AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Chemistry
A buffer solution contain
\( \mathbf{0 . 8} \boldsymbol{M} \boldsymbol{N} \boldsymbol{H}_{\mathbf{4}} \boldsymbol{O} \boldsymbol{H} \boldsymbol{\&} \)
\( \mathbf{0 . 2 M} N \boldsymbol{H}_{4} \boldsymbol{C l}, \boldsymbol{K} \boldsymbol{a}\left(\boldsymbol{N} \boldsymbol{H}_{4}^{+}\right)=\mathbf{5} \times \mathbf{1 0}^{-10} \)
Find \( p H \) of the solution \( (\log 2=0.3) \&(\log 3=0.48) \)
A . 9.9
B. 8.7
\( c .9 .6 \)
D. 4.
Subject: Chemistry
Which of the following species have undistorted octahedral structures?
1. \( \boldsymbol{S F}_{\mathbf{6}} \)
2. \( \boldsymbol{P F}_{\mathbf{6}}^{-} \)
3. \( \boldsymbol{S} \boldsymbol{i} \boldsymbol{F}_{\boldsymbol{6}}^{2-} \)
4. \( \boldsymbol{X} \boldsymbol{e} \boldsymbol{F}_{\boldsymbol{6}} \)
A. 2,3 and 4
B. 1,3 and 4
\( c .2 \) and 3
D. 1,2 and 3
Subject: Maths
Assertion
The equation \( \boldsymbol{f}(\boldsymbol{x})\left(\boldsymbol{f}^{\prime \prime}(\boldsymbol{x})\right)^{2}+ \)
\( \boldsymbol{f}(\boldsymbol{x}) \boldsymbol{f}^{\prime}(\boldsymbol{x}) \boldsymbol{f}^{\prime \prime \prime}(\boldsymbol{x})+\left(\boldsymbol{f}^{\prime}(\boldsymbol{x})\right)^{2} \boldsymbol{f}^{\prime \prime}(\boldsymbol{x})= \)
0 has atleast 5 real roots
Reason
The equation \( f(x)=0 \) has atleast 3
real distinct roots
\& if \( f(x)=0 \) has \( k \)
real distinct roots, then \( f^{\prime}(x)=0 \) has
atleast k-1 distinct roots.
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
Assuming that shear stress of base of a mountain is equal to force per unit area to its weight, calculate the maximum possible height of a mountain on the earth if breaking stress of a typical rock
is \( 30 \times 10^{7} N m^{-2} \) and specific gravity
is \( 3 \times 10^{3} k g / m^{3} \)
\( A \cdot 10 \mathrm{km} \)
B. \( 8 \mathrm{km} \)
\( c \cdot 7 k m \)
\( D .6 \mathrm{km} \)
Subject: Maths
If \( [\sin x]+[\sqrt{2} \cos x]=-3, x \in[0,2 \pi] \)
([.] denotes the greatest integer function), then \( x \) belongs to
A \( \cdot\left(\pi, \frac{5 \pi}{4}\right) \)
B . \( \left[\pi, \frac{5 \pi}{4}\right] \)
c. \( \left(\frac{5 \pi}{4}, 2 \pi\right) \)
D・ \( \left[\frac{5 \pi}{4}, 2 \pi\right] \)
Subject: Physics
The value of universal gas constant is
\( 8.3 J / \)mole\( / K, \) the mean kinetic
energy of \( 32 g m \) of oxygen at \( -73^{\circ} C \) will
be
\( \mathbf{A} \cdot 480 J \)
в. \( 4980 J \)
c. \( 2490 J \)
D. \( 100 J \)
Subject: Physics
Two slits in Young's experiment have widths in the ratio \( 1: 25 . \) The ratio of
intensity at the maxima and minima in the interference pattern, \( \frac{\boldsymbol{I}_{\max }}{\boldsymbol{I}_{\min }} \) is
A \( \cdot \frac{4}{9} \)
B. \( \frac{9}{4} \)
c. \( \frac{121}{49} \)
D. \( \frac{49}{121} \)
Subject: Physics
Magnetic flux through a circuit of
resistance \( 20 \Omega \) is changed from 20 Wb to \( 40 \mathrm{Wb} \) in \( 5 \mathrm{ms} \). Charge passed through the circuit during this time is
A . \( 1 \mathrm{c} \)
B. 2
c. zero
D. \( 0.5 \mathrm{c} \)
Subject: Maths
(i) Find the area bounded by the curve \( \boldsymbol{y}=\boldsymbol{x}(\mathbf{1}-\boldsymbol{x}) \) between the points where
it crosses the x-axis.
