AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Chemistry
Assertion
Hybridization of \( \left[\boldsymbol{A u C l}_{4}\right]^{\Theta} \) is \( \boldsymbol{s p}^{3} \)
Reason
Hybridization of Au in above complex
compound does not depend upon nature
of ligand.
A. Statement-1 is true, statement-2 is true and statement-2 is correct explanation for statement-1.
B. Statement-1 is true, statement-2 is true and statement-2 is NOT the correct explanation for statement-1
C. Statement-1 is true, statement-2 is false.
D. Statement-1 is false, statement-2 is true.
Subject: Chemistry
A graph of volume of hydrogen released
vs time for the reaction between zinc
and dil. \( H C l \) is given. Find the
instantaneous rate of reaction at 40 sec
is :
A. \( \frac{V_{3}-V_{2}}{40} \)
B. \( \frac{V_{2}-V_{1}}{20} \)
c. \( \frac{V_{3}-V_{1}}{40} \)
D. cannot be determined
Subject: Chemistry
If equal volume of \( B a C l_{2} \) and \( N a F \) solutions are mixed, which of these
combination will give a precipitate? \( \boldsymbol{K}_{s p} \) of \( \boldsymbol{B a} \boldsymbol{F}_{2}=\mathbf{1 . 7} \times \mathbf{1 0}^{-\mathbf{7}} \)
Subject: Maths
Ten rational numbers between \( \frac{-2}{5} \) and \( \frac{1}{2} \)
\( \operatorname{are} \frac{-7}{20}, \frac{-6}{20}, \frac{-5}{20}, \frac{-4}{20}, \frac{-3}{20}, \frac{-2}{20}, \frac{-1}{20}, 0 \ldots, \frac{1}{20}, \frac{2}{20} \)
If true then enter 1 and if false then
enter \( \mathbf{0} \)
Subject: Biology
Assertion
Histones are basic proteins of major importance in packaging of eukaryotic DNA. DNA and histones comprise chromatin forming the bulk of
eukaryotic chromosome.
Reason
Histones are of five major types: \( \mathrm{H} 1 \) H2A, H2B, H3 and H4.
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: Maths
In a city, three daily newspapers \( A, B, C \) are published. \( 42 \% \) of the people in that city read \( A, 51 \% \) read \( B \) and \( 69 \% \) read \( C .30 \)
\( \% \) read \( A \) and \( B ; 28 \% \) read \( B \) and \( C ; 36 \% \)
read \( A \) and \( C ; 8 \% \) do not read any of the
three newspapers. The percentage of persons who read all the three papers is
A . \( 25 \% \) \%
B. 18\%
c. \( 20 \% \)
D. none of these
Subject: Physics
Mass of a planet is \( 5 \times 10^{24} \mathrm{kg} \) and
radius is \( 6.1 \times 10^{6} \mathrm{m} . \) The energy
needed to send a 2 kg body into space from its surface, would be.
A. 9 joule
B. 18 joule
C. \( 2.2 \times 10^{8} \) joule
D. \( 1.1 \times 10^{8} \) joul
Subject: Maths
\( \frac{1}{2.3}+\frac{1}{4.5}+\frac{1}{6.7}+\ldots \infty= \)
A \( \cdot 1+\log _{e} 2 \)
B . \( 1-\log _{\mathrm{e}} 2 \)
c. \( 2+\log _{\mathrm{e}} 2 \)
D. \( 2-\log _{\mathrm{e}} 2 \)
Subject: Physics
In the following circuit diagram, what is
the value recorded by the voltmeter if
the potential across the diode is \( 1 V \) and
both ammeter and voltmeter are ideal?
A \( .4 .5 \mathrm{v} \)
B. 5.5 v
c. 3.2
D. \( 8.4 \mathrm{V} \)
Subject: Chemistry
Find the number of acid(s) which can
form its meta derivative from the
following:
\( \boldsymbol{H}_{3} \boldsymbol{B} \boldsymbol{O}_{3}, \boldsymbol{H}_{3} \boldsymbol{P} \boldsymbol{O}_{4}, \boldsymbol{H}_{2} \boldsymbol{S} \boldsymbol{O}_{4}, \boldsymbol{H}_{2} \boldsymbol{S} \boldsymbol{O}_{3} \)
Subject: Chemistry
Suppose that a hypothetical atom gives
a red, green, blue and violet line
spectrum. Which jump according to the
figure would give off the red spectral
line?
