AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Chemistry
Match the column I with II and column I
and mark the appropriate choice.
Column I

İ
Uncertainty of an
(i)
(A) \( \quad \) object
(B) Bohr's radius of an
(ii) \( \frac{h}{4 \pi m} \) orbit
Angular
(C) momentum of an
(iii) \( \frac{h}{m v} \) electron
(D) de Broglie
(iv) \( n \cdot \frac{h}{2 \pi} \) wavelength
A \( \cdot(A) \rightarrow(i i i),(B) \rightarrow(i v),(C) \rightarrow(i),(D) \rightarrow(i i) \)
в. \( (A) \rightarrow(i i),(B) \rightarrow(i),(C) \rightarrow(i v),(D) \rightarrow(i i i) \)
C. \( (A) \rightarrow(i v),(B) \rightarrow(i i i),(C) \rightarrow(i),(D) \rightarrow(i i) \)
D. \( (A) \rightarrow(i),(B) \rightarrow(i i),(C) \rightarrow(i v),(D) \rightarrow(i i i) \)
Subject: Chemistry
Assertion
Ney York City may submerge due to global warming.
Reason
Due to global warming, glaciers are melting and due to this sea-level will be
certainly increasing which may cause flooding of cities situated at the bank of
the sea. New York is one of them.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
C. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect
Subject: Maths
Let \( f(x)=\sin ^{23} x-\cos ^{22} x \) and
\( \boldsymbol{g}(\boldsymbol{x})=\mathbf{1}+\frac{\mathbf{1}}{\mathbf{2}} \tan ^{-\mathbf{1}}|\boldsymbol{x}| \)
Then, the number of values of \( x \) in
interval \( [-10 \pi, 20 \pi] \) satisfying the equation \( f(x)=\operatorname{sgn}(g(x)), \) is \( 5 a \) Then
\( a \) is
Subject: Physics
A ball moving with a velocity v hits a massive wall moving towards the ball with a velocity u. An elastic impact
lasts for time \( \Delta t \), Then :
This question has multiple correct options
A. the average elastic force acting on the ball is \( [m(u+ \)
\( v)] / \Delta t \)
B. the average elastic force acting on the ball is \( [2 m(u+ \)
\( v)] / \Delta t \)
c. the kinetic energy of the ball increases by 2 mu \( (u+v) \)
D. the kinetic energy of the ball remains the same after the collision
Subject: Maths
There are 30 tickets numbered from 1 to
30 in a box. A ticket is drawn at random.
If \( A \) is the event that the number on the
ticket is a prime number less than 15 write the sample space \( S, n(S) \) the event \( \boldsymbol{A} \) and \( \boldsymbol{n}(\boldsymbol{A}) \)
Subject: Maths
\( A B C D \) is a rectangle and \( \angle B O C= \)
\( 66^{\circ} . \) The value of \( x \) is
A \( \cdot 104^{\circ} \)
B. \( 114^{\circ} \)
\( c \cdot 60^{\circ} \)
\( D \cdot 33^{\circ} \)
Subject: Physics
Assertion
More force is required to push a body up
a rough inclined plane than that to
move the same body down the same
plane
Reason
The friction always acts parallel to
inclined plane downwards
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
When \( C l_{2} \) is passed through cold dil
NaOH, the products are :
\( \begin{array}{llll}\text { A. } N a C l, & \text { NaOCl } & \text { and } & H_{2} O\end{array} \)
B. NaCl, \( \quad N a C l_{2} \) and \( H_{2} O \)
\( \begin{array}{lll}\text { C. } N a C l, & N a C l_{3} & \text { and } & H_{2} O\end{array} \)
D. \( N a C l, \quad N a C l_{4} \quad \) and \( \quad H_{2} O \)
Subject: Chemistry
Name the following coordination entities and draw the structures of their
steroisomers:
(i) \( \left[\boldsymbol{C o}(\boldsymbol{e n})_{2} \boldsymbol{C l}_{2}\right]^{+}(\boldsymbol{e n}=\boldsymbol{e t h a n e}- \)
1, 2 - diamine)
(ii) \( \left[\boldsymbol{C r}\left(\boldsymbol{C}_{2} \boldsymbol{O}_{4}\right)_{3}\right]^{3-} \)
(iii) \( \left[\boldsymbol{C o}\left(\boldsymbol{N} \boldsymbol{H}_{3}\right)_{3} \boldsymbol{C l}_{3}\right] \)
(Atomic number \( \boldsymbol{C r}=\mathbf{2 4}, \boldsymbol{C o}=\mathbf{2 7}) \)
Subject: Chemistry
Which of the following statements are
correct for an electron that has \( n=4 \)
and \( m=-2 ? \)
This question has multiple correct options
A. The electron may be in a \( d \) -orbital
B. The electron is in the \( 3^{r d} \) -orbital
C . The electron may be in a \( p \) -orbital
D. The electron must have the spin quantum number \( = \) \( 1 / 2 \)
Subject: Biology
Which of the following are correct?