(ii) Find the area between the curves
\( \boldsymbol{y}=\boldsymbol{x} \) and \( \boldsymbol{y}=\boldsymbol{x}^{3} \)
Subject: Physics
Ratio of \( S I \) unit of torque to its CGS unit is
\( \mathbf{A} \cdot 10^{5}: 1 \)
B . \( 10^{7}: 1 \)
\( \mathbf{c} \cdot 10^{6}: 1 \)
D. \( 10^{17}: 1 \)
Subject: Chemistry
The reaction of \( X e F_{6} \) with silica \( \left(S i O_{2}\right) \) gives:
A. \( X e O_{3} \) and \( S i F_{4} \)
B. \( X e F_{4} \) and \( S i F_{4} \)
c. \( X e O F_{2} \) and \( S i F_{4} \)
D. \( X e O F_{4} \) and \( S i F_{4} \)
Subject: Maths
If a complex number z satisfies the equation \( z+\sqrt{\mathbf{2}}|z+\mathbf{1}|+\mathbf{i}=\mathbf{0}, \) where
\( \boldsymbol{i}=\sqrt{-\mathbf{1}}, \) then \( |\boldsymbol{z}| \) is equal to.
A .
B. 2
\( c \cdot \sqrt{3} \)
D. \( \sqrt{5} \)
Subject: Physics
A rod of weight \( \boldsymbol{w} \) is supported by two parallel knife edges \( A \& B \) and is in
equilibrium in a horizontal position. The
knives are at a distance \( d \) from each
other. The center of mass of the rod is at
a distance \( x \) from \( A \). The normal
reactions at \( A \) and \( B \) will be
A \( . N_{A}=2 w(1-x / d), N_{B}=w x / d \)
B . \( N_{A}=w(1-x / d), N_{B}=w x / d \)
c. \( N_{A}=2 w(1-x / d), N_{B}=2 w x / d \)
D. \( N_{A}=w(2-x / d), N_{B}=w x / d \)
Subject: Chemistry
A mixture of \( N a_{2} C_{2} O_{4}(A) \) and
\( K H_{2} C_{2} O_{4} \cdot 2 H_{2} O(B) \) required equal
volumes of \( 0.1 \mathrm{M} K M n O_{4} \) and \( 0.1 \mathrm{M} \)
NaOH separately. Molar ratio of \( A \) and
\( B \) in the mixture is :
A . 1: 1
B. 1: 5.5
c. 5.5: 1
D. 3.1 : 1
Subject: Physics
Brine has a density of \( 1.2 g / c c .40 c c \) of it
are mixed with \( 30 c c \) of water. The
density of solution is
A \( .2 .11 g / c c \)
в. \( 1.11 g / c c \)
c. \( 12.2 g / c c \)
D. \( 20.4 g / c c \)
Subject: Chemistry
Calculate the wavelength of the first number of Balmer series of hydrogen spectrum (R for hydrogen \( =1.09678 \times 10 \) \( \left.7 m^{-1}\right) \)
A \( \cdot 2188 \times 10^{-10} \mathrm{m} \)
B. 656 \( \times 10^{-10} \mathrm{m} \)
c. \( 6564 \times 10^{-10} \mathrm{m} \)
D. None of these
Subject: Maths
A particle is in motion along a curve \( 12 y-x^{3} . \) The rate of change of its
ordinate exceeds that of abscissa in
This question has multiple correct options
A \( .-2<x<2 \)
B. \( x=\pm 2 \)
c. \( x<-2 \)
D. \( x>2 \)
Subject: Chemistry
When \( A g N O_{3} \) is added to a solution of
\( \boldsymbol{C o}\left(\boldsymbol{N} \boldsymbol{H}_{3}\right)_{5} \boldsymbol{C l}_{3}, \) the precipitate of \( \boldsymbol{A} \boldsymbol{g} \boldsymbol{C l} \)
shows two ionized chloride ions. This
means:
This question has multiple correct options
A. only two chlorine atoms satisfy primary valency and one secondary valency
B. one chlorine atom satisfies primary as well as secondary valency
c. two chlorine atoms satisfy primary valency
D. three chlorine atoms satisfy secondary valency
Subject: Maths
Food Corporation of India stacks of bags containing wheat in the shape of cuboidal blocks in an open field on
wooden platform and these blocks are covered with tarpaulin. If there be 10 blocks, each having dimensions
\( 10 m \times 5 m \times 3 m, \) then find the cost of
the tarpaulin used to cover these blocks
at the rate of RS. 12.5 per \( m^{2} \). Assuming that there is negligible wastage of tarpaulin in folds.
