AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Chemistry
Which amongst the following reactions cannot be used for the preparation of the halogen acid?
A \( \cdot 2 K B r+H_{2} S O_{4}(\text { conc }) \rightarrow K_{2} S O_{4}+2 H B r \)
в. \( 2 \mathrm{NaCl}+\mathrm{H}_{2} \mathrm{SO}_{4}(\text { conc. }) \rightarrow \) NaH \( \mathrm{SO}_{4}+\mathrm{HCl} \)
c. \( N a H S O_{4}+N a C l(\text {conc.}) \rightarrow N a_{2} S O_{4}+H C l \)
D. \( C a F_{2}+H_{2} S O_{4}(\text {conc.}) \rightarrow C a S O_{4}+2 H F \)
Subject: Chemistry
The \( X-X \) bond length is \( 1.00 \dot{A} \) and \( C-C \) bond length is 1.54 A. If
electronegativities of ' \( X^{\prime} \) and ' \( C^{\prime} \) are 3.0
and 2.0 respectively, the \( C-X \) bond
length is likely to be:
A. 1.27 an a
в. 1.18 \( \dot{A} \)
c. \( 1.08 \AA \)
D. \( 1.28 \dot{A} \)
Subject: Chemistry
Among the quantities, density \( (\rho) \) temperature(T), enthalpy(H), heat
capacity \( \left(C_{\rho}\right), \) volume (V) and pressure
(P), a set of intensive variables are :
A. \( (\rho, T, H) \)
в. \( (H, T, V) \)
\( \mathbf{c} \cdot\left(V, T, C_{\rho}\right) \)
D. \( (\rho, T, P) \)
Subject: Chemistry
The difference between the heat of
reaction at constant pressure and constant volume for the reaction
\( \mathbf{2} C_{6} \boldsymbol{H}_{6}(l)+\mathbf{1 5} \boldsymbol{O}_{2}(\boldsymbol{g}) \rightarrow \mathbf{1 2} \boldsymbol{C} \boldsymbol{O}_{2}(\boldsymbol{g})+ \)
\( 6 H_{2} O(l) \) at \( 25^{\circ} C \) in \( k J \) is:
A . -7.43
в. 3.72
c. -3.72
D. 7.43
Subject: Physics
A steel cable with a radius \( 2 c m \)
supports a chairlift at a ski area. If the
maximum stress is not to exceed
\( 10^{8} N \quad m^{-2}, \) the maximum load the
cable can support is
A \( \cdot 4 \pi \times 10^{5} N \)
B \( \cdot 4 \pi \times 10^{4} N \)
C \( .2 \pi \times 10^{5} N \)
D. \( 2 \pi \times 10^{4} N \)
Subject: Maths
A line d.c's proportional to (2,1,2)
meets each of the lines \( \boldsymbol{x}=\boldsymbol{y}+\boldsymbol{a}=\boldsymbol{z} \)
and \( x+a=2 y=2 z . \) Then the
coordinates of each of the points of
intersection are given by
A . \( (3 a, 2 a, 3 a) ;(a, a, 2 a) \)
в. \( (3 a, 2 a, 3 a) ;(a, a, a) \)
C. \( (3 a, 3 a, 3 a) ;(a, a, a) \)
D. \( (2 a, 3 a, 3 a) ;(2 a, a, a) \)
Subject: Chemistry
The de-Broglie's wavelength of electron present in first Bohr orbit of 'H' atom is :
A \( \cdot 0.529 \) a
B \( \cdot 4 \times 0.529 \)
c. \( 2 \pi \times 0.529 \) 能
D. \( \frac{0.529}{2 \pi} \stackrel{\circ}{A} \)
Subject: Chemistry
If heat of formation of \( C a C l_{2} \) and \( N a C l \)
are 191 and 97.5 kcal, the heat of
reaction for \( \boldsymbol{C a} \boldsymbol{C l}_{2}+\boldsymbol{2} \boldsymbol{N} \boldsymbol{a} \longrightarrow \)
\( 2 N a C l+C a \) is:
Subject: Physics
Three capacitance of capacity \( 10 \mu F, 5 \mu F \) are connected in parallel.