(i) Sponges: Cellular level of organisation
(ii) Cnidaria : Tissue level of
organisation
(iii) Platyhelminthes: Organ level of organisation
(iv) Annelids, Arthropods, Molluscs, Echinoderms and Chordates: Organ
system level of organisation.
A. (i) and (ii) only
B. (ii) and (iv) only
C. (ii) and (iii) only
D. (i), (ii), (iii) and (iv)
Subject: Chemistry
Which is the correct for the following reaction:
\( \boldsymbol{B}(\boldsymbol{O} \boldsymbol{H})_{3}+\boldsymbol{H}_{2} \boldsymbol{O} \rightarrow\left[\boldsymbol{B}(\boldsymbol{O} \boldsymbol{H})_{4}\right]^{-}+ \)
\( \boldsymbol{H}^{+} \)
A. \( B(O H)_{3} \) is a Lewis acid
B. \( B(O H)_{3} \) is a Lewis base
C. \( B(O H)_{3} \) is amphoteric
D. None of the above
Subject: Physics
A thin uniform rod of length \( L \) is bent at its mid point as shown in figure. The distance of the centre of mass from the
point \( \boldsymbol{L} \) is
A \( \cdot \frac{L}{4} \)
в. \( \frac{L}{4} \sin (\theta / 2) \)
c. \( \frac{L}{4} \cos (\theta / 2) \)
D. \( \frac{L}{2} \cos (\theta / 2) \)
Subject: Physics
A gas under constant pressure of \( 4.5 \times \)
\( 10^{5} P a \) when subjected to \( 800 K J \) of
heat, changes the volume from \( 0.5 m^{3} \) to \( 2.0 m^{3} . \) The change in
the internal energy of the gas:
\( \mathbf{A} \cdot 6.75 \times 10^{5} J \)
B . \( 5.25 \times 10^{5} J \)
c. \( 3.25 \times 10^{5} J \)
D. \( 1.25 \times 10^{5} J \)
Subject: Maths
If \( \int \frac{2 x^{2}+3}{\left(x^{2}-1\right)\left(x^{2}+4\right)} d x= \)
\( a \log \left(\frac{x-1}{x+1}\right)+b \tan ^{-1}\left(\frac{x}{2}\right)+c, \) then
values of a and \( b \) are
A. (1,-1)
в. (-1,1)
c. \( \left(\frac{1}{2},-\frac{1}{2}\right. \)
D. \( \left(\frac{1}{2}, \frac{1}{2}\right) \)
Subject: Chemistry
Statement 1: After a period of time in a
closed container, the rate of evaporation
of a liquid will equal the rate of condensation.
Statement 2: An equilibrium will be
established between a liquid and its
vapor in a closed container held at constant temperature.
A. Statement 1 and Statement 2 are correct and Statement 2 is the correct explanation of Statement 1
B. Both the Statement 1 and Statement 2 are correct and Statement 2 is NOT the correct explanation of Statement 1
c. Statement 1 is correct but Statement 2 is not correct.
