AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Biology
Assertion
Fertilization of bryophytes require water for antherozoids.
Reason
They are amphibians of plant kingdom.
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: Biology
Use the following diagram to complete
the statement about the human
nephron-
A. The composition of the filtrate would be must like plasma in the tubule next to the
B. The urine would be most concentrated in the collecting duct next to letter
C. Most of the glomerular filtrate is reabsorbed into pentubular capillary next to the
D. Conducting of urine to pelvis of the kidney from the structure next to the letter
E. Most water is reabsorbed by the structure next to the letter
Subject: Maths
Find \( \boldsymbol{f} \circ \boldsymbol{g} \) and \( \boldsymbol{g} \) o \( \boldsymbol{f}, \) if \( \boldsymbol{f}(\boldsymbol{x})= \)
\( \boldsymbol{x}^{2}, \boldsymbol{g}(\boldsymbol{x})=\cos \boldsymbol{x} \)
Subject: Chemistry
Which of the following reaction occur when urea is added to soil as a fertilizer?
A. \( N H_{2} C O N H_{2} \longrightarrow H N C O+N H_{3} \)
B. \( N H_{2} C O N H_{2}+H_{2} O \longrightarrow 2 N H_{3}+C O_{2} \)
c. \( 2 N H_{2} C O N H_{2} \longrightarrow H_{2} N C O N H C O N H_{2}+N H_{3} \)
D. Both 1 and 2
Subject: Chemistry
When \( I_{2} \) dissociated to its form the
following reaction occurs:
\( \boldsymbol{I}_{2(g)} \rightleftharpoons 2 \boldsymbol{I}_{(g)} ; \triangle \boldsymbol{H}^{0}=+\mathbf{1 5 0 k J} \)
The reaction is favoured at ?
A. low temperature
B. high temperature
c. no change with temperature
D. high pressure.
Subject: Chemistry
Which of the following statements is
not true about \( K M n O_{4} ? \)
A. Its solution is unstable in acidic medium.
B. A green coloured solution containing \( M n O_{3}^{+} \) ions is
formed when a small quantity of \( K M n O_{4} \) is added to
concentrated \( H_{2} S O_{4} \)
C. \( M n O_{4}^{-} \) changes to \( M n^{2+} \) in basic solution
D. It acts as a self-indicator in the titration with \( F e^{2+} \) or
\( C_{2} O_{4}^{2-} \)
Subject: Maths
\( M C Q: \sin \left(\sin ^{-1} \frac{5 \pi}{6}\right)+ \)
\( \cos ^{-1}\left(\cos \frac{5 \pi}{3}\right)+\tan ^{-1}\left(\tan \frac{7 \pi}{3}\right) \)
\( A \cdot \frac{5 \pi}{6} \)
в. \( \frac{\pi}{3} \)
c. \( \frac{7 \pi}{6} \)
\( D \cdot \frac{29 \pi \pi \pi}{6} \)
Subject: Chemistry
Equal volumes of molar hydrochloric acid and sulphuric acid are neutralized
by dilute NaOH solution and \( \boldsymbol{x} \) kcal
and \( y k c a l \) of heat are liberated
respectively. Which of the following is
true?