The total capacity will be :
\( \mathbf{A} \cdot 10 \mu F \)
в. \( 5 \mu F \)
\( \mathbf{c} \cdot 20 \mu F \)
D. None of the above
Subject: Chemistry
Assertion \( (A): H P O_{3} \) is monobasic acid
Reason(R) : The salts of \( H P O_{3} \) are called meta-phosphates The correct answer is:
A. Both (A) and (R) are true and (R) is the correct explanation of (A)
B. Both (A) and (R) are true and (R) is not the correct explanation of (A)
c. (A) is true and (R) is false
D. (A) is false but (R) is true
Subject: Physics
Given solid sphere is in pure rolling on a
rough surface. Pick correct statement(s): (Take \( \left.\pi=\frac{22}{7}\right) \)
This question has multiple correct options
A. There are two points in sphere having velocity in vertical direction
B. There is no point in sphere having velocity in vertical direction
C . Ratio of distance travelled by A and O is \( \frac{14}{11} \) in one
complete round
D. Ratio of distance travelled by A and O is 1 in one complete round
Subject: Chemistry
AT \( 25^{\circ} C, \) a solution containing 0.2 g of polyisobutylene in \( 100 \mathrm{mL} \) of benzene developed a rise of \( 2.4 \mathrm{mm} \) at osmotic equilibrium. The molar mass of polyisobutylene if the density of the solution is \( 0.88 \mathrm{g} / \mathrm{mL} \) is :
A \( \cdot 2.39 \times 10^{5} g m o l^{-1} \)
B . \( 7.36 \times 10^{5} \mathrm{g} \) mol \( ^{-1} \)
c. \( 5.45 \times 10^{5} g \) mol \( ^{-1} \)
D. None of these
Subject: Chemistry
The straight chain polymer is formed by
\( \mathbf{A} \cdot \) hydrolysis of \( \left(C H_{3}\right)_{2} S i C l_{2} \) followed by condensation polymerization
B. hydrolysis of \( \left(C H_{3}\right)_{3} \) SiCl followed by condensation polymerization
C . hydrolysis of \( C H_{3} S i C l_{3} \) followed by condensation polymerization
D. hydrolysis of \( \left(C H_{3}\right)_{4} \) Si followed by addition polymerization
Subject: Chemistry
Following statements regarding the periodic trends of chemical reactivity of
alkali metals and the halogens are
given.Which of these statements give
the correct picture?
A. In alkali metals, the reactivity increases but for halogens it decreases with increase in atomic number down the group.
B. The reactivity decreases in the alkali metals but increases in the halogens with increase in atomic number down the group.
C. In both the alkali metals and the halogen the chemical reactivity decreases with increase in atomic number down the group.
D. Chemical reactivity increases with increase in atomic number down the group.
Subject: Maths
A bag contains \( (2 n+1) \) coins. It is
known that \( n \) of these coins have a head
on both sides, whereas the remaining \( n+1 \) coins are fair. A coin is picked up
at random from the bag and tossed. If the probability that the toss results in a head is \( \frac{31}{42}, \) then \( n \) is equal to
A . 10
B. 11
c. 12
D. 13
Subject: Physics
A cycle tube has volume \( 2000 \mathrm{cm}^{3} \)
Initially the tube is filled to \( 3 / 4 \) th of its
volume by air at pressure of \( 105 N / m^{2} \)
It is to be inflated to a pressure of \( 6 x \) \( 10^{5} N / m^{2} \) under isothermal conditions.
The number of strokes of pump, which
\( \operatorname{gives} 500 c m^{3} \) air in each stroke,
to inflate the tube is
A . 2
B. 12
\( c \cdot 42 \)
D. 1
Subject: Chemistry
When \( 6 \times 10^{22} \) electrons are used in the
electrolysis of a metalic salt, \( 1.9 \mathrm{gm} \) of the metal is deposited at the cathode The atomic weight of that metal Is 57 So oxidation state of the metal in the
salt is:
\( A \cdot+2 \)
\( B \cdot+3 \)
\( c \cdot+1 \)
\( D \cdot+4 \)
Subject: Physics
A ray of light is incident on a glass slab
making an angle of \( 60^{0} \) with the surface. Calculate the angle of
refraction in glass and the velocity of light in glass if the refractive index of glass and the velocity of light in air are 1.5 and \( 3.0 \times 10^{8} \mathrm{m} / \mathrm{s} \) respectively.