\( A \cdot 3 \rightarrow 1 \)
B \( .2 \rightarrow 1 \)
\( c \cdot 4 \rightarrow 1 \)
\( D \cdot 3 \rightarrow 2 \)
Subject: Physics
A lamp consumes only \( 50 \% \) of maximum power applied in an AC circuit. What will be the phase difference between applied voltage and circuit current?
A \( \cdot \frac{\pi}{3} r a d \)
B. \( \frac{\pi}{6} r a d \)
c. \( \frac{\pi}{4} r a d \)
D. \( \frac{\pi}{2} r a d \)
Subject: Physics
By imparting heat to a body, its
temperature rises by \( 15^{\circ} \mathrm{C} \). What is the corresponding rise in temperature on kelvin scale?
\( \mathbf{A} \cdot 288 K \)
в. \( 15 K \)
\( c .30 K \)
D. \( 7.5 K \)
Subject: Maths
If \( \boldsymbol{f}: \boldsymbol{R} \rightarrow(-1,1) \) is defined by \( \boldsymbol{f}(\boldsymbol{x})= \)
\( \frac{-\boldsymbol{x}|\boldsymbol{x}|}{\mathbf{1}+\boldsymbol{x}^{2}} \) then \( \boldsymbol{f}^{-1}(\boldsymbol{x}) \) equals
\( ^{A} \cdot \sqrt{\frac{|x|}{1-|x|}} \)
в. \( \quad-\operatorname{sgn}(x) \sqrt{\frac{|x|}{1-|x|}} \)
\( ^{\mathrm{c}} \cdot \sqrt{\frac{x}{1-x}} \)
D. None of these
Subject: Maths
Q 1 ) If the polynomial \( a z^{3}+4 z^{2}+3 z- \)
4 and \( z^{3}-4 z+a \) leave the same
remainder when divided by \( z-3, \) find
the value of \( a \)
\( Q \) 2) If both \( x-2 \) and \( x-\frac{1}{2} \) are the
factors of \( p x^{2}+5 x+r, \) show that \( p=r \)
Q 3) Without actually division prove that \( 2 x^{4}-5 x^{3}+2 x^{2}-x+2 \) is
divisible by \( x^{2}-3 x+2 \)
Subject: Physics
A block of mass \( m=1 k g \) has speed
\( v=4 m / s \) at \( \theta=60^{\circ} \) on a circular track
of radiu \( R=2 m \) as shown in figure.
Coefficient of kinetic friction between
the block and the track is \( \mu_{k}=0.5 \) tangential acceleration of the block at this instant is approximately.
A \( .2 .1 m / s^{2} \)
В \( \cdot 5 m / s^{2} \)
\( \mathrm{c} \cdot 1.2 \mathrm{m} / \mathrm{s}^{2} \)
D. \( 3 m / s^{2} \)
Subject: Physics
An electrical appliance is rated
\( \mathbf{1 5 0 0} W, \mathbf{2 5 0} V . \) This appliance is
connected to \( 250 V \) mains. Calculate
the current drawn.
A . \( 5 A \)
в. \( 10 A \)
\( c \cdot 6 A \)
D. 2A\$
Subject: Maths
If \( x=\phi(t), y=\psi(t), \) then \( \frac{d^{2} y}{d x^{2}} \) is
A \( \cdot \frac{\phi^{\prime} \psi^{\prime \prime}-\psi^{\prime} \phi^{\prime \prime}}{\left(\phi^{\prime}\right)^{2}} \)
B. \( \frac{\phi^{\prime} \psi^{\prime \prime}-\psi^{\prime} \phi^{\prime \prime}}{\left(\phi^{\prime}\right)^{3}} \)
c. \( \frac{\phi^{\prime \prime}}{\psi^{\prime \prime}} \)
D. \( \frac{\psi^{\prime \prime}}{\phi^{\prime \prime}} \)
Subject: Chemistry
Choose the incorrect statement:
\( \mathbf{A} \cdot B e C O_{3} \) is kept in the atmosphere of \( C O_{2} \) since it is thermally unstable.
