AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Chemistry
The \( K_{a} \) values of formic acid and acetic
acid are respectively \( 1.77 \times 10^{-4} \) and
\( 1.75 \times 10^{-5} . \) The ratio of the acid
strength of \( 0.1 M \) acid is:
A . 10
в. 3.178
c. 0.3
D. \( 0 . \)
E. 100
Subject: Physics
A long string having a cross-sectional
area \( 0.80 m m^{2} \) mm2and density,
\( 12.5 g / c c \) is subjected to a tension of
\( 64 N \) along the positive \( x \) -axis. One end of this string is attached to a vibrator at \( x=0 \) moving in transverse direction at
a frequency of \( 20 H z . A t t=0, \) the source is at a maximum displacement
\( \boldsymbol{y}=1.0 \mathrm{cm} . \) What is the displacement of
the particle of the string at \( x=50 c m \) at
time \( t=0.05 s ? \)
A \( .0 .71 \mathrm{cm} \)
B. \( 0.91 \mathrm{cm} \)
c. \( 0.58 \mathrm{cm} \)
D. \( 0.31 \mathrm{cm} \)
Subject: Physics
Angular velocity of rod about \( \boldsymbol{O} \) is
\( \frac{3 \sqrt{5}<F>(\Delta t)}{M L} \)
B. \( \frac{2 \sqrt{5}<F>(\Delta t)}{M L} \)
c. \( \frac{2 \sqrt{3}<F>(\Delta t)}{M L} \)
D. \( \frac{3 \sqrt{3}<F>(\Delta t)}{M L} \)
Subject: Physics
A sample of hydrogen atoms gas contains 100 atoms \( A \| \) the atoms are
excited to the seventh state. The total
energy released by all the atoms is \( \frac{4800}{49} \) Ry( Where Ry \( =13 \) eV) then discuss the following things
a) Maximum energy of the emitted
photon will be less then \( \frac{4800}{49} R y \)
b)Maximum energy of the emitted
photon may be grater than \( \frac{48}{49} R y \)
c)The value of \( n=6 \)
d)total number of photon that can be emitted this sample may be less than 600
Subject: Maths
A motor car is going due north at a speed of \( 50 \mathrm{km} / \mathrm{hr} \). It makes a \( 90^{\circ} \) left
turn without changing the speed. The change in the velocity of the car is about.
A. \( 50 \sqrt{2} \mathrm{km} / \mathrm{hr} \)
B. \( 70 \mathrm{km} / \mathrm{hr} \)
c. \( 80 \mathrm{km} / \mathrm{hr} \)
D. zero
Subject: Physics
A body is projected at \( t=0 \) with a
velocity \( 10 m s^{1} \) at an angle of 60 with
the horizontal.The radius of curvature of
its trajectory at \( t=1 s \) is \( R . \) Neglecting
air resistance and taking acceleration due to gravity \( g=10 \) ms2, the value of
\( \boldsymbol{R} \) is :
A \( .2 .4 m \)
B. \( 10.3 m \)
\( c .2 .8 m \)
D. \( 5.1 \mathrm{m} \)
Subject: Maths
Let \( f \) be a polynomial function such
that \( \boldsymbol{f}(\mathbf{3} \boldsymbol{x})=\boldsymbol{f}^{\prime}(\boldsymbol{x}) \cdot \boldsymbol{f}^{\prime \prime}(\boldsymbol{x}), \) for all \( \boldsymbol{x} \in \)
\( \boldsymbol{R} \). Then:
A \( \cdot f(2)+f^{\prime}(2)=28 \)
B . \( f^{\prime \prime}(2)-f^{\prime}(2)=0 \)
\( \mathbf{c} \cdot f^{\prime \prime}(2)-f(2)=4 \)
D \( \cdot f(2)-f^{\prime}(2)+f^{\prime \prime}(2)=10 \)
Subject: Physics
The equation of a plane progressive wave is \( \boldsymbol{y}=\mathbf{0 . 9} \sin \mathbf{4} \boldsymbol{\pi}\left[\boldsymbol{t}-\frac{\boldsymbol{x}}{\mathbf{2}}\right], \) when it is
reflected at a rigid support, its amplitude becomes \( 2 / 3 \) of its previous value. The equation of the reflected wave is :
A \( \cdot y=0.9 \sin 4 \pi\left[t+\frac{x}{2}\right. \)
B・ \( y=-0.6 \sin 4 \pi\left[t+\frac{x}{2}\right] \)
c. \( y=0.9 \sin 8 \pi\left[t-\frac{x}{2}\right. \)
D. \( y=0.6 \sin 4 \pi\left[t+\frac{x}{2}\right] \)
Subject: Chemistry
Refer to the given paragraph and
answer the following question. Plant P is
the only source of food for the caterpillars of a butterfly species, \( Q \) Plant P depends on the adults of the butterfly species \( Q \) for pollination. Infact, animal \( Q \) is the only pollinator of plant \( P \) in nature. Animal \( R \) feeds
exclusively on the caterpillars of the butterfly species, Q. Animal R In turn is the prey of animal S.Which of the
following is likely to happen if animal
is hunted to extinction?