A \( \cdot 28^{\circ} 30^{\prime}, 3 \times 10^{8} \mathrm{ms}^{-1} \)
B . \( 40^{\circ} 20^{\prime}, 2.5 \times 10^{8} \mathrm{ms}^{-1} \)
C. \( 35^{\circ} 15^{\prime}, 2 \times 10^{8} \mathrm{ms}^{-1} \)
D. \( 28^{\circ} 30^{\prime}, 2.5 \times 10^{8} \mathrm{ms}^{-1} \)
Subject: Physics
When the temperature of an iron sphere
of mass \( 1 \mathrm{kg} \) falls from \( 30^{\circ} \mathrm{C} \) to \( 25^{\circ} \mathrm{C} \) the 550 calories of heat are released The
heat capacity of iron sphere will be in
cal/o \( _{C} \)
A . 110
B. 220
\( c \cdot 330 \)
D. 440
Subject: Chemistry
Which of the following complex will show optical activity?
A \( \cdot \operatorname{trans}-\left[\operatorname{Co}\left(N H_{3}\right)_{4} C l_{2}\right]^{+} \)
B . \( \left[\operatorname{Cr}\left(\text { H }_{2} \text { O }\right)_{6}\right]^{3+} \)
c. \( \operatorname{cis}-\left[\operatorname{Co}\left(N H_{3}\right)_{2}(e n) 2\right]^{3} \)
D. \( \operatorname{trans}-\left[\operatorname{Co}\left(N H_{3}\right)_{2}(e n)_{2}\right]^{3+} \)
Subject: Physics
The phase difference between two
points is \( \pi / 3 . \) If the frequency of wave is \( 50 \mathrm{Hz}, \) then what is the distance between two points? \( (\operatorname{given} v=330 \mathrm{m} / \mathrm{s}) \)
\( A \cdot 2.2 \mathrm{m} \)
в. \( 1.1 \mathrm{m} \)
c. \( 0.6 \mathrm{m} \)
D. \( 1.7 \mathrm{m} \)
Subject: Maths
\( \frac{\sin 70^{\circ}+\cos 40^{\circ}}{\cos 70^{\circ}+\sin 40^{\circ}}= \)
A \( \cdot \frac{1}{\sqrt{3}} \)
B. \( \sqrt{3} \)
\( c \cdot \frac{1}{2} \)
D.
Subject: Maths
Solve \( \int \frac{1}{\sqrt{9-25 x^{2}}} d x \)
A. \( \frac{1}{5} \sin ^{-1}\left(\frac{5 x}{3}\right)+C \)
B \( \cdot \sin ^{-1}\left(\frac{5 x}{3}\right)+C \)
c. \( \frac{1}{5} \sin ^{-1}\left(\frac{3 x}{5}\right)+C \)
D. \( \sin ^{-1}\left(\frac{3 x}{5}\right)+C \)
Subject: Physics
A particle of mass ' \( m^{\prime} \) and charge \( ^{\prime} q^{\prime} \) is accelerated through a potential
difference of \( ^{\prime} V^{\prime} \) volt. Its energy is...
