AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Maths
Find the intersection of \( A \) and \( B \) by
representing using by Venn diagram:
\( \boldsymbol{A}=\{\boldsymbol{a}, \boldsymbol{b}, \boldsymbol{c}\}, \boldsymbol{B}=\{1,2, \boldsymbol{9}\} \)
\( A \cdot \phi \)
в. \( a, b, c, 1,2,9 \)
c. \( a, c, 1,9 \)
D. None of these
Subject: Maths
Let \( \vec{u} \) be a vector on rectangular system
with sloping angle \( 60^{\circ} . \) Suppose that \( |\vec{u}-\hat{i}| \) is geometric mean of \( |\vec{u}| \) and \( |\vec{u}-2 \hat{i}|, \) where \( \vec{i} \) is the unit vector along
\( x \) -axis, then \( |\vec{u}| \) has the value equal to \( \sqrt{a}-\sqrt{b}, \) where \( a, b \in N . \) Find the value \( \frac{(\boldsymbol{a}+\boldsymbol{b})^{3}+(\boldsymbol{a}-\boldsymbol{b})^{3}}{\mathbf{7}} \)
Subject: Physics
What reading would you expect of a square-wave current, switching rapidly between \( +0.5 A \) and \( -0.5 A, \) when
passed through an ac ammeter?
\( \mathbf{A} \cdot \mathbf{0} \)
B. \( 0.5 A \)
c. 0.25
D. \( 1.0 A \)
Subject: Chemistry
Which is the correct increasing order of
bond dissociation enthalpy of \( \boldsymbol{C}-\boldsymbol{X} \)
bond?
A. \( C-F, C-C l, C-B r, C-I \)
в. \( C-I, C-F, C-C l, C-B r \)
c. \( C-C l, C-F, C-B r, C-I \)
D. \( C-I, C-B r, C-C l, C-F \)
Subject: Physics
An electrical heater and a capacitor are joined in series across a \( 220 V, 50 H z \)
\( A C \) supply. The
potential difference across the heater is
\( 90 V . \) The potential difference across the
capacitor will be about
\( \mathbf{A} \cdot 200 V \)
B. \( 130 V \)
\( \mathrm{c} \cdot 110 \mathrm{V} \)
D. \( 90 V \)
Subject: Chemistry
The chemical formula of plaster of paris
is:
A \( \cdot C a S O_{4} \cdot 2 H_{2} O \)
в. \( \operatorname{CaSO}_{4} \)
\( \mathrm{c} \cdot \mathrm{CaSO}_{4} \cdot \mathrm{H}_{2} \mathrm{O} \)
\( ^{\mathrm{D}} \cdot_{C a S O_{4}} \cdot \frac{1}{2} H_{2} O \)
Subject: Physics
suspended from a point \( A \) by an inextensible string of length L. Ball is
drawn to a side and held at same level
as \( A \) but at a distance \( \frac{\sqrt{3}}{2} L \) from \( A \) as
shown. Now the ball is released. Then:
(assume string applies only that much jerk which is required so that velocity
along string becomes zero).
This question has multiple correct options
A. speed of ball just before experiencing jerk is \( \sqrt{g L} \)
B. speed of ball just after experiencing jerk is \( \frac{\sqrt{3 g L}}{2} \)
C. Impulse applied by string \( \frac{\sqrt{g L}}{10} \)
D. ball will experience jerk after reaching to point B
Subject: Chemistry
The statement(s) that is/are true for the
halides of oxygen \( \left(X_{2} O\right) \) is/are:
A. the bond angles of \( X_{2} O \) (where \( X \) is halogen) are in the decreasing order \( F_{2} O>C l_{2} O>B r_{2} O \)
B. the halides of oxygen (except \( F_{2} O \) ) are easily hydrolyzedd
C. the halides of oxygen \( \left(X_{2} O\right) \) have square planar geometry
D. the molecules have linear shape
Subject: Maths
If \( \theta \) is the angle between \( \bar{a} \) and \( \bar{b} \), then \( \frac{|\bar{a} \times \bar{b}|}{\bar{a} \cdot \bar{b}} \) equals
A \( \cdot \tan \theta \)
B. - \( \tan \theta \)
\( c \cdot \cot \theta \)
D. - cot \( \theta \)
Subject: Maths
Find the value of \( \boldsymbol{p}(\boldsymbol{x})=\boldsymbol{x}^{2}-\boldsymbol{x}+\mathbf{1} \) at
\( \boldsymbol{x}=\mathbf{2} \)
\( A \cdot 3 \)
B. - -
\( c \)
D. -
Subject: Physics
A point moves rectilinearly in one
direction. Above figure shows the
distance \( s \) traversed by the point as a
function of the time \( t . \) Using the plot,
find the maximum velocity.
