AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Biology
Select the correct option representing
the excretory organs present in (i) earthworm, (ii) centipede,(iii) prawn,
and (iv) flatworm.
A. (i) Malpighian tubules
(ii) Flame cell (iii) Nelphridia
(iv) Green gland
B. (i) Flame cell (ii)Green gland (iii) Malpighian tubules
(iv) Nephridia
C. (i) Nephridia (ii)Malpighian tubules (iii) Green gland
(iv) Flame cell
D. (i)Green gland (ii) Nephridia (iii) Flame cell (iv) Malpighian tubules
Subject: Maths
Calculate M.D about Mean for the given
data
\begin{tabular}{lcccc} 
Size of item & 4 & 6 & 8 & 10 \\
\hline
\end{tabular}
\[
\text { Frequency } \quad 2 \quad 1 \quad 3
\]
6
A . 6.12
в. 5.12
c. 2.44
D. 3.44
Subject: Physics
A sphere contracts in volume by \( 0.01 \% \) when taken to the bottom of lake \( 1 k m \)
deep. If the density of water is \( 1 g m / c c \)
the bulk modulus of water is
A \( \cdot 9.8 \times 10^{5} \mathrm{N} / \mathrm{m}^{2} \)
B. \( 9.8 \times 10^{8} \mathrm{N} / \mathrm{m}^{2} \)
c. \( 9.8 \times 10^{10} \mathrm{N} / \mathrm{m}^{2} \)
D. 9.8 \( \times 10^{6} \mathrm{N} / \mathrm{m}^{2} \)
Subject: Maths
Let \( \boldsymbol{A}=(\mathbf{1}, \mathbf{2}, \mathbf{2}), \boldsymbol{B}=(\mathbf{2}, \mathbf{3}, \mathbf{6}) \) and \( \boldsymbol{C}= \)
\( (3,4,12) . \) The direction cosines of a line
equally inclined with \( O A, O B \) and \( O C \)
where \( \boldsymbol{O} \) is the origin, are
A \( \cdot \frac{1}{\sqrt{2}}, \frac{-1}{\sqrt{2}}, 0 \)
B. \( \frac{1}{\sqrt{2}}, \frac{1}{\sqrt{2}}, 0 \)
c. \( \frac{1}{\sqrt{3}}, \frac{-1}{\sqrt{3}}, \frac{1}{\sqrt{3}} \)
D. \( \frac{1}{\sqrt{3}}, \frac{-1}{\sqrt{3}}, \frac{-1}{\sqrt{3}} \)
Subject: Physics
A square-shaped wire loop of mass \( m \)
resistance \( \boldsymbol{R} \) and side a moving with
speed \( v_{0}, \) parallel to the \( x \) -axis, enters a
region of uniform magnetic field \( B \) which is perpendicular to the plane of the loop. The speed of the loop changes with distance \( x(x<a) \) in the field, as
A \( \cdot v_{0}-\frac{B^{2} a^{2}}{R m} x \)
B. \( _{v_{0}-\frac{B^{2} a^{2}}{2 R m} x} \)
c. \( _{v_{0}+} \frac{B^{2} a}{R m} x \)
D. \( v \)
Subject: Physics
If \( \vec{a} \) and \( \vec{b} \) are two vectors then the value of \( (\vec{a}+\vec{b}) \times(\vec{a}-\vec{b}) \) is:
A \( \cdot 2(\vec{b} \times \vec{a}) \)
B. \( -2(\vec{b} \times \vec{a}) \)
c. \( \vec{b} \times \vec{a} \)
D. \( \vec{a} \times \vec{b} \)
Subject: Chemistry
The chemical formula of diaspore, an ore of aluminium, is:
A. \( A l_{2} O_{3} .3 H_{2} O \)
в. \( A l_{2} O_{3} .2 H_{2} O \)
c. \( A l_{2} O_{3} . H_{2} O \)
D. \( A l_{2} O_{3} \)
Subject: Chemistry
One mole of non volatile solute is
dissolved in two moles of water. The
vapour pressure of the solution relative to that of water is:
A \( \cdot \frac{2}{3} \)
в. \( \frac{1}{3} \)
\( c \cdot \frac{1}{2} \)
D. \( \frac{3}{1} \)
Subject: Chemistry
A radioactive material of half-life \( \boldsymbol{T} \) was
produced in a nuclear reactor at different instants, the quantity
produced second time was twice of that produced first time. If now their present
activities are \( A_{1} \) and \( A_{2} \) respectively then their age difference equals:
\( ^{\mathbf{A}} \cdot \frac{T}{\ln 2}\left|\ln \frac{A_{1}}{A_{2}}\right| \)
\( ^{\mathbf{B}} \cdot \quad^{ }\left|\ln \frac{A_{1}}{A_{2}}\right| \)
\( c \)
\[
\frac{T}{\ln 2}\left|\ln \frac{A_{2}}{2 A_{1}}\right|
\]
D.