A. Animal R wit continuously feed on animal Q which may lead to coex-tinction of both \( \mathrm{P} \) and \( \mathrm{Q} \) with time.
B. The populations of both animals \( Q \) and \( R \) will increase, however the population of plant P will decrease with time
C. Population of animal R will Increase while population of animal Q will decrease with time.
D. Both (A) and (C)
Subject: Chemistry
Find the number of nonbonding molecular orbital(s) from the following (lf \( x \) is inter nuclear axis):
\( \boldsymbol{s}+\boldsymbol{p}_{\boldsymbol{y}}, \boldsymbol{p}_{\boldsymbol{y}}+\boldsymbol{p}_{\boldsymbol{y}}, \boldsymbol{p}_{\boldsymbol{x}}+\boldsymbol{p} \boldsymbol{x}, \boldsymbol{d}_{\boldsymbol{x} \boldsymbol{y}}+ \)
\( \boldsymbol{s}, \boldsymbol{d} \boldsymbol{x} \boldsymbol{y}+\boldsymbol{p}_{\boldsymbol{x}}, \boldsymbol{p}_{\boldsymbol{y}}+\boldsymbol{p}_{\boldsymbol{x}} \)
Subject: Chemistry
For the estimation of sulphur by Carius method, the organic compound is heated in Carius tube with:
A \( . B a C l_{2} / H C l \)
в. \( B a C l_{2} / H_{2} S O_{4} \)
c. \( A g C l / H C l \)
D. \( \operatorname{CaCl}_{2} / \mathrm{HCl} \)
Subject: Physics
The shape of the string is drawn at \( t=0 \)
and the area of the pulse enclosed by the string and the \( x \) -axis is measured. It
will be equal to
\( \mathbf{A} \cdot 2 c m^{2} \)
B. \( 2.5 \mathrm{cm}^{2} \)
c. \( 4 \mathrm{cm}^{2} \)
D. \( 5 \mathrm{cm}^{2} \)
Subject: Physics
\( P \) is a point moving with constant speed \( 10 m / s \) such that its velocity
vector always maintains an angle \( 60^{\circ} \)
with line \( O P \) as shown in figure \( (O \) is a fixed point in space). The initial distance between \( O \) and \( P \) is \( 100 m \).