Subject: Chemistry
The solubility of \( M g(O H)_{2} \) in pure
water is \( 9.57 \times 10^{-3} g L^{-1} . \) Calculate its
solubility in \( g L^{-1} \) in \( 0.02 M \)
\( M g\left(N O_{3}\right)_{2} \) solution.
Subject: Physics
Transverse waves on a string have wave speed \( 12.0 \mathrm{m} / \mathrm{s}, \) amplitude \( 0.05 \mathrm{m} \) and wavelength 0.4 m. The waves travel in
the \( +x \) direction and at \( t=0, \) the \( x=0 \)
end of the string has zero displacement and is moving upwards. Find the transverse displacement of a point at \( x \) \( =0.25 \mathrm{m} \) at time \( t=0.15 \mathrm{s} \)
A. \( -4.54 \mathrm{cm} \)
B. \( -5.54 \mathrm{cm} \)
c. \( -3.54 \mathrm{cm} \)
D. \( -9.54 \mathrm{cm} \)
Subject: Maths
Prove the following by using the principle of mathematical induction for all \( \boldsymbol{n} \in \boldsymbol{N} \)
\( \mathbf{1}+\mathbf{3}+\mathbf{3}^{2}+----+\mathbf{3}^{n-1}= \)
\( \frac{\left(3^{N}-1\right)}{2} \)
Subject: Chemistry
Which of the following is a cyaclic oxoacid?
A. \( \mathrm{H}_{4} \mathrm{P}_{2} \mathrm{O}_{7} \)
в. \( \mathrm{H}_{4} \mathrm{P}_{2} \mathrm{O}_{6} \)
\( \mathrm{c} \cdot \mathrm{H}_{3} \mathrm{P}_{3} \mathrm{O}_{9} \)
D. \( \mathrm{H}_{5} \mathrm{P}_{5} \mathrm{O}_{15} \)
Subject: Physics
A student measures the level of
radiation emitted by a radioactive
sample.

The table shows the readings she
records on the counter over a short
period of time.
Counter
reading/
\( \mathbf{9 6} \)
98
counts per minute
The sample is removed and the counter
then shows a background radiation
reading of 4 counts per minute.
What is the best estimate for the
average count rate due to the
radioactive sample?