A \( . q V \)
в. \( m q V \)
c. \( \left(\frac{q}{m}\right) v \)
D. \( \frac{q}{m V} \)
Subject: Maths
\( \frac{-7}{5}+\left(\frac{2}{-11}+\frac{-13}{25}\right)= \)
\( \left(\frac{-7}{5}+\frac{2}{-11}\right)+\frac{-13}{25} \)
This property is
A . closure
B. commutative
c. associative
D. identity
Subject: Maths
If \( f(x)=\left|\begin{array}{cc}x & \lambda \\ 2 \lambda & x\end{array}\right|, \) then \( f(\lambda x)-f(x) \) is
equal to:
A \( \cdot x\left(\lambda^{2}-1\right) \)
B \( \cdot 2 \lambda\left(x^{2}-1\right) \)
C \( \cdot \lambda^{2}\left(x^{2}-1\right) \)
D. \( \lambda\left(x^{2}-1\right) \)
E \( \cdot x^{2}\left(\lambda^{2}-1\right) \)
Subject: Chemistry
The value of \( \log _{10} \mathrm{K} \) for a reaction \( \boldsymbol{A} \longrightarrow \boldsymbol{B} \) is :
\( \left(\text { Given }: \Delta_{\mathrm{r}} \mathbf{H}_{298 \mathrm{K}}^{\circ}=\right. \)
\( -\mathbf{5 4 . 0 7 k J m o 1}^{-1}, \quad \Delta_{\mathbf{r}} \mathbf{S}_{298 K}^{0}= \)
\( 10 \mathrm{JK}^{-1} \mathrm{mol}^{-1} \) and
\( \mathbf{R}=\mathbf{8 . 3 1 4} \mathbf{J K}^{-1} \mathbf{m o 1}^{-1} ; \quad \mathbf{2 . 3 0 3} \times \)
\( 8.314 \times 298=5705) \)
A. 5
B. 10
c. 95
D. 100
Subject: Chemistry
Calculate the solubility of \( A g C N \) in a
buffer solution of \( \boldsymbol{p} \boldsymbol{H}=\mathbf{3 . 0} \)
\( \boldsymbol{K}_{s p}(\boldsymbol{A} \boldsymbol{g} \boldsymbol{C} \boldsymbol{N})=\mathbf{1 . 2} \times \)
\( \mathbf{1 0}^{-16}, \boldsymbol{K}_{\boldsymbol{a}}(\boldsymbol{H} \boldsymbol{C N})=\mathbf{4 . 8} \times \mathbf{1 0}^{-\mathbf{1 0}} . \) There
is no \( C N^{-} \) or \( A g^{+} \) ion in the buffer
previously.
Subject: Maths
Find \( \boldsymbol{A}-\boldsymbol{B} \)
\( \boldsymbol{A}=\left[\begin{array}{ccc}\mathbf{2} & \mathbf{2} & \mathbf{0} \\ \mathbf{3} & \mathbf{- 4} & \mathbf{5} \\ \mathbf{2} & \mathbf{3} & \mathbf{- 7}\end{array}\right] \) and \( \boldsymbol{B}= \)
\( \left[\begin{array}{ccc}\mathbf{3} & \mathbf{3} & \mathbf{1} \\ \mathbf{4} & \mathbf{- 5} & \mathbf{4} \\ \mathbf{3} & \mathbf{2} & \mathbf{- 4}\end{array}\right] \)
Subject: Chemistry
Assertion
\( \ln S O_{2}, \) the bond angle is \( 119^{\circ} \) whereas
in \( S O_{3}, \) the bond angle is \( 120^{\circ} \)
Reason
\( \boldsymbol{S} \) atom in both \( \boldsymbol{S O}_{2} \) and \( \boldsymbol{S O}_{3} \) is \( \boldsymbol{s} \boldsymbol{p}^{2} \)
hybridized.
A. If both assertion and reason are CORRECT and reason is the CORRECT explanation of the assertion.
B. If both assertion and reason are CORRECT, but reason
is NOT THE CORRECT explanation of the assertion.