D. Statement 1 is not correct but Statement 2 is correct
E. Both the Statement 1 and Statement 2 are not correct
Subject: Maths
Prove that
\[
\boldsymbol{f}(\boldsymbol{x})=\left\{\begin{array}{rl}
\frac{\boldsymbol{x}^{2}-\boldsymbol{2 5}}{\boldsymbol{x}-\mathbf{5}}, & \boldsymbol{w} \boldsymbol{h} \boldsymbol{e} \boldsymbol{n} \quad \boldsymbol{x} \neq \mathbf{5} \\
\boldsymbol{1 0}, \boldsymbol{w h e n} & \boldsymbol{x}=\mathbf{5}
\end{array}\right.
\]
continuous at \( \boldsymbol{x}=\mathbf{5} \)
Subject: Maths
For non zero vectors \( a, b \) and \( c, \) if \( a+ \) \( b+c=0 \) then which relation true:
A \( a=b=c=0 \)
0
В. \( a . b=b . c=c . a \)
\( \mathbf{c} \cdot a \times b=b \times c=c \times a \)
D. None
Subject: Physics
Find the \( x \) coordinate of the particle at
the moment of time \( t=6 s \)
\( \mathbf{A} \cdot x=0.4 m \)
B. \( x=0.24 m \)
c. \( x=0.42 \mathrm{m} \)
D. \( x=0.44 \mathrm{m} \)
Subject: Maths
\( \frac{\boldsymbol{x}^{\boldsymbol{4}}-\mathbf{5} \boldsymbol{x}^{\boldsymbol{2}}+\mathbf{1}}{\left(\boldsymbol{x}^{\mathbf{2}}+\mathbf{1}\right)^{\mathbf{3}}}= \)
\( \mathbf{A} \cdot \frac{1}{\left(\mathbf{x}^{2}+1\right)}-\frac{1}{\left(\mathbf{x}^{2}+1\right)^{2}}+\frac{7}{\left(\mathbf{x}^{2}+1\right)^{3}} \)
\( \mathbf{B} \cdot \frac{1}{\left(\mathbf{x}^{2}+1\right)}-\frac{7}{\left(\mathbf{x}^{2}+1\right)^{2}}+\frac{7}{\left(\mathbf{x}^{2}+1\right)^{3}} \)
\( \mathbf{C} \cdot \frac{7}{\left(\mathbf{x}^{2}+1\right)}-\frac{7}{\left(\mathbf{x}^{2}+1\right)^{2}}+\frac{1}{\left(\mathbf{x}^{2}+1\right)^{3}} \)
\( \frac{7}{\left(\mathbf{x}^{2}+1\right)}-\frac{1}{\left(\mathbf{x}^{2}+1\right)^{2}}-\frac{1}{\left(\mathbf{x}^{2}+1\right)^{3}} \)
Subject: Maths
The real part of \( (i-\sqrt{3})^{13} \) is
A \( \cdot 2^{-10} \sqrt{3} \)
B. \( -2^{12} \sqrt{3} \)
\( \mathrm{c} \cdot 2^{-12} \sqrt{3} \)
D. \( -2^{-12} \sqrt{3} \)
E \( .-2^{10} \sqrt{3} \)
Subject: Chemistry
Slowest reaction among the following under identical conditions is:
A \( \cdot N a O H+H C l \rightarrow N a C l+H_{2} O \)
B. \( H^{+}+O H^{-} \rightarrow H_{2} O \)
\( \mathrm{c} \cdot 2 \mathrm{N} \mathrm{O}+\mathrm{O}_{2} \rightarrow 2 \mathrm{N} \mathrm{O}_{2} \)
D. \( C H_{4}+2 O_{2} \rightarrow C O_{2}+2 H_{2} O \)
Subject: Maths
The least positive value of \( x \) satisfying \( \frac{\sin ^{2} 2 x+4 \sin ^{4} x-4 \sin ^{2} x \cos ^{2} x}{4-\sin ^{2} 2 x-4 \sin ^{2} x}=\frac{1}{9} \)
is
A \( \cdot \frac{\pi}{3} \)
B. \( \frac{\pi}{6} \)
c. \( \frac{2 \pi}{3} \)
D. \( \frac{5 \pi}{6} \)
Subject: Biology
Which one of the following is the correct percentage of (the two out of
four) greenhouse gases that contribute to the total globa
warming?