A. 96 counts per minute
B. 98 counts per minute
C . 100 counts per minute
D. 104 counts per minute
Subject: Maths
A tangent \( \mathrm{PQ} \) at a point \( \mathrm{P} \) of a circle of radius \( 5 \mathrm{cm} \) meets a line through the centre 0 at a point \( Q, \) so that \( O Q=12 \)
cm. Length of PQ is :
A. \( \sqrt{112} \mathrm{cm} \)
B . \( \sqrt{113} \mathrm{cm} \)
c. \( \sqrt{85} \mathrm{cm} \)
D. \( \sqrt{119} \mathrm{cm} \)
Subject: Physics
A ray of light takes grazing incidence on the first face of a prism and the
emergent ray is normal to the \( 2^{n d} \) face
of the prism. If \( \mathrm{D} \) is angle of deviation then the refracting angle of the prism is equal to
A \( \cdot 90^{\circ}-2 D \)
B. \( 90^{\circ}-D \)
c. \( 90^{\circ}-\frac{D}{2} \)
D. \( 180^{\circ}-2 D \)
Subject: Chemistry
\( \ln \Psi_{321} \) the sum of angular momentum, spherical nodes and angular mode is:
A \( \cdot \frac{\sqrt{6 h}+4 \pi}{2 \pi} \)
в. \( \frac{\sqrt{6 h}}{2 \pi}+3 \)
c. \( \frac{\sqrt{6 h}+2 \pi}{2 \pi} \)
D. \( \frac{\sqrt{6 h}+8 \pi}{2 \pi} \)
Subject: Chemistry
\( \left[\boldsymbol{P t}\left(\boldsymbol{N} \boldsymbol{H}_{3}\right)\left(\boldsymbol{N} \boldsymbol{H}_{2} \boldsymbol{O H}\right)(\boldsymbol{p} \boldsymbol{y})\left(\boldsymbol{N} \boldsymbol{O}_{2}\right)\right] \boldsymbol{N} \boldsymbol{O} \)
has square planar shape and has three geometrical isomer
A. True
B. False
Subject: Physics
The resistance of a wire at room
temperature \( 30^{\circ} \mathrm{C} \) is found to be \( 10 \Omega \)
Now to increase the resistance by \( 10 \% \) the temperature of the wire must be:
[The temperature coefficient of resistance of the material of the wire is
\( \left.0.002 \text { per }^{\circ} C\right] \)
A \( \cdot 36^{\circ} \mathrm{C} \)
в. \( 83^{\circ} \) С
\( \mathbf{c} \cdot 63^{\circ} C \)
D. \( 33^{\circ} \mathrm{C} \)
Subject: Chemistry
Arrange the following compounds in decreasing order of reactivity towards nucleophilic addition reaction. \( \begin{array}{cc}o & o \\ \boldsymbol{C H}_{3}-\stackrel{\|}{\boldsymbol{C}}-\boldsymbol{C H}_{3} & \boldsymbol{C H}_{3}-\underset{I I}{C}-\boldsymbol{C l}\end{array} \)
\( \boldsymbol{C H}_{3}-\underset{\boldsymbol{I} I I}{\boldsymbol{C}}-\boldsymbol{N} \boldsymbol{H}_{2} \quad \boldsymbol{C H}_{3}-\underset{\boldsymbol{I} \boldsymbol{V}}{\boldsymbol{C}}-\boldsymbol{O} \boldsymbol{H} \)
\( \boldsymbol{C H}_{3}-\stackrel{\|}{\boldsymbol{C}}-\underset{\boldsymbol{V}}{\boldsymbol{O}}-\stackrel{\|}{\boldsymbol{C}}-\boldsymbol{C H}_{3} \)
A \( . I I>V>I>I V>I I I \)
В. \( I I I>I V>I>V>I I \)
c. \( I I>I>V>I I I>I V \)
D. \( I V>I I I>V>I>I I \)
Subject: Maths
If \( a^{2}+b^{2}+c^{2}=1, x^{2}+y^{2}+z^{2}=1 \)
where \( a, b, c, x, y, z \) are real, prove that \( \boldsymbol{a} \boldsymbol{x}+\boldsymbol{b} \boldsymbol{y}+\boldsymbol{c} \boldsymbol{z} \leq \mathbf{1} \)
Subject: Physics
A charge of \( 4 \times 10^{-8} C \) is uniformly
distributed over the surface of sphere of
radius \( 1 \mathrm{cm} . \) Another hollow sphere of
radius \( 5 \mathrm{cm} \) is concentric with the
smaller sphere. Find the intensity of the
electric field \( \left(\text { in } N C^{-1}\right) \) at a distance
\( 2 c m \) from the centre. \( k=9 \times 10^{-9} S I \)
Subject: Physics
Two spheres each of mass \( 10^{5} k g \) and
radius \( 10 m \) are kept in contact. Find the force of gravitation acting between them.