B. \( B e \) dissolves in alkali forming \( \left[\operatorname{Be}(O H)_{4}\right]^{2-} \)
C. \( B e F_{2} \) forms a complex ion with \( N a F \) in which \( B e \) goes with the cation.
D. \( B e F_{2} \) forms a complex ion with \( N a F \) in which \( B e \) goes with the anion.
Subject: Chemistry
Details of some gases taken at \( 273 \mathrm{K} \)
temperature and 1 atm pressure are given in the table.
\( \begin{array}{lll}\text { Gas } & \text { Volume (L) } & \text { Number of moles } \\ \text { Hydrogen } & 224 & 10 \\ \text { Helium } & 112 & 5 \\ \text { Oxygen } & 224 & 10 \\ & & \end{array} \) Ammonia 56 2.5
(a) On the basis of which gas law, the volume and the number of moles are
given in the table?
(b) Represent this gas law in mathematical form.
(c) Among these, if the pressure of hydrogen gas is changed to 2 atm. Calculate the new volume.
Subject: Physics
A negatively charged rod is brought close to two metal spheres which are in
contact with each other, and the
spheres are separated in the presence
of the rod. Then
A. The sphere close to the rod acquires a negative charge and the other sphere acquires a positive charge
B. The sphere close to the rod acquires a positive charge and the other sphere acquires a negative charge
c. Both the spheres will acquire positive charge
D. Both the spheres will acquire negative charge
Subject: Physics
Two identical pulses move in opposite directions with same uniform speeds on a stretched string. The width and kinetic energy of each pulse is \( L \) and \( k \)
respectively. At the instant they completely overlap, the kinetic energy of
the width \( L \) of the string where they
overlap is
\( A \cdot k \)
B. \( 2 k \)
c. \( 4 k \)
D. \( 8 k \)
Subject: Physics
In a potentiometer arrangement, a cell of emf \( 1.5 V \) gives a balance point at
\( 27 \mathrm{cm} \) length of wire. If the cell is replaced by another cell and balance
point shifts to \( 54 c m, \) the emf of the second cell is
A . \( 3 V \)
в. \( 1.5 V \)
c. \( 0.75 V \)
D. \( 2.25 V \)
Subject: Maths
The position vectors of \( \boldsymbol{A}, \boldsymbol{B}, \boldsymbol{C}, \boldsymbol{D} \) are
\( \vec{a}, \vec{b}, 2 \vec{a}+3 \vec{b} \) and \( \vec{a}-2 \vec{b} \) respectively
Show that \( \overrightarrow{D B}=3 \vec{b}-\vec{a} \) and \( \overrightarrow{A C}= \) \( \vec{a}+3 \vec{b} \)
Subject: Chemistry
Indicate whether the following
conversions represent an oxidation, a reduction or none (neither oxidation nor
reduction)
(i) \( \boldsymbol{H} \boldsymbol{C l O}_{3} \) to \( \boldsymbol{H} \boldsymbol{C l} \boldsymbol{O}_{\mathbf{4}} \)
\( (\text { ii }) N H_{4}^{+} \) to
\( N H_{3} \)
(iii) \( N O_{2} \) to \( N_{2} O_{4} \)
\( (\text { iv }) \boldsymbol{H} \boldsymbol{S} \boldsymbol{O}_{3}^{-} \) to \( \boldsymbol{S} \boldsymbol{O}_{4}^{2-} \)
\( (v) H_{2} O_{2} \) to \( H_{2} O \)
A \( \cdot \) (i) Oxidation
(ii) Reduction
(iii) None (iv) None (v) Oxidation
B. (i) Oxidation (ii) None (iii) None (iv) Oxidation (v) Reduction
c. (i) Reduction
(ii) Oxidation
(iii) Reduction (iv) None (v) Reduction
D. (i) Oxidation (ii) Reduction (iii) None (iv) Reduction (v) Reduction
Subject: Physics
toppr
Q Type your question
piston can enter a cylınaer tıgntıy ana
without friction, and initially it is at the
bottom of the cylinder. \( 750 g m \) of water
is now poured into the pipe so that the
piston and pipe are lifted up as show.
