AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Physics
The angle between the two vectors \( -2 \hat{i}+3 \hat{j}+\hat{k} \) and \( \hat{i}+2 \hat{j}-4 \hat{k} \) is:
A \( \cdot 0^{\circ} \)
B. \( 90^{\circ} \)
\( c \cdot 180^{\circ} \)
\( D \cdot 45^{\circ} \)
Subject: Physics
A disc arranged in a vertical plane has two groves of same length directed along the vertical chord \( A B \) and \( C D \) as
shown in the fig. The same particles slide down along \( A B \) and \( C D . \) The ratio
of the time \( t_{A B} / t_{C D} \) is then
A . 1: 2
B. \( 1: \sqrt{2} \)
\( c \cdot 2: 1 \)
D. \( \sqrt{2}: 1 \)
Subject: Maths
The d.r's of the line of intersection of the
planes \( \boldsymbol{x}+\boldsymbol{y}+\boldsymbol{z}-\mathbf{1}=\mathbf{0} \) and \( \mathbf{2} \boldsymbol{x}+ \)
\( 3 y+4 z-7=0 \) are
A .1,2,-3
в. 2,1,-3
c. 4,2,-6
D. 1,-2,1
Subject: Maths
If \( \boldsymbol{x}=\mathbf{2} \) and \( \boldsymbol{y}=\mathbf{3}, \) then find the value of \( \left[\frac{1}{x^{x}}+\frac{1}{y^{y}}\right] \)
A \( \cdot \frac{-31}{108} \)
в. \( \frac{31}{108} \)
c. \( \frac{125}{171} \)
D. \( \frac{153}{222} \)
Subject: Physics
A ray of light from a liquid \( (\mu=\sqrt{3}) \) is
incident on a system of two right angled prism of refractive indices \( \sqrt{3} a n d \sqrt{2} \)
as shown in the figure. The light suffers zero net deviation when it emerges into
air from surface CD. If the angle of incidence (in degrees) is \( 5 n . \) Find \( n \) ?
Subject: Physics
The radiant energy from the sun, incident normally at the surface of
earth, is \( 20 k c a l / m^{2}- \) min. What would have been the radiant energy incident normally on the earth, if the sun had
a temperature twice of the present one?
A \( .40 \mathrm{kcal} /\left(\mathrm{m}^{2}-\mathrm{min}\right) \)
B. 80 kcal/(m^-min)
c. \( 160 \mathrm{kcal} /\left(\mathrm{m}^{2}-\mathrm{min}\right) \)
D. 320 kcal/(m^-min)
Subject: Chemistry
Q Type your question
molecules unite with \( \boldsymbol{H}_{2} \boldsymbol{O} \) to form
\( N H_{4} O H \) molecules. \( N H_{4} O H \) again
dissociates into \( N H_{4}^{+} \) and \( O H^{-} \) ions.