A \( \cdot 5.67 \times 10^{-3} N \)
N \( .5 .67 \times 10^{-3} .6 \times 10^{-3} \)
в. \( 6.67 \times 10^{-3} N \)
c. \( 3.67 \times 10^{-3} N \)
D. 2.67 \( \times 10^{-3} N \)
Subject: Biology
A carrier protein transfers a solute across the phospholipid bilayer via facilitated diffusion behaves much like
an enzyme-substrate reaction. A distintction between the process by
which an enzyme converts substrate to product and facilitated transport is
A. Solutes are able to undergo transport without chemical modification
B. Solutes are restricted to flow in one direction depending on the orientation of the carrier protein.
C. Solutes are directly transported without interacting with or influencing the conformational state of the carrier protein.
D. Solutes are transported whether or not there is a competitive or noncompetitive inhibitor present.
Subject: Physics
The efficiency of a transformer is \( 98 \% \) The primary voltage and current are \( 200 V \) and \( 6 A . \) If the secondary voltage is \( 100 V \), the secondary current is :
A . \( 11.76 A \)
B. \( 12.25 A \)
c. \( 3.06 A \)
D. \( 2.94 A \)
Subject: Chemistry
When 1 mol gas is heated at constant volume temp. is raised from 298 to 308
K. Heat supplied to the gas is 500 J. Then which statement is correct?
\( A \cdot q=w=500 \mathrm{J}, \mathrm{U}=0 \)
B. \( q=U=500 \), \( w=0 \)
\( c \cdot q=w=600,1, U=0 \)
D. \( U=0, q=w=400 \)
Subject: Chemistry
The lattice energies of \( \boldsymbol{K} \boldsymbol{F}, \boldsymbol{K} \boldsymbol{C l}, \boldsymbol{K} \boldsymbol{B r} \)
and \( K I \) follows the order:
A. \( K F>K C l>K B r>K I \)
B. \( K I>K B r>K C L>K F \)
c. \( K F>K C l>K I>B r \)
D. \( K I>K B r>K F>K C l \)
Subject: Maths
Let \( a, b, c \) are \( 7^{t h}, 11^{t h} \) and \( 13^{t h} \) terms of
non constant AP. If \( a, b, c \) are also in GP, then find \( \frac{\boldsymbol{a}}{\boldsymbol{c}} \)
\( \mathbf{A} \cdot \mathbf{1} \)
B. 2
\( c \cdot 3 \)
D. 4
Subject: Physics
An object of mass ' \( m \) ' is kept on a
horizontal platform. The platform is
oscillating vertically with amplitude ' \( a \) '
and period 'T". The weight of object at lowest position is:
A \( . m g+m a \omega^{2} \)
B. \( m a \omega^{2} \)
\( \mathrm{c} \cdot m g \)
D. \( m g-m a \omega^{2} \)
Subject: Chemistry
If the equilibrium constant of the reaction of weak acid \( \boldsymbol{H} \boldsymbol{A} \) with strong
base is \( 10^{9} \), then \( \mathrm{pH} \) in \( 0.1 M \) NaA is:
A . 5
B. 9
\( c \cdot 7 \)
D.
Subject: Physics
Electric field outside a long wire carrying charge q is proportional to:
A \( \cdot \frac{1}{r} \)
в. \( \frac{1}{r^{2}} \)
c. \( \frac{1}{r^{\frac{1}{35}}} \)
D. \( \frac{1}{r^{\frac{1}{32}}} \)
Subject: Chemistry
Which of the following compounds will undergo Cannizzaro reaction?
