldsymbol{O}_{7}^{4-} \) is :
\( A \cdot+3 \)
\( B \cdot+4 \)
\( c \cdot+5 \)
\( D \cdot+6 \)
Subject: Maths
Check whether the first polynomial is a factor of the second polynomial by
applying the division algorithm. \( x^{3}- \)
\( \mathbf{3} \boldsymbol{x}+\mathbf{1}, \boldsymbol{x}^{\mathbf{5}}-\mathbf{4} \boldsymbol{x}^{\mathbf{3}}+\boldsymbol{x}^{\mathbf{2}}+\mathbf{3} \boldsymbol{x}+\mathbf{1} \)
A. Yes
B. No
c. Ambiguous
D. Data insufficient
Subject: Maths
\( A \) and \( B \) are two events such that
\( \boldsymbol{P}(\boldsymbol{A} \cup \boldsymbol{B})=\frac{\mathbf{3}}{\mathbf{4}}, \boldsymbol{P}(\boldsymbol{A} \cap \boldsymbol{B})= \)
\( \frac{1}{4}, P(\bar{A})=\frac{2}{3} ; \operatorname{then} P(\bar{A} \cap B) \) is
A \( .1 / 12 \)
в. \( 5 / 12 \)
c. \( 4 / 9 \)
D. \( 1 / 3 \)
Subject: Chemistry
The concentration of \( O H^{-} \) ions in a
solution with the \( \boldsymbol{H}^{+} \) ions
concentration of \( 1.3 \times 10^{-4} \mathrm{M} \) is?
A \( .7 .7 \times 10^{-4} \)
B . \( 1.3 \times 10^{-4} \) М
c. \( 2.6 \times 10^{-8} \) М
D. \( 7.7 \times 10^{-11} \) М
Subject: Physics
Using general logic for electric field, the flux of \( \vec{g} \) through any closed surface is given by :
A \( \cdot \oint \vec{g} \cdot d \vec{s}=4 \pi G m_{\text {endosed }} \)
в. \( \oint \vec{g} \cdot d \vec{s}=-4 \pi G m_{\text {endosed }} \)
c. \( \oint \vec{g} \cdot d \vec{s}=G m_{\text {enclosed}} \)
D \( \cdot \oint \vec{g} \cdot d \vec{s}=-G m_{\text {endose}} \)
Subject: Physics
The length of a wire is \( l_{1} \) when tension is
\( T_{1} \) and \( l_{2} \) when tension is \( T_{2} \). The natura length of the wire is
A \( \cdot \frac{l_{1}+l_{2}}{2} \)
B. \( \sqrt{l_{1} l_{2}} \)
c. \( \frac{l_{1} T_{2}-l_{2} T_{1}}{T_{2}-T_{1}} \)
D. \( \frac{l_{1} T_{2}+l_{2} T_{1}}{T_{2}+T_{1}} \)
E \( \cdot \frac{l_{1} T_{1}-l_{2} T_{2}}{T_{1}-T_{2}} \)
Subject: Chemistry
How many of the following is/are not obtained as one of the hydrolysis
products of \( X e F_{2} \) with water?
\( \boldsymbol{X} \boldsymbol{e} \boldsymbol{O}_{3}, \boldsymbol{X} \boldsymbol{e}, \boldsymbol{H} \boldsymbol{F}, \boldsymbol{O}_{2} \)
A.
B. 3
\( c \cdot 4 \)
D.
Subject: Maths
\( \mathbf{S} \) and \( \mathbf{S}^{\prime} \) are the foci of the ellipse
\( 25 x^{2}+16 y^{2}=1600, \) then the sum of
the distances from \( \mathrm{S} \) and \( \mathrm{S}^{\prime} \) to the point
\( (4 \sqrt{3}, 5) \) is:
A . 20
B. 15
c. 40
D. 30
Subject: Biology
Both avian and mammalian hearts are
four chambered. The anatomy and physiology of heart is described by
A. Blood always enters into an atrium and then is pumped into a ventricle
B. Blood pressure alternates between systolic pressure and diastolic pressure
C. The atria provide one pump and the ventricles provide a second pump
D. The heart sends blood out through arteries and retrieves blood through veins
E. The heart pumps blood simultaneously through a pulmonary circuit and a systemic circuitt
Subject: Chemistry
The elements \( X \) and \( Y \) form two
compounds, \( \boldsymbol{X} \boldsymbol{Y}_{2} \) and \( \boldsymbol{X}_{3} \boldsymbol{Y}_{2} . \mathbf{0 . 1} \) mol of
former weighs 10 g while 0.05 mole of the latter weighs 9 g. Find the atomic
weight of \( \boldsymbol{X} \)
Subject: Biology
Mendel studied the inheritance
patterns of 12 different pairs of
characters of the pea plant. He could
ascertain the independent assortment
for only 7 of these 12 pairs of characters
by repeated experiments. What can be
deduced from this?
