AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Physics
Assertion: Radio waves can'be
polarised.

Reason: Sound waves in air are
longitudinal in nature.
A. If both assertion and reason are true but the reason is the correct explanation of assertion
B. If both assertion and reason are true but the reason is not the correct explanation of assertion
c. If assertion is true but reason is false
D. If both the assertion and reason are false
E. If reason is true but assertion is false
Subject: Maths
The function \( \boldsymbol{f}:(-\infty,-1) \rightarrow\left(\mathbf{0}, e^{5}\right] \)
defined by \( f(x)=e^{x^{3}-3 x+2} \) is
A. many-one and onto
B. many-one and into
c. one-one and onto
D. one-one and into
Subject: Chemistry
Which of the following equations corresponds to the definition of
enthalpy of formation at \( 298 K ? \)
A \( \cdot C(\text { graphite })+2 H_{2}(g)+\frac{1}{2} O_{2}(g) \longrightarrow C H_{3} O H(l) \)
B \( \cdot 2 C(\text { graphite })+4 H_{2}(g)+O_{2}(g) \longrightarrow 2 C H_{3} O H(l) \)
c. \( C(\text { diamond })+2 H_{2}(g)+\frac{1}{2} O_{2}(g) \longrightarrow C H_{3} O H(l) \)
D. \( C(\text { graphite })+2 H_{2}(g)+\frac{1}{2} O_{2}(l) \longrightarrow C H_{3} O H(g) \)
Subject: Chemistry
The solubility of \( N a C l(s) \) in water at
\( 298 K \) is about 6 moles per litre.

Suppose you add 1 mole of \( N a C l(s) \) to a litre of water. For the reaction:
\( N a C l(s)+H_{2} O \rightarrow N a C l(a q) \)
A. \( \Delta G>0, \Delta S>0 \)
в. \( \Delta G<0, \Delta S>0 \)
c. \( \Delta G>0, \Delta S<0 \)
D. \( \Delta G<0, \Delta S<0 \)
Subject: Maths
For the probability distribution function
of random variable \( X, x_{1}, x_{2}, x_{3}, \dots x_{n} \)
are the values \( X \) takes, and \( p\left(x_{i}\right) \)
denote the probability of \( x_{i} \) then which
one of the following is true.? This question has multiple correct options
\( \mathbf{A} \cdot p\left(x_{i}\right)>0 \)
в. \( p\left(x_{i}\right)<0 \)
\( \mathbf{c} \cdot \sum p\left(x_{i}\right)=1 \)
D. \( \sum x_{i}=1 \)
Subject: Chemistry
Which of the following statement is not
correct?
\( \mathbf{A} \cdot L a(O H)_{3} \) is less basic than \( L u(O H)_{3} \)
B. In Lanthanoid series ionic radius of \( \mathrm{Ln}^{3+} \) ions
decreases
C. La is actually an element of transition series rather than Lanthanoid series
D. Atomic radii of Zr and Hf are same because of
Lanthanoid contraction
Subject: Chemistry
Which one of the following complexes is an outer orbital complex?
\( A \)
\( \left[F e(C N)_{4}\right]^{6-} \)
в. \( \left[F e(C N)_{6}\right]^{4} \)
c. \( \left[\mathrm{Co}\left(\mathrm{NH}_{3}\right)_{6}\right]^{3+} \)
D. \( \left[N i\left(N H_{3}\right)_{6}\right]^{2+} \)
Subject: Chemistry
Assertion: Preservatives are added to
food items
Reason : Preservatives inhibit the
growth of microorganisms
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. Both Assertion and Reason are incorrect
D. Assertion is correct but Reason is incorrect
E. Assertion is incorrect but Reason is correct
Subject: Physics
Imagine an atom made of a proton and a hypothetical particle of double the mass of the electron but having the same charge as the electron. Apply Bohr atom model and consider all possible transitions of this hypothetical particle to the first excited level. The longest
wavelength photon that will be emitted has wavelength [Rydberg Constant = R] equal to
A. \( \frac{9}{5 R} \)
в. \( \frac{36}{5 R} \)
c. \( \frac{18}{5 R} \)
D. \( \frac{4}{R} \)
Subject: Maths
The centroid of triangle \( \boldsymbol{A}(\mathbf{3}, \mathbf{4}, \mathbf{5}) ; \boldsymbol{B}(\mathbf{6}, \mathbf{7}, \mathbf{2}) ; \boldsymbol{C}(\mathbf{0},-\mathbf{5}, \mathbf{2}) \) is
A \( .(3,2,3) \)
в. (5,2,1)
c. (2,5,1)
D. (3,4,1)
Subject: Chemistry
Which of the following compounds is not coloured?