C. If assertion is CORRECT, but reason is INCORRECT
D. If assertion is INCORRECT, but reason is CORRECT.
Subject: Chemistry
\( M n O_{4}^{2-}(1 \text { mole }) \) in neutral aqueous medium is disproportionate to:
A \( \cdot 2 / 3 \) mole of \( M n O_{4}^{-} \) and \( 1 / 3 \) mole of \( M n O_{2} \)
B . 1/3 mole of \( M n O_{4}^{-} \) and 2/3 mole of \( M n O_{2} \)
c. \( 1 / 3 \) 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: Chemistry
Work done in an isothermal reversible
expansion of 1 mole \( C l_{2} \) from 1 ltr to 50
litre at \( 273 K \) for \( C l_{2}, a= \)
\( \mathbf{0 . 6 5 5} \) litre \( ^{\mathbf{2}} \) MPa mol \( ^{-\mathbf{2}}, \boldsymbol{b}= \)
\( \left.0.055 \text { litre } m o l^{-1}\right) \)
\( \mathbf{A} \cdot-8.365 k J / m o l \)
в. \( 32.55 k J / \) mol
c. \( 8.365 k J / m o l \)
D. \( 83.65 k J / \) mol
Subject: Physics
toppr
Q Type your question_
constant speed. The field deflects the
particle, a distance h above the original
line of flight as shown in the Figure. The
particle leaves the field region with
momentum, if \( h<<d, \) of about :
\( \frac{q B d^{2}}{2 h}, \) making an angle \( \frac{2 h}{d} \) with initial direction
B. \( \frac{q B h^{2}}{2 d}, \) making an angle \( \frac{2 h}{d} \) with initial direction
\( \frac{q B d}{2}, \) making an angle \( \frac{2 d}{h} \) with initial direction
\( \frac{q B h}{2}, \) making an angle \( \frac{2 d}{h} \) with initial direction
Subject: Physics
slowly neated tIII all the mercury spılls
over
\( P_{a t m}=76 \mathrm{cm} \) of Hg column
Statement 1: The temperature of gas continuously increases.

Statement 2: According to first law of
thermodynamics \( d Q=d U+d W \)
where symbols have their usual
meaning.
A. Statement1 is true, statement 2 is true and statement 2 is correct explanation for statement 1
B. Statement1 is true, statement 2 is true and statement 2 is NOT the correct explanation for statement
c. Statement 1 is true statement 2 is false
D. Statement 1 is false, statement 2 is true
Subject: Physics
Two pith balls carrying equal charges are suspended from a common point by strings of equal length, the equilibrium separation between them is r. Now the
strings are rigidly clamped at half the height. The equilibrium separation between the balls now become:
\( A \)
B. \( \left(\frac{r}{3 \sqrt{2}}\right) \)
c. \( \left(\frac{2 r}{\sqrt{3}}\right) \)
D. \( \frac{2 r}{3} \)
Subject: Physics
In a winter season, a heat pump is used to warm the room. A heat pump works \( 60 \mathrm{J} \) on the pump while it absorbs \( 90 \mathrm{J} \)
of heat. How much heat is delivered to
the house?
A. 5,400 J
B. 150 J
c. 30 J
D. 1.5 J
E . 0.67 J
Subject: Physics
Two light rays \( P \) and \( Q \) are incident an
optical device \( ^{\prime} X^{\prime} \) which finally goes
along \( ^{\prime} \boldsymbol{R}^{\prime} \) and \( ^{\prime} \boldsymbol{S}^{\prime} . \) Identify optical device
\( \boldsymbol{X}^{\prime} \)
A. Concave lens
B. Concave mirror
c. Convex lens
D. Convex mirror
Subject: Physics
\( \boldsymbol{C H}_{4}(\boldsymbol{g})+\mathbf{2} \boldsymbol{O}_{2}(\boldsymbol{g}) \rightarrow \boldsymbol{C} \boldsymbol{O}_{2}(\boldsymbol{g})+ \)
\( 2 H_{2} O(g)+800 k J . \) If a mole of \( O_{2}(g) \) is
consumed in the reaction, what energy
is produced?