\[
T \mid \ln \frac{A_{2}}{2 A_{1}}
\]
Subject: Chemistry
The product formed when \( H_{2} O_{2} \) reacts
with acidified \( \boldsymbol{K}_{2} \boldsymbol{C r}_{2} \boldsymbol{O}_{7} \) is:
A \( \cdot K_{2} C r_{2} O_{4} \)
в. \( C r O_{3} \)
\( \mathbf{c} \cdot \operatorname{Cr}(O H)_{3} \)
D. \( C r O_{5} \)
Subject: Physics
A person with normal near point \( 25 \mathrm{cm} \) using a compound microscope with objective of focal length \( 8.0 \mathrm{mm} \) and an eye piece of focal length \( 2.5 \mathrm{cm} \) can bring an object placed at \( 9.0 \mathrm{mm} \) from the objective in sharp focus. The separation between two lenses and
magnification respectively are
A \( .9 .47 \mathrm{cm}, 88 \)
B. 3.36 \( \mathrm{cm}, 44 \)
c. \( 6.00 \mathrm{cm}, 22 \)
D. 7.49 cm, 11
Subject: Biology
One day the contractor's workers appeared in the forest to cut the trees
but the men folk were absent. However,
the women from the village reached the forest quickly and elapsed the tree trunks preventing the workers from felling the trees. Thus, the forest trees
were saved.

The incident was originated in a remote village called "Reni" in Garhwal in the
early 1970 s. By which name is this andolan known as?
A. Amritadevi Andolan
B. Vankatai Andolan
c. Prakruti Samrakshan Andolan
D. Chipko Andolan
Subject: Maths
The value of \( \int \frac{d x}{\left(1-x^{2}\right)^{3 / 2}} \) equals
\( \mathbf{A} \cdot x \sqrt{1-x^{2}}+c \)
B \( \cdot \frac{x}{2 \sqrt{1-x^{2}}}+c \)
\( \mathbf{C} \cdot \frac{x}{\sqrt{1-x^{2}}}+c \)
D. \( \frac{2 x}{\sqrt{1-x^{2}}}+c \)
Subject: Chemistry
\( \mathbf{A} \)
0.1 molal aqueous solution of a weak
acid is \( 30 \% \) ionized. If \( K_{f} \) for water is
\( 1.86^{\circ} \mathrm{C} / \mathrm{m}, \) the freezing point of the solution will be:
B \( .-0.18^{\circ} \mathrm{C} \)
c. \( -0.54^{\circ} \mathrm{C} \)
D. \( -0.36^{\circ} \mathrm{C} \)
Subject: Maths
\( \left[\begin{array}{lll}\boldsymbol{x} & \mathbf{1} & -\mathbf{1}\end{array}\right]\left[\begin{array}{lll}\mathbf{0} & \mathbf{1} & -\mathbf{1} \\ \mathbf{2} & \mathbf{1} & \mathbf{3} \\ \mathbf{1} & \mathbf{1} & \mathbf{1}\end{array}\right]\left[\begin{array}{l}\boldsymbol{x} \\ -\mathbf{1} \\ \mathbf{1}\end{array}\right]=\mathbf{0} \)
then find \( x \)
Subject: Maths
\( \operatorname{Given} f(x)=\frac{a x+b}{x+1}, \lim _{x \rightarrow \infty} f(x)=1 \) and
\( \lim _{x \rightarrow 0} f(x)=2, \) then \( f(-2) \) is
\( A \cdot 0 \)
B.