A \( \cdot N a_{2}\left[C u C l_{4}\right] \)
B . \( N a_{2}\left[C d C l_{2}\right] \)
\( \mathbf{c} \cdot\left[\operatorname{Cr}\left(H_{2} O\right)_{6}\right] C l_{3} \)
D. all of the above
Subject: Physics
A hydrogen atom \( \left(\operatorname{mass}=1.66 \times 10^{-27}\right. \)
kg, ionization potential = \( 13.6 e V \) ), moving with a velocity of \( 6.24 \times \) \( 10^{4} m s^{-1} \) makes a completely inelastic
head-on collision with another
stationary hydrogen atom. Both atoms are in the ground state before collision.
Up to what state either of one atom may
be excited?
Subject: Physics
Thin films like soap bubbles and oil
floating on water can create colorful
patterns. Which of the following explanations most accurately describes why this happens?
A. Thin films contain many different colored chemicals
B. Thin films diffract and refract light so that it sets up interference patterns
c. Thin films provide reflection from the front and back surfaces, and this creates interference patterns
D. Thin films polarize light which interferes with the unpolarized light to create colors
E. Thin films absorb some colors and allow others to reflect
Subject: Physics
A water jet, whose cross sectional are is
'a' strikes a wall making an angle ' \( \boldsymbol{\theta}^{\prime} \)
with the normal and rebounds
elastically. The velocity of water of
density 'd' is v. Force exerted on wall is
A \( \cdot 2 a v^{2} d \cos \theta \)
B. \( 2 a v^{2} d \sin \theta \)
c. 2 avd \( \cos \theta \)
D. avd cose
Subject: Maths
A symmetrical die is thrown 6 times. If getting an odd number is a success, the probability of at the most 5 successes
is
A \( \cdot \frac{5}{64} \)
в. \( \frac{15}{64} \)
c. \( \frac{63}{64} \)
D. \( \frac{36}{64} \)
Subject: Physics
Assertion
If a charged particle enters from outside at right angles in uniform
magnetic field.The maximum time spent in magnetic field may be \( \frac{\pi m}{B q} \)
Reason

It can complete only semi-circle in the magnetic field.
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: Chemistry
Balance the following equation.
\( \boldsymbol{F} \boldsymbol{e} \boldsymbol{S}_{2}+\boldsymbol{O}_{2} \rightarrow \boldsymbol{F} \boldsymbol{e}_{2} \boldsymbol{O}_{3}+\boldsymbol{S} \boldsymbol{O}_{2} \)
Subject: Maths
\( \left|\begin{array}{ccc}1 ! & 2 ! & 3 ! \\ 2 ! & 3 ! & 4 ! \\ 3 ! & 4 ! & 5 !\end{array}\right|=2016 K \)
then value of \( \boldsymbol{K} \) is
A . 24
B. 84
c. \( \frac{1}{24} \)
D. \( \frac{1}{84} \)
Subject: Maths
Draw the graph for the linear equation \( 3 y+5=0 \) and select the correct
option:
A. The line is parallel to the \( x \) -axis and passes through \( \left(0,-\frac{5}{3}\right) \)
B. The line is parallel to the \( y \) -axis and passes through \( \left(0,-\frac{5}{3}\right) \)
c. The line is parallel to the \( x \) -axis and passes through \( \left(0, \frac{5}{3}\right) \)
D. The line is parallel to the \( y \) -axis and passes through \( \left(0, \frac{5}{3}\right) \)
Subject: Maths
The value of \( \lim _{x \rightarrow 1} \frac{x^{m}-1}{x^{n}-1} \) is?