A \( .200 k J \)
\( J \)
в. \( 400 k J \)
c. \( 800 k J \)
D. 1200 k \( J \)
E. \( 1600 k J \)
Subject: Chemistry
Consider the reversible reaction
\( \boldsymbol{H} \boldsymbol{C} \boldsymbol{N}(\boldsymbol{a} \boldsymbol{q}) \leftrightharpoons \boldsymbol{H}^{+}(\boldsymbol{a} \boldsymbol{q})+\boldsymbol{C} \boldsymbol{N}^{-}(\boldsymbol{a} \boldsymbol{q}) \) at
equilibrium. The addition of \( C N^{-}(a q) \)
at equilibrium would:
A. reduce \( H C N \) (aq) concentration
B. decrease \( H^{+} \) ion concentration
c. increase equilibrium constant
D. decrease equilibrium constant
Subject: Physics
The value of \( \mu_{o} \) is
\( \mathbf{A} \cdot 2 \pi \times 10^{-7} H m^{-1} \)
B \( \cdot 4 \pi \times 10^{-7} \mathrm{Hm}^{-1} \)
\( \mathbf{c} \cdot 8 \pi \times 10^{-7} \mathrm{Hm}^{-1} \)
D \( \cdot \pi \times 10^{-7} \mathrm{Hm}^{-1} \)
Subject: Physics
A string of length \( 2 \mathrm{L} \), obeying Hooke's Law, is stretched so that its extension is
L. The speed of the transverse was traveling on the string is v. If the string is further stretched so that the extension in the string becomes 4L. The speed transverse wave traveling on the string will be.
A \( \cdot \sqrt{2} v \)
B.
c. \( 2 \sqrt{2} v \)
D. \( 2 v \)
Subject: Maths
\( \operatorname{Let} \overrightarrow{\boldsymbol{a}}=\hat{\boldsymbol{i}}+\hat{\boldsymbol{j}}+\hat{\boldsymbol{k}}, \overrightarrow{\boldsymbol{b}}=\hat{\boldsymbol{i}}-\hat{\boldsymbol{j}}+\hat{\boldsymbol{k}} \) and
\( \vec{c}=\hat{i}-\hat{j}-\hat{k} \) be three vectors. A vector \( \vec{v} \) in the plane of \( \vec{a} \) and \( \vec{b}, \) whose projection on \( \vec{c} \) is \( \frac{1}{\sqrt{3}}, \) is given by
A \( \cdot \hat{i}-3 \hat{j}+3 \hat{k} \)
B . \( -3 \hat{i}-3 \hat{j}-3 \hat{k} \)
\( \mathbf{c} \cdot_{3 \hat{i}-\hat{j}+3 \hat{k}} \)
D \( \cdot \hat{i}+3 \hat{j}-3 \hat{k} \)
Subject: Chemistry
Which of the following options are
correct regarding the complex
\( \left[\boldsymbol{F} \boldsymbol{e}(\boldsymbol{C} \boldsymbol{N})_{\boldsymbol{6}}\right]^{\boldsymbol{3}-} \operatorname{and}\left[\boldsymbol{F} \boldsymbol{e}(\boldsymbol{C} \boldsymbol{N})_{\boldsymbol{6}}\right]^{\boldsymbol{4}-} \)
This question has multiple correct options
A. number of unpaired electrons are 1 and 0 respectively.
B. number of unpaired electrons are 0 and 1 respectively.
C. magnetic moment are \( \sqrt{3} B M \) and 0 respectively.
D. magnetic moment are 0 and \( \sqrt{3} B M \) respectively.
Subject: Chemistry
Graph between log k and 1/T [k is rate
constant \( \left(s^{-1}\right) \) and \( T \) the temperature
(K) \( ] \) is a straight line with \( 0 X=5, \theta= \)
\( \tan ^{-1}(1 / 2.303) . \) Hence \( -E_{a} \) will be :
A . 2.303 2 cal
B. 2/2.303 cal
c. 2 cal
D. None
Subject: Maths
If \( f(x)=\left\{\begin{array}{l}\frac{1-\sqrt{2} \sin x}{\pi-4 x} x \neq \frac{\pi}{4} \frac{\pi}{4} \\ a, x=\frac{\pi}{4}\end{array}\right. \)
is continuous at \( x=\frac{\pi}{4} \) then \( a= \)
\( \mathbf{A} \cdot \mathbf{4} \)
B. 2
c. 1
D.