Then
This question has multiple correct options
\( A \)
the height \( H \) of water in the cylinder is \( -n \)
B. the height \( H \) of water in the cylinder is \( \frac{11}{32 \pi} m \)
c. the height \( h \) of water in the pipe is \( \frac{2}{\pi} \)
the height \( h \) of water in the pipe is \( \frac{11}{32 \pi} m \)
Subject: Chemistry
In addition reactions of aldehydes, the carbonyl carbon atom changes from:
A \( \cdot s p^{3} \) to \( s p^{2} \)
B \( \cdot s p^{2} \) to \( s p^{3} \)
c. \( s p \) to \( s p^{3} \)
D. \( s p^{3} \) to sp
Subject: Chemistry
Which of the following is an endothermic
reaction?
\( \mathbf{A} \cdot 2 H_{2}+O_{2} \rightarrow 2 H_{2} O \)
\( \mathbf{B} \cdot C_{(g r a p h i t e)}+H_{2} O_{\rightarrow} C O_{(g)}+H_{2(g)} \)
\( \mathbf{c} \cdot 2 N a O H+H_{2} S O_{4} \rightarrow N a_{2} S O_{4}+2 H_{2} O \)
D. \( C_{2} H_{5} O H+3 O_{2} \rightarrow 2 C O_{2}+3 H_{2} O \)
Subject: Physics
Four particles, each of mass \( 1 \mathrm{kg} \) are placed at the corners of a square OABC of side \( 1 \mathrm{m} .0 \) is at the origin of the coordinate system. OA and OC are aligned along positive X-axis and positive Y-axis respectively. the position the vector of the center of mass is (in
\( \mathrm{m}) \)
Subject: Maths
A function \( \boldsymbol{f}:(-\mathbf{3}, \mathbf{7}) \rightarrow \boldsymbol{R} \) is defined as
follows:
\( f(x)=\left\{\begin{array}{cc}4 x^{2}-1 ; & -3 \leq x<2 \\ 3 x-2 ; & 2 \leq x \leq 4 \\ 2 x-3 ; & 4<x \leq 6\end{array}\right. \)
Find:
\( \boldsymbol{f}(\mathbf{1})-\boldsymbol{f}(-\boldsymbol{3}) \)
Subject: Chemistry
The equivalent conductance of \( N a C l \) at
concentration \( C \) and at infinite dilution
\( \operatorname{are} \lambda_{C} \) and \( \lambda_{\infty}, \) respectively. The correct
relationship between \( \lambda_{C} \) and \( \lambda_{\infty} \) is
given as:
(here the constant B is positive)
A \( \cdot \lambda_{C}=\lambda_{\infty}-(B) \sqrt{C} \)
B . \( \lambda_{C}=\lambda_{\infty}+(B) \sqrt{C} \)
c. \( \lambda_{C}=\lambda_{\infty}-(B) C \)
D. \( \lambda_{C}=\lambda_{\infty}+(B) C \)
Subject: Chemistry
Which of the following pair gives
effervescence with \( N a H C O_{3} ? \)
\( \boldsymbol{C H}_{3} \boldsymbol{C O C l} \)
\( (I) \)
\( \boldsymbol{C H}_{3} \boldsymbol{C O C H}_{3} \)
\( (I I) \)
\( \boldsymbol{C H}_{3} \boldsymbol{C O O C H}_{3} \)
\( (I I I) \)
\( \boldsymbol{C H}_{3} \boldsymbol{C O O C O C H} \)
\( (I V) \)
A. I and II
B. I and IV
c. ॥ and III
D. I and III
Subject: Chemistry
Copper pyrites, \( C u F e S_{2}, \) is the important source of copper. 10 g of it was leached with dil. \( H_{2} S O_{4} \) and solution diluted to 1 L
\( 10 \mathrm{mL} \) of this solution required \( 10 \mathrm{mL} \) of
0.02 \( \mathrm{M} \mathrm{KMnO}_{4} \) in acidic solution. What
is \% of \( F e \) in \( C u F e S_{2} ? \)
Subject: Physics
A string vibrates according to equation