\( A \cdot \frac{m}{n} \)
в. \( \frac{n}{m} \)
c. \( \frac{n^{2}}{m^{2}} \)
D. \( \frac{m^{2}}{n^{2}} \)
Subject: Maths
Given that \( i z^{2}=1+\frac{2}{z}+\frac{3}{z^{2}}+\frac{4}{z^{3}}+\frac{5}{z^{4}}+ \)
\( \ldots . \) and \( z=n \pm \sqrt{-i}, \) find \( \lfloor 100 n\rfloor \)
Subject: Physics
A current i, indicated by the crosses in
figure, is established in a strip of
copper of height h and width w. A
uniform field of magnetic induction B is applied at right angle to the strip.
f the drift velocity \( v_{d} \) of the electrons is
\( \boldsymbol{v}_{\boldsymbol{d}}=\mathbf{1 . 4} \times \mathbf{1 0}^{-\boldsymbol{x}} \boldsymbol{m} \boldsymbol{s}^{-1} . \) Find \( \mathbf{x} \)
Subject: Maths
The population of a town is 1200 in
2010. From 2010 to 2015, the
population of the town increased by \( 10 \% \) per year. Whats the population of the town in \( 2015 ? \)
A .4932 .612
B . 3932.612
c. 2932.612
D. 1932.612
Subject: Chemistry
The correct statement about \( I C l_{5} \) and
\( \boldsymbol{I} \boldsymbol{C l}_{4}^{-} \) is:
A \( \cdot I C l_{5} \) is trigonal bipyramidal and \( I C l_{4}^{-} \) is tetrahedral
B. \( I C l_{5} \) is square pyramidal and \( I C l_{4} \) is tetrahedral
C . \( I C l_{5} \) is square pyramidal and \( I C l_{4}^{-} \) is square planar
D. both are isostructural
Subject: Chemistry
Identify the correct statement about nomenclature of alkylidene dihalides.
A. Dihaloalkanes in which two halogen atoms of the same type are present on the same carbon atom are called alkylidene dihalides.
B. In common naming system these are called as alkylene dihalides
c. In the IUPAC system, the locants for the two halogen atoms are prefixed to the name of dihaloalkane.
D. Both \( A \) and \( C \)
Subject: Maths
If \( |\boldsymbol{x}|<1 \) then \( \mathbf{7}^{\text {th}} \) term in the expansion
of \( (1-x)^{-2} \) is
A \( \cdot 7 x^{8} \)
В . \( 7 x^{6} \)
\( c \cdot 6 x^{7} \)
D. \( 6 x^{6} \)
Subject: Physics
Two infinitely long parallel plates of equal areas \( 6 \mathrm{cm}^{2} \) are separated by a distance of \( 1 \mathrm{cm} . \) While one of the plates has a charge of \( +10 n C \) and the other
has \( -10 n C . \) The magnitude of the
electric field between the plates, if \( \varepsilon_{0}= \) \( \frac{10^{-9}}{36 \pi} F / m \) is?
A. \( 0.6 \pi V / m \)
в. \( 6 \pi k V / m \)
c. \( 600 \pi k V / m \)
D. \( 60 \pi V / m \)
E . \( 6 \pi \)
Subject: Physics
The angle between two vectors \( \vec{A}= \) \( 4 \hat{i}+3 \hat{j}-2 \hat{k} \) and \( \vec{B}=-8 \hat{i}-6 \hat{j}+4 \hat{k} \) is
\( \mathbf{A} \cdot \pi / 4 \)
в. \( \pi / 3 \)
\( c \)
D. \( \pi / 2 \)
Subject: Physics
An enclosure of volume 3 litre contains 16
\( \mathrm{gms} \) of oxygen, \( 7 \mathrm{gms} \) of nitrogen and 11 gms of carbon di-oxide at \( 27^{\circ} \mathrm{C} \). The
pressure exerted by the mixture is approximately
A. 1 atmosphere
B. 3 atmosphere
c. 9 atmosphere
D. 8.3 atmosphere
Subject: Maths
In an acute angled triangle \( A B C, A P \) is
the altitude. Circle drawn with AP as its
diameter cuts the sides \( A B \) and \( A C \) at \( D \)
and \( \mathrm{E} \), respectively, then length DE is equal to
A \( \cdot \frac{\Delta}{2 R} \)
в. \( \frac{\Delta}{3 R} \)
c. \( \frac{\Delta}{4 R} \)
D. \( \frac{\Delta}{R} \)
Subject: Chemistry
Thermal stability of \( B a C O_{3}, C a C O_{3} \)