After what time shall \( P \) reach \( O \)
A . \( 10 s \)
B. \( 15 s \)
c. \( 20 s \)
D. \( 20 \sqrt{3} s \)
Subject: Maths
Two different vectors having same
magnitude:
\( \mathbf{A} \cdot \hat{i}+2 \hat{j}+3 \widehat{k}, 3 \hat{i}+2 \hat{j}+\widehat{k} \)
в. \( \hat{i}+\widehat{j}-\widehat{k}, 2 \hat{i}-\widehat{j}-\bar{k} \)
c. \( \hat{i}-2 \hat{j}+2 \widehat{k}, \hat{i}+\widehat{j}+\widehat{k} \)
D. None
Subject: Physics
The pressure at point \( C \) is given by
A \( \cdot \frac{3 P_{0}}{2^{0.4}} \)
в. \( \frac{3 P_{0}}{2^{1.4}} \)
c. \( 3 P_{0} \times 2^{0.4} \)
D. \( 3 P_{0} \times 2^{1.4} \)
Subject: Maths
If \( \frac{1}{\sqrt{2}}<x<1, \) then \( \cos ^{-1} x+ \)
\( \cos ^{-1}\left(\frac{x+\sqrt{1-x^{2}}}{\sqrt{2}}\right) \) is equal to
A \( \cdot 2 \cos x^{-1} \)
B. \( 2 \cos ^{-1} x \)
\( c \cdot \frac{\pi}{4} \)
\( D \)
Subject: Physics
The magnification of an object placed in front of a convex lens of focal length 20 \( \mathrm{cm} \) is is \( +2 . \) To obtain a magnification of
\( -2, \) The object has to be moved a distance equal to:
\( A \cdot 10 \mathrm{cm} \)
B. 20 cm
\( c .30 \mathrm{cm} \)
D. \( 40 \mathrm{cm} \)
Subject: Chemistry
What amount of sodium propanoate should be added to one litre of an
aqueous solution containing 0.02 mole
of propanoic acid \( \left[\boldsymbol{K} \boldsymbol{a}=\mathbf{1 . 3 4} \times \mathbf{1 0}^{-\mathbf{5}} \mathbf{a t}\right. \)
\( \left.25^{\circ} \mathrm{C}\right] \) to obtain a buffer solution of \( \mathrm{pH} \)
4.75
A \( \cdot 4.52 \times 10^{-2} \) м
В. \( 3.52 \times 10^{-2} \) м
c. \( 2.52 \times 10^{-2} \) м
D. \( 1.52 \times 10^{-2} \) м
Subject: Maths
A shop-keeper sells a badminton racket
marked Rs. 30 at \( 15 \% \) discount and
gives a shuttle cock costing Rs. 1.50 free with each racket. He then makes a
profit of \( 20 \% \). His cost price per racket is
A . Rs. 15
B. Rs. 16
c. Rs. 18
D. Rs. 20
Subject: Maths
\( \boldsymbol{A}=\{1,2,3,4\} \) and \( \boldsymbol{B}=\{\boldsymbol{a}, \boldsymbol{b}, \boldsymbol{c}\} . \) The
relations from \( \boldsymbol{A} \) to \( \boldsymbol{B} \) is
A \( \cdot\{(1,2),(1,3),(2,3),(2,4),(3,4),(3,1)\} \)
B \( \cdot\{(a, b),(a, c),(b, a),(b, c),(c, a)\} \)
c. \( \{(1, a),(1, b)(1, c),(2, a),(2, b),(2, c),(3, a),(3, b),(3, c),(4 \)
D \cdot \( \{(a, 1),(1,3),(b, 2),(c, 3),(b, 3),(b, 4)\} \)
Subject: Maths
The length \( x \) of rectangle is decreasing at the rate of \( 5 \mathrm{cm} / \mathrm{minute} \) and the
width \( y \) is increasing at the rate of 4 \( \mathrm{cm} / \mathrm{minute} . \) When \( \boldsymbol{x}=\mathbf{8} \mathrm{cm} \) and \( \boldsymbol{y}=\mathbf{6} \)
\( \mathrm{cm}, \) find the rates of change of the area of the rectangle.