A \( \cdot \mathrm{N}_{2} \mathrm{O} 6 \%, \mathrm{CO}_{2} 86 \% \)
B. Methane 20\%, N_0 18\%\%
c. СFC 14\%, Methane 20\%
D. \( \operatorname{co}_{2} \) 40\%, сFС \( 30 \% \)
Subject: Chemistry
The ionic bonds \( X^{+} Y^{-} \) are formed
when
(I) electron affinity of \( Y \) is high
(II) ionization energy of \( \boldsymbol{X} \) is low
(III) lattice energy of \( \boldsymbol{X} \boldsymbol{Y} \) is high
(IV) lattice energy of \( \boldsymbol{X} \boldsymbol{Y} \) is low
A . I and II
B. I and III
c. ।, ॥ and III
D. All
Subject: Physics
For current entering at \( \mathbf{A}, \) the electric
field at a distance \( \mathbf{r} \) ' from A is:
A \( \cdot \frac{\rho \mathrm{I}}{2 \pi \mathrm{r}^{2}} \)
в. \( \frac{\rho \mathrm{I}}{4 \pi^{2}} \)
c. \( \frac{\rho \mathrm{I}}{8 \pi \mathrm{r}^{2}} \)
D. \( \frac{\rho}{\mathrm{r}^{2} \mathrm{I}} \)
Subject: Maths
\( \frac{1}{10} \) of a rod is coloured red, \( \frac{1}{20} \) orange \( \frac{1}{30} \) yellow, \( \frac{1}{40} \) green, \( \frac{1}{50} \) blue, \( \frac{1}{60} \) black
and the rest are violet. If the lenght of the violet portion is \( 12.08 \mathrm{m} \), then what
is the lenght of the rod?
A. 16 m
B. 18 m
c. \( 20 \mathrm{m} \)
D. 30
Subject: Physics
A body has a charge of \( -2 \mu C \). If it has
\( 2.5 \times 10^{13} \) protons, then how many
electrons the body has?
A \( \cdot 1.25 \times 10^{13} \)
B. \( 2.5 \times 10^{13} \)
c. \( 3.75 \times 10^{13} \)
D. None of these
Subject: Physics
The objective lens of a compound microscope produces magnification of
10. In order to get an overall
magnification of 100 when image is formed at \( 25 \mathrm{cm} \) from the eye, the focal
length of the eye lens should be : (in \( c m \) )
A . 4
B. 10
c. \( \frac{25}{9} \)
D. 9
Subject: Physics
The effective resistance between points
P and Q of the electrical circuit shown in
the figure is
A \( \cdot \frac{2 R r}{R+r} \)
B. \( \frac{8 R(R+r)}{3 R+r} \)
\( c \cdot 2 r+4 R \)
D. \( \frac{5 R}{2}+2 \)
Subject: Maths
\( \ln \triangle A B C, D \) is the mid-point \( B C . \) If a line is drawn in such a way that it
bisects \( A D \) and \( A D \) and \( A C \) at \( E \) and
\( X \) respectively, then prove that \( \frac{\boldsymbol{E} \boldsymbol{X}}{\boldsymbol{B} \boldsymbol{E}}= \)
\( \frac{1}{3} \)
Subject: Maths
If \( f(x)=\left\{\begin{array}{cl}\frac{\sin 5 x}{x^{2}+2 x}, & x \neq 0 \\ k+\frac{1}{2}, & x=0\end{array} \) is \right.
continuous at \( x=0, \) then the value of \( k \)
is
\( \mathbf{A} \cdot \mathbf{1} \)
B. - 2
\( c \cdot 2 \)
D.