A. \( C H_{3} C H O \)
в. \( C H_{3} \) СОСН\( _{3} \)
\( \mathbf{c} \cdot C_{6} H_{5} C H O \)
D. \( C_{6} H_{5} C H_{2} C H O \)
Subject: Physics
At a certain point in a pipeline the
velocity is \( 1 m / s \) and gauge pressure is
\( \mathbf{3} \times \mathbf{1 0}^{\mathbf{5}} \quad \boldsymbol{N} / \boldsymbol{m}^{2} . \) Find the gauge
pressure at a second point in the line \( 20 m \) lower than the first, if the cross-
section at the second point is half that at the first. The liquid in the pipe is
water
Subject: Physics
The breaking stress of aluminium is
\( \mathbf{7} . \mathbf{5} \times \mathbf{1 0}^{7} \mathbf{N m}^{-2} . \) The greatest length of
aluminium wire that can hang vertically without breaking is
(Density of aluminium is \( 2.7 \times \) \( \left.10^{3} k g m^{-3}\right) \)
A \( \cdot 283 \times 10^{3} m \)
В. \( 28.3 \times 10^{3} m \)
c. \( 2.72 \times 10^{3} m \)
D. \( 0.283 \times 10^{3} m \)
Subject: Maths
\( \operatorname{Let} \boldsymbol{A}=\left[\begin{array}{ll}\mathbf{0} & \boldsymbol{a} \\ \mathbf{0} & \mathbf{0}\end{array}\right] \) and \( (\boldsymbol{A}+\boldsymbol{I})^{50} \)
\( \mathbf{5} \mathbf{0} \boldsymbol{A}=\left[\begin{array}{ll}\boldsymbol{a} & \boldsymbol{b} \\ \boldsymbol{c} & \boldsymbol{d}\end{array}\right] . \) Then the value of \( \boldsymbol{a}+ \)
\( \boldsymbol{b}+\boldsymbol{c}+\boldsymbol{d} \) is
A . 2
B.
\( c \cdot 4 \)
D. none of these
Subject: Biology
6-furfuryl amino purine, \( 2-4 \)
dichlorophenoxy acetic acid and indole-
3 acetic acid are examples respectively
for
A. Synthetic auxin, kinetin and natural auxin
B. Gibberellin, natural auxin and kinetin
C. Natural auxin, kinetin and synthetic auxin
D. Kinetin, synthetic auxin and natural
E. Natural auxin, gibberellin and kinetin
Subject: Physics
A transverse wave is described by the equation \( \boldsymbol{y}=\boldsymbol{y}_{0} \sin 2 \pi\left(\boldsymbol{f} \boldsymbol{t}-\frac{\boldsymbol{\pi}}{\boldsymbol{\lambda}}\right) . \) The
maximum particle velocity is equal to four times the wave velocity if :
A \( \cdot \lambda=\frac{\pi y_{0}}{4} \)
B. \( \lambda=\frac{\pi y_{0}}{2} \)
c. \( \lambda=\pi y_{0} \)
D. \( \lambda=2 \pi y_{0} \)
Subject: Chemistry
Solubility product of \( B a S O_{4} \) in water
\( 57^{\circ} \mathrm{C} \) is:
A . \( 5 \times 10^{-19} \)
В. \( 3.125 \times 10^{-13} \)
\( \mathrm{c} .5 .625 \times 10^{-13} \)
D. \( 2.25 \times 10^{-12} \)
Subject: Physics
Calculate the electric potential at point
\( R \) on the \( x- \) axis
A . 0
B. \( V=\frac{q}{4 \pi \epsilon_{o} \sqrt{a^{2}+y^{2}}} \)
c. \( V=\frac{q}{4 \pi \epsilon_{o}}\left(\frac{1}{x+a}-\frac{1}{x-a}\right) \)
\( V=\frac{q}{4 \pi \epsilon_{o}}\left(\frac{1}{x+a}+\frac{1}{x-a}\right) \)
Subject: Chemistry
Which of the following is not the
configuration of Lanthanoid?
\( \mathbf{A} \cdot[X e] 4 f^{10} 6 s^{2} \)
B \( \cdot[X e] 4 f^{1} 5 d^{1} 6 s^{2} \)
\( \mathbf{c} \cdot[X e] 4 f^{14} 5 d^{10} 6 s^{2} \)
\( \mathbf{D} \cdot[X e] 4 f^{7} 5 d^{1} 6 s^{2} \)
Subject: Maths
If \( 0<x<1, \) then \( \tan ^{-1}\left(\frac{\sqrt{1-x^{2}}}{1+x}\right) \) is
equal to
\( ^{\mathbf{A} \cdot} \frac{1}{2} \cos ^{-1} x \)
B. \( \cos ^{-1} \frac{\sqrt{1+x}}{2} \)
c. \( \sin ^{-1} \sqrt{\frac{1-x}{2}} \)
D. \( \frac{1}{2} \sqrt{\frac{1+x}{1-x}} \)
Subject: Biology
Consider the four entries below:
I. Right auricle
II. Left auricle
III. Right ventricle
IV. Left ventricle
The above are the four chambers of
human heart in which the blood
returned to the bean by great veins flows in a sequential order. What is the correct sequentional order?