and \( M g C O_{3} \) is:
А. \( B a C O_{3}>C a C O_{3}>M g C O_{3} \)
в. \( B a C O_{3}>M g C O_{3}>C a C O_{3} \)
с. \( C a C O_{3}>M g C O_{3}>B a C O_{3} \)
D. \( M g C O_{3}>C a C O_{3}>B a C O_{3} \)
Subject: Chemistry
A monoprotic acid in \( 1.00 M \) solution is
\( 0.001 \% \) ionised. The dissociation
constant of acid is:
A \( \cdot \alpha^{2} C+\alpha K-K=0 \)
B . \( \alpha^{2} C-\alpha K-K=0 \)
c. \( \alpha^{2} C-\alpha K+K=0 \)
D \( \cdot \alpha^{2} C+\alpha K+K=0 \)
Subject: Physics
A body of mass 2 g, moving along the positive \( x- \) axis in gravity free space
with velocity \( 20 \mathrm{cms}^{-1} \) explodes at \( x= \) \( \mathbf{1} \mathbf{m}, \boldsymbol{t}=\mathbf{0} \) into two pieces of masses \( \frac{\mathbf{2}}{\mathbf{3}} \)
\( \mathrm{g} \) and \( \frac{4}{3} \) g. After \( 5 \mathrm{s} \), the lighter piece is at the point \( (3 m, 2 m,-4 m) . \) Then the position of the heavier piece at this moment, in metres is
в. (1.5,-2,-2)
\begin{tabular}{l} 
c. (1.5,-1,-1) \\
\hline
\end{tabular}
D. None of these
Subject: Physics
Two marks on a glass rod \( 10 \mathrm{cm} \) apart are found to increase their distance by \( 0.08 \mathrm{mm} \) when the rod is heated from
\( 0^{\circ} \mathrm{C} \) to \( 100^{\circ} \mathrm{C} \). A flask made of the same
glass as that of rod measures a volume
of \( 100 \mathrm{cc} \) at \( 0^{\circ} \mathrm{C} \). The volume it
measures at \( 100^{\circ} \mathrm{C} \) in cc is
A . 100.24
B. 100.12
c. 100.36
D. 100.48
Subject: Maths
Construct a \( \triangle \boldsymbol{X} \boldsymbol{Y} \boldsymbol{Z} \) in which \( \boldsymbol{X} \boldsymbol{Y}=\boldsymbol{4} . \mathbf{5} \)
\( \mathrm{cm}, Y Z=5 \mathrm{cm} \) and \( Z X=6 \mathrm{cm} \)
Subject: Chemistry
Assertion
In natural tris chelating complex,
\( \left[\boldsymbol{C o}(\boldsymbol{a c a c})_{3}\right], \) in each ring the two \( \mathrm{M}-\mathrm{O} \)
bonds are equal to length, as are two \( \mathrm{C} \) O and the two C-C bonds because,
Reason

In each ring resonance takes place.
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
\( \operatorname{Let} f^{\prime}(x)=e^{x^{2}} \) and \( f(0)=10 . \) If \( A< \)
\( f(1)<B \) can be concluded from the
mean value theorm, then the largest value of \( (\boldsymbol{A}-\boldsymbol{B}) \) equals
\( A \)
B. \( 1-e \)
\( \mathbf{c} \cdot e-1 \)
D. \( 1+e \)
Subject: Chemistry
\( \mathbf{0 . 1 6} \boldsymbol{g} \boldsymbol{N}_{\mathbf{2}} \boldsymbol{H}_{4}\left(\boldsymbol{K}_{\boldsymbol{b}}=\mathbf{4} \times \mathbf{1 0}^{-\mathbf{6}}\right) \) are
dissolved in water and the total volume
made up to 500 m \( L \). Calculate the
percentage of \( N_{2} H_{4} \) that has reacted to water in this solution.
Subject: Biology
Select the correct match
\( \begin{array}{lll}\text { Hormone } & \text { Target Organ } & \text { Source } \\ \text { CCK-PZ } & \begin{array}{l}\text { Gallbladder and } \\ \text { pancreas }\end{array} & \begin{array}{l}\text { Small } \\ \text { intestine }\end{array} \\ \text { GIP } & \begin{array}{l}\text { Gastrointestinal } \\ \text { tract }\end{array} & \text { Pancreas } \\ \text { Gastrin } & \text { Liver and stomach } & \text { Duodenum } \\ \text { Secretin } & \begin{array}{l}\text { Liver and } \\ \text { gallbladder }\end{array} & \text { Duodenum }\end{array} \)
Subject: Chemistry
Match the following.