A \( . x=y \)
B・ \( x=\frac{y}{2} \)
c. \( x=2 y \)
D. None of these
Subject: Physics
A string is stretched between fixed points separated by \( 75 \mathrm{cm} \). It is observed to have resonant frequencies
of \( 420 H z \) and \( 315 H z . \) There are no
other resonant frequencies between these two. Then, the lowest resonant
frequency for this string is
A. \( 10.5 ~ H z \)
в. \( 105 \mathrm{Hz} \)
c. \( 1.05 \mathrm{Hz} \)
D. \( 1050 \mathrm{Hz} \)
Subject: Chemistry
\( \boldsymbol{H}_{2(g)}+\frac{1}{2} \boldsymbol{O}_{2(g)} \rightarrow \boldsymbol{H}_{2} \boldsymbol{O}_{(l)} ; \boldsymbol{\Delta} \boldsymbol{H}= \)
\( -286.2 k J ; H_{2} O_{(l)} \rightarrow H_{(a q)}^{+}+O H_{(a q)}^{-} \)
\( \Delta H=+57.3 k J . \) Enthalpy of ionisation
of \( O H^{-} \) in aqueous solution is:
B . \( +228.5 k J \)
c. \( -343.5 k J \)
D. zero
Subject: Maths
The differential equation of system of concentric circles with centres (1,2) is
A \( \cdot \frac{d y}{d x}=\frac{x-1}{x-2} \)
B. \( \frac{d y}{d x}=\frac{x-1}{2-x} \)
c. \( \frac{d y}{d x}=\frac{x-1}{2-y} \)
D. \( \frac{d y}{d x}=\frac{x-1}{y-2} \)
Subject: Chemistry
Arrange the oxides of manganese
according to increasing acidic strength.
\( \mathbf{A} \cdot M n O<M n_{3} O_{4}<M n_{2} O_{3}<M n O_{2}<M n_{2} O_{7} \)
B. \( M n_{2} O_{7}<M n O_{2}<M n_{2} O_{3}<M n_{3} O_{4} \)
\( \mathbf{c} \cdot M n O_{2}<M n_{2} O_{7}<M n_{3} O_{4}<M n_{2} O_{3}<M n O \)
D. \( M n_{3} O_{4}<M n_{2} O_{3}<M n_{2} O_{7}<M n O_{2}<M n O \)
Subject: Physics
The value of \( ^{\prime} g^{\prime} \) at a depth of \( 80 k m \) will
be (Radius of earth \( =\mathbf{6 4 0 0 k m} \) and
value of \( ^{\prime} g^{\prime} \) on the surface of earth is
\( \left.10 m / s^{2}\right) \)
A. \( 990 \mathrm{cm} / \mathrm{s}^{2} \)
В \( .980 \mathrm{cm} / \mathrm{s}^{2} \)
\( \mathrm{c} \cdot 970 \mathrm{cm} / \mathrm{s}^{2} \)
D. \( 1000 \mathrm{cm} / \mathrm{s}^{2} \)
Subject: Maths
The value of \( 60^{\circ} \) in centesimal system is
A \( \cdot \frac{100^{9}}{3} \)
в. \( \frac{200^{9}}{3} \)
c. \( \frac{140^{9}}{3} \)
D. \( \frac{160^{9}}{3} \)
Subject: Physics
A resistance of \( 2 \Omega \) is connected across one gap of a metre bridge (the length of the wire is \( 100 \mathrm{cm} \) ) and an unknown
resistance greater than \( 2 \Omega \) is connected across the other gap. When these resistances are interchanged, the balance point shifts by \( 20 \mathrm{cm} \) Neglecting any corrections, the unknown resistance is:
A . \( 4 \Omega \)
в. 3 \( \Omega \)
\( c \cdot 5 \Omega \)
D. \( 6 \Omega \)
Subject: Chemistry
\( M n O_{4}^{2-}(1 \text { mole }) \) in neutral aqueous medium disproportionate to
A \( \cdot 2 / 3 \) mole \( M n O_{4}^{-} \) and \( 1 / 3 \) mole \( M n O_{2} \)
B . 1/3 mole \( M n O_{4}^{-} \) and \( 2 / 3 \) mole \( M n O_{2} \)
\( \mathrm{c} \cdot 1 / 3 \) mole of \( M n_{2} O_{7} \) and \( 1 / 3 \) mole of \( M n O_{2} \)
D. \( 2 / 3 \) mole of \( M n_{2} O_{7} \) and \( 1 / 3 \) mole of \( M n O_{2} \)
Subject: Physics
A ball of mass m approaches a wall of \( \operatorname{mass} M(>>m) \) with the speed \( 4 \mathrm{m} / \mathrm{s} \)
along normal to the wall. The speed of wall is \( 1 \mathrm{m} / \mathrm{s} \) towards the ball. The speed of the ball after an elastic collision with
the wall is-
A. \( 5 \mathrm{m} / \mathrm{s} \) away from the wall
B. 3 m/s away from the wall
c. \( 9 \mathrm{m} / \mathrm{s} \) away from the wall
D. \( 6 \mathrm{m} / \mathrm{s} \) away from the wall
Subject: Physics
Two trains are each 50 m long moving parallel towards each other at speeds \( 10 m / s \) and \( 15 m / s \) respectively. After what time will they pass each other?