Subject: Chemistry
When \( K C N \) is added to \( C u S O_{4} \)
solution, there is formation of the stable
water soluble complex. This complexis:
A \( \cdot K_{4}\left[C u(C N)_{6}\right. \)
В \( \cdot K_{3}\left[C u(C N)_{4}\right] \)
\( \mathbf{c} \cdot_{K_{2}}\left[C u(C N)_{4}\right] \)
D \( \cdot K\left[C u(C N)_{3}\right] \)
Subject: Chemistry
The decomposition of \( 2 N_{2} O_{5} \rightarrow \)
\( 2 N_{2} O_{4}+O_{2} \) is at \( 200^{\circ} C . \) If the initial
pressure is \( 114 \mathrm{mm} \) and after \( 25 \mathrm{min} \). of
the reaction the total pressure of gaseous mixture is \( 133 \mathrm{mm} \). Calculate
the average rate of the reaction in
a) \( \operatorname{atm} \min ^{-1} \)
b) \( \operatorname{mol} L^{-1} s^{-1} \)
respectively.
A \( .0 .002,8.58 \times 10^{-7} \)
В. \( 0.001,8.58 \times 10^{-7} \)
c. \( 0.002,8.58 \times 10^{-4} \)
D. \( 0.001,8.58 \times 10^{-3} \)
Subject: Physics
A truck is moving with a constant velocity of \( 54 k m h^{-1} . \) In which direction
(angle with the direction of motion of
truck) should a stone be projected up
with a velocity of \( 20 \mathrm{ms}^{-1} \), from the
floor of the truck, so as to appear at
right angles to the truck, for a person standing on earth?
A \( \cdot \cos ^{-1}\left(-\frac{3}{4}\right) \)
B. \( \cos ^{-1}\left(-\frac{1}{4}\right) \)
\( ^{\mathbf{c}} \cdot \cos ^{-1}\left(-\frac{2}{3}\right) \)
D \( \cdot \cos ^{-1}\left(\frac{3}{4}\right) \)
Subject: Physics
A bar magnet of magnetic moment \( M \) is
divided into ' \( n \) ' equal parts by cutting
parallel to length. Then one part is suspended in a uniform magnetic field of
strength \( 2 T \) and held making an angle \( 60^{0} \)
with the direction of the field. When
the magnet is released, the kinetic energy of the magnet in the equilibrium position
is:
A. \( \frac{M}{n} \)
B. \( M n \) J
c. \( \frac{M}{n^{2}} \)
D. \( M n^{2} \)
Subject: Chemistry
The vapour pressure of an aqueous solution is found to be 750 torrs at
certain temperature 'T'. If 'T' is the temperature at which pure water boils under atmospheric pressure and same solution show elevation in the boiling
point \( \Delta T_{b}=1.04 K, \) find the
atmospheric pressure?
\( \left[\boldsymbol{K}_{\boldsymbol{b}}=\mathbf{0 . 5 2} \boldsymbol{K} \boldsymbol{k g m o l}-\mathbf{1}\right] \)
A . 77
в. 779
\( c .782 \)
D. 746
Subject: Chemistry
The rate constant for two parallel
reactions were found to be \( 1.0 \times \)
\( 10^{-2} d m^{3} m o l^{-1} s^{-1} \) and \( 3.0 \times 10^{-2} d m^{3} \)
\( m o l^{-1} s^{-1} . \) If the corresponding energies
of activation of the parallel
reactions are \( 60.0 \mathrm{KJ} \mathrm{mol}^{-1} \) and \( 70.0 \mathrm{KJ} \)
mol \( ^{-1} \) respectively, then what is the apparent overall energy of activation?
B. 65.0 KJ \( m o l^{-1} \)
c. 67.5 к \( \operatorname{mol}^{-1} \)
D. 100.0 K」 \( m o l^{-} \)
Subject: Chemistry
An organic compound weighing 0.244 g on combustion with dry oxygen produces 0.616 g of \( C O_{2} \) and 0.108 g of \( H_{2} O . \) Determine the percentage
composition of the oxygen in compound
A . \( 11.16 \% \)
B . 26.23\%
c. \( 30.41 \% \)
D. 25.66\%
Subject: Chemistry
Match the column I with column II and
mark the appropriate choice.