In solution therefore, we have \( \boldsymbol{N} \boldsymbol{H}_{3} \)
molecules, \( N H_{4} O H \) molecules and \( N H_{4}^{+} \) ions and the following equilibrium exist:
\( N H_{3}(g) \) (pressure \( P \) and concentration
\( c \) ) Initially \( \rightleftharpoons N H_{3}(l)+H_{2} O \rightleftharpoons \)
\( N H_{4} O H \rightleftharpoons N H_{4}^{+}+O H^{-} \)
Let \( c_{1} \) mol \( / L \) of \( N H_{3} \) pass in liquid state which on dissolution in water
froms \( c_{2} \) mol \( / L \) of \( N H_{4} O H . \) The
solution contains \( c_{3} \) mol \( / L \) of \( N H_{4}^{+} \) ions. The dissociation constant of
\( N H_{4} O H \) can be given as:
\( ^{\mathrm{A}} \cdot_{K_{b}}=\frac{\left(c_{3}\right)^{2}}{\left(c_{2}-c_{3}\right)} \)
B. \( _{K_{b}}=\frac{\left(c_{3}\right)^{2}}{c_{2}} \)
\( ^{\mathbf{c}} \cdot_{K_{b}}=\frac{c_{3}}{\left(c_{2}-c_{3}\right)} \)
D. \( _{K_{b}}=\frac{c_{3}}{\left(c_{1}-c_{2}\right)} \)
Subject: Physics
A vessel contains air at a temperature
of \( 15^{0} C \) and \( 60 \% \) R.H. What will be the
R.H if it is heated to \( 20^{0} C ? \) (S.V.P at
\( 15^{0} C \) is \( 12.67 \& \) at \( 20^{0} C \) is \( 17.36 \mathrm{mm} \) of
Hg respectively)
A . 262\%
B . 26.2\%
c. \( 44.5 \% \)
D. 46.2\%
Subject: Maths
Assertion \( \operatorname{Let} A=\left[\begin{array}{ll}a & b \\ b & a\end{array}\right] \) and \( B=\left[\begin{array}{ll}p & q \\ r & s\end{array}\right] \)
If \( b=0, \) then \( A B=B A \)
Reason

If \( b \neq 0, \) then \( A B=B A \)
\( \Leftrightarrow \boldsymbol{p}=\boldsymbol{s} \boldsymbol{a} \boldsymbol{n} \boldsymbol{d} \boldsymbol{q}=\boldsymbol{r} \)
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
A conductance cell was filled with a
0.02 M KCl solution which has a specific conductance of \( 2.768 \times \)
\( 10^{-3} \) oh \( m^{-1} c m^{-1} . \) If its resistance is
82.4 ohm at \( 25^{\circ} \mathrm{C}, \) then the cell constant
is:
A. \( 0.2182 \mathrm{cm}^{-1} \)
В. \( 0.2281 \mathrm{cm}^{-1} \)
c. \( 0.2821 \mathrm{cm}^{-1} \)
D. 0.2381 \( c m^{-1} \)
Subject: Physics
Pick out the isoelectronic species from the following:
\( (\boldsymbol{I}) \boldsymbol{C} \boldsymbol{H}_{3}^{+} \)
\( (\boldsymbol{I I}) \boldsymbol{H}_{3} \boldsymbol{O}^{+} \)
\( (I I I) N H_{3} \)
A. I and II
B. III and IV only
c. I and III
D. II, III, IV
Subject: Maths
\( \lim _{x \rightarrow 0^{+}} \frac{\sqrt{1+x}-\sqrt{1-x}}{\sqrt{1+x^{2}}-\sqrt{1-x^{2}}} \) equals to
A. 1
B. \( \frac{1}{2} \)
\( c \cdot \infty \)
\( D \)
Subject: Chemistry
At \( 700 K, K_{p}=0.140 \) for the reaction
\( \boldsymbol{C I F}_{3}(\boldsymbol{g}) \rightleftharpoons \boldsymbol{C l F}(\boldsymbol{g})+\boldsymbol{F}_{2}(\boldsymbol{g}) \cdot \) Calculate
the equilibrium partial pressure of
\( C l F_{3}, C l F, \) and \( F_{2} \) if only \( C l F_{3} \) is
present initially, at a partial pressure of
1.47 atm.