List-I \( \quad \) List-II (Monomer)
A) Sucrose
i) \( \beta \) -D-Galactose and \( \beta \) -D-Glucose
B) Cellulose
ii) \( \alpha \) -D-Glucose and \( \beta \) -D-Fructose
c) Starch
iii) \( \beta \) -D-Glucose
D) Lactose
iv) \( \alpha \) -D-Glucose
A. A-i; B-ii; C-iii; D-iv
B. A-ii; B-i; C-iii; D-iv
c. A-ii; B-iii; C-iv; D-i
D. A-iv; B-iii; C-i; D-ii
Subject: Maths
The solution of differential equation
\( x \cos ^{2} y d x=y \cos ^{2} x d y \) is
A \( \cdot x \tan x-y \tan y-\log \left(\frac{\sec x}{\sec y}\right)=c \)
B. \( y \tan x-x \tan y-\log (\sec x \cdot \sec y)=c \)
c. \( x \tan x-y \tan y+\log (\sec x \cdot \sec y)=c \)
D. None of the above
Subject: Maths
If \( \boldsymbol{y}^{\prime}-\mathbf{3} \boldsymbol{y}^{\prime}+\mathbf{2} \boldsymbol{y}=\mathbf{0} \) where \( \boldsymbol{y}(\mathbf{0})= \)
1 \( , y^{\prime}(0)=0, \) then the value of \( y \) at \( x= \)
\( \log 2 \) is
A .
B. - -
\( c \cdot 2 \)
D.
Subject: Physics
Water jet is coming out of a hose pipe of diameter \( 20 \mathrm{cm} \) with speed \( 20 \mathrm{cm} / \mathrm{sec} \)
It strike a man inelastically. Find the force exerted by water jet on the person.
A . \( 5.04 N \)
B. \( 1.26 N \)
c. \( 2.52 N \)
D. \( 9.4 N \)
Subject: Chemistry
Which of the following is/are true statement(s)?

This question has multiple correct options
A. Water vapour is absorbed by anhydrous calcium chloride while it is adsorbed by silica gel.
B. \( N H_{3} \) is absorbed by water but adsorbed by charcoal
c. Sugar is decolourized by animal charcoal based on adsorption
D. water is absorbed by conc. \( H_{2} S O_{4} \)
Subject: Physics
The diameter of iron wheel is \( 1 \mathrm{cm} \). If its
temperature is increased by \( 700^{\circ} \mathrm{C} \)
What is the increase in circumference
of the wheel?
\( \left(\alpha=12 \times 10^{-6} /^{\circ} \mathrm{C}\right) \)
A . \( 0.0264 \mathrm{cm} \)
B. \( 0.264 \mathrm{cm} \)
c. \( 2.64 \mathrm{cm} \)
D. \( 26.4 \mathrm{cm} \)
Subject: Maths
Two sets of candidates are competing for the positions on the board of directors of a company. The probabilities that first and second sets will win are 0.6 and 0.4 respectively. If the first set wins the probability of introducing a new product is 0.8 and the corresonding probability if the second set wins is 0.3. The probability that the new product will be introduced
is \( 0.1 k . \) Find the value of \( k \)
Subject: Maths
\( \sum_{r=1}^{n} r(n-r) \)
\( \mathbf{A} \cdot \frac{1}{6} n(n+1)(2 n+1) \)
B \( \cdot\left(\frac{n(n+1)}{2}\right)^{2} \)
C \( \cdot \frac{n^{2}(n+1)}{6} \)
D. \( \frac{n\left(n^{2}-1\right)}{6} \)
Subject: Chemistry
What changes occur when acidified \( C r_{2} O_{7}^{2-} \) ion reacts with \( H_{2} O_{2} \) solution
in presence of ether solvent?
A. orange colour of solution turns blue
B. Oxidation state of \( C r \) atom increases
c. oxidation state of \( C r \) atom remains constant
D. Orange colour turns green
Subject: Chemistry
Assertion
Combustion of \( N_{2} \) to give NO is
endothermic.
Reason
Bond energy of \( N_{2} \) is very high.