\( ^{\mathrm{A}} \cdot_{5} \sqrt{\frac{2}{3}} s e c \)
B. 4 sec
\( \mathbf{c} \cdot 2 \sec \)
D. 6 sec
Subject: Maths
Simplify using associative property :
\( \frac{-8}{9} \times\left(\frac{27}{32} \times \frac{-8}{21}\right) \)
A \( \cdot \frac{2}{7} \)
B. \( \frac{-2}{7} \)
\( c \cdot \frac{-8}{21} \)
D. \( \frac{-3}{4} \)
Subject: Physics
If a particle is executing \( S H M \) on a
straight line. \( A \) and \( B \) are two points at which its velocity is zero. It passes
through a certain point \( \boldsymbol{P}(\boldsymbol{A} \boldsymbol{P}<\boldsymbol{P B}) \)
at successive intervals of 0.5 sec and
1.5 sec with a speed of \( 3 \mathrm{m} / \mathrm{s} \). The maximum speed of the particle is
A. \( 3 m / s \)
B. \( 3 \sqrt{2} \mathrm{m} / \mathrm{s} \)
\( \mathbf{c} \cdot 3 \sqrt{3} m / s \)
D. \( 6 m / s \)
Subject: Chemistry
Sequence of acidic character
is
\( \mathbf{A} \cdot S O_{2}>C O_{2}>C O>N_{2} O_{5} \)
B \( \cdot S O_{2}>N_{2} O_{5}>C O>C O_{2} \)
\( \mathrm{c} \cdot N_{2} \mathrm{O}_{5}>S \mathrm{O}_{2}>\mathrm{CO}>\mathrm{CO}_{2} \)
\( \mathrm{D} \cdot N_{2} O_{5}>S O_{2}>C O_{2}>C O \)
Subject: Maths
The area of \( \square O A P B \) is:
A \( .24 \mathrm{cm}^{2} \)
B. \( 36 \mathrm{cm}^{2} \)
c. \( 48 \mathrm{cm}^{2} \)
D. \( 60 \mathrm{cm}^{2} \)
Subject: Physics
The magnetic moment of a bar magnet is
0.256 amp.m \( ^{2} \). Its pole strength is 400
milli amp. m. It is cut into two equal
pieces and these two pieces are arranged
at right angles to each other with their unlike poles in contact (or like poles in contact). The resultant magnetic
moment of the system is
A \( \cdot \sqrt{2} \times 256 \times 10^{-3} A m^{2} \)
B . \( 250 \times 10^{-3} \mathrm{Am}^{2} \)
c. \( \frac{256}{\sqrt{2}} \times 10^{-3} \mathrm{Am}^{2} \)
D \( \cdot \frac{128}{\sqrt{2}} \times 10^{-3} \mathrm{Am}^{2} \)
Subject: Physics
Let \( \ell, r, c \) and \( v \) represent inductance, resistance, capacitance and voltage, respectively. The dimension of \( \frac{\ell}{r c v} \) is
SI units will be:
A. \( [L T A] \)
B . \( \left[L A^{-2}\right] \)
\( \mathbf{c} \cdot\left[A^{-1}\right] \)
D \cdot \( \left[L T^{2}\right] \)
Subject: Physics
It is well known that a raindrop or a small pebble falls under the influence of the downward gravitational force and the opposing resistive force. The resistive force is known to be
proportional to the speed of the drop. Consider a drop or small pebble of 1 g falling (from rest) from a diff of height \( 1.00 \mathrm{km} . \) It hits the ground with a speed
of \( 50.0 \mathrm{m} s^{-1} . \) What is the work done by
the unknown resistive force?