Subject: Physics
A potential difference of \( 5 V \) is applied
across a conductor of length \( 10 \mathrm{cm} . \) If
drift velocity of electrons is \( 2.5 \times \)
\( 10^{-4} m / s, \) then electron mobility will be
A \( .5 \times 10^{-4} \mathrm{m}^{2} \mathrm{V}^{-1} \mathrm{s}^{1} \)
B. \( 5 \times 10^{-6} \mathrm{m}^{2} \mathrm{V}^{-1} \mathrm{s}^{1} \)
c. \( 5 \times 10^{-2} \mathrm{m}^{2} \mathrm{V}^{-1} \mathrm{s}^{1} \)
D. zero
Subject: Maths
\( \boldsymbol{f}(\boldsymbol{x})=\boldsymbol{4}-(\boldsymbol{6}-\boldsymbol{x})^{2 / 3} \) in \( [\mathbf{5}, \boldsymbol{7}] \)
A. Lagrange's theorem is applicable
B. Rolle's theorem is applicable
C. Lagrange's theorem is applicable but not the Roll's theorem
D. Both theorem are not applicable
Subject: Physics
Displacement current goes through the gap between the plates of a capaitor when the charge of the capacitor:
(i) does not change
(ii) change with time
(iii) increases
(iv) decreases
\( A \cdot(i),(\text { iii }) \) and \( (\text { iv }) \)
B. (i), and (ii) and (iv)
c. ( ii ), (iii) and (iv)
D. (i), (ii) and (iii)
Subject: Chemistry
The acidic nature of halogen acids in methanoic acid is:
\( \boldsymbol{H} \boldsymbol{F}>\boldsymbol{H} \boldsymbol{C l}>\boldsymbol{H} \boldsymbol{B r}>\boldsymbol{H} \boldsymbol{I} . \) If true
write 1 , else write 0 .
Subject: Maths
\( A(-a, 0) ; B(a, 0) \) are fixed points. \( C \) is a point which divides internally \( A B \) in a constantly ration \( \tan \alpha . \) If \( A C \& C B \)
subtend equal angles at \( P, \) that the
equation of the locus of \( \boldsymbol{P} \) is \( \boldsymbol{x}^{2}+\boldsymbol{y}^{2}+ \)
\( 2 a x \sec 2 \alpha+a^{2}=0 \)
Subject: Physics
A power transmission line feeds input power at \( 2300 V \) to a step-down transformer, with its primary winding having 4000 turns. What should be the
number of turns in the secondary winding in order to get output power at
\( \mathbf{2 3 0} \boldsymbol{V} ? \)
A . 300
в. 250
\( c .400 \)
D. 450
Subject: Physics
In dyplcal wnealsuone nelwork trie
resistance in cyclic order are \( \boldsymbol{A}= \)
\( \mathbf{1 0} \mathbf{\Omega}, \boldsymbol{B}=\mathbf{5} \mathbf{\Omega}, \boldsymbol{C}=\mathbf{4} \mathbf{\Omega} \) and \( \boldsymbol{D}=\mathbf{4} \mathbf{\Omega} \)
for the bridge to be balanced :-
(a) \( 10 \Omega \) should be connected in parallel
with \( \mathbf{A} \)
(b) \( 10 \Omega \) should be connected in series
with \( \mathbf{A} \)
(c) \( 5 \Omega \) should be connected in series
with B
(d) \( 5 \Omega \) should be connected in parallel
with B
\( A \cdot a, b \)
B. b, c
\( c \cdot a, c \)
D. al
Subject: Chemistry
What is the IUPAC name for the
following compound? \( O \)
\( \boldsymbol{H} \stackrel{\|}{\boldsymbol{C}}-\boldsymbol{O}-\stackrel{\|}{\boldsymbol{C} \boldsymbol{H}} \)
A. propanoic anhydride
B. methanoic anhydride
c. formyl formate
D. oxomethanoate
Subject: Chemistry
Find the number of acid(s) which are
having hypo prefix in their name from the following:
\( \boldsymbol{H}_{3} \boldsymbol{P} \boldsymbol{O}_{4}, \boldsymbol{H}_{3} \boldsymbol{P} \boldsymbol{O}_{3}, \boldsymbol{H}_{3} \boldsymbol{P} \boldsymbol{O}_{2}, \boldsymbol{H} \boldsymbol{C l O}, \boldsymbol{H}_{4} \boldsymbol{P}_{2} \)
Subject: Maths
M is the midpoint of \( \overline{A B} \). The coordinates of \( A \) are (-2,3) and the coordinates of \( \mathrm{M} \) are \( (1,0) . \) Find the coordinates of B.