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
\( a, b, c \) are three positive numbers and
\( a b c^{2} \) has greatest value \( \frac{1}{64} . \) Then
A \( \cdot a=b=\frac{1}{2}, c=\frac{1}{4} \)
В \( \cdot a=b=\frac{1}{4}, c=\frac{1}{2} \)
c. \( a=b=c=\frac{1}{3} \)
D. none of these
Subject: Maths
Assertion
The relation \( \boldsymbol{R} \) given by
\( \boldsymbol{R}=\{(\mathbf{1}, \mathbf{3}),(\mathbf{4}, \mathbf{2}),(\mathbf{2}, \mathbf{4}),(\mathbf{2}, \mathbf{3}),(\mathbf{3}, \mathbf{1})\} \)
on a set \( A=\{1,2,3,4\} \) is not
symmetric.
Reason
For symmetric relation \( \boldsymbol{R}=\boldsymbol{R}^{-1} \)
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
Expand the polynomial: \( \left(3 x^{2}-1\right)\left(x^{2}+\right. \)
\( \boldsymbol{x}+\mathbf{1}) \)
A \( \cdot 3 x^{4}+3 x^{3}+3 x^{2}+x^{2}-x-1 \)
B. \( 3 x^{4}+3 x^{3}+x^{2}-x^{2}-x-1 \)
c. \( 3 x^{4}+3 x^{3}+2 x^{2}-x-1 \)
D. \( 3 x^{4}-3 x^{3}+3 x^{2}-x^{2}-x-1 \)
Subject: Physics
Assertion
Inertia is the property by virtue of which the body is unable to change by itself, its state of rest or motion and its
direction of motion.
Reason
The bodies do not change their state
unless acted upon by an unbalanced external force
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
In a sequence of 21 terms, the first 11
term are in \( A . P \) with common
difference 2 and the last 11 terms are in
\( G . P . \) with common ratio \( 2 . \) If the middle
term of the \( A . P . \) is equal to the middle
term of \( G . P . \) The find the middle term
of the entire sequence.
Subject: Maths
Let \( y=y(x) \) be the solution of the differential equation \( \frac{\boldsymbol{d} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}}+\boldsymbol{2} \boldsymbol{y}=\boldsymbol{f}(\boldsymbol{x}) \)
where \( \boldsymbol{f}(\boldsymbol{x})=\left\{\begin{array}{ll}\mathbf{1}, & \boldsymbol{x} \in[\mathbf{0}, \mathbf{1}] \\ \mathbf{0}, & \text { otherwise }\end{array}\right. \)
If \( \boldsymbol{y}(\mathbf{0})=\mathbf{0}, \) then \( \boldsymbol{y}\left(\frac{\mathbf{3}}{\mathbf{2}}\right) \) is
\( ^{A} \cdot \frac{e^{2}-1}{2 e^{3}} \)
в. \( \frac{e^{2}-1}{e^{3}} \)
c. \( \frac{1}{2 e} \)
D. \( \frac{e^{2}+1}{2 e^{4}} \)
Subject: Maths
A chord of a circle is \( 12 \mathrm{cm} \) which is at a distance of \( 8 \mathrm{cm} \) from center. Find the length of the chord of the same circle
which is at a distance of \( 6 \mathrm{cm} \) from the
centre
\( A \cdot 20 \mathrm{cm} \)
B. \( 24 \mathrm{cm} \)
\( c .16 \mathrm{cm} \)
D. \( \mathrm{cm} \)
Subject: Maths
In the figure (not drawn to scale), BCF is
an isosceles triangle with \( \mathrm{FC}=\mathrm{FB}, \mathrm{EBF} \)
and \( A B C \) are straight lines, EB is paralle
to GC. Find \( x \).
A \( .264^{\circ} \)
B. \( 84^{\circ} \)
\( c \cdot 118^{\circ} \)
D. 200
Subject: Physics
Assertion
Ratio of maximum intensity and minimum intensity in interference is 25
1. Hence amplitude ratio of two waves should be 3: 2
Reason
\( \frac{\boldsymbol{I}_{m a x}}{\boldsymbol{I}_{m i n}}=\left(\frac{\boldsymbol{A}_{1}+\boldsymbol{A}_{2}}{\boldsymbol{A}_{1}-\boldsymbol{A}_{2}}\right)^{2} \)
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
The radius of curvature of concave
mirror is \( 24 \mathrm{cm} \) and the image is magnified by 1.5 times. The object distance is
A. \( 20 \mathrm{cm} \)
B. \( 8 \mathrm{cm} \)
\( c \cdot 16 \mathrm{cm} \)
D. \( 24 \mathrm{cm} \)
Subject: Physics
A sphere and a disc of same radii and
mass are rolling on an inclined plane
without slipping. \( a_{s} \& a_{d} \) are
acceleration and \( g \) is acceleration due
to gravity. Then which statement is
correct?