A \( \cdot P_{C I F}=P_{F_{2}}=0.389 \) atm, \( P_{C I P_{3}}=1.08 \mathrm{atm} \)
B . \( P_{C I F}=0.45 \) at \( m, P_{F_{2}}=0.276 \) atm, \( P_{C l F_{3}}=2.30 \) at
C \( \cdot P_{C I F}=0.50 \) at \( m, P_{F_{2}}=0.389 \) at \( m, P_{C l F_{3}}=1.67 \) at \( m \)
D. \( P_{C I F}=P_{F_{2}}=0.678 \) atm, \( P_{C I F_{3}}=3.04 \mathrm{atm} \)
Subject: Physics
5 bullets, each of mass 10 gm are fired per second, vertically upwards, such that a plate of mass 200 gm floats in air. If the bullets rebound with the same
velocity back vertically downwards, the velocity with which each bullet is fired
in \( \mathrm{ms}^{-1} \) is:
(Take \( \left.g=10 m s^{-2}\right) \)
A . 10
B. 30
c. 20
D. 40
Subject: Physics
A Sound wave with an amplitude of \( 3 c m \)
starts moving towards right from origin
and gets reflected at a rigid wall after a
second. If the velocity of the wave is
\( 340 m s^{-1} \) and it has a wavelength of \( 2 m \)
the equations of incident and reflected
waves are
A \( \cdot y=3 \times 10^{-2} \sin \pi(340 t-x), y=-3 x \)
\( 10^{-2} \sin \pi(340 t+x) \) towards left
B . \( y=4 \times 10^{-2} \sin \pi(340 t+x), y=-4 \times \)
\( 10^{-2} \sin \pi(340 t+x) \) towards left
C . \( y=5 \times 10^{-2} \sin \pi(340 t-x), y=-5 \times \)
\( 10^{-2} \sin \pi(340 t-x) \) towards left
D . \( y=6 \times 10^{-2} \sin \pi(340 t-x), y=-6 \times \)
\[
10^{-2} \sin \pi(340 t+x) \text { towards left }
\]
Subject: Physics
Ten positively charged particles are
kept fixed on the \( x- \) axis at points \( x= \)
\( 10 \mathrm{cm}, 20 \mathrm{cm}, 30 \mathrm{cm}, \ldots ., 100 \mathrm{cm} . \) The
first particle has a charge \( 1.0 \times 10^{-8} C \)
the second \( 8 \times 10^{-8} C, \) the third \( 27 \times \)
\( 10^{-8} C \) and so on. The tenth particle has
a charge \( 1000 \times 10^{-8} C . \) Find the
magnitude of the electric force acting on a \( 1 C \) charge placed at the origin.
\( \mathbf{A} \cdot 5.94 \times 10^{5} N \)
B . \( 5.49 \times 10^{5} N \)
c. \( 9.45 \times 10^{5} N \)
D. \( 4.95 \times 10^{5} N \)
Subject: Chemistry
Which of the following reactions is called slaking of lime?
A \( \cdot C a C O_{3} \rightarrow C a O+C O_{2} \)
в. \( C a O+2 H C l \rightarrow C a C l_{2}+H_{2} O \)
c. \( C a O+H_{2} O \rightarrow C a(O H)_{2}+ \) heat
D. \( C a C O_{3}+N a C l \rightarrow N a_{2} C O_{3}+C a C l_{2} \)
Subject: Chemistry
Wave number of spectral line for a given
transition is \( x c m^{-1} \) for \( H e^{+}, \) then its
value for \( B e^{3+} \) (isoelectronic of \( \boldsymbol{H} \boldsymbol{e}^{+} \) )
for same transition is:
A \( \cdot \frac{x}{4} c m^{-1} \)
B. \( x \mathrm{cm}^{-1} \)
\( c \cdot 4 x c m^{-1} \)
D. \( 16 x \mathrm{cm}^{-1} \)
Subject: Physics
A tension of \( 22 \mathrm{N} \) is applied to a copper
wire of cross-sectional area \( 0.02 \mathrm{cm}^{2} \)
Young's modulus of copper is \( 1.1 \times \) \( 10^{11} N / m^{2} \) and Poisson's ratio \( 0.32 . \) The
decrease in cross sectional area will be:
A \( \cdot 1.28 \times 10^{-6} \mathrm{cm}^{2} \)
в. \( 1.6 \times 10^{-6} \mathrm{cm}^{2} \)
c. \( 2.56 \times 10^{-6} \mathrm{cm}^{2} \)
D. \( 0.64 \times 10^{-6} \mathrm{cm}^{2} \)
Subject: Physics
A balloon is rising with constant acceleration \( 2 m / s e c^{2} . \) Two stones are
released from the balloon at the interval
of 2 sec. Find out the distance between
the two stones 1 se \( c \). after the release of
second stone.