A. \( 1.5 \mathrm{m} / \mathrm{s} \)
B. \( 2.5 \mathrm{m} / \mathrm{s} \)
\( \mathbf{c} \cdot 2 m / s \)
D. \( 5 \mathrm{m} / \mathrm{s} \)
Subject: Maths
Let \( f \) and \( g \) be two real valued functions
and \( S=\{x \mid f(x)=0\} \) and \( T= \)
\( \{x \mid g(x)=0\}, \) then \( S \cap T \) represent the
set of roots of
A \( . f(x) g(x)=0 \)
B \( \cdot(f(x))^{2}+(g(x))^{2}=0 \)
c. \( f(x)+g(x)=0 \)
D. \( \frac{f(x)}{g(x)}=0 \)
Subject: Chemistry
A gas is heated through \( 1^{\circ} \mathrm{C} \) in a closed vessel and so the pressure increases by \( 0.4 \% . \) The initial temperature of the gas
was:
A . \( -23^{0} C \)
В. \( +23^{0} C \)
c. \( +250^{\circ} \mathrm{C} \)
D. \( +523^{0} C \)
Subject: Chemistry
\( 0.29 g \) of an organic compound containing phosphorous gave 0.887 g of \( M g_{2} P_{2} O_{7} \) by the usual analysis. Calculate the percentage of phosphorous in the compound.
A . 45.8\%
B. 85.48\%
c. \( 83.7 \% \)
D. 72.2\%
Subject: Chemistry
The mole fraction of \( H N O_{3} \) in an
aqueous binary solution is \( 0.15> \) The
ratio of moles of \( H N O_{3} \) to \( H_{2} O \) in the
solution is nearly:
\( \mathbf{A} \cdot 17: 3 \)
B. 3: 17
c. 1: 1
D. 15: 100
Subject: Physics
A fully loaded Boeing aircraft has a mass of \( 3.3 \times 10^{5} \mathrm{kg}, \) its total wing area
is \( 500 m^{2} . \) It is in level flight with speed of \( 960 \mathrm{km} / \mathrm{h} \)
(a) Estimate the pressure difference between the lower and upper
surfaces of the wings.
(b) Estimate the
fractional increase in the speed of the
air on the upper surface of the wing relative to lower surface. (The density of
\( \left.\operatorname{air} \text { is } \rho=1.2 k g m^{-3}\right) \)
Subject: Chemistry
The salt \( A l(O H)_{3} \) is involved in the following two equilibria.
\( \boldsymbol{A l}(\boldsymbol{O H})_{3}(\boldsymbol{s}) \rightleftharpoons \boldsymbol{A l}^{3+}(\boldsymbol{a q})+ \)
\( \mathbf{3} \boldsymbol{O} \boldsymbol{H}^{-}(\boldsymbol{a} \boldsymbol{q}) ; \boldsymbol{K}_{s p} \)
\( A l(O H)_{3}(s)+O H(a q) \rightleftharpoons \)
\( \boldsymbol{A l}(\boldsymbol{O} \boldsymbol{H})_{4}^{-}(\boldsymbol{a} \boldsymbol{q}) ; \boldsymbol{K}_{c} \)
Which of the following relationship is correct when the solubility is minimum?
\( ^{\mathbf{A}}\left[O H^{-}\right]=\left(\frac{K_{s p}}{K_{C}}\right)^{1 / 3} \)
\( ^{\mathrm{B}}\left[O H^{-}\right]=\left(\frac{K_{C}}{K_{s p}}\right)^{1 / 4} \)
\( ^{\mathrm{c}}\left[O H^{-}\right]=\sqrt{\left(\frac{K_{s p}}{K_{C}}\right)^{1 / 4}} \)
D. None of these
Subject: Chemistry
\( 1.2375 \mathrm{g} \) of cupric oxide on being heated in a current of hydrogen gave 0.9322 g of the metal In another experiment \( 0.9369 \mathrm{g} \) of pure copper was dissolved in nitric acid Excess of acid evaporated and the residue has ignited The weight of the cupric oxide left was 1.2469 g. Which law of chemical combination is
shown by the above results?