\( \mathbf{A} \cdot a_{s}>a_{d}>g \)
В \( \cdot g>a_{s}>a_{d} \)
\( \mathbf{c} \cdot a_{s}>g>a_{d} \)
D \( \cdot a_{d}>a_{s}>g \)
Subject: Physics
Two condensers of capacities \( 10 \mu F \) and \( 20 \mu F \) have potential differences of \( 20 \mathrm{V} \)
and \( 10 \mathrm{V} \) respectively. The total charge is
A \( .200 \mu C \)
в. \( 600 \mu C \)
c. \( 400 \mu C \)
D. zero
Subject: Physics
Find the density of lattice, A compound
AB has a rock type structure with \( A: B= \)
1 : 1. The formula mass of AB is 6.023 Y
amu and the closed \( A \) -B distance is
\( \boldsymbol{Y}^{1 / 3} \mathrm{nm} \)
A \( \cdot 4 \mathrm{kg} / m^{3} \)
в. \( 5 \mathrm{kg} / \mathrm{m}^{3} \)
c. \( 40 \mathrm{kg} / \mathrm{m}^{3} \)
D. \( 50 \mathrm{kg} / \mathrm{m}^{3} \)
Subject: Maths
If \( \mathbf{A}=(-\mathbf{1}, \mathbf{6}, \mathbf{6}), \mathbf{B}=(-\mathbf{4}, \mathbf{9}, \mathbf{6}), \mathbf{G}= \)
\( \frac{1}{3}(-5,22,22) \) and \( G \) is the centroid of
the \( \Delta A B C \) then the name of the
triangle \( \mathbf{A B C} \) is
A. an isosceles triangle
B. a right angled triangle
c. an equilateral triangle
D. a right-angled isosceles triangle
Subject: Chemistry
When \( N a \) and \( L i \) placed in dry air we
get :
A. \( N a O H, N a_{2} O, L i_{2} O \)
в. \( N a_{2} C O_{3}, N a_{2} O_{2}, L i_{2} O \)
c. \( N a_{2} O, L i_{3} N, N H_{3} \)
D. \( N a_{2} O, L i_{2} O, L i_{3} N \)
Subject: Maths
The probability distribution of a random variable is given below:
\[
\begin{array}{llll}
\boldsymbol{X}=\boldsymbol{x} & 0 & 1 & 2 \\
P(X= & 0 & K & 2 K
\end{array}
\]
\( 2 k \quad 3 K \)
\[
x)
\]
\[
\text { Then } \boldsymbol{P}(\mathbf{0}<\boldsymbol{X}<\mathbf{5})=
\]
A \( \cdot \frac{1}{10} \)
B. \( \frac{3}{10} \)
\( c \cdot \frac{8}{10} \)
D. \( \frac{7}{10} \)
Subject: Maths
\( \int \frac{d x}{9+16 \sin ^{2} x} \) is equal to
A \( \cdot \frac{1}{3} \tan ^{-1}\left(\frac{3 \tan x}{5}\right)+c \)
B \( \cdot \frac{1}{5} \tan ^{-1}\left(\frac{\tan x}{15}\right)+c \)
c. \( \frac{1}{15} \tan ^{-1}\left(\frac{\tan x}{5}\right)+c \)
D. \( \frac{1}{15} \tan ^{-1}\left(\frac{5 \tan x}{3}\right)+c \)
Subject: Chemistry
The gases \( (\mathrm{B}),(\mathrm{C}) \) and \( (\mathrm{D}), \) respectively
are:
A. \( H C \equiv C H, C O_{2} \) and \( H_{2} \)
B. \( H C \equiv C H, H_{2} \) and \( C O_{2} \)
c. \( C H_{3}-C \equiv C-C H_{3}, C O_{2} \) and \( H_{2} \)
D. \( C H_{3}-C \equiv C-H, H_{2} \) and \( C O_{2} \)