Subject: Maths
\( \frac{3+\cot 76^{0} \cot 16^{0}}{\cot 76^{0}+\cot 16^{0}} \) is equal to
This question has multiple correct options
\( A \cdot \tan 16^{0} \)
B \( \cdot \cot 76^{0} \)
\( \mathbf{C} \cdot \tan 46^{\circ} \)
\( \mathbf{D} \cdot \cot 44^{0} \)
Subject: Chemistry
For the fuel cell reaction, \( 2 H_{2}+O_{2} \rightarrow \)
\( 2 H_{2} O, \Delta G=-475 k J \)
The value of \( \boldsymbol{E}^{o} \) cell is:
A . \( 1.23 \mathrm{v} \)
B. 2.46
c. \( 0.615 \mathrm{v} \)
D. 0.31
Subject: Chemistry
In the graph \( (1), A, B \) and \( C \) respectively
are:
\( A \cdot S O_{3}, S O_{2} \) and \( O_{2} \)
B. \( S O_{3}, O_{2} \) and \( S O_{2} \)
\( c \cdot S O_{2}, O_{2} \) and \( S O_{3} \)
D. \( O_{2}, S O_{2} \) and \( S O_{3} \)
Subject: Chemistry
Rate law for the following reaction; Ester \( +\boldsymbol{H}^{+} \rightleftharpoons \) Acids \( + \) Alcohol; is
\( \frac{d x}{d t}=k[\text { ester }]^{1}\left[H^{+}\right]^{0} . \) What would be the
effect on the rate if concentration of \( \boldsymbol{H}^{+} \)
ion is doubled?
A. Same
B. Doubled
c. Half
D. Data insufficient
Subject: Maths
If \( \boldsymbol{f}: \boldsymbol{Z} \rightarrow \boldsymbol{Z} \) is defined by \( \boldsymbol{f}(\boldsymbol{x})= \)
\( \left\{\begin{array}{ll}\frac{x}{2} & \text { if } x \text { is even } \\ 0 & \text { if } x \text { is odd }\end{array} \text { then } f \) is \right.
A. onto but not one to one
B. One to one but not onto
c. one to one and onto
D. Neither one to one nor onto
Subject: Chemistry
The following are the formulae for three compounds 2,3 -dichorobutane written
in non-eclipsed conformations. In each
instance, tell which compounds are enanatiomers and which are meso:
\( \mathbf{a} \)
A. (a) and (c) are enantiomers;(b) is meso
B. (a) and
(b) are enantiomers;(c) is meso
\( c \cdot(b) \) and
(c) are enantiomers;(c) is meso
D. none of these
Subject: Chemistry
Which of the following are examples of
pseudo unimolecular reactions?
\( \mathbf{A} \cdot C H_{3} C O_{2} C_{2} H_{5}+H_{2} O \rightarrow C H_{3} C O_{2} H+C_{2} H_{5} O H \)
\( \mathbf{B} \cdot C_{12} H_{22} O_{11}+H_{2} O \rightarrow C_{6} H_{12} O_{6}+C_{6} H_{12} O_{6} \)
\( \mathbf{c} \cdot C H_{3} C O C l+H_{2} O \rightarrow C H_{3} C O_{2} H+H C l \)
D. All of the above
Subject: Physics
If
A.C. voltage is applied to a pure capacitor, then voltage across the
capacitor
A \( \cdot \) Leads the current by phase angle \( \left(\frac{\pi}{2}\right) \) rad.
B. Leads the current by phase angle \( (\pi) \) rad.
C - Lags behind the current by phase angle \( \left(\frac{\pi}{2}\right) \) rad.