\( c \cdot 2 \)
\( D \)
Subject: Maths
If \( k \) is a scalar and \( A \) is an \( n \times n \) square
matrix, then \( |\boldsymbol{k} \boldsymbol{A}|= \)
A \( \cdot k|A|^{n} \)
в. \( k|A| \)
c \( \cdot k^{n}\left|A^{n}\right| \)
D \( \cdot k^{n}|A| \)
Subject: Chemistry
Assertion
The plots of \( \log \frac{x}{m} \) vs \( \log P \) are linear
Reason

Adsorption increases linearly with increase in pressure at lower range.
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 angular frequency of the damped
oscillator is given by \( \omega= \) \( \sqrt{\left(\frac{k}{m}-\frac{r^{2}}{4 m^{2}}\right)} \) where \( k \) is the spring
constant, \( m \) is the mass of the oscillator
and \( r \) is the damping constant. If the ratio \( \frac{r^{2}}{m k} \) is \( 8 \% \), the changed in time
period compared to the undamped oscillator is approximately as follows:
A. Increases by \( 1 \% \)
B. Decreases by 1\%
c. Decreases by \( 8 \% \)
D. increases by 8\%
Subject: Physics
The density of a rod gradually decreases from one end to the other. It is pivoted at
an end so that it can move about a
vertical axis through the pivot. A horizontal force \( \boldsymbol{F} \) is applied on the free end in a direction perpendiclar to the
rod. The quantities, that do not depend on which end of the rod is pivoted, are :
A . angular acceleration
B. angular velocity when the rod completes one rotation
c. angular momentum when the rod completes one rotation
D. torque of the applied force.
Subject: Chemistry
For metal carbonyls which of the
following is correct?
A. Filled d-orbital of metal axially overlaps with vacant anti-bonding orbitals of \( C O \)
B. Filled d-orbital of metal laterally overlaps with vacant bonding orbitals of \( C O \)
C. Filled d-orbital of metal laterally overlaps with antibonding orbitals of \( C O \)
D. Filled d-orbital of metal laterally overlaps with filled molecular orbitals of \( C O \)
Subject: Physics
distance travelled by the ball upto that instant, when lift and ball were of same
height from ground take \( g=10 m / s^{2} \)
A \( \cdot \frac{350}{9} m \)
в. \( \frac{700}{9} \mathrm{m} \)
c. \( \frac{175}{9} m \)
D. None of the above
Subject: Chemistry
In which of the following conditions is the potential for the following half-cell
reaction maximum?
\( 2 H^{+}+2 e^{-} \longrightarrow H_{2} \)
\( \mathbf{A} \cdot 1.0 M H C l \)
B. A solution having \( p H=4 \)
c. Pure water
D. \( 1.0 M \) NaOH
Subject: Maths
A circular grass lawn of \( 35 m \) in radius
has a path \( 7 m \) wide running around it
on the outside. The area ofthe path is?