\( \mathbf{A} \cdot 48 m \)
в. \( 84 m \)
\( c .40 m \)
D. \( 60 m \)
Subject: Physics
When the bulb of a constant volume
hydrogen thermometer is placed in melting ice, the pressure recorded is \( 80 \mathrm{cm} \mathrm{Hg} \) and when immersed is boiling water, it is \( 113 \mathrm{cm} \) Hg. When the bulb is placed in another boiling liquid, the pressure recorded is
\( 143 \mathrm{cm} \) Hg.What is the boiling point of the liquid?
Subject: Maths
Draw the graphs of the following
equations:
\( \mathbf{2} \boldsymbol{x}-\mathbf{3} \boldsymbol{y}+\mathbf{6}=\mathbf{0} \)
\( 2 x+3 y-18=0 \)
\( \boldsymbol{y}-\mathbf{2}=\mathbf{0} \)
Find the vertices of the triangle so obtained. Also, find the area of the
triangle.
Subject: Chemistry
The reaction \( 2 N O+B r_{2} \rightarrow 2 N O B r \)
is supposed to follow the following mechanism
(i) \( N O+B r_{2} \rightleftharpoons N O B r_{2} \)
(ii) \( N O B r_{2}+N O \stackrel{s l o w}{\rightarrow} 2 N O B r \)
The rate law expression is:
A \( \cdot r=K^{\prime}[N O]^{2}\left[B r_{2}\right] \)
B . \( r=K^{\prime}[N O]^{2}\left[B r_{2}\right]^{2} \)
c. \( r=K^{\prime}[N O]\left[B r_{2}\right. \)
D . \( r=K^{\prime}[N O]^{1}\left[B r_{2}\right] \)
Subject: Chemistry
Select correct statement for \( \boldsymbol{B} \boldsymbol{r} \boldsymbol{F}_{5} \)
A. All fluorine atoms are in same plane
B. Four fluorine atoms and \( B r \) atom is in same plane
C. Four fluorine atoms are in same plane
D. It has all \( F-B r-F \) bond angles at \( 90^{\circ} \)
Subject: Physics
t is given that rate of heat transfer in convection is directly proportional to area of plate across which fluid flows \( \boldsymbol{A} \) , density of fluid \( (\rho), \) velocity of flow \( (V \) ,temperature difference
\( (t) \) with
proportionality constant of 2 units.Also fluid is flowing across edge to edge on a square plate of side length of 0.1 unit with density of fluid is 10 units and
velocity of 2 units. Then what will be the rate of heat conducted through the plate if temperature difference between plate and fluid is unity?(assume that all \( u n i t s \) are in international standards
Subject: Maths
If \( \boldsymbol{x}^{\boldsymbol{m}} \cdot \boldsymbol{y}^{\boldsymbol{n}}=(\boldsymbol{x}+\boldsymbol{y})^{\boldsymbol{m}+\boldsymbol{n}} \) then \( \frac{\boldsymbol{d} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}}= \)
A. \( \frac{y}{x} \)
B. \( -\frac{y}{x} \frac{y}{x} \)
c. \( \frac{m y}{x} \)
D. \( \frac{n y}{x} \)
Subject: Maths
In the figure below. PQR is a right-
angle triangle right angled at \( Q . X Y \) is
parallel to \( \boldsymbol{Q} \boldsymbol{R} . \boldsymbol{P} \boldsymbol{Q}=\boldsymbol{6} \mathrm{cm}, \boldsymbol{P Y}=\mathbf{4} \mathrm{cm} \)
and \( P X: X Q=1: 2 . \) Calculate the
lengths of \( \boldsymbol{P R} \) and \( \boldsymbol{Q} \boldsymbol{R} \)
A. \( P R=12 \mathrm{cm} ; Q R=10.392 \mathrm{cm} \)
B. \( P R=13 \mathrm{cm} ; Q R=11.392 \mathrm{cm} \)
c. \( P R=11 \mathrm{cm} ; Q R=12.392 \mathrm{cm} \)
D. none of the above
Subject: Chemistry