A \( \cdot(-1 / 2,3 / 2) \)
в. (4,-3)
c. (-4,3)
D. (-5,6)
E. none of these
Subject: Maths
The table shows a five-day forecast indicating high (H) and Low(L) temperatures in Fahrenheit. Organise the temperatures in a matrix where the
first and second rows represent the High and Low temperatures respectively and identify which day will be the
warmest?
\begin{tabular}{|c|c|c|c|c|}
\hline Mon & Tue & wed & Thu & Fri \\
\hline\( \sum_{i}^{m} \) & \( \sum_{i}^{m} \) & \( \sum_{i}^{m} \) & \( \sum_{i}^{m} \) & \( \sum_{j}^{m} \) \\
\hline \( \mathrm{H} 88 \) & \( \mathrm{H} 90 \) & \( \mathrm{H} 86 \) & \( \mathrm{H} 84 \) & \( \mathrm{H} 85 \) \\
\hline \( \mathrm{L} 54 \) & \( \mathrm{L} 56 \) & \( \mathrm{L} 53 \) & \( \mathrm{L} 52 \) & \( \mathrm{L} 52 \) \\
\hline
\end{tabular}
Subject: Chemistry
\( 6 \times 10^{22} \) gas molecules each of mass
\( 10^{-24} \mathrm{kg} \) are taken in a vessel of 10 litre. What is the pressure exerted by gas molecules if the root mean speed of gas molecules is \( 100 \mathrm{m} / \mathrm{s} ? \)
A. 20Pa
В. \( 2 \times 10^{4} \) Ра
c. \( 2 \times 10^{5} \) Ра
D. \( 2 \times 10^{7} \) Ра
Subject: Physics
A lift starts from the top of a mine shaft and descends with a constant speed of \( 10 m / s .4 s \) later a boy throws a stone vertically upwards from the top of the shaft with a speed of \( 30 m / s . \) If stone
hits the lift at a distance \( x \) below the
shaft write the value of \( \frac{x}{3}(\text { in } \mathrm{m} \) ). (Take:
\( \left.\boldsymbol{g}=\mathbf{1 0 m} / \boldsymbol{s}^{2}\right](\text { Give value of } \mathbf{2 0} \sqrt{\mathbf{6}}=\mathbf{4 9}) \)
Subject: Maths
\( \boldsymbol{F}(\boldsymbol{x}, \boldsymbol{y})=\boldsymbol{x}^{3}+\boldsymbol{y}^{3}+\boldsymbol{3} \boldsymbol{x}^{2} \boldsymbol{y}+\boldsymbol{3} \boldsymbol{x} \boldsymbol{y}^{2} \cdot \mathrm{I} \)
this homogeneous function
Subject: Physics
Assertion
Net charge given to a conductor resides on its outer surface under electrostatic
conditions.
Reason
Electric field lines do not enter a
conductor under electrostatic
conditions.
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
A body of mass \( 2 \mathrm{kg} \) is at rest. A force of \( 4 \hat{i}+3 \hat{j}-5 \hat{k} \) N acts on it and displaces through \( 2 \hat{i}+\hat{j}+2 \hat{k} \) m. The velocity acquired by the body is:
A \( \cdot 0 \mathrm{ms}^{-1} \)
B. \( 1 \mathrm{ms}^{-1} \)
\( \mathbf{c} \cdot 2 m s^{-1} \)
D. \( 10 \mathrm{ms}^{-1} \)
Subject: Physics
The kinetic energy of a body of mass \( \boldsymbol{m} \)
moving with a velocity \( v \) is given by:
A \( \cdot m v^{2} \)
в. \( \frac{1}{2} m v^{2} \)
\( \mathrm{c} \cdot 2 \mathrm{mv}^{2} \)
D. \( \frac{1}{2} m^{2} v^{2} \)
Subject: Chemistry
Assertion
For a reaction at equilibrium,the Gibb's free energy of reaction is minimum at constant temperature and pressure.
Reason
The Gibb's free energy of both reactants and products increases and become
equal at equilibrium.

Read the above assertion and reason
and choose the correct option regarding
¡t.