\( y=\sin \frac{\pi x}{3} \cos 40 \pi t . \) The potential
energy of the string will be zero at times
\( ^{A} \cdot \frac{1}{20} s \) and \( \frac{1}{40} s \)
B. \( \frac{1}{40} s \) and \( \frac{1}{80} s \)
\( ^{\mathrm{c}} \cdot \frac{1}{80} s \) and \( \frac{3}{80} s \)
D. \( \frac{1}{40} s \) and \( \frac{3}{40} s \)
Subject: Physics
The angular speed of rotation of earth about its axis at which the weight of man standing on the equator becomes half of its weight at the poles is given by:
A. 0.034 rads\( ^{-1} \)
B. \( 8.75 \times 10^{-4} \)rads\( ^{-1} \)
c. \( 1.23 \times 10^{-2} \mathrm{rads}^{-1} \)
D. \( 7.65 \times 10^{-7} \)rads\( ^{-1} \)
Subject: Physics
What is known as Ocean thermal
energy?
A. The Sun's heat warms the surface water a lot more
than the deep ocean water which creates ocean's naturally available temperature gradient
B. The Moon's heat warms the surface water a lot more
than the deep ocean water which creates ocean's naturally available temperature gradient.
C. The Solar cell's heat warms the surface water a lot more than the deep ocean water which creates ocean's naturally available temperature gradient.
D. None
Subject: Maths
If \( \boldsymbol{A}=\{\boldsymbol{x}, \boldsymbol{y}\} \) and \( \boldsymbol{B}=\{\mathbf{3}, \mathbf{4}, \mathbf{5}, \mathbf{7}, \mathbf{9}\} \) and
\( \boldsymbol{C}=\{\mathbf{4}, \mathbf{5}, \mathbf{6}, \mathbf{7}\}, \) find \( \boldsymbol{A} \times(\boldsymbol{B} \cap \boldsymbol{C}) \)
A \( \cdot\{(x, 4),(x, 5),(x, 7),(y, 4),(y, 5),(y, 7)\} \)
B - \( \{(x, 3),(x, 5),(x, 7),(y, 4),(y, 5),(y, 7)\} \)
c \( \cdot\{(x, 4),(x, 5),(x, 7),(y, 4),(y, 5),(y, 9)\} \)
D. none of the above
Subject: Physics
At what depth in an ocean will a bubble of air have one fifth the volume it will
have on reaching the surface?
(Atmosphere pressure \( -\mathbf{7 6} \) cm of \( \mathrm{Hg} \) and density of \( \boldsymbol{H} \boldsymbol{g}=\mathbf{1 3 . 6} \boldsymbol{g} \boldsymbol{c m}^{-\mathbf{3}} \mathbf{)} \)
Subject: Maths
Divide: \( \boldsymbol{x}^{\boldsymbol{6}}-\boldsymbol{1} \) by \( \boldsymbol{x}^{\boldsymbol{3}}-\boldsymbol{2} \boldsymbol{x}^{2}+\boldsymbol{2} \boldsymbol{x}-\boldsymbol{1} \)
Subject: Maths
Solve the following pair of equations:
\( \frac{5 y}{2}-\frac{x}{3}=8 \)
\( \frac{y}{2}+\frac{5 x}{3}=12 \)
\( \mathbf{A} \cdot x=2 ; y=7 \)
B. \( x=4 ; y=3 \)
\( \mathbf{c} \cdot x=6 ; y=4 \)
D. \( x=7 ; y=3 \)
Subject: Physics
An electrical device draws \( 2 \mathrm{kW} \) power from ac mains voltage \( 223 \mathrm{V}(\mathrm{rms}) . \) The current differs lags in phase by \( \phi= \)
\( \tan ^{-1}[]-\frac{3}{4}[\mathbb{1}] \) as compared to voltage. The
resistance \( R \) in the circuit is
A . \( 15 \Omega \)
в. 20 \( \Omega \)
\( c .25 \Omega \)
D. 30 \( \Omega \)
Subject: Physics
In a double-slit experiment, instead of taking slits of equal width, one slit is made twice as wide as the other. Then,
in the interference pattern?