A. The pea plant could have atleast seven pairs of chromosomes.
B. The pea plant can have a maximum of seven pairs of chromosomes.
C. The pea plant has exactly seven pairs of chromosomes.
D. The pea plant can have haploid chromosome number between 7 and 12 only.
Subject: Maths
If \( 4 \hat{i}+7 \widehat{j}+8 \widehat{k}, 2 \hat{i}+3 \widehat{j}+4 \widehat{k} \) and \( 2 \hat{i}+ \)
\( \mathbf{5} \widehat{\boldsymbol{j}}+\mathbf{7} \widehat{\boldsymbol{k}} \) are the position vectors of the
vertices \( A, B \) and \( C \) respectively, of
triangle \( A B C, \) then the position vector of the point where the bisector of angle
\( A \) meets \( B C \) is
A \( \cdot \frac{2}{3}(-6 \hat{i}-8 \hat{j}-6 \widehat{k}) \)
B \( \cdot \frac{2}{3}(6 \hat{i}+8 \hat{j}+6 \widehat{k}) \)
c. \( \frac{1}{3}(6 \hat{i}+13 \hat{j}+18 \widehat{k}) \)
D \( \cdot \frac{1}{3}(5 \hat{j}+12 \widehat{k}) \)
Subject: Physics
In the given circuit find the ratio of \( i_{1} \) to
\( i_{2} . \) Where \( i_{1} \) is the initial \( (\text { at } t=0) \)
current, and \( i_{2} \) is steady state \( (\text { at } t= \)
\( \infty) \) current through the battery.
A . \( 1 . \)
В. 0.8
c. 1.2
D. 1.5
Subject: Chemistry
Which of the following factors may be
regarded as the main cause of
lanthanide contraction?
A. Poor shielding of one of \( 4 f \) electron by another in the subshell
B. Effective shielding of one of 4 f electrons by another in the subshell
C. Poorer shielding of 5d electrons by 4f electrons
D. Greater shielding of 5d electrons by 4f electrons
Subject: Maths
Length of two sides of a \( \triangle A B C \) is \( A B=6 \mathrm{cm} \) and \( B C=7 \mathrm{cm} . \) Then
which of the following can represent the third side of the triangle ? Also, construct the triangle formed by these three sides
A. \( 8 \mathrm{cm} \)
в. \( 13 \mathrm{cm} \)
c. \( 14 \mathrm{cm} \)
D. \( 15 \mathrm{cm} \)
Subject: Physics
Why do we study the Dispersion
phenomenon using a glass prism and
not a glass slab?
A. Light doesn't undergo any deviation inside a glass slab; so cannot be used to study Disprsion
B. All of the dispersion that takes place at the first interface is exactly reversed at the second parallel surface, 'undoing' the effect of the first interface.
C. Dispersion occurs only in prism and not in glass slab
D. None of the above
Subject: Physics
Assertion
In Young's interference experiment fringes become brighter if one of the slits is covered by cellophone paper.
Reason
The intensity of light emerging from the slit increases and the two interfering
beams have unequal intensities.
A. Statement I is True and Statement 2 is True and is correct explanation of Statement 1
B. Statementl is True and Statement 2 is True but not the correct explanation of Statement t.
c. statement lis False and statement 2 is False
D. Statement lis True and Statement 2 is False
Subject: Maths
Assertion: An isosceles \( \Delta \) is right angled.
Reason \( : \angle A=\angle B=45^{\circ} \) and \( \angle C= \)
\( \mathbf{9 0}^{\circ} \)
Which of the following statement is
true?
A. A is true and \( \mathrm{R} \) is the correct explanation of
B. A is true and R is not the correct explanation of
c. A is false
D. None of these
Subject: Physics
A rectangular loop carrying a current \( i \) is placed in a uniform magnetic field \( B \). The area enclosed by the loop is \( A \). If there are \( n \) turns in the loop, the torque acting on the loop is given by
\( \mathbf{A} \cdot n i(\bar{A} \times \bar{B}) \)
в. \( n i(\overline{A . \bar{B}}) \)
\( \frac{i(\bar{A} \times \bar{B})}{n} \)
D. \( \frac{i(\bar{A} . \bar{B})}{n} \)
Subject: Physics
Light travels through a glass plate of
thickness 't' and refractive index 'n'. If c
is the velocity of light in vacuum, then the time taken by light to travel through the thickness of the plate will be
A \( \cdot \frac{n t}{c} \)
B. \( \frac{t}{n c} \)
c. \( \frac{t c}{n} \)
D. \( \frac{c}{n t} \)
Subject: Chemistry
Regarding dipole-dipole attractions the
incorrect statement is:
This question has multiple correct options
A. dipole-dipole attractions are more, if the molecules have height dipole moment values.
B. in liquid \( H B r \) dipole-dipole attractions are present
C. dipole-dipole interaction energy between stationary polar molecules as in solids \( \propto r^{-3} \)
D. dipole-dipole interaction energy between rotating molecules \( \propto r^{6} \)
Subject: Physics
The possible relationship between
magnitudes of \( " \boldsymbol{V}_{1} \) " and \( " \boldsymbol{V}_{2} \) " is :
\( \mathbf{A} \cdot V_{1}>V_{2} \)
\( \mathbf{B} \cdot V_{1}<V_{2} \)
\( \mathbf{c} \cdot V_{1}=V_{2} \)
D. Both A and C
Subject: Chemistry
A certain reaction is non-spontaneous at \( 300 \mathrm{K} \). The entropy change during the reaction is \( 120 J K^{-1} \). Then the
minimum value of \( \Delta H \) for the reaction
and the nature of the reaction will be:
A. 36.0 kj; endothermic
B. 36.0 kJ; exothermic
c. \( 2.8 \mathrm{kJ} \); endothermic
D. \( -2.8 \mathrm{kJ} \); exothermic
Subject: Chemistry
The correct order of increasing \( s \) character (in percentage) in the hybrid orbitals of the given molecules/ions is (assume all hybrid orbitals are exactly equivalent):
\( \boldsymbol{C H}_{2} \quad \boldsymbol{X} \boldsymbol{e F}_{4} \quad \boldsymbol{B r} \boldsymbol{F}_{3} \quad \boldsymbol{N C l}_{3} \quad: \boldsymbol{C C l}_{2} \)
\( \mathbf{A} \cdot\|<\| \mathbf{I}<\mid V<1=\mathbf{V} \)
B. \( |>V>|||>|V>| \mid \)
\( c \cdot\|1<\|<1<V<1 V \)
D. \( \|<I V<\| 1<1<V \)
Subject: Chemistry
The enthalpies of formation of \( N_{2} O \) and
\( N O \) are 28 and \( 90 k J m o l^{-1} \)
respectively. The enthalpy of the
reaction, \( 2 N_{2} O(g)+O_{2}(g) \longrightarrow \)
\( 4 N O(g) \) is equal to :
\( A \cdot 8 k J \)
B. 88 kJ
c. \( -16 k J \)
D. 304 kJ
Subject: Physics
A thin uniform tube is bent into a circle
of radius \( r \) in the vertical plane. Equal volumes of two immiscible liquids,
whose densities are \( \rho_{1} \) and \( \rho_{2}\left(\rho_{1}>\rho_{2}\right) \)
fill half the circle. The angle \( \theta \) between
the radius vector passing through the common interface and the vertical is:
\( \boldsymbol{\theta}=\tan ^{-1}\left[\frac{\pi}{2}\left(\frac{\rho_{1}-\rho_{2}}{\rho_{1}+\rho_{2}}\right)\right] \)
B. \( \quad \theta=\tan ^{-1} \frac{\pi}{2}\left(\frac{\rho_{1}-\rho_{2}}{\rho_{1}+\rho_{2}}\right) \)
\( ^{\mathrm{C}} \theta=\tan ^{-1} \pi\left(\frac{\rho_{1}}{\rho_{2}}\right) \)
D. None of above
Subject: Chemistry
An ideal aqueous solution containing liquid \( \boldsymbol{A}(M \cdot W \boldsymbol{t}=\mathbf{1 2 8}) \mathbf{6 4 \%} \) by weight
has a vapour pressure of \( 145 m m H g \). If
the vapour pressure of \( \boldsymbol{A} \) is \( \boldsymbol{x} \) mm of \( H g \) and that of water is \( 155 m m H g \) at the same temperature. Then find \( \frac{x}{5} . \) The solutions is ideal.
Subject: Physics
The plane of a dip circle is set in the geographical meridian and the apparent dip is \( \theta_{1} \). If it is set in a vertical plane perpendicular to the geographical meridian, then the
apparent dip becomes \( \theta_{2} \). The angle of declination \( \alpha \) at the given place is given by :
A. \( \tan \alpha=\sqrt{\left(\tan \theta_{1} \tan \theta_{2}\right)} \)
B. \( \tan \alpha=\frac{\tan \theta_{1}}{\tan \theta_{2}} \)
\( c \cdot \tan \alpha=\tan \theta_{1}+\tan \theta_{2} \)
D. \( \tan \alpha=\frac{\tan \theta_{2}}{\tan \theta_{1}} \)