A. Law of constant proportions
B. Law of multiple proportions
c. Law of conservation of mass
D. Law of constant volumes
Subject: Physics
A ray of monochromatic green light
enters a liquid from air, as shown in
figure. The angle 1 is \( 45^{\circ} \) and angle 2 is
\( 30^{\circ} \) Find the refractive index of light.
\( A \)
B. \( \sqrt{0.5} \)
\( c \cdot \sqrt{2} \)
D.
Subject: Physics
Two rods of same length and same area
of cross section are joined. Temperature
of two ends are as shown in figure. As
we move along the rod, temperature are as shown in following.
\( \mathbf{A} \cdot K_{1}>K_{2} \)
B \( . K_{1}=K_{2} \)
\( \mathbf{c} \cdot K_{1}<K_{2} \)
D. None of these
Subject: Maths
Find the angle between \( 3 \vec{i}+4 \vec{j}, 2 \vec{j}-5 \vec{k} \)
\( ^{\mathrm{A}} \cdot \cos ^{-1} \frac{8}{5 \sqrt{29}} \)
B. \( \sin ^{-1} \frac{8}{5 \sqrt{29}} \)
c. \( \cos ^{-1} \frac{-1}{5 \sqrt{29}} \)
D. \( \sin ^{-1} \frac{-1}{5 \sqrt{29}} \)
Subject: Physics
Q Type your question
constant angular velocity \( \boldsymbol{\omega}=\frac{1}{\sqrt{L C}} \)
with the help of an external agent. A
uniform magnetic field B exists in
space and is directed into the plane of
the figure. (circuit part remains at rest
(left part is at rest) ). Then,
This question has multiple correct options
A the rms value of current in the circuit is \( \frac{\pi B a^{2}}{R \sqrt{2 L C}} \)
B. the rms value of current in the circuit is \( \frac{\pi B a^{2}}{2 R \sqrt{L C}} \)
c. the maximum energy stored in the capacitor is \( \frac{\pi^{2} B^{2} a^{4}}{8 R^{2} C} \)
D. the maximum power delivered by the external agent is \( \frac{\pi^{2} B^{2} a^{4}}{4 L C R} \)
Subject: Chemistry
The equilibrium concentration of \( [\boldsymbol{B}]_{e q} \) for the reversible reaction \( \boldsymbol{A} \rightleftharpoons \boldsymbol{B} \) can
be evaluated by the expression:
A \( \cdot K_{c}[A]_{e}^{-1} \)
B. \( \frac{K_{f}}{K_{b}}[A]_{e}^{-1} \)
\( \mathbf{c} \cdot K_{f} K_{b}^{-1}[A]_{e} \)
D. \( K_{f} K_{b}[A]^{-1} \)
Subject: Physics
Assertion: The drift velocity of electrons in a metallic wire will decrease, if the
temperature of the wire is increased.
Reason: On increasing temperature, conductivity of metallic wire decreases.