A. The intensities of both maxima and the minima increase
B. The intensity of the maxima increases and the minima has zero intensity
c. The intensity of the maxima decreases and that of the minima increases
D. The intensity of the maxima decreases and the minima has zero intensity
Subject: Chemistry
Which set does not show correct
matching?
A \( \cdot S c^{3+}:[N e] 3 s^{2} 3 p^{6}: \) zero group
B . \( F e^{2+}:[A r] 3 d^{6} \) : VIII group
C \( \cdot C r:[A r] 3 d^{5} 4 s^{1}: \) VIB group
D. All of the above
Subject: Maths
A regular hexagon of maximum possible area is cut off from an equilateral triangle. The ratio of the area of the triangle to the area of hexagon will be-
A \( \cdot \sqrt{\frac{3}{2}} \)
B. \( \frac{\sqrt{6}}{2} \)
c. \( \frac{3}{\sqrt{2}} \)
D. \( \frac{3}{2} \)
Subject: Maths
If \( f \) is a continuous function on the real
line. Given that \( x^{2}+(f(x)-2) x- \) \( \sqrt{3} \cdot f(x)+2 \sqrt{3}-3=0 . \) Then the value
of \( f(\sqrt{3}) \)
A. can not be determined
B. \( 2(1-\sqrt{3} \)
c. zero
D. \( \frac{2(\sqrt{3}-2)}{\sqrt{3}} \)
Subject: Maths
Suppose a girl throws a die. If she gets a
5 or \( 6, \) she tosses a coin three times and
notes the number of heads. If she gets
1,2,3 or \( 4, \) she tosses a coin once and
notes whether a head or tail is obtained.
If she obtained exactly one head, what
is the probability that she threw 1,2,3 or 4 with the die?
Subject: Chemistry
The redox reaction involving the reducing power of hydrogen sulphide is:
\[
\begin{array}{c}
\boldsymbol{S}+\mathbf{2} \boldsymbol{H}^{+}+\mathbf{2} \boldsymbol{e}^{-} \rightarrow \\
\boldsymbol{H}_{2} \boldsymbol{S}, \quad \boldsymbol{E}_{\boldsymbol{S} / \boldsymbol{H}_{2} \boldsymbol{S}}^{\circ}=+\mathbf{0 . 1 4} \boldsymbol{V}
\end{array}
\]
Two other half equations are:
\[
\boldsymbol{F} e^{3+}+\boldsymbol{e}^{-} \rightarrow \boldsymbol{F} \boldsymbol{e}^{2+} \quad \boldsymbol{E}_{\boldsymbol{F} e^{3+} / \boldsymbol{F} e^{2+}}^{\mathrm{O}}=
\]
\[
\begin{array}{l}
+\mathbf{0 . 7 7} V \\
B r_{2}+2 e^{-} \rightarrow 2 B r^{-} \quad E_{B r_{2} / B r^{-}}^{0}=
\end{array}
\]
\( \mathbf{1 . 0 7} V \)
Under standard conditions, hydrogen sulphide reacts with iron \( (I I I) \) ions If this statement is true enter 1 , else
enter 0
Subject: Maths
ff \( x \) follows the Binomial distribution
with parameters \( n=6 \) and \( p \) and
\( \mathbf{9} P(X=4)=P(X=2), \) then \( p \) is
A \( \cdot \frac{1}{4} \)
B.