Subject: Physics
On connecting a battery to the two corners of a diagonal of a square
conductor frame of side \( a \) the
magnitude of the magnetic field at the centre will be:
A . zero
в. \( \frac{\mu_{0}}{\pi a} \)
c. \( \frac{2 \mu_{0}}{\pi a} \)
D. \( \frac{4 \mu_{0}}{\pi a} \)
Subject: Maths
Assertion(A): If the tangent at any point
\( P \) on the curve \( x y=a^{2} \) meets the axes
at \( A \) and \( B \) then \( A P: P B=1: 1 \)
Reason(R): The tangent at \( P(x, y) \) on
the curve \( \boldsymbol{X}^{\boldsymbol{m}} \cdot \boldsymbol{Y}^{\boldsymbol{n}}=\boldsymbol{a}^{\boldsymbol{m}+\boldsymbol{n}} \) meets the
axes at \( A \) and \( B \). Then the ratio of \( P \)
divides \( \overline{A B} \) is \( n: m \)
A. Both A and R are true R is the correct explanation of
B. Both A and R are true but R is not correct explanation of A
c. A is true but R is false
D. A is false but R is true
Subject: Maths
f \( \triangle_{1}= \)
\( \mid \begin{array}{ccc}a_{1}^{2}+b_{1}+c_{1} & a_{1} a_{2}+b_{2}+c_{2} & a_{1} a_{3}+c \\ b_{1} b_{2}+c_{1} & b_{2}^{2}+c_{2} & b_{2} b_{3} \\ c_{3} c_{1} & c_{3} c_{2} & c_{3}^{2}\end{array} \)
and \( \triangle_{2}=\left|\begin{array}{lll}a_{1} & b_{1} & c_{1} \\ a_{2} & b_{2} & c_{2} \\ a_{3} & b_{3} & c_{3}\end{array}\right|, \) then \( \frac{\triangle_{1}}{\triangle_{2}} \) is
equal to
A \( \cdot a_{1} b_{2} c_{3} \)
B. \( a_{1} a_{2} a_{3} \)
\( c \cdot a_{3} b_{2} c \)
D. \( a_{1} b_{1} c_{1}+a_{2} b_{2} c_{2}+a_{3} b_{3} c_{3} \)
Subject: Physics
A rubber ball of mass \( 10 g m \) and volume
\( 15 c m^{3} \) dipped in water to a depth of
10m. Assuming density of water
uniform throughout the depth, find
(a) the acceleration of the ball, and
(b) the time taken by it to the surface if it is released from rest. take \( g= \)
\( 980 \mathrm{cm} / \mathrm{s}^{2} \)
(b) \( 2.02 \sec \)
B . (a) \( 4.9 \mathrm{m} / \mathrm{s}^{2} \)
(b) \( 2.02 \sec \)
c. (a) \( 4.9 \mathrm{m} / \mathrm{s}^{2} \)
(b) \( 12.02 \mathrm{sec} \)
D. (a) \( 8.9 m / s^{2} \)
(b) \( 2.02 \sec \)
Subject: Physics
An vehicle has a mass of 1500 kg. What must be the force between the vehicle
and the road if the vehicle is to be
stopped with a negative acceleration of \( 1.7 m s^{-2} ? \)
A. \( 2550 N \) in a direction opposite to that of the vehicle
B. \( 2550 N \) in a direction same to that of the vehicle
c. \( 1550 N \) in a direction opposite to that of the vehicle
D. \( 1550 N \) in a same opposite to that of the vehicle
Subject: Chemistry
The freezing point depression of a \( 0.109 M a q . \) solution of formic acid is
\( -0.21^{\circ} \mathrm{C} . \) The equilibrium constant for
the reaction is \( 1.44 \times 10^{-x} \)