A. Both (A) and (R) are true and
(R) is the correct explanation of
B. Both (A) and (R) are true but (R) is not the correct explanation of A
c. (A) is true but (R) is false
D. (A) is false but (R) is true
Subject: Maths
\( \left|\begin{array}{ccc}1 & \sin \theta & 1 \\ -\sin \theta & 1 & \sin \theta \\ -1 & -\sin \theta & 1\end{array}\right| \) then
\( \mathbf{A} \cdot \Delta=0 \)
B. \( \Delta \in(0, \infty) \)
c. \( \Delta \in[-1,2] \)
D. \( \Delta \in[2,4] \)
Subject: Physics
If the radius of curvature of the curved
surface of a planoconvex lens is \( 50 \mathrm{cm} \)
its focal length is \( (\mu=1.5) \)
A . \( -0.5 m \)
в. \( -0.75 m \)
c. \( -1.25 m \)
D. \( -0.25 m \)
E. \( 1 m \)
Subject: Physics
A ball is dropped on the floor from a height of \( 10 \mathrm{m} \). It rebounds to a height of \( 2.5 \mathrm{m} \).If the ball is in contact with the
floor for 0.01 sec, then average acceleration during contact is
\( \mathbf{A} \cdot 2100 m / s^{2} \)
B. \( 1400 \mathrm{m} / \mathrm{s}^{2} \)
\( \mathbf{c} \cdot 700 m / s^{2} \)
D. \( 400 \mathrm{m} / \mathrm{s}^{2} \)
Subject: Maths
\( \mathbf{f} \boldsymbol{\alpha}^{2}+\boldsymbol{\beta}^{2}+\boldsymbol{\gamma}^{2}=\mathbf{1}, \) then highest
integral value of \( \boldsymbol{\alpha} \boldsymbol{\beta}+\boldsymbol{\beta} \boldsymbol{\gamma}+\boldsymbol{\alpha} \boldsymbol{\gamma} \) is
Subject: Maths
\( f(a+b+c=27, \) then what is the value
of \( (a-7)^{3}+(b-9)^{3}+(c-11)^{3}- \)
\( \mathbf{3}(\boldsymbol{a}-\mathbf{7})(\boldsymbol{b}-\mathbf{9})(\boldsymbol{c}-\mathbf{1 1}) ? \)
A . 0
B. 9
c. 27
D. 81
Subject: Physics
Q Type your question-
the figure. The coefficient of friction,
between the particle and the rough
track equals \( \mu . \) The particle is released,
from rest, from the point \( \boldsymbol{P} \) and it comes
to rest at a point \( R \). The energies, lost by
the ball, over the parts, \( P Q \) and \( Q R \), of
the track, are equal to each other, and
no energy is lost when particle changes
direction from \( P Q \) to \( Q R \) The values of
the coefficient of friction \( \mu \) and the
distance \( x(=Q R), \) are respectively
close to.
A. 0.2 and 6.5 m
B. 0.2 and 3.5 m
c. 0.29 and \( 3.5 m \)
D. 0.29 and 6.5
Subject: Chemistry
In a constant volume calorimeter, 5 g of
a gas with molecular weight 40 was
burnt in excess of oxygen at \( 298 \mathrm{K} \). The temperature of the calorimeter was
found to increase from \( 298 \mathrm{K} \) to \( 298.75 \mathrm{K} \)
due to combustion process. Given that the heat capacity of the calorimeter is
\( 2.5 \mathrm{kJ} K^{-1} \), the numerical value for the
\( \Delta U \) of combustion of the gas in \( \mathrm{kJ} \)
\( m o l^{-1} \) is:
A . 15
B. 12
c. 90
D. 8
Subject: Physics
If the work done in blowing a soap
bubble of volume \( ^{\prime} V^{\prime} \) is \( W \), then the
work done in blowing is soap bubble of
volume \( ^{\prime} 2 V^{\prime} \) is
A \( .4 W \)
B. \( 8 W \)
\( \mathbf{c} \cdot 2^{1 / 3} W \)
\( \mathbf{D} \cdot 4^{1 / 3} W \)
Subject: Chemistry
What transition in \( H e^{+} \) ion shall have
the same wave number as the first line
in Balmar series of H atom?
\( \mathbf{A} \cdot 7 \rightarrow 5 \)
B . \( 5 \rightarrow 3 \)
\( c \cdot 6 \rightarrow 4 \)
\( \mathbf{D} \cdot 4 \rightarrow 2 \)
Subject: Chemistry
The dissociation constant of acetic acid
at a given temperature is \( 1.69 \times 10^{-5} \)
The degree of dissociation of \( 0.01 M \)
acetic acid in the presence of \( 0.01 M \)
HCl is equal to:
A . 0.41
в. 0.13
c. \( 1.69 \times 10^{-3} \)
D. 0.013
Subject: Physics
In an experiment the following observations were recorded
\( \boldsymbol{L}=\mathbf{2 . 8 9 0} \) metre
\( \mathbf{M}=\mathbf{3 . 0} \mathbf{k g} \)
\( \ell=0.87 \mathrm{cm} \)
\( \mathbf{D}=\mathbf{0 . 0 4 1} \mathrm{cm} \)
\( \mathbf{g}=\mathbf{9 8 1 c m} / \mathbf{s e c ^ { 2 }} \)
and the formula used for calculatlon of Young's modulus \( (\mathrm{Y}) \) is \( \mathrm{Y}=\frac{\mathrm{MgL}}{\pi \mathrm{r}^{2} l} \)
What is the maximum possible error
expressed in percentage?