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
A \( 20 \mathrm{kg} \) object is lifted through a height of \( _{-1}-\ldots- \) m when 784 J of work is
done on it.
[Assume \( \left.\boldsymbol{g}=\mathbf{9 . 8 m} / \boldsymbol{s}^{2}\right] \)
\( A \cdot 2 \)
B. 4
c. 7.84
D. 3.92
Subject: Chemistry
CO is practically non-polar since:
A. the \( \sigma \) -electron drift from \( C \) to \( O \) is almost nullified by the \( \pi \) -electron drift from \( O \) to \( C \)
B. the \( \sigma \) -electron drift from \( O \) to \( C \) is almost nullified by the \( \pi \) -electron drift from \( C \) to \( O \)
C. the bond moment is low
D. there is a triple bond between \( C \) and \( O \)
Subject: Physics
A square of side L meters lies in the \( x-y \)
plane in a region where the magnetic field is given by \( \overline{\boldsymbol{B}}=\boldsymbol{B}_{0}(\mathbf{2} \hat{\boldsymbol{i}}+\boldsymbol{3} \hat{\boldsymbol{j}}+ \)
\( 4 \hat{k}) T \) Where \( B_{0} \) is constant. The
magnitude of flux passing through the
square is:
\( \mathbf{A} \cdot 2 B_{0} L^{2} \mathbf{W} \mathbf{b} \)
B. 3 \( B_{0} L^{2} \) wh
\( \mathbf{c} \cdot 4 B_{0} L^{2} \mathbf{w} \mathbf{b} \)
D. \( \sqrt{2} 9 B_{0} L^{2} \) wh
Subject: Chemistry
Write balanced redox reactions of the
following:
4 moles of \( S n^{2+}(a q) \) reduces \( I O_{4}^{-} \) to
\( \boldsymbol{I}^{-}(\boldsymbol{a} \boldsymbol{q}) \)
A \( \cdot 4 S n^{2+}+I O_{4}^{-}+8 H^{+} \rightarrow 6 S n^{4+}+I^{-}+4 H_{2} O \)
B . \( 4 S n^{2+}+I O_{8}^{-}+8 H^{+} \rightarrow 4 S n^{4+}+I^{-}+4 H_{2} O \)
c. \( 4 S n^{2+}+I O_{4}^{-}+8 H^{+} \longrightarrow 4 S n^{4+}+I^{-}+4 H_{2} O \)
D. none of these
Subject: Physics
What are the speeds of two objects if they move uniformly towards each other, they get \( 4 \mathrm{m} \) closer in each second and if they move uniformly in the same direction with the original speeds they get \( 4 \mathrm{m} \) closer in each \( 10 \mathrm{sec} ? \)
A. \( 2.8 \mathrm{m} / \mathrm{s} \) and \( 1.2 \mathrm{m} / \mathrm{s} \)
B. 5.2 \( \mathrm{m} / \mathrm{s} \) and \( 4.6 \mathrm{m} / \mathrm{s} \)
c. \( 3.2 \mathrm{m} / \mathrm{s} \) and \( 2.1 \mathrm{m} / \mathrm{s} \)
D. 2.2 \( \mathrm{m} / \mathrm{s} \) and \( 1.8 \mathrm{m} / \mathrm{s} \)
Subject: Physics
Plane of both loops circle and ellipse are held perpendicularly to the uniform magnetic field of strength B, Compare the magnetic flux passing through both
loops if \( \phi_{c}, \) the magnetic flux through
the circular loop and \( \phi_{E}, \) the magnetic
flux through the elliptical loop given
that area of both loops are same.