A . ॥, Iv, , ॥ ॥
в . ।, ॥I, и, Iv
c. ।, ॥, ॥ा, ।v
D. ॥, II, , , Iv
Subject: Maths
Which of the following is correct?
\( A \cdot \sin 1^{\circ}>\sin 1 \)
B. \( \sin 1^{\circ}<\sin 1 \)
\( \mathbf{c} \cdot \sin 1^{\circ}=\sin 1 \)
D \( \cdot \sin 1^{\circ}=\frac{\pi}{180} \sin 1 \)
Subject: Chemistry
The energy of a photon is given as
\( 3.03 \times 10^{-19} \) J/atom. The wavelength of
the photon is :
\( A \cdot 6.56 \mathrm{nm} \)
B. 65.6 nm
c. \( 0.656 \mathrm{nm} \)
D. 656 nm
Subject: Maths
Solve the equation obtained \( x^{2}-x- \)
\( 6=0 \) and hence find the dimensions of
the verandah. Verandah is in
rectangular shape having area and perimeter equal.
A. \( x=3 ; \) length \( =6 \mathrm{m} \) and breadth \( =3 \mathrm{m} \)
B. \( x=3 ; \) length \( =6 \mathrm{m} \) and breadth \( =4 \mathrm{m} \)
c. \( x=3 ; \) length \( =4 \mathrm{m} \) and breadth \( =3 \mathrm{m} \)
D. \( x=4 ; \) length \( =6 \mathrm{m} \) and breadth \( =3 \mathrm{m} \)
Subject: Physics
A current \( I \) flows through a uniform
wire of diameter \( d \) when the mean
electron drift velocity is \( v . \) The same
current will flow through a wire of diameter \( \frac{d}{2} \) made of the same material if the mean drift velocity of the electron
is
A. \( \frac{v}{4} \)
в. \( \frac{v}{2} \)
\( c \cdot 2 v \)
D. \( 4 v \)
Subject: Physics
\( 10 g \) of lce at \( -20^{0} C \) is added to \( 10 g \) of
water at \( 50^{0} C . \) The amount of ice and
water, present at equilibrium, are respectively
A . \( 0,20 g \)
в. \( 5 g, 15 g \)
c. \( 5 g, 10 g \)
D. \( 10 g, 10 g \)
Subject: Physics
A nurse measures the blood pressure of
a seated patient to be \( 190 \mathrm{mm} \) of Hg.
A. the blood pressure at the patient's feet is less than 190 \( \mathrm{mm} \) of \( \mathrm{Hg} \)
B. the actual pressure is about 0.25 times the atmospheric pressure.
C. the blood pressure at the patient's neck is more than \( 190 \mathrm{mm} \) of \( \mathrm{Hg} \)
D. the actual pressure is about 1.25 times the atmospheric pressure.
Subject: Chemistry
One mole of \( \boldsymbol{H}_{2} \boldsymbol{O} \) and one mole of \( \boldsymbol{C O} \)
are taken in 10 L vessel and heated to
725 K. At equilibrium, \( 40 \% \) of water (by mass) reacts with \( C O \) according to the
equation.
\( \boldsymbol{H}_{2} \boldsymbol{O}(\boldsymbol{g})+\boldsymbol{C O}(\boldsymbol{g}) \rightleftharpoons \boldsymbol{H}_{2}(\boldsymbol{g})+ \)
\( \boldsymbol{C O}_{2}(\boldsymbol{g}) \)
Calculate the equilibrium constant for the reaction.