A \( \cdot 1,496 m^{2} \)
B . \( 1,450 m^{2} \)
c. \( 1,576 m^{2} \)
D. \( 1,694 m^{2} \)
Subject: Chemistry
1 mole of stachyose on hydrolysis yields:
A. 1 mole of glucose +1 mole of fructose +2 mole of galactose
B. 2 mole of glucose + 1 mole of fructose + 1 mole of galactose
c. 1 mole of glucose +2 mole of fructose +1 mole of galactose
D. 2 mole of glucose +2 mole of fructose
Subject: Chemistry
The first ionization energy for \( L i \) is 5.4 eV and electron affinity of \( C l \) is \( 3.61 \mathrm{eV} \) The \( \Delta H \) (in \( \mathrm{kJ} / \mathrm{mol} \) ) for the reaction
\( \boldsymbol{L} \boldsymbol{i}(\boldsymbol{g})+\boldsymbol{C l}(\boldsymbol{g}) \rightarrow \boldsymbol{L} \boldsymbol{i}^{+}(\boldsymbol{g})+\boldsymbol{C l}^{-}(\boldsymbol{g}) \) is:
(If the resulting ions do not combine with each other)
\( A \cdot 70 \)
в. 100
c. 172
D. 270
Subject: Chemistry
The standard free energies of formation
of \( \boldsymbol{H}_{2} \boldsymbol{O}_{(l)}, \boldsymbol{C} \boldsymbol{O}_{2}(g) \) an n-pentane are
\( -237.2 k J,-394.4 k J,-8.2 k J . \) Then
the value of \( E^{0} \) for pentane-oxygen fuel
cell is:
A . \( 1.1 V \)
в. \( 0.1 V \)
\( c .2 .0 V \)
D. 2.3V
Subject: Chemistry
The emf \( \left(E^{\circ}\right) \) of the following cells are:
\( \boldsymbol{A} \boldsymbol{g} / \boldsymbol{A} \boldsymbol{g}^{+}(\mathbf{1} \boldsymbol{M}) \| \)
\( \boldsymbol{C u}^{2+}(\mathbf{1} \boldsymbol{M}) \mid \boldsymbol{C u} ; \boldsymbol{E}^{\circ}=-\mathbf{0 . 4 6} \boldsymbol{v o l t} \)
\( \boldsymbol{Z} \boldsymbol{n} / \boldsymbol{Z} \boldsymbol{n}^{\boldsymbol{2}+}(\boldsymbol{1} \boldsymbol{M}) \| \)
\( \boldsymbol{C u}^{2+}(\mathbf{1} \boldsymbol{M}) \mid \boldsymbol{C u} ; \boldsymbol{E}^{\circ}=+\mathbf{1 . 1 0} \boldsymbol{v o l t} \)
Calculate the emf of the cell:
\( \boldsymbol{Z} \boldsymbol{n}\left|\boldsymbol{Z} \boldsymbol{n}^{2+}(\boldsymbol{1} \boldsymbol{M}) \| \boldsymbol{A} \boldsymbol{g}^{+}(\boldsymbol{1} \boldsymbol{M})\right| \boldsymbol{A} \boldsymbol{g} \)
Subject: Physics
A convex lens of focal length \( 16 \mathrm{cm} \) is completely immersed in water.lf the refractive indices of material of lens
and water are 1.5 and 1.33 respectively, then its focal length be :
\( \mathbf{A} \cdot 16 \mathrm{cm} \)
B . \( 62.59 \mathrm{cm} \)
\( \mathbf{c} \cdot 18 c m \)
D. \( 24.24 \mathrm{cm} \)
Subject: Maths
Factorize by the grouping method:
\( 16(a+b)^{2}-4 a-4 b \)
A \( .4(a-3 b)(4 a+4 b-1) \)
B . \( 4(2 a+b)(a+4 b-3) \)
c. \( 4(a-b)(4 a-4 b-1) \)
D. \( 4(a+b)(4 a+4 b-1) \)
Subject: Physics
In the circuit shown here, the cell is
ideal with emf of 2 volt. Then
This question has multiple correct options
A. no current flows in the galvanometer
B. a current of \( 0.2 A \) flows through galvanometer
c. potential difference across \( C_{1} \) is \( 1.2 V \)