A . 6.36\%
B. 4.8\%
c. अ\%
D. 1\%
Subject: Physics
A long solenoid of radius \( R \) carries a time (t)-dependent current \( \boldsymbol{I}(\boldsymbol{t})= \)
\( \boldsymbol{I}_{0} \boldsymbol{t}(\mathbf{1}-\boldsymbol{t}) \cdot \mathbf{A} \) ring of radius \( 2 \boldsymbol{R} \) is placed
coaxially near its middle. During the
time interval \( 0 \leq t \leq 1, \) the induced
current \( \left(I_{R}\right) \) and the induced
\( \boldsymbol{E} \boldsymbol{M} \boldsymbol{F}\left(\boldsymbol{V}_{\boldsymbol{R}}\right) \) in the ring change as:
\( \mathbf{A} \cdot \) At \( t=0.5 \) direction of \( I_{R} \) reverses and \( V_{R} \) is zero.
B. Direction if \( I_{R} \) remains unchanged and \( V_{R} \) is zero at \( t=0.25 \)
C . At \( t=0.25 \) direction of \( I_{R} \) reverses and \( V_{R} \) is maximum.
D. Direction of \( I_{R} \) remains unchanged and \( V_{R} \) is maximum at \( t=0.5 \)
Subject: Maths
Find the equation of the tangent and the normal to the following curves at the indicated points.
\( \boldsymbol{y}=\boldsymbol{x}^{4}-\boldsymbol{6} \boldsymbol{x}^{3}+1 \mathbf{3} \boldsymbol{x}^{2}-\mathbf{1 0} \boldsymbol{x}+\mathbf{5} \) at \( \boldsymbol{x}= \)
\( \mathbf{1} \)
Subject: Chemistry
In the following reactions:
\( (i) P C l_{5}+S O_{2} \rightarrow A+B \)
\( (i i) A+M e C O O H \rightarrow C+S O_{2}+ \)
\( \boldsymbol{H} \boldsymbol{C l} \)
\( (i i i) 2 C+M e_{2} C d \rightarrow 2 D+C D C l_{2} \) The
compound (C) is:
A. \( M e-C H-C l_{2} \)
в. \( M e-C H_{2}-C l \)
c. \( M e-\underset{\| O}{C}-C l \)
D. \( M e-C-C l_{3} \)
Subject: Physics
The electric field for \( \boldsymbol{R}_{1}<\boldsymbol{r}<\boldsymbol{R}_{2} \) is
\( \operatorname{given} \operatorname{by} \boldsymbol{E}=\frac{Q}{\boldsymbol{X} \boldsymbol{\pi} \varepsilon_{0} r^{2}}\left[\frac{r^{3}-\boldsymbol{R}_{1}^{3}}{R_{2}^{3}-\boldsymbol{R}_{1}^{3}}\right] . \) Find \( \mathbf{X} ? \)
Subject: Chemistry
Select the oxidant in the given
reactions.