D. Lags behind the current by phase angle \( (\pi) \) rad.
Subject: Physics
A heavy rod of length \( L \) and weight \( W \) is
suspended horizontally by two vertical ropes as shown. The first rope is
attached to the left end of the rod while
the second rope is attached a distance \( \boldsymbol{L} \)
\( \overline{4} \) from right end. The tension in the
second rope is :
A \( \cdot \frac{W}{2} \)
в. \( \frac{W}{4} \)
c. \( \frac{W}{3} \)
D. \( \frac{2 W}{3} \)
E. \( W \)
Subject: Chemistry
The formula of the compound which gives violet colour in Lassiagnes test for sulphur with sodium nitroprusside is :
A \( \cdot N a_{4}\left[F e(C N)_{5} N O S\right] \)
B . \( N A_{3}\left[F e(C N)_{5} N O S\right] \)
c. \( \operatorname{Na}_{2}\left[\operatorname{Fe}(C N)_{5} S\right] \)
D. \( N a_{4}\left[F e(C N)_{4} S\right] \)
Subject: Chemistry
Assertion: The more negative the standard reduction potential, the more is its ability to displace hydrogen from acids.

Reason: Ability to displace hydrogen from acids translates to the strength of the reductant.
A. Both Assertion and Reason are true and Reason is the correct explanation of Assertion
B. Both Assertion and Reason are true but Reason is not the correct explanation of Assertion
c. Assertion is true but Reason is false
D. Assertion is false but Reason is true
E. Both Assertion and Reason are false
Subject: Chemistry
Assertion
In the titration of \( N a_{2} C O_{3} \) with \( H C l \)
using methyl orange indicator, the volume required at the equivalence
point is twice that of the acid required using phenolphthalein indicator.
Reason
Two mole of \( H C l \) are required for the
complete neutralization of one mole of
\( N a_{2} C O_{3} \)
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is incorrect but Reason is correct
D. Both Assertion and Reason are correct
Subject: Maths
\( \int \frac{x^{2}}{\left(x^{2}+2\right)\left(x^{2}+3\right)} d x= \)
\( \mathbf{A} \cdot-\sqrt{2} \tan ^{-1} x+\sqrt{3} \tan ^{1} x+c \)
B \( \cdot-\sqrt{2} \tan ^{-1}\left(\frac{x}{\sqrt{2}}\right)+\sqrt{3} \tan ^{-1}\left(\frac{x}{\sqrt{3}}\right)+c \)
C \( \cdot \sqrt{2} \tan ^{-1}\left(\frac{x}{\sqrt{2}}\right)+\sqrt{3} \tan ^{-1}\left(\frac{x}{\sqrt{3}}\right)+c \)
D. None of these
Subject: Maths
Maximum value of \( \prod\left(1+\frac{b-c}{a}\right)^{a} \) is \( \lambda \) where \( a, b, c \) are integral sides of a
triangle, \( \lambda+2 \) is/are divisible by
This question has multiple correct options
A . 2
B. 3
c. 1
D. 5
Subject: Physics
The velocity of the wave
\( \mathbf{A} \cdot 80 \mathrm{cm} / \mathrm{sec} \)
B. \( 112 \mathrm{cm} / \mathrm{sec} \)
c. \( 120 \mathrm{cm} / \mathrm{sec} \)
D. \( 140 \mathrm{cm} / \mathrm{sec} \)
Subject: Maths
If \( |\boldsymbol{x}|<\mathbf{1} \) then the coefficient of \( \boldsymbol{x}^{\mathbf{5}} \) in
the expansion of \( \frac{3 x}{(x-2)(x+1)} \) is
A \( \cdot \frac{33}{32} \)
B. \( -\frac{33}{32} \)
\( c \cdot \frac{31}{32} \)
D. \( -\frac{3}{32} \)
Subject: Physics
The equation of a simple harmonic motion is given by \( \boldsymbol{x}=\mathbf{6} \sin \mathbf{1 0 t}+ \)
\( 8 \cos 10 t, \) where \( x \) is in \( \mathrm{cm}, \) and \( t \) is in
seconds. Find the resultant amplitude
A . 20
B . 10
c. 30
D. 50
Subject: Maths
If \( A \) and \( B \) are two disjoint sets and \( N \) is
the universal set then \( \boldsymbol{A}^{c} \cup \)
\( \left[(\boldsymbol{A} \cup \boldsymbol{B}) \cap \boldsymbol{B}^{c}\right] \) is
\( A \cdot \phi \)
B. A
\( c . \) в
D.