\( \boldsymbol{H} \boldsymbol{C O O H}(\boldsymbol{a q}) \rightleftharpoons \boldsymbol{H}^{+}(\boldsymbol{a q})+ \)
\( H C O O^{\ominus}(a q) \)
\( \boldsymbol{K}_{f} \) for water \( =\mathbf{1 . 8 6} \boldsymbol{k g} \boldsymbol{m o l}^{-1} \boldsymbol{K} \)
Value of \( x \) is:
Subject: Physics
A spring of force constant \( \mathrm{k}=300 \mathrm{N} / \mathrm{m} \) connects two blocks having masses 2 kg and 3 kg, lying on a smooth horizontal plane. If the spring block system is released from a stretched position, find the number of complete oscillations in 1 minute. Take \( \pi=\sqrt{10} \)
A .44
B. 150
\( c \cdot 34 \)
D. 55
Subject: Maths
\( A B C D E \) is a pentagon. the resultant of the forces \( \overrightarrow{A B}+\overrightarrow{B C}+\overrightarrow{D C}+\overrightarrow{E D}+ \)
\( \overrightarrow{A E}=k \overrightarrow{A C}, \) then find the value of \( k \)
Subject: Chemistry
The \( I U P A C \) name for the complex
\( \left[\mathrm{Co}\left(\mathrm{NO}_{2}\right)\left(\mathrm{NH}_{3}\right)_{5}\right] \mathrm{Cl}_{2} \) is:
A. pentaamminenitrito-N-cobalt(III) chloride
B. nitrito-N-pentaamminecobalt(III) chloride
C . pentaamminenitrito-N-cobalt(II) chloride
D. pentaamminenitrito-N-cobalt(I) chloride
Subject: Maths
Using ruler and compasses only, construct a \( \triangle A B C \) having given
\( \angle A B C=60^{0}, \angle A C B=45^{0} \) and the
perpendicular from \( \boldsymbol{A} \) to \( \boldsymbol{B} \boldsymbol{C} \) equal to
\( 2.5 \mathrm{cm} . \) The length of \( A B \) is
A \( .2 .1 \mathrm{cm} \)
B. \( 2.9 \mathrm{cm} \)
\( c .3 .5 \mathrm{cm} \)
D. \( 4.2 \mathrm{cm} \)
Subject: Maths
Show that the function \( \boldsymbol{f}(\boldsymbol{x})= \) \( \left\{\begin{array}{ll}3 x-2 & \text { if } 0<x \leq 1 \\ 2 x^{2}-x & \text { if } 1<x \leq 2 \\ 5 x-4 & \text { if } x>2\end{array}\right. \)
is continuous at \( x=2 \)
Subject: Chemistry
The ease of formation of free radicals
follows the order:
A \( \cdot 3^{\circ}>2^{\circ}>1^{\circ}>\dot{C} H_{3} \)
в. \( \dot{C H}_{3}>1^{\circ}>2^{\circ}>3^{\circ} \)
c. \( 1^{\circ}>2^{\circ}>3^{\circ}>\dot{C} H \)
D \( \cdot 2^{\circ}>1^{\circ}>3^{\circ}>\dot{C} H_{3} \)
Subject: Maths
Let \( m \) and \( n(m<n) \) be the roots of the
equation \( \boldsymbol{x}^{2}-\mathbf{1 6 x}+\mathbf{3 9}=\mathbf{0 .} \) If four
terms \( p, q, r \) and \( s \) are inserted between
\( m \) and \( n \) form an \( A P, \) then what is the
value of \( \boldsymbol{p}+\boldsymbol{q}+\boldsymbol{r}+\boldsymbol{s} ? \)
A . 29
B. 30
\( c \cdot 32 \)
D. 35
Subject: Chemistry
From the stability constant (hypothetical values) given below,
predict which is the strongest ligand?