D. potential difference across \( C_{2} \) is \( 1.0 \% \).
Subject: Physics
A particle of mass \( m \) is executing
oscillations about the origin on the \( x- \) axis. It's potential energy is \( \boldsymbol{U}(\boldsymbol{x})= \)
\( \boldsymbol{k}|\boldsymbol{x}|^{3}, \) where \( \boldsymbol{k} \) is a positive constant. If
the amplitude of oscillation is \( a \), then
its time period \( \boldsymbol{T} \) is:
A . proportional to \( \frac{1}{\sqrt{a}} \)
B. independent of \( a \)
c. proportional to \( \sqrt{a} \)
D. proportional to \( a^{3 / 2} \)
Subject: Chemistry
At \( 1000 K, K_{w} \) value can be:
\( \mathbf{A} \cdot 1 \times 10^{-6.98} \)
В . \( 1 \times 10^{-7} \)
c. \( 1 \times 10^{-71} \)
D. \( 1 \times 10^{-14} \)
Subject: Chemistry
At equilibrium,in solution a certain
\( \operatorname{acid}, \boldsymbol{H} \boldsymbol{A}, \) yields \( [\boldsymbol{H} \boldsymbol{A}]=\mathbf{0 . 9 4} \boldsymbol{M} \) and
\( \left[A^{-}\right]=0.060 M . \) On the basis of the
above data given
(A) Calculate \( K_{a} \)
(B) Is this acid stronger or weaker than
sulfurous acid \( \left(\boldsymbol{K}_{\boldsymbol{a}}=\mathbf{1 . 7} \times \mathbf{1 0}^{-\mathbf{2}}\right) ? \)
(C) Calculate \( K_{b} \)
(D) Calculate pH
Subject: Physics
During blood transfusion the needle is inserted in a vein where the gauge
pressure is 2000 Pa. At what height must the blood container be placed so that the blood mayjust enter the vein? Density of whole blood is 1.06
\( \times 10^{3} k g / m^{3} \)
A. \( 0.1 \mathrm{m} \)
B. 0.2 \( m \)
\( c .0 .5 \mathrm{cm} \)
D. 0.7 \( m \)
Subject: Biology
Choose the correct answer from the
alternatives given.

Which is the best definition of active
transport?
A. Movement of molecules from an area of their higher concentration to an area of their lower concentration
B. Movement of water across a semi-permeable membrane from an area of high water concentration to an area of lower water concentration
C. Movement of molecules from an area of their lower
concentration to an area of their higher concentration
D. Movement of a substance against its concentration through the release of energy from ATP
Subject: Physics
A glass rod when rubbed with silk cloth
acquires a charge \( 1.6 \times 10^{-13} C . \) What
is the charge on the silk cloth?
A \( .-1.6 \times 10^{-19} C \)
В. \( 1.6 \times 10^{-13} C \)
c. \( -1.6 \times 10^{-13} C \)
D. \( 1.6 \times 10^{-19} C \)
Subject: Biology
The typical floral formula of Gramineae
is
\( A \)
\( \mathrm{Br} \% \mathrm{GP}_{2} \mathrm{A}_{3} \mathrm{G}_{1} \)
в. \( \mathrm{Br} \oplus \widehat{\mathrm{G}} \mathrm{P}_{2} \mathrm{A}_{3} \mathrm{G}(2) \)
\( \mathrm{c} \cdot \mathrm{Br} \oplus \mathrm{GP}_{2} \mathrm{A}_{2} \mathrm{G}(3) \)
D. \( \mathrm{Br} \oplus \oint \mathrm{P}_{2} \mathrm{A}_{3} \mathrm{G}_{3} \)
Subject: Chemistry
Which of the following are true for the first order reaction?