\( c \cdot \frac{1}{2} \)
D. \( \frac{2}{3} \)
Subject: Maths
If \( \sqrt{\boldsymbol{x}}-\sqrt{\mathbf{1 2}}=\sqrt{\mathbf{4}}-\sqrt{\boldsymbol{x}}, \) then find \( \boldsymbol{x} \)
A. \( 1+\sqrt{3} \)
B. \( 2+2 \sqrt{3} \)
c. \( 4+\sqrt{3} \)
D. \( 4+2 \sqrt{3} \)
Subject: Maths
Two candidates attempt to solve a
quadratic equation of the \( a x^{2}+b x+ \)
\( c=0 \) One starts with a wrong value of \( b \)
and find the roots to be 2 and 6 . The
other starts with the wrong values of \( c \)
and find the roots to be \( +2,-9 . \) The correct roots of the equation are
Subject: Maths
Given \( \frac{\pi}{2}<\alpha<\pi, \) then the expression \( \sqrt{\frac{1-\sin \alpha}{1+\sin \alpha}}+\sqrt{\frac{1+\sin \alpha}{1-\sin \alpha}}= \)
A \( \frac{1}{\cos \alpha} \)
B. \( -\frac{2}{\cos \alpha} \)
c. \( \frac{2}{\cos \alpha} \)
D. None of these
Subject: Maths
The domain of the function
\( \sin ^{-1}\left(\log _{2}\left(\frac{x}{3}\right)\right) \) is
A \( \cdot \frac{1}{2}, 3 \)
B. \( \frac{1}{2}, 4 \)
c. \( \frac{3}{2}, 6 \)
D. \( \frac{1}{2}, 2 \)
Subject: Chemistry
For the given data
\( \boldsymbol{A}+\boldsymbol{B} \rightleftharpoons \boldsymbol{C}+\boldsymbol{D} ; \boldsymbol{E}^{o}=\boldsymbol{a} \boldsymbol{v} \boldsymbol{o l} \boldsymbol{t} ; \boldsymbol{K}_{c}=\boldsymbol{K}_{1} \)
\( \mathbf{2} \boldsymbol{A}+\mathbf{2} \boldsymbol{B} \rightleftharpoons \mathbf{2} \boldsymbol{C}+\mathbf{2} \boldsymbol{D} ; \boldsymbol{E}^{\boldsymbol{o}}= \)
\( \boldsymbol{b} \boldsymbol{v} \boldsymbol{o l} \boldsymbol{t} ; \boldsymbol{K}_{c}=\boldsymbol{K}_{2} \)
Select the correct choices:
This question has multiple correct options
\( \mathbf{A} \cdot a=b \)
В. \( K_{2}=K_{1}^{2} \)
\( \mathbf{c} \cdot a \neq b \)
\( \mathbf{D} \cdot b=a^{2} \)
Subject: Maths
If \( \boldsymbol{a}=\left[\begin{array}{ll}\mathbf{1} & \mathbf{2} \\ \mathbf{4} & \mathbf{2}\end{array}\right], \) than show that \( |\mathbf{2} \boldsymbol{A}|= \)
\( \mathbf{4}|\boldsymbol{A}| \)
Subject: Chemistry
Assertion
\( 14 C \) is an isotope of carbon.
Reason
\( 14 C \) and \( 14 N \) have the same mass
number.
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 incorrect but Reason is correct
D. Both Assertion and Reason are incorrect
Subject: Maths
A polynomial \( P \) is positive for \( x>0 \) and
the area of the region bounded by \( \boldsymbol{P}(\boldsymbol{x}) \)
the \( x- \) axis and the vertical lines \( x=0 \)
and \( x=\lambda \) is \( \frac{\lambda^{2}(\lambda+3)}{3} \) squnit. Then
polynomial \( \boldsymbol{P}(\boldsymbol{x}) \) is:
A \( \cdot x^{2}+2 x \)
B. \( x^{2}+2 x+1 \)
c. \( x^{2}+x+1 \)
D. \( x^{3}+2 x^{2}+2 \)
Subject: Chemistry
Four one litre flasks are separately filled
with gases \( O_{2}, F_{2}, C H_{4} \) and \( C O_{2} \) under same conditions.

The ratio of the number of molecules in
these gases are:
\( \mathbf{A} \cdot 2: 2: 4: 3 \)
B. 1: 1: 1: 1
\( \mathbf{c} \cdot 1: 2: 3: 4 \)
D. 2: 2: 3: 4
Subject: Chemistry
The b.p. of a solution of \( 5 g \) of sulphur in
100g of carbon disulphide is \( 0.476^{\circ} \)
above that of pure solvent. Determine
the moles of sulphur in this solvent. The
b.p. of pure carbon disulphide is
\( 46.30^{\circ} \mathrm{C} \) and its heat of vaporation is
84.1 calories per gram.