\( \mathbf{A} \cdot C u^{2+}+4 N H_{3} \rightarrow\left[C u\left(N H_{3}\right)_{4}\right]^{2+}, K=4.5 \times 10^{11} \)
B. \( C u^{2+}+4 C N^{-} \rightarrow\left[C u(C N)_{4}\right]^{2-}, K=2.0 \times 10^{27} \)
\( \mathbf{c} \cdot C u^{2+}+2 e n \rightarrow\left[C u(e n)_{2}\right]^{2+}, K=3.0 \times 10^{15} \)
D \( \cdot C u^{2+}+4 H_{2} O \rightarrow\left[C u\left(H_{2} O\right)_{4}\right]^{2+}, K=9.5 \times 10^{8} \)
Subject: Physics
An \( A C \) voltage source of variable
angular frequency \( \omega \) and fixed
amplitude \( V_{0} \) is connected in series
with a capacitance \( C \) and an electric bulb of resistance \( \boldsymbol{R} \) (inductance zero)
When \( \omega \) is increased
A. the bulb glows dimmer
B. the bulb glows brighter
C. total impedance of the circuit is unchanged
D. total impedance of the circuit increases
Subject: Physics
The flux passing through the surface \( S_{5} \)
will be
\( \mathbf{A} \cdot-0.135 N m^{2} C^{-} \)
B. \( -0.054 N m^{2} C^{-1} \)
\( c \cdot 0.081 N m^{2} C^{-1} \)
) \( 0.054 N m^{2} C^{-1} \)
Subject: Physics
Calculate the work done to rise a body of \( 30 \mathrm{kg} \) to a height of \( 50 \mathrm{m}\left(\mathrm{g}=10 \mathrm{m} \mathrm{s}^{-2}\right) \)
(in kJ)
A . 100
B.
c. 15
D. 0.5
Subject: Chemistry
The volume of water to be added to
\( 100 \mathrm{cm}^{3} \) of \( 0.5 \mathrm{M} H_{2} \mathrm{SO}_{4} \) to get
decimolar concentration is :
A. \( 500 \mathrm{ml} \)
B. 100 \( \mathrm{ml} \)
c. \( 400 \mathrm{ml} \)
D. 300 m1
Subject: Physics
Assertion
On going away from a point charge or a small electric dipole, electric field decreases at the same rate in both the
cases.
Reason
Electric field is inversely proportional to
square of distance from the charge or on electric dipole.
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: Biology
Assertion
The phloem present in the xylem elements is called protophloem.
Reason
The phloem elements develop in the middle of xylem elements are secondary in nature
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion.
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Assertion is incorrect but Reason is correct
Subject: Maths
One hundred identical coins, each with
probability, \( p, \) of showing up heads are
tossed once. If \( 0<p<1 \) and the
probability of heads showing on fifty coins is equal to that of heads showing on 51 coins, then the value of \( p \) is :
A . \( 1 / 2 \)
B . \( 49 / 101 \)
c. \( 50 / 101 \)
D. \( 51 / 101 \)
Subject: Physics
\( 50 g \) of oil of specific heat capacity \( 2.2 J / g^{o} C \) is cooled from \( 350^{\circ} C \) to
\( 25^{\circ} \mathrm{C} . \) Calculate the heat energy given
out by the oil
A . \( 35.75 J \)
B. \( 35,75000 J \)
c. \( 35,75 J \)
D. \( 35,750 J \)
Subject: Maths
A straight line drawn through (1,2)
intersects \( x+y=4 \) at a distance \( \frac{\sqrt{6}}{3} \)
from \( (1,2) . \) The angle made by the line with the positive direction of \( x \) -axis
is \( \alpha . \) Find the greater of the two values
of \( \boldsymbol{\alpha} \)
A . \( 105^{\circ} \)
B \( \cdot 75^{\circ} \)
\( c \cdot 60^{0} \)
D. \( 15^{\circ} \)
Subject: Physics
A horizontal telegraph wire \( 0.5 k m \) long
running east and west in a part of a circuit whose resistance is \( 2.5 \Omega \). The