This question has multiple correct options
A \( \cdot t_{3 / 4}=2 t_{1 / 2} \)
B . \( t_{15 / 16}=4 t_{1 / 2} \)
C \( \cdot t_{15 / 16}=3 t_{3 / 4} \)
D. \( t_{7 / 8}=2 t_{3 / 4} \)
Subject: Physics
The relation between volume \( V \), pressure
\( \mathrm{P} \) and absolute temperature \( \mathrm{T} \) of an ideal
gas is \( \mathrm{PV}=\mathrm{xT} \), where \( \mathrm{xis} \) a constant. The
value of \( x \) depend upon
A. the mass of the gas molecule
B. the average kinetic energy of the gas molecules
C. P, V and T
D. the number of gas molecules in volume \( V \)
Subject: Maths
Find variance for the following data:
\( \begin{array}{lllll}\text { Wages } & \begin{array}{l}125- \\ 175\end{array} & \begin{array}{l}\text { 175- } \\ 225\end{array} & \begin{array}{l}\text { 225- } \\ 275\end{array} & \begin{array}{l}\text { 275- } \\ 325\end{array}\end{array} \)
workers 2 १९ 14
A . 7935.69
в. 7935.56
c. 7835.89
D. 7835.16
Subject: Physics
(i) \( \ln \) a process 10 gm of ice at \( -5^{\circ} C \) is
converted into steam at \( 100^{\circ} \mathrm{C} \). If
specific heat of water 1 cal \( g^{-1 \circ} C^{-1}, \) the heat required to rise the temperature of water 10 g from \( 0^{\circ} \mathrm{C} \) to \( 100^{\circ} \mathrm{C} \)
A . \( 100 c a l \)
в. 1000call
\( \mathbf{c} \cdot 10^{4} \) cal
D. \( 10^{5} \) cal
Subject: Maths
The maximum value of \( \mathbf{f}(\mathbf{x})= \) \( \frac{1}{2 e^{x}+e^{-x}} \) is:
A \( \cdot \frac{1}{2 \sqrt{2}} \)
B. \( 2 \sqrt{2} \)
\( c \cdot \frac{1}{2} \)
D. \( \frac{\mathrm{e}}{2 \mathrm{e}^{2}+1} \)
Subject: Maths
A boat in a circular lake lies at its
centre. The perpendicular distance of the boat is \( 10 \mathrm{m} \) from a bridge lying in
\( 40 \mathrm{m} \) distance across the circular lake.
Find the distance that the boat will have
to travel to reach to the extreme point of left side of bridge is \( m \sqrt{5} \mathrm{m} \). Then, \( m \) is
A . \( 20 \mathrm{m} \)
в. \( 10 \mathrm{m} \)
\( c .-10 m \)
D. both B \&
Subject: Chemistry
Following reaction can take place in both direction \( A \stackrel{k_{1}}{_{k_{2}}} B, \) It is given that for the forward reaction:
\( [\mathrm{B}] \)
Rate
\( 0.01 M \quad 1 \times 10^{-2} M s^{-1} \)
\( 0.02 M \quad 2 \times 10^{-2} M s^{-1} \)
Hence, net reaction rate of B is:
Rate
\( \mathbf{A} \cdot k_{1} \)
\( \mathbf{B} \cdot k_{1}-k_{2} \)
\( \mathbf{c} \cdot k_{1}[A]-k_{2} \)
D. none of these
Subject: Physics
If a simple pendulum has significant amplitude (up to a factor of \( 1 / \) e of original) only in the period between \( t= \) \( 0 s \) to \( t=\tau s, \) then \( \tau \) may be called the
average life of the pendulum. When the spherical bob of the pendulum suffers a retardation (due to viscous drag) proportional to its velocity, with b' as the constant proportionality, the average life time of the pendulum in seconds (assuming damping is small) in second :-
A. \( \frac{0.693}{b} \)
B. \( b \)
c. \( \frac{1}{b} \)
D. \( \frac{2}{b} \)
Subject: Chemistry
Baking powder is more commonly used to make cakes or bread "rise". Filler in
baking powder is:
A. \( \operatorname{NaH} \mathrm{CO}_{3} \)
в. \( \operatorname{Ca}\left(\text { На }_{2} \text { РО }_{4} \) ) \right.