\( \boldsymbol{K} \boldsymbol{I} \boldsymbol{O}_{3}+\boldsymbol{5} \boldsymbol{K} \boldsymbol{I}+\boldsymbol{6} \boldsymbol{H} \boldsymbol{C l} \rightarrow \boldsymbol{3} \boldsymbol{I}_{2}+ \)
\( 6 K C l+3 H_{2} O \)
Subject: Chemistry
For the ionic reaction of hydrochloric acid with the following alkenes, predict the correct sequence of reactivity as measured by reaction rates:
\( (\boldsymbol{I}) \boldsymbol{C l C H}=\boldsymbol{C H}_{2} \)
\( (\boldsymbol{I I})\left(\boldsymbol{C H}_{3}\right)_{2} \boldsymbol{C}=\boldsymbol{C H}_{2} \)
\( (I I I) O H C C H=C H_{2} \)
\( (\boldsymbol{I} \boldsymbol{V})(\boldsymbol{N} \boldsymbol{C})_{2} \boldsymbol{C}=\boldsymbol{C}(\boldsymbol{C} \boldsymbol{N})_{2} \)
A. IV > |> ||| > ||
B. |>IV> || > ||
c. \( \||>\|>| V> \)
D. II>1>111>1V
Subject: Maths
Assertion \( \operatorname{Let} \boldsymbol{A}=\left[\begin{array}{ll}\boldsymbol{a}_{11} & \boldsymbol{a}_{12} \\ \boldsymbol{a}_{21} & \boldsymbol{a}_{22}\end{array}\right], \boldsymbol{X}=\left[\begin{array}{l}\boldsymbol{x}_{1} \\ \boldsymbol{x}_{2}\end{array}\right], \boldsymbol{Y}= \)
\( \left[\begin{array}{l}\boldsymbol{y}_{1} \\ \boldsymbol{y}_{2}\end{array}\right] \)
If \( \boldsymbol{X}^{\prime} \boldsymbol{A} \boldsymbol{X}=\boldsymbol{0} \) for each \( \boldsymbol{X}, \) then \( \boldsymbol{A} \) must
be a symmetric matrix.
Reason
If \( \boldsymbol{A} \) is symmetric and \( \boldsymbol{X}^{\prime} \boldsymbol{A} \boldsymbol{X}=\mathbf{0} \) for
\( \operatorname{each} X, \) then \( A=0 \)
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
For the reaction, \( \boldsymbol{C a} \boldsymbol{C O}_{3}(\boldsymbol{s}) \rightleftharpoons \)
\( \boldsymbol{C a O}(\boldsymbol{s})+\boldsymbol{C O}_{2}(\boldsymbol{g}), \boldsymbol{K}_{\boldsymbol{p}}=\boldsymbol{p}_{C O_{2}} \)
A. True
B. False
Subject: Chemistry
In the estimation of nitrogen by Kjeldahl's method. 2.8 gm of an organic compound required 20 millimole of
\( H_{2} S O_{4} \) for the complete neutralisation
of \( N H_{3} \) gas evolved. The percentage of nitrogen in the sample is:
A . 20\%
B . 10\%
c. 40\%
D. 30\%
Subject: Maths
The blood groups of 30 students of Class VIII are recorded as follows:
\( \boldsymbol{A}, \boldsymbol{B}, \boldsymbol{O}, \boldsymbol{O}, \boldsymbol{A} \boldsymbol{B}, \boldsymbol{O}, \boldsymbol{A}, \boldsymbol{O}, \boldsymbol{B}, \boldsymbol{A}, \boldsymbol{O}, \boldsymbol{B}, \boldsymbol{A}, \boldsymbol{O} \)
\( \boldsymbol{A}, \boldsymbol{A B}, \boldsymbol{O}, \boldsymbol{A}, \boldsymbol{A}, \boldsymbol{O}, \boldsymbol{O}, \boldsymbol{A B}, \boldsymbol{B}, \boldsymbol{A}, \boldsymbol{O}, \boldsymbol{B}, \boldsymbol{A} \)
Use this table to determine the
probability that a student of this class, selected at random, has blood group
\( A B \)
Subject: Maths
\( \int \frac{\cos x}{\sqrt[3]{\sin ^{2} x}} d x= \)
A \( \cdot 3 \sqrt[3]{\sin x}+c \)
B. \( 3 \sqrt[3]{\sin ^{2} x}+c \)
c. \( \sqrt[3]{\sin x}+c \)
D. \( \sqrt[3]{\sin ^{2} x}+c \)
Subject: Chemistry
The isomer(s) of \( \left[\boldsymbol{C o}\left(\boldsymbol{N} \boldsymbol{H}_{3}\right)_{4} \boldsymbol{C l}_{2}\right] \) that
has/have a \( C l-C o-C l \) angle of \( 90^{\circ} \)
is/are:
A. trans only
B. meridional and trans
c. cis and trans
D. cis only
Subject: Maths
Construct the following quadrilaterals. Quadrilateral PLAN \( P L=4 \mathrm{cm} \)