wire falls to \( g=10.0 m / s^{2} \) and \( B= \)
\( 2 \times 10^{-5} w e b e r / m^{2}, \) then the current
induced in the circuit is
A. 0.7 amp
B. 0.04 amp
c. 0.02 amp
D. \( 0.01 a m p \)
Subject: Physics
The magnitude of the impulse developed by a mass of \( 0.2 \mathrm{kg} \) which changes its velocity from \( 5 \hat{i}+3 \hat{j}+7 \hat{k} \) \( \mathrm{m} / \mathrm{s} \) to \( 2 \hat{\boldsymbol{i}}+\boldsymbol{3} \hat{\boldsymbol{j}}+\hat{\boldsymbol{k}} \)
A . \( 2.7 \mathrm{N}-\mathrm{s} \)
B. 1.3N-s
c. \( 0.9 N- \) s
D. 3.6N-s
Subject: Physics
A particle of mass \( m \) is moving in a circular path of constant radius r such
that its centripetal acceleration \( a_{c} \) is
varying with time \( t \) as \( a_{c}=k^{2} r t^{2}, \) where
k is a constant. The power delivered to the particle by the forces acting on it is:
A. zero
B. \( m k^{2} r^{2} t^{2} \)
\( \mathrm{c} \cdot m k^{2} r^{2} t \)
\( \mathbf{D} \cdot m k^{2} r t \)
Subject: Physics
Starting from rest a wheel rotates with
uniform angular acceleration \( 2 \pi r a d / s^{2} \)
After \( 4 s, \) if the angular acceleration ceases to act, its angular displacement
in the next \( 4 s \) is:
B. \( 16 \pi \) rad
\( \mathbf{c} \cdot 24 \pi \quad r a d \)
D. \( 32 \pi \) rad
Subject: Physics
A source \( S \) and a detector \( D \) of high
frequency waves are a distance d apart
on the ground. The direct wave from S is found to be in phase at D with the wave
from \( S \) that is reflected rays make the
same angle with the reflecting layer. When the layer rises a distance \( h, \) no
signal is detected at D. Neglect absorption in the atmosphere and find the relation between \( \mathrm{d}, \mathrm{h}, \mathrm{H} \) and the wavelength \( \lambda \) of the waves.
Subject: Chemistry
Choose the correct statement. The use
\( ^{12} C \) scale has superseded the older scale of atomic mass based on
\( ^{16} \boldsymbol{O} \) isotope, one important advantage of the former being:
A. The atomic masses on \( ^{12} C \) scale became whole
numbers
B. 12 C is more abundant in the earths crust than \( ^{16} \) O
c. The difference between the physical and chemical atomic masses got narrowed down significantly
D. \( 12 \mathrm{C} \) is situated midway between metals and nonmetals in the periodic table
Subject: Maths
Find the determinant of given matrix \( \left[\begin{array}{ccc}\boldsymbol{a}-\boldsymbol{b}-\boldsymbol{c} & \boldsymbol{2} \boldsymbol{a} & \boldsymbol{2} \boldsymbol{a} \\ \boldsymbol{2} \boldsymbol{b} & \boldsymbol{b}-\boldsymbol{c}-\boldsymbol{a} & \boldsymbol{2} \boldsymbol{b} \\ \boldsymbol{2} \boldsymbol{c} & \boldsymbol{2} \boldsymbol{c} & \boldsymbol{c}-\boldsymbol{a}-\boldsymbol{b}\end{array}\right] \)
A \( \cdot 2(a+b+c)^{3} \)
В. \( (a-b-c)^{3} \)
\( \mathbf{D} \cdot(a+b+c)^{3} \)
Subject: Chemistry
The reaction \( : 2 A \rightarrow 2 B+C \) occurs by
the mechanism:
\( \boldsymbol{A} \stackrel{\boldsymbol{k}_{1}}{\longrightarrow} \boldsymbol{B}+\boldsymbol{x}(\boldsymbol{s} \boldsymbol{l} \boldsymbol{o} \boldsymbol{w}) \)
(1)
\( \boldsymbol{x} \stackrel{\boldsymbol{k}_{2}}{\longrightarrow} \boldsymbol{B}+\boldsymbol{C}(\text {fast}) \)
(2)
Which of the following step is incorrect?