Subject: Physics
A block of mass \( 10 k g \) is pulled by force \( F=100 N . \) It covers a distance \( 500 m \)
in 10 sec. From initial point. This motion is observed by three observers \( A, B \) and C as shown in figure.

Find out work done by the force \( F \) in \( 10 s \)
as observed by \( \mathrm{C} \)
A . \( 0 . J \)
в. \( 50000 J \)
c. \( 20000 J \)
D. \( 40000 J \)
Subject: Physics
A bus can be stopped by applying a retarding force \( F \) when it is moving with speed \( v \) on a level road. The distance covered by it before coming to rest is \( s \) If the load of the bus increases by \( 50 \% \) because of passengers, for the same speed and same retarding force, the distance covered by the bus to come to rest shall be:
A . \( 1.5 s \)
в. \( 2 s \)
\( c \cdot 1 s \)
D. 2.5
Subject: Chemistry
The density of \( N H_{3} \) at \( 30^{\circ} C \) and 5 atm
pressure is:
A \( \cdot 3.417 \mathrm{mg} \mathrm{L}^{-1} \)
в. \( 3.417 g^{-1} L \)
c. \( 3.417 g L^{-1} \)
D. 3.417 kg L \( ^{-1} \)
Subject: Chemistry
The graph between \( \log \frac{X}{m} \) v/s log P is straight-line inclined at an angle \( 45^{\circ} \) with intercept 0.30. What will be the rate of adsorption at pressure of 0.4
atm?
A. 0.4
в. 0.6
\( c \cdot 0.8 \)
D. 0.9
Subject: Physics
When the tension in a metal wire is \( T_{1} \)
its length is \( l_{1}, \) when the tension is \( T_{2} \)
its length is \( l_{2} \). The natural length of
wire is :
A. \( T_{1} l_{1}+T_{2} l_{2} \)
в. \( \frac{l_{1} T_{2}-l_{2} T_{1}}{T_{2}-T_{1}} \)
\( \overbrace{\frac{l_{1} T_{2}-l_{2} T_{1}}{T_{2}+T_{1}}}^{\text {in }} \)
D. \( \frac{T_{2}}{T_{1}}\left(l_{1}+l_{2}\right) \)
Subject: Chemistry
An oxygen cylinder of volume 30 litres has an initial gauge pressure of 15 atm
and a temperature of \( 27^{\circ} \mathrm{C} \). After some
oxygen is withdrawn from the cylinder
the gauge pressure drops to 11 atm and
its temperature drops to \( 17^{\circ} \mathrm{C} \)

Estimate the mass of oxygen taken out of the cylinder. \( \left(R=8.31 J m o l^{-1} K^{-1}, \) molecular \right.
mass of \( \boldsymbol{O}_{2}=\boldsymbol{3} \boldsymbol{2} \boldsymbol{u} \)
Subject: Chemistry
Plaster of paris in contact with water sets to a hard mass whose composition
is :
A. \( \operatorname{CaSO}_{4} \)
в. \( \operatorname{CaSO}_{4} . \mathrm{H}_{2} \mathrm{O} \)
\( \mathrm{c} \cdot \operatorname{CaSO}_{4} \cdot 2 \mathrm{H}_{2} \mathrm{O} \)
D. \( \operatorname{CaSO}_{4} \cdot \operatorname{Ca}(O H)_{2} \)
Subject: Chemistry
A plot of \( \ln K \) against \( \frac{1}{T}(\text { abscissa }) \) is expected to be a straight line with intercept on ordinate axis equal to:
A \( \cdot \frac{\Delta S^{o}}{2.303 R^{n}} \)
в. \( \frac{\Delta S^{\circ}}{R} \)
c. \( -\frac{\Delta S^{\circ}}{R} \)
D. \( R \times \Delta S^{o} \)