Subject: Physics
Assertion
High energy particles from outer space, on entering the earth's atmosphere
causes ionisation of the atoms of the
gases present in the atmosphere.
Reason

One goes higher the atmospheric
pressure decreases.
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
\( \operatorname{Let} \boldsymbol{F}(\boldsymbol{k})= \)
\( \left(1+\sin \frac{\pi}{2 k}\right)\left(1+\sin (k-1) \frac{\pi}{2 k}\right)(1+\sin \)
The value of \( \boldsymbol{F}(\mathbf{1})+\boldsymbol{F}(\mathbf{2})+\boldsymbol{F}(\mathbf{3}) \) is
equal to
A \( \cdot \frac{3}{16} \)
B.
\( c \cdot \frac{5}{16} \)
D. \( \frac{7}{16} \)
Subject: Physics
If a body of mass \( 200 g \) falls from a
height \( 200 m \) and its total potential
energy is conserved into kinetic energy, at the point of contact of the body with the surface, then decrease in potential
energy of the body at the contact is
\begin{tabular}{l} 
A. 9005 \\
\hline
\end{tabular}
в. \( 500 J \)
c. \( 400 J \)
D. \( 200 J \)
Subject: Biology
fungal cell with different parts labelled as \( A, B, C \) and \( D . \) Which of the following statements are true with regard to the
fungal cell structure?
(i) A contains mucopolysaccharides
which are also present in exoskeleton of insects and crustaceans.
(ii) D are usually more than one in number in case of aseptate hyphae.
(iii) Carotenes and xanthophylls are
present in \( C, \) which harvest light energy
for photosynthesis.
(iv) \( \mathrm{B} \) is the reserve food material,
usually stored in the form of starch and
oil.
A. (i) and (ii)
B. (iii) and (iv)
C. (i), (ii) and (iv)
D. (ii), (iii) and (iv)
Subject: Chemistry
toppr
Q Type your question
\( N H_{4} O H \) molecules. \( N H_{4} O H \) again
dissociates into \( N H_{4}^{+} \) and \( O H^{-} \) ions.
In solution therefore, we have \( N H_{3} \)
molecules, \( N H_{4} O H \) molecules and
\( N H_{4}^{+} \) ions and the following equilibrium exist:
\( N H_{3}(g) \) (pressure \( P \) and concentration
\( \boldsymbol{c} \) ) Initially \( \rightleftharpoons \boldsymbol{N} \boldsymbol{H}_{3}(l)+\boldsymbol{H}_{2} \boldsymbol{O} \rightleftharpoons \)
\( N H_{4} O H \rightleftharpoons N H_{4}^{+}+O H^{-} \)
Let \( c_{1} \) mol \( / L \) of \( N H_{3} \) pass in liquid
state which on dissolution in water
froms \( c_{2} \) mol \( / L \) of \( N H_{4} O H \). The solution contains \( c_{3} \) mol \( / L \) of \( N H_{4}^{+} \) ions

If \( P \) is the partial pressure of ammonia at equilibrium, then which of the following is constant?
\( ^{A} \cdot \frac{P}{c_{1}} \)
в. \( \frac{p}{c_{0}} \)
\( c \cdot \frac{p}{c_{2}} \)
D. \( \frac{p}{c_{3}} \)
Subject: Maths
If \( z \in C, \) the minimum value of \( |z|+ \)
\( |z-5| \) is attained by
This question has multiple correct options
\( \mathbf{A} \cdot z=0 \)
B . \( z=5 \)
c. \( z=5 / 2 \)
D. For all \( z \in[0,5] \)
Subject: Maths
If \( A \) and \( B \) are \( 3 \times 3 \) matrices and
\( |\boldsymbol{A}| \neq \mathbf{0}, \) then
This question has multiple correct options
A \( \cdot|A B|=0 \Rightarrow|B|=0 \)
B . \( |A B| \neq 0 \Rightarrow|B| \neq 0 \)
C \( \cdot\left|A^{-1}\right|=|A|^{-1} \)
D. \( |2 A|=2|A| \)
Subject: Chemistry
Element \( A \) reacts with oxygen to form a
compound \( A_{2} O_{3} \). If 0.359 gram of \( A \) reacts to give 0.559 gram of the compound, then atomic weight of \( \boldsymbol{A} \) will
be:
A. 5
B. 43.08
c. 49.7
D. 47.9
Subject: Maths
Let \( a, b, c \in R \) be such that \( a+b+ \)
\( \boldsymbol{c}>\mathbf{0} \) and \( \boldsymbol{a b c}=\mathbf{2 .} \) Let \( \boldsymbol{A}=\left[\begin{array}{lll}\boldsymbol{a} & \boldsymbol{b} & \boldsymbol{c} \\ \boldsymbol{b} & \boldsymbol{c} & \boldsymbol{a} \\ \boldsymbol{c} & \boldsymbol{a} & \boldsymbol{b}\end{array}\right] \)
If \( A^{2}=I, \) then value of \( a^{3}+b^{3}+c^{3} \) is
\( A \cdot 7 \)
B.