\( \boldsymbol{L} \boldsymbol{A}=\mathbf{6 . 5} \boldsymbol{c m} \)
\( \angle P=90^{\circ} \)
\( \angle A=110^{\circ} \)
\( \angle N=85^{\circ} \)
Subject: Maths
The position vector of a point \( \boldsymbol{P} \) such
that \( \overline{O P} \) is inclined to \( O X \) at \( 45^{\circ} \) and to
\( O Y \) at \( 60^{\circ} \) and \( O P=12 \) units, is
\( \mathbf{A} \cdot 6(\sqrt{2} \hat{i}+\hat{j} \pm \hat{k}) \)
B . \( 3(\sqrt{2} \hat{\imath}+\hat{j} \pm \hat{k}) \)
c. \( 2(\sqrt{2} \hat{i}+\hat{j} \pm \hat{k}) \)
D . \( 12(\sqrt{2} \hat{i}+\hat{j} \pm \hat{k}) \)
Subject: Maths
Find the coordinates of the points which divide the line segment joining the points (-4,0) and (0,6) in 4 equal
parts This question has multiple correct options
A \( \cdot\left(-3, \frac{3}{2}\right) \)
в. (-2,3)
\( ^{c} \cdot\left(-1, \frac{9}{2}\right) \)
D. All of the above
Subject: Maths
A quadratic equation \( a x^{2}+b x+c=0 \)
with distinct coefficients is formed. It a
b, c are chosen from the numbers 2,3,5 then the probability that the equation has real roots is
A \( \cdot \frac{1}{3} \)
B. \( \frac{2}{5} \)
\( c \cdot \frac{1}{4} \)
D.
E \( \cdot \frac{2}{3} \)
Subject: Chemistry
Carbonic acid \( \left(\boldsymbol{H}_{2} \boldsymbol{C} \boldsymbol{O}_{3}\right), \) a diprotic acid
has \( \boldsymbol{K}_{a_{1}}=\mathbf{4 . 0} \times \mathbf{1 0}^{-\mathbf{7}} \) and \( \boldsymbol{K}_{a_{2}}= \)
\( \mathbf{7} . \mathbf{0} \times \mathbf{1 0}^{-11} . \) What is the \( \left[\boldsymbol{H} \boldsymbol{C O}_{\mathbf{3}}^{-}\right] \) of \( \mathbf{a} \)
\( 0.025 \mathrm{M} \) solution of carbonic acid?
A \( .7 .8 \times 10^{-3} \)
B. \( 6.6 \times 10^{-4} \)
c. \( 10^{-10} \)
D. \( 1.0 \times 10^{-4} \)
Subject: Physics
Choose the correct answer from
alternatives given. If \( \vec{E} \) and \( \vec{B} \) represent electric and magnetic field vectors of an electromagnetic wave, the direction of propagation of the wave is along
\( \mathbf{A} \cdot \vec{B} \times \vec{E} \)
в. \( \vec{B} \)
\( c \cdot \vec{E} \)
D. \( \vec{E} \times \vec{B} \)
Subject: Chemistry
The total number of diprotic acids among the following is:
\( \boldsymbol{H}_{3} \boldsymbol{P} \boldsymbol{O}_{4}, \boldsymbol{H}_{2} \boldsymbol{S} \boldsymbol{O}_{4}, \boldsymbol{H}_{3} \boldsymbol{P} \boldsymbol{O}_{3}, \boldsymbol{H}_{2} \boldsymbol{C} \boldsymbol{O}_{3}, \boldsymbol{H}_{2} \)
\( \mathbf{A} \cdot \mathbf{6} \)
B. 5
\( c \cdot 4 \)
\( D \)
Subject: Physics
A current I flows in the anticlockwise
direction through a square loop of side a lying in the xoy plane with its center at the origin. The magnetic induction at the center of the square loop is
A \( \cdot \frac{2 \sqrt{2} \mu_{0} I}{\pi a} \hat{e}_{x} \)
B. \( \frac{2 \sqrt{2} \mu_{0} I}{\pi a} \hat{e}_{z} \)
\( ^{\mathrm{c}} \cdot \frac{2 \sqrt{2} \mu_{0} I}{\pi a^{2}} \hat{e}_{z} \)
D. \( \frac{2 \sqrt{2} \mu_{0} I}{\pi a^{2}} \hat{e}_{x} \)
Subject: Physics
A \( 0.098-k g \) block slides down a
frictionless track as shown in Fig. The time taken by the block to move
from \( A \) to \( B \) is:
\( ^{A} \cdot \frac{1}{\sqrt{g}} \)
в. \( \frac{2}{\sqrt{g}} \)
c. \( \frac{3}{\sqrt{g}} \)
D. \( \frac{4}{\sqrt{g}} \)
Subject: Physics
Light moves from air into water. The
light makes an angle of \( 47^{\circ} \) with the normal in the air. What angle will it
make with the normal in the water?