and \( \begin{array}{ll}\text { column } & \text { column I } \\ 1\end{array} \)
Interstitial
hydride \( A \) 4 A Nat
\[
C H_{4}
\]
ii Molecular
hydride В
\( C \)
\( V H_{0.56} \)
\( B_{2} H_{6} \) iii lonic hydride Electron
deficient
hydride iv
A. \( (A) \rightarrow(i i i),(B) \rightarrow(i v),(C) \rightarrow(i i)(D) \rightarrow(i) \)
B. \( (A) \rightarrow(i i),(B) \rightarrow(i v),(C) \rightarrow(i i i)(D) \rightarrow(i) \)
c. \( (A) \rightarrow(i),(B) \rightarrow(i i),(C) \rightarrow(i v)(D) \rightarrow(i i i) \)
D. \( (A) \rightarrow(i i i),(B) \rightarrow(i i),(C) \rightarrow(i)(D) \rightarrow(i v) \)
Subject: Maths
\( \mid f \hat{i}+\hat{j}+\hat{k}, 2 \hat{i}+5 \hat{j}, 3 \hat{i}+2 \hat{j}-3 \hat{k} \) and
\( \hat{\mathbf{i}}-\mathbf{6} \hat{\mathbf{j}}-\hat{\boldsymbol{k}} \) are the position vectors of
points \( A, B, C \) and \( D \) respectively, then find the angle between \( \overrightarrow{A B} \) and \( \overrightarrow{C D} \)
Subject: Maths
If \( \sec ^{-1} x+\sec ^{-1} y+\sec ^{-1} z=3 \pi \)
then \( \boldsymbol{x} \boldsymbol{y}+\boldsymbol{y} \boldsymbol{z}+\boldsymbol{z} \boldsymbol{x}= \)
\( \mathbf{A} \cdot \mathbf{0} \)
B. -
\( c .3 \)
\( D \)
Subject: Physics
Two like magnetic poles of strength 10 and \( 40 S I \) units are separated by a
distance \( 30 c m . \) The intensity of magnetic field is Zero on the line joining them.
A. At a point \( 10 \mathrm{cm} \) from stonger pole.
B. At a point \( 20 \mathrm{cm} \) from stonger pole.
c. At a mid-point.
D. At infinity.
Subject: Chemistry
If the equilibrium constant for \( \boldsymbol{A}_{2}+ \)
\( B_{2} \rightleftharpoons 2 A B \) is \( K, \) then equilibrium
constant for \( \frac{1}{2} A_{2}+\frac{1}{2} B_{2} \rightleftharpoons A B \) is \( \sqrt{K} \)
If true enter \( 1, \) if false enter 0
Subject: Maths
ff \( f, g: R \rightarrow R \) be two functions defined
as \( \boldsymbol{f}(\boldsymbol{x})=|\boldsymbol{x}|+\boldsymbol{x} \) and \( \boldsymbol{g}(\boldsymbol{x})=|\boldsymbol{x}|-\boldsymbol{x} \) for
all \( x \in R \). Then, find \( f \circ g \) and \( g \circ f \) Hence, find \( \boldsymbol{f} \circ \boldsymbol{g}(-\boldsymbol{3}), \boldsymbol{f} \circ \boldsymbol{g}(\boldsymbol{5}) \) and \( \boldsymbol{g} \)
\( \boldsymbol{f}(-2) \)
Subject: Chemistry
Which one of the following equations does not correctly represent the first law of thermodynamics for the given
process?
A. Isothermal process: \( q=-w \)
B. Cyclic process: \( q=-w \)
C. Isochoric process: \( \Delta U=q \)
D. Adiabatic process: \( \Delta U=-w \)
E. Expansion of gas into vacuum: \( \Delta U=q \)
Subject: Physics
A uniform thin rod of length \( l \) is
standing on a smooth horizontal
surface. A slight disturbance causes
the lower end to slip to the smooth
surface and the rod starts falling. Based
on this information mark the correct
option.
A. The center of mass will move along a straight line.
B. The path followed by the end of the rod which is in contact with the ground is circular
C. the path followed by the end of the rod (which is not in contact with the ground) is circular
D. The angular velocity of the rod when it is about to hit about to hit the ground is \( \sqrt{\frac{3 g}{2 l}} \)