The emf of the cell involving the following reaction, \( 2 A g^{+}+H_{2} \longrightarrow \)
\( 2 A g+2 H^{+} \) is 0.80 volt. The standard
oxidation potential of silver electrode is:
B. \( 0.50 \mathrm{v} \)
c. \( -0.30 v \)
D. \( 0.40 \mathrm{v} \)
Subject: Physics
When disc B is brought in contact with
disc \( A, \) they acquire a common angular velocity in time t. The average frictional torque on one disc by the other during this period is:
A \( \cdot \frac{2 I \omega}{3 t} \)
B. \( \frac{9 \text { I }}{\text { ? }} \)
c. \( \frac{9 \mathrm{Ic}}{4 \mathrm{t}} \)
\( D \cdot \frac{31}{2 t} \)
Subject: Maths
If \( \boldsymbol{A}=(\mathbf{6}, \mathbf{7}, \mathbf{8}, \mathbf{9}), \boldsymbol{B}=(\mathbf{4}, \mathbf{6}, \mathbf{8}, \mathbf{1 0}) \) and
\( C=\{x: x \in N: 2<x \leq 7\} ; \) find :
\( \boldsymbol{B}-\boldsymbol{B} \)
\( A \cdot \phi \)
B . \{0\}
c. \{6,7\}
D. \{4\}
Subject: Chemistry
Assertion \( (A): H_{2} S \) is more volatile than
\( \boldsymbol{H}_{2} \boldsymbol{O} \)
Reason (R): Oxygen atom is smaller in size as compared to sulphur.
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
c. \( A \) is true but \( R \) is false
D. \( A \) is false but \( R \) is true
Subject: Chemistry
For a reaction to be spontaneous in neither direction, which of the following is/are correct regarding the closed
system?
(1) \( (\Delta G)_{T, P}=0 \)
(2) \( (\Delta G)_{T, P}<0 \)
(3) \( (\Delta G)_{U, V}=0 \)
(4) \( (\Delta G)_{U, V}>0 \)
codes:
A. 1,2,3 are correct
B. 1 and 2 are correct
c. 2 and 4 are correct
D. 1 and 3 are correct
Subject: Chemistry
Which complex is most stable?
\( \mathbf{A} \cdot\left[C u(C N)_{2}\right]^{-} K_{d}=1 \times 10^{-16} \)
B \( \cdot\left[F e(C N)_{6}\right]^{4-} K_{d}=1 \times 10^{-37} \)
\( \mathbf{c} \cdot\left[F e(C N)_{6}\right]^{3-} K_{d}=1 \times 10^{-44} \)
\( \mathbf{D} \cdot\left[A g(C N)_{2}\right]^{-} K_{d}=1 \times 10^{-20} \)
Subject: Chemistry
The Glycosidic linkage present in
sucrose is between:
A. \( C-1 \) of \( \alpha \) - glucose and \( C-2 \) of \( \beta \) -fructose
B. C-1 of \( \beta \) -galactose and C-4 of \( \alpha \) -glucose
C. \( C-1 \) of \( \alpha \) -glucose and \( C-4 \) of \( \beta \) - fructose
D. \( \mathrm{C}-1 \) of \( \alpha \) -glucose and \( \mathrm{C}-4 \) of \( \alpha \) -glucose
Subject: Physics
A man of mass \( m \) walks from end \( A \) to
the other end \( B \) of a boat of mass \( M \)
and length \( l . \) The coefficient of friction
between the man and the boat is \( \mu \) and
neglect any resistive force between the
boat and the water.
This question has multiple correct options
A. If the man runs at his maximum acceleration, the acceleration of the boat is \( (m / M) g \)
B. The maximum time take by the men to reach the other end of the boat is \( \sqrt{\frac{2 M l}{(M+m) \mu g}} \)
c. If the man runs at his maximum acceleration, the acceleration of the boat is \( \frac{m}{m+M} \mu g \)
D. The minimum time take by the men to reach the other end of the boat is \( \sqrt{\frac{2 m l}{(M+m) \mu g}} \)
Subject: Chemistry
Assertion
Salt dissolved in water lowers the
freezing point.