The index of refraction for air is 1.00
The index of refraction for water is 1.33
A \( \cdot 47^{\circ} \)
B. 77
\( c \cdot 43 \)
D. 25
\( E \cdot 33 \)
Subject: Maths
If the mean deviation of number \( 1,1+ \)
\( \boldsymbol{d}, \mathbf{1}+\mathbf{2} \boldsymbol{d}, \dots, \mathbf{1}+\mathbf{1 0 0} \boldsymbol{d} \) from their mean
is \( 255, \) then the \( d \) is equal to:
A . \( 10 . \)
B. 20.2
c. 20
D. 10
Subject: Physics
A piece of iron of mass 0.05 kg is
heated to a temperature of \( 200^{\circ} \mathrm{C} \) and
dropped into a beaker containing \( 0.4 \mathrm{kg} \)
of water at \( 20^{\circ} \mathrm{C} \). If the final
temperature of water and iron is \( 22.4^{\circ} \mathrm{C} \)
find the specific heat capacity of iron.
A . \( 354.04 J k g^{-1} K^{-1} \)
B. \( 454.04 J k g^{-1} K^{-1} \)
c. \( 554.04 J k g^{-1} K^{-1} \)
D. \( 654.04 J k g^{-1} K^{-1} \)
Subject: Physics
Find the heat radiated per second by a body of surface area \( 12 \mathrm{cm}^{2} \) kept in
thermal equilibrium in a room at
temperature \( 20^{\circ} \mathrm{C} \). The emissivity of the
surface is 0.8 and \( \sigma=6 x \)
\( 10^{-8} W m^{-2} K^{-4} \)
A . 4.2
B . 0.42
c. 0.042
D. 42
Subject: Maths
If \( A \) and \( B \) are two disjoint sets and \( N \) is
universal set, then \( \boldsymbol{A}^{\circ} \cup\left[(\boldsymbol{A} \cup \boldsymbol{B}) \cap \boldsymbol{B}^{\circ}\right] \)
is
\( A \cdot \phi \)
в. \( A \)
\( c . B \)
D. \( N \)
Subject: Chemistry
Insulin is dissolved in a suitable solvent
and the osmotic pressure \( \pi \) in atm of
solutions of various concentrations \( C \) in
\( g / c m^{3} \) is measured at \( 27^{\circ} \mathrm{C} \). The slope of plot of \( \pi \) against \( C \) is found to be
\( 4.1 \times 10^{-3} \operatorname{atm} \mathrm{cm}^{3} g^{-1} . \) The molecular
mass of insulin is?
A \( .6 \times 10^{3} \)
B. \( 3 \times 10^{6} \)
\( c \cdot 6 \times 10^{5} \)
D. \( 3 \times 10^{3} \)
Subject: Physics
A force of \( 25 \mathrm{N} \) acts on a body at rest for
\( 0.2 s \) and a force of \( 70 N \) acts for the next
\( 0.1 \mathrm{s} \) in opposite direction. If the final
velocity of the body is \( 5 m s^{-1}, \) the mass
of the body is:
\( A \cdot 1 \mathrm{kg} \)
B. \( 2 \mathrm{kg} \)
c. \( 0.8 \mathrm{kg} \)
D. \( 0.4 \mathrm{kg} \)
Subject: Physics
If \( \triangle E \) is the heat of reaction for
\( C_{2} H_{3} O H_{(1)}+3 O_{2(g)} \rightarrow 2 C O_{2(s)}+ \)
\( \mathbf{3} \boldsymbol{H}_{2} \mathbf{0}_{(1)} \) at constant volume, the \( \triangle \boldsymbol{H} \)
Heat of reaction at constant pressure) at constant temperature is:
A \( . \triangle H=\triangle E+2 R T \)
B. \( \triangle H=\triangle E-2 R T \)
c. \( \triangle H=\Delta E+R T \)
D. \( \triangle H=\triangle E-R T \)