\( c \cdot 0 \)
\( D \)
Subject: Physics
A capacitor of capacitance \( 2 \mu F \) is
charged to a voltage of \( 6 \mathrm{V} \). The charge
on its plates is:
A . \( 1.2 \times 10^{-5} C \)
B . \( 3 \times 10^{-6} C \)
c. \( \frac{1}{3} \times 10^{-6} C \)
D. \( \frac{1}{12} \times 10^{-6} \mathrm{C} \)
Subject: Physics
A motor car is travelling at speed of \( 30 m / s \) on a circular road of radius
\( 500 m . \) If the speed of the car is
increasing at the rate of \( 2.0 m / s^{2} \), then
the total acceleration will be
A \( \cdot 1.8 m / s^{2} \)
B \( \cdot 2 m / s^{2} \)
c. \( 2.7 m / s^{2} \)
D. \( 3.8 m / s^{2} \)
Subject: Maths
\( f(x)=\left|\begin{array}{ccc}a^{-x} & e^{x \log _{e} a} & x^{2} \\ a^{-3 x} & e^{3 x \log _{e} a} & x^{4} \\ a^{-5 x} & e^{5 x \log _{e} a} & 1\end{array}\right|, \) then
A \( \cdot g(x)+g(-x)=0 \)
B . \( g(x)-g(-x)=0 \)
C. \( g(x) \times g(-x)=0 \)
D. none of these
Subject: Physics
A \( 60 p F \) capacitor is fully charged by a
\( 20 V \) supply. It is then disconnected
from the supply and is connected to another uncharged \( 60 p F \) capacitor in
parallel. The electrostatic energy that is
lost in this process by the time the charge is redistributed between them is \( (\operatorname{in} n J) \)
Subject: Maths
\( f \) is a function defined as \( \sum_{k=1}^{n} f(a+ \) \( \boldsymbol{k})=\mathbf{1 6}\left(\mathbf{2}^{n}-\mathbf{1}\right) \) and \( \boldsymbol{f}(\boldsymbol{x}+\boldsymbol{y})= \)
\( f(x) \cdot f(y) \) and \( f(1)=2 \) then integral
value of \( \boldsymbol{a} \)
A . 3
B. 0
\( c \cdot 2 \)
D.
Subject: Physics
An inductor \( 20 \mathrm{mH} \), a capacitor \( 100 \mu \mathrm{F} \) and a resistor \( 50 \Omega \) are connected in
series across a source of emf, \( \mathrm{V}=10 \)
\( \sin 314 t . \) The power loss in the circuit is?
A . 2.74 w
в. 0.79 w
c. \( 1.13 \mathrm{w} \)
D. \( 0.43 \mathrm{w} \)
Subject: Physics
A block of mass m slides with velocity
of \( 10 m / s \) on a rough horizontal surface It comes to rest after converting a distance of 50 meters. If \( g \) is \( 10 m / s e c^{2} \) then the coefficient of dynamic friction between the block and the surface is
A . \( 0 . \)
B. 1
c. 10
D. 5