\( \mathbf{A} \cdot \phi_{c}=2.5 \phi_{E} \)
B \( \cdot \phi_{c}=\sqrt{2.5} \)
\( \mathbf{c} \cdot \phi_{c}=\phi_{E} \)
\( \mathbf{D} \cdot \phi_{E}=\sqrt{2.5} \phi_{c} \)
E \( \cdot \phi_{E}=2.5 \phi_{c} \)
Subject: Maths
The complete range of values of \( ^{\prime} a^{\prime} \) such that \( \left(\frac{1}{2}\right)^{|x|}=x^{2}-a \) is satisfied for maximum number of values of \( \boldsymbol{x} \) is
B \( \cdot(-\infty, \infty) \)
c. (-1,1)
D. \( (-1, \infty) \)
Subject: Maths
The value of \( c \) in Lagrange's theorm for
the function \( f(x)=\log \sin x \) in the
interval \( [\boldsymbol{\pi} / \mathbf{6}, \mathbf{5} \boldsymbol{\pi} / \mathbf{6}] \) is
\( \mathbf{A} \cdot \pi / 4 \)
в. \( \pi / 2 \)
\( \mathrm{c} \cdot 2 \pi / 3 \)
D. none of these
Subject: Maths
The equation of a plane which passes through the point of intersection of lines \( \frac{x-1}{3}=\frac{y-2}{1}=\frac{z-3}{2}, \) and \( \frac{x-3}{1}= \)
\( \frac{\boldsymbol{y}-\mathbf{1}}{\mathbf{2}}=\frac{\boldsymbol{z}-\mathbf{2}}{\mathbf{3}} \) and at greatest
distance from point (0,0,0) is-
A. \( 4 x+3 y+5 z=25 \)
B. \( 4 x+3 y+5 z=50 \)
c. \( 3 x+4 y+5 z=49 \)
D. \( x+7 y-5 z=2 \)
Subject: Physics
The propagation of a sound wave in a gas is given by the equation \( \frac{\boldsymbol{d}^{2} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{t}^{2}}=\frac{\boldsymbol{k}}{\boldsymbol{l}} \cdot \frac{\boldsymbol{d}^{2} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}^{2}} \)
Then the velocity of sound is given by
A \( \cdot \frac{k}{l} \)
в. \( \frac{l}{k} \)
c. \( \sqrt{\left(\frac{k}{l}\right)} \)
D. \( \sqrt{\left(\frac{l}{k}\right)} \)
Subject: Chemistry
One mole of nitrogen and three moles of hydrogen are mixed in a 4 litre container. If 0.25 percent of nitrogen is converted to ammonia by the following reaction
\( N_{2}(g)+3 H_{2}(g) \rightleftharpoons 2 N H_{3}(g) \)
What will be the value of \( K \) for the
following equilibrium? \( \frac{1}{2} N_{2}(g)+\frac{3}{2} H_{2}(g) \rightleftharpoons N H_{3}(g) \)
A \( \cdot 1.49 \times 10^{-5} L \) mol \( ^{-1} \)
В . \( 2.22 \times 10^{-10} L \) mol \( ^{-1} \)
D. None of these
Subject: Maths
Assertion
STATEMENT-1: \( 1.3 .5 \ldots . .(2 n-1)> \)
\( \boldsymbol{n}^{\boldsymbol{n}}, \boldsymbol{n} \boldsymbol{\epsilon} \boldsymbol{N} \)
Reason
STATEMENT-2: The sum of the first \( n \)
odd natural numbers is equal to \( n^{2} \)
A. Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-
B. Statement-1 is True, Statement-2 is True; Statementis Not a correct explanation for Statement-
c. statement- - is True, Statement-2 is False
D. Statement- 1 is False, Statement- 2 is True
Subject: Chemistry
The density \( \left(\operatorname{in} g m l^{-1}\right) \) of a 3.60 M
sulphuric acid solution that is \( 29 \% \)
\( H_{2} S O_{4}\left(\text { Molar mass }=98 \mathrm{g} \mathrm{mol}^{-1}\right) \mathrm{by} \)
mass will be:
A .1 .64
B. 1.88
c. 1.22
D. 1.45
Subject: Physics
Assertion
It is harder to open and shut the door if
we apply force near the hinge.