c. starch
D. \( \operatorname{NaAl}\left(S O_{4}\right)_{2} \)
Subject: Physics
A Carnot engine has an efficiency of \( 1 / 6 \) When the temperature of the sink is
reduced by \( 62^{\circ} \mathrm{C} \), its efficiency is
doubled. The temperatures of the source and the sink are, respectively
A \( \cdot 124^{\circ} \mathrm{C}, 62^{\circ} \mathrm{C} \)
B . \( 37^{\circ} C, 99^{\circ} \mathrm{C} \)
c. \( 62^{\circ} \mathrm{C}, 124^{\circ} \mathrm{C} \)
D. \( 99^{\circ} \mathrm{C}, 37^{\circ} \mathrm{C} \)
Subject: Maths
A triangle \( A B C \) is placed so that the
mid-points of the sides are on the \( x, y, z \)
axes. Lengths of the intercepts made by the plane containing the triangle on
these axes are respectively \( \boldsymbol{\alpha}, \boldsymbol{\beta}, \boldsymbol{\gamma} \)
Coordinates of the centroid of the
triangle \( \boldsymbol{A B C} \) are
A \( \cdot(-\alpha / 3, \beta / 3, \gamma / 3) \)
B. \( (\alpha / 3,-\beta / 3, \gamma / 3) \)
c. \( (\alpha / 3, \beta / 3,-\gamma / 3) \)
D. \( (\alpha / 3, \beta / 3, \gamma / 3) \)
Subject: Physics
A ship moves along the equator to the
east with velocity \( v_{0}=30 k m / h . \) The
southeastern wind blows at an angle
\( \varphi=60^{\circ} \) to the equator with velocity
\( \boldsymbol{v}=\mathbf{1 5} \boldsymbol{k m} / \boldsymbol{h} . \) The angle \( \boldsymbol{\varphi}^{\prime} \) between the
equator and the wind direction in the
reference frame fixed to the ship is (in degrees)
Subject: Chemistry
Select correct statement(s).
This question has multiple correct options
A. Nickel (II) compounds tend to be thermodynamically more stable than platinum (II)
B. Platinum (IV) compounds are relatively more stable than nickel (IV) compounds
\( \mathbf{C} \cdot K_{2} P t^{I V} C l_{6} \) exists
D. \( K_{2} N i^{I V} C l_{6} \) exists
Subject: Chemistry
Assertion
Cellulose is not digested by human beings
Reason
Cellulose is a polymer of \( \beta \) -D-glucose
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
The set of isoelectronic ions amongst
the following is:
A. \( N a^{+}, C l^{-}, O^{2-} \)
B . \( K^{+}, C a^{2+}, F^{-} \)
c. \( C l^{-}, K^{+}, S^{2} \)
D. \( H^{+}, B e^{2+}, N a^{+} \)
Subject: Chemistry
For the gas phase reaction, \( C_{2} H_{4}+ \)
\( \boldsymbol{H}_{2} \rightleftharpoons \boldsymbol{C}_{2} \boldsymbol{H}_{6},(\boldsymbol{\Delta} \boldsymbol{H}=-\mathbf{3 2 . 7 k c a l}) \)
carried out in a vessel, the equilibrium
concentration of \( C_{2} H_{4} \) can be increased by :

This question has multiple correct options
A. increasing the temperature
B. decreasing the pressure
c. removing some \( H_{2} \)
D. adding some \( C_{2} H_{6} \)
Subject: Maths
If \( \bar{a}, \bar{b}, \bar{c} \) be three unit vectors, such that \( \bar{a}+\bar{b}+\bar{c} \) is also a unit vector and \( \alpha_{1} \)
\( \alpha_{2}, \alpha_{3} \) be the angles between \( \bar{a} \) and \( \bar{b}, \bar{b} \)
and \( \bar{c}, \bar{c} \) and \( \bar{a} \) respectively, then \( \alpha_{1}, \alpha_{2} \)
\( \boldsymbol{\alpha}_{3} \)
A. All are acute angles
B. All are right angles
C. Has at least one among them obtuse
D. None of these
Subject: Physics