Reason
The change in freezing point is given by:
\( \Delta \boldsymbol{T}_{\boldsymbol{f}}=\boldsymbol{i} \boldsymbol{K}_{\boldsymbol{f}} \boldsymbol{m} \)
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
The \( P . V .^{\prime} s \) of the vertices of a \( \triangle A B C \)
\( \operatorname{are} \bar{i}+\bar{j}+\bar{k}, 4 \bar{i}+\bar{j}+\bar{k}, 4 \bar{i}+5 \bar{j}+\bar{k} \)
The \( P . V . \) of the circumcentre of \( \triangle A B C \)
is
A \( \cdot \frac{5}{2} \bar{i}+3 \bar{j}+\bar{k} \)
В \( \cdot 5 \bar{i}+\frac{3}{2} \bar{j}+\bar{k} \)
c. \( 5 \bar{i}+3 \bar{j}+\frac{1}{2} \bar{k} \)
D. \( \bar{i}+\bar{j}+\bar{k} \)
Subject: Chemistry
Equal masses of hydrogen gas and oxygen gas are placed in a closed
container at a pressure of \( 3.4 a t m . \) The
contribution of hydrogen gas to the total
pressure is:
A . \( 1.7 a t m \)
B. \( 0.2 a t m \)
c. \( 3.2 a t m \)
D. 3.02atm
Subject: Physics
A \( 2 k W \) electric heater is placed in 2.5
kg of water at \( 25^{\circ} \mathrm{C} \). calculate the time
taken to increase the temperature by
\( 50^{\circ} \mathrm{C} \)
A. 4 min 38 sec
B. 5 min 03 sec
c. 2 min
D. 159 sec
Subject: Biology
Assertion
Tapeworm, roundworm and pinworm are
endoparasites of human intestine.
Reason
Improperly cooked food is the source of
all intestinal infections.
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
\( \boldsymbol{a} \neq \boldsymbol{p}, \boldsymbol{b} \neq \boldsymbol{q}, \boldsymbol{c} \neq \boldsymbol{r} \) and \( \left|\begin{array}{lll}\boldsymbol{p} & \boldsymbol{b} & \boldsymbol{c} \\ \boldsymbol{a} & \boldsymbol{q} & \boldsymbol{c} \\ \boldsymbol{a} & \boldsymbol{b} & \boldsymbol{r}\end{array}\right|=0 \)
then the value of \( \frac{\boldsymbol{p}}{\boldsymbol{p}-\boldsymbol{a}}+\frac{\boldsymbol{q}}{\boldsymbol{q}-\boldsymbol{b}}+ \)
\( \frac{r}{r-c} \) is equal to
\( A \)
B. 2
\( c \cdot 3 \)
D.
Subject: Chemistry
Which of the following reactions do not
involve oxidation or reduction:
A \( \cdot 2 R b+2 H_{2} O \rightarrow 2 R b O H+H_{2} \)
в. \( 2 C u I_{2} \rightarrow 2 C u+I_{2} \)
c. \( N H_{4} C l+N a O H \rightarrow N a C l+N H_{3}+H_{2} O \)
D. None of these.
Subject: Maths
A bag contains 5 red balls and 8 blue
balls. It also contains 4 green and 7
black balls. If a ball is drawn at random,
then find the probability that it is not green
A \( \cdot \frac{5}{6} \)
B. \( \frac{1}{4} \)
\( c \cdot \frac{1}{6} \)
D. \( \frac{7}{4} \)
Subject: Physics
The escape velocity of a body from earth is about \( 11.2 \mathrm{km} / \mathrm{s} \). Assuming the mass and radius of the earth to be about 81
and 4 times the mass and radius of the
moon, the escape velocity in \( \mathrm{km} / \mathrm{s} \) from the surface of the moon will be:
A . 0.54
B. 2.48
\( c \cdot 11 \)
D. 49.5
Subject: Physics
A comb run through ones hair attracts
small bits of paper. What happens, if
the hair are wet or if