Reason
Torque is maximum at hinge of the
door
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
Arrange the following in increasing
order of solubility in \( \boldsymbol{H}_{2} \boldsymbol{O} \)
\( \boldsymbol{A} \boldsymbol{g} \boldsymbol{C l}, \boldsymbol{A} \boldsymbol{g} \boldsymbol{B r}, \boldsymbol{A} \boldsymbol{g} \boldsymbol{I}, \boldsymbol{A} \boldsymbol{g} \boldsymbol{F} \)
A. \( A g I<A g B r<A g C l<A g F \)
B. \( A g I<A g B r<A g F<A g C l \)
c. \( A g I<A C l<A g B r<A g F \)
D. None of these
Subject: Chemistry
A gas is compressed from a volume of
\( 2 m^{3} \) to a volume of \( 1 m^{3} \) at a constant
pressure of \( 100 N / m^{2} . \) Then it is heated at constant volume by supplying \( 150 J \)
of energy. As a result, the internal
energy of the gas:
A. Increases by \( 250 \mathrm{J} \)
B. Decreases by 250 J
c. Increases by \( 50 \mathrm{J} \)
D. Decreases by \( 50 \mathrm{J} \)
Subject: Maths
\( \frac{\cos (90-\theta) \sec (90-\theta) \tan \theta}{\operatorname{cosec}(90-\theta) \sin (90-\theta) \cot (90-\theta)} \)
\( \frac{\tan (90-\theta)}{\cot \theta}=\dots \)
\( A \)
B. -
\( c \cdot 2 \)
D. -2
Subject: Chemistry
If \( C a O \) caustic soda then which of the
following option is correct?
A \( \cdot M g\left(C r O_{4}\right)_{2}: \) Refractory metal
B. \( C a H_{2} \) :Radioactive element
c. Radium: Do not impart any colour
D. \( M g O: \) constituent of sorel cement
Subject: Chemistry
Which of the following compound is obtained on heating potassium
ferrocyanide with concentrated \( \boldsymbol{H}_{2} \boldsymbol{S} \boldsymbol{O}_{4} \) ?
A \( \cdot C O_{2} \)
в. \( C O \)
\( \mathbf{c} \cdot C_{2} H_{2} \)
D. \( (C N)_{2} \)
Subject: Physics
A ray of light \( O P \) passes through a right
angled prism as shown in the adjacent
diagram. State the angles of incidence at the faces \( A C \) and \( B C . \) Given critical
angle is \( 42^{\circ} \)
A . Angle of incidence at the face \( A C=45^{\circ} \) and angle of
incidence at the face \( B C=90^{\circ} \)
B. Angle of incidence at the face \( A C=90^{\circ} \) and angle of
incidence at the face \( B C=45^{\circ} \)
C. Angle of incidence at the face \( A C=45^{\circ} \) and angle of
incidence at the face \( B C=0^{\circ} \)
D. Angle of incidence at the face \( A C=0^{\circ} \) and angle of
incidence at the face \( B C=45^{\circ} \)
Subject: Chemistry
Consider the following reaction:
ethanol \( \frac{P B r_{3}}{\longrightarrow} X \frac{a l c . K O H}{\longrightarrow} \)
\( \boldsymbol{Y} \stackrel{(i) \boldsymbol{H}_{2} S \boldsymbol{O}_{4}, \text {room temp}(i \boldsymbol{i}) \boldsymbol{H}_{2} \boldsymbol{O} / \text {heat}}{\boldsymbol{X}} \boldsymbol{Z} \)
The product \( Z \) is:
A. \( C H_{3} C H_{2}-O-C H_{2}-C H_{3} \)
B. \( C H_{3}-C H_{2}-O-S O_{3} H \)
c. \( C H_{3} C H_{2} O H \)
D. \( C H_{2}=C H_{2} \)
Subject: Physics
A solenoid of self-inductance \( 1.2 H \) is in
series with a tangent galvanometer of reduction factor \( 0.9 A \). They are connected to a battery and the tangent
galvanometer shows a deflection of \( 53^{\circ} \)
The energy stored in the magnetic field of the solenoid is:
\( \left(\tan 53^{\circ}=4 / 3\right) \)
\begin{tabular}{l} 
A. 0.8645 \\
\hline
\end{tabular}
в. \( 0.72 J \)
c. \( 0.173 J \)
D. \( 1.44 J \)