A square card of side length \( 1 \mathrm{mm} \) is being seen through a magnifying lens of focal length \( 10 \mathrm{cm} . \) The card is placed at a distance of \( 9 \mathrm{cm} \) from the lens. The apparent area of the card through the lens is
\( \mathbf{A} \cdot 1 \mathrm{cm}^{2} \)
B. \( 0.81 \mathrm{cm}^{2} \)
c. \( 0.27 \mathrm{cm}^{2} \)
D. \( 0.60 \mathrm{cm}^{2} \)
Subject: Maths
Show that the function \( \boldsymbol{f}(\boldsymbol{x})= \) \( \left\{\begin{array}{cll}3-x, & \text { if } & x<1 \\ 2, & \text { if } & x=1 \text { is continuous at } \\ 1+x, & \text { if } & x>1\end{array}\right. \)
\( \boldsymbol{x}=\mathbf{1} \)
Subject: Chemistry
The polymerisation of propene to linear polypropene is represented by the reaction
where \( n \) ahs large integral value, the average enthalpies of bond dissociation for \( (C==C) \) and \( (C--C) \) at \( 298 k \)
are +590 and \( +331 k J m o l^{-1} \)
respectively. The enthalpy of polymerisation is \( -360 k J m o l^{-1} \). Find
the value of \( n \)
\[
n\left(\begin{array}{l}
\mathrm{CH}_{3} \\
\mathrm{CH}=\mathrm{CH}_{2}
\end{array}\right) \longrightarrow-\left(\begin{array}{l}
\mathrm{CH}_{3} \\
1 \\
\mathrm{CH}--\mathrm{CH}_{2}-
\end{array}\right)_{n}
\]
A \( . n=5 \)
в. \( n=2 \)
\( c \cdot n=7 \)
D. None of these
Subject: Physics
One end of a uniform wire of length \( \boldsymbol{L} \) and of weight \( W \) is attached rigidly to a
point in the roof and \( W_{1} \) weight is suspended from looser end. If \( A \) is area
of cross-section of the wire, the stress in the wire at a height \( \frac{L}{4} \) from the upper end is
\( \mathbf{A} \cdot \frac{W_{1}+W}{a} \)
B. \( \frac{W_{1}+3 W / 4}{a} \)
c. \( \frac{W_{1}+W / 4}{a} \)
D. \( \frac{4 W_{1}+3 W}{a} \)
Subject: Physics
The mean free path and rms velocity of
a nitrogen molecule at a temperature \( 17 \mathrm{C} \) are \( 1.2 \times 10^{-7} \mathrm{m} \) and
\( 5 \times 10^{2} \mathrm{m} / \mathrm{s} \) respectively.The time
between two successive collisions
A . \( 2.4 \times 10^{-10} \mathrm{s} \)
B . \( 1.2 \times 10^{-10} \mathrm{s} \)
c. \( 3.4 \times 10^{-13} \) s
D. 3.4 \( \times 10^{-10} \) s
Subject: Maths
In the adjoining figure, \( A B \) and \( C D \) are
parallel lines. The transversals \( P Q \) and
\( R S \) intersect at \( U \) on the line \( A B . \) Given
that \( \angle D W U=110^{\circ} \) and \( \angle C V P=70^{\circ} \)
find the measure of \( \angle Q U S \)
Subject: Physics
A rectangular coil of 300 turns has an
average area of \( 25 \mathrm{cm} \times 10 \mathrm{cm} . \) The coil
rotates with a speed of 50 cps in uniform magnetic field of strength \( 4 \times \) \( 10^{-2} T \) about an axis perpendicular to
the field. The peak value of the induced emf is \( (\text { in } v o l t) \)
A. \( 300 \pi \)
B. 3000 \( \pi \)
\( c .3 \pi \)
D. \( 30 \pi \)
Subject: Maths
\( \operatorname{Let} f(x)=\cos \left(\tan ^{-1} 2 x\right)- \)
\( \sin \left\{\tan ^{-1}\left(\frac{1}{2 x+1}\right)\right\} \) and \( a= \)
\( \cos \left(\tan ^{-1}\left(\sin \left(\cot ^{-1} 2 x\right)\right)\right) \) and \( b= \)
cos \( \left(\frac{\pi}{2}+\cos ^{-1} 2 x\right) \cdot \) If \( f(x)=0, \) then
\( b= \)
A. \( \frac{1}{\sqrt{2}} \)
B. \( -\frac{\sqrt{3}}{2} \)
c. \( \frac{\sqrt{3}}{2} \)
D. \( -\frac{1}{\sqrt{2}} \)