A. molecularity of the reaction is one
B. the order of the reaction with respect to A is two
C . the rate law is : \( v=k_{1}[A] \)
D. \( k_{2}>k_{1} \)
Subject: Maths
If \( A, B \) are two events with \( P(A \cup B)= \)
\( \mathbf{0 . 6 5}, \boldsymbol{P}(\boldsymbol{A} \cap \boldsymbol{B})=\mathbf{0 . 1 5}, \) then find the
value of \( \boldsymbol{P}\left(\boldsymbol{A}^{C}\right)+\boldsymbol{P}\left(\boldsymbol{B}^{C}\right) \)
Subject: Maths
\( \boldsymbol{n}[\boldsymbol{P}(\boldsymbol{A})]=\boldsymbol{n}[\boldsymbol{P}(\boldsymbol{B})], \) then \( A \) and \( \mathrm{B} \) are
sets
A . Equal
B. Overlapping
c. Equivalent
D. Dissoint
Subject: Physics
A pure inductor \( L, \) a capacitor \( C \) and \( a \)
resistance \( R \) are connected across a
battery of emf \( \mathrm{E} \) and internal resistance
as shown in Fig. Switch \( S_{w} \) is closed at
\( t=0, \) select the correct alternative(s)
A. current through resistance R is zero all the time
B. current through resistance R is zero at \( t=0 \) and \( t- \)
c. maximum charge stored in the capacitor is \( c E \)
D. maximum energy stored in the inductor is equal to the maximum energy stored in the capacito
Subject: Chemistry
Which of the following sets of compounds follow law of multiple proportions?
A. \( N O, N O_{2} \) and \( N_{2} O_{5} \)
в. \( C O, C O_{2} \) and \( C H_{4} \)
c. \( N H_{3}, H_{2} O \) and \( N O_{2} \)
D. \( H_{2} O, C O_{2} \) and \( C H_{4} \)
Subject: Physics
A man throws the bricks to the height of \( 12 m \) where they reach with a speed of
\( 12 m / s . \) If he throws the bricks such that theyjust reach this height, then what percentage of energy will he save?
A . \( 19 \% \)
B. 38\%
c. \( 57 \% \)
D. 76\%
Subject: Chemistry
The high temperature \( (\approx 1200 K) \)
decomposition of \( \boldsymbol{C} \boldsymbol{H}_{3} \boldsymbol{C O O H}(\boldsymbol{g}) \)
occurs as follows, as per simultaneous 1
stercactions. \( \boldsymbol{C H}_{3} \boldsymbol{C O O H} \stackrel{\boldsymbol{K}_{1}}{\longrightarrow} \boldsymbol{C} \boldsymbol{H}_{4}+\boldsymbol{C O}_{2} \)
\( \boldsymbol{C H}_{3} \boldsymbol{C O O H} \stackrel{\boldsymbol{K}_{2}}{\longrightarrow} \boldsymbol{C H}_{2} \boldsymbol{C O}+\boldsymbol{H}_{2} \boldsymbol{O} \)
What would be the \( \% \) of \( \mathrm{CH}_{4} \) by mole in the product mixture (excluding
\( \left.\boldsymbol{C H}_{3} \boldsymbol{C O O H}\right) ? \)
A \( \cdot \frac{50 k_{1}}{\left(k_{1}+k_{2}\right)} \)
В. \( \frac{100 k_{1}}{\left(k_{1}+k_{2}\right)} \)
c. \( \frac{200 k_{1}}{\left(k_{1}+k_{2}\right)} \)
D. It depends on time
Subject: Physics
The image of a square hole in a screen illuminated by light is obtained on another screen with the help of a converging lens. The distance of the
hole from the lens is \( 40 \mathrm{cm} \). If the area
of the image is nine times that of the
hole, the focal length of the lens is :
\( \mathbf{A} \cdot 30 \mathrm{cm} \)
B. \( 50 \mathrm{cm} \)
c. \( 60 \mathrm{cm} \)
D. \( 75 \mathrm{cm} \)