Subject: Chemistry
A solution is prepared by dissolving
\( 11 g \) glucose in \( 250 c m^{3} \) water at \( 30^{\circ} C \)
what is mass percent glucose in
solution. The density of water at \( 30^{\circ} \) is \( \mathbf{0 . 9 9 6} \boldsymbol{g} / \boldsymbol{c m}^{\mathbf{3}} \)
Subject: Chemistry
Silt in water remains suspended. It is
removed by sedimentation and filtration. For increasing its sedimentation aluminium sulphates and calcium hydroxide (slaked lime) are added. As a result sticky aluminium hydroxide.
A. Destroys slit particles
B. Attracts the particles of slitt
C. Mixes with slit particles
D. Makes slit particles increases in size and deposit at the bottom
Subject: Maths
If \( \boldsymbol{f}(\boldsymbol{x})=\cos (\log \boldsymbol{x}), \) then
\( f\left(\frac{1}{x}\right) f\left(\frac{1}{y}\right)- \)
\( \frac{1}{2}\left\{f\left(\frac{x}{y}\right)+f(x y)\right\}= \)
\( A \cdot \log x \)
B. \( \cos (\log x) \)
\( c \cdot \sin (\log x) \)
D.
Subject: Chemistry
When \( 20 g F e_{2} O \) is reacted with \( 50 g \) of
\( \boldsymbol{H} \boldsymbol{C l}, \boldsymbol{F e} \boldsymbol{C l}_{3} \) and \( \boldsymbol{H}_{2} \boldsymbol{O} \) are formed. The
amount of unreacted \( \boldsymbol{H} \boldsymbol{C l} \) is \( (\boldsymbol{F e}=\mathbf{5 6}) \)
A. \( 27.375 g \)
в. \( 22.625 g \)
c. \( 30 g \)
D. \( 4.75 g \)
Subject: Maths
Area of region \( \left\{(x, y) \in R^{2}: y \geq \sqrt{|x+3|}, 5 y \leq x+9\right. \)
is equal to
A \( \cdot \frac{1}{6} \)
B. \( \frac{4}{3} \)
\( c \cdot \frac{3}{2} \)
D.
Subject: Chemistry
Statement I: \( H C l \) is considered to be an
acid.
Statement II: \( \boldsymbol{H} \boldsymbol{C l} \) is a proton donor.
A. Both Statement 1 and Statement 2 are correct and
Statement 2 is the correct explanation of Statement 1.
B. Both 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: Chemistry
If \( N_{1}, N_{2}, N_{3}, \dots \) are the number of
molecules with molecular masses
\( M_{1}, M_{2}, M_{3}, \ldots \) respectively, then
mass average molar mass is expressed
as :
\( ^{\mathbf{A}} \cdot \frac{\sum N i M i^{2}}{\sum N i M i} \)
в. \( \frac{\sum N i M i}{\sum N i} \)
c. \( \frac{\sum M i^{2}}{\sum N i} \)
D. \( \frac{\sum N i M i}{\sum M i} \)
Subject: Physics
A car is traveling in plane curved road of radius 125 m. If the coefficient of
friction between the tyres and road is
0.5 and \( g=10 m / s^{2} . \) The maximum
speed to avoid skidding is:
A . \( 50 \mathrm{m} / \mathrm{s} \)
в. \( 25 \mathrm{m} / \mathrm{s} \)
c. \( 20 m / s \)
D. 10 \( m / s \)
Subject: Physics
A wedge of mass \( 10 \mathrm{kg} \) is moving
rightwards. A block of mass \( 10 k g \) is
placed on it. Friction coefficient
between wedge and block is \( 0.8 . \) Then
\( \left[\text {take } g=10 m / s^{2}\right] \)
This question has multiple correct options
A. If wedge is moving with constant velocity then friction acting on block is 64N
B. If wedge is moving with constant velocity then acceleration of block is zero
C. If wedge is moving with \( a=2 \hat{i} m / s^{2} \) then friction
acting on block is \( 44 \mathrm{N} \)
D. If wedge is moving with \( a=10 \hat{i} m / s^{2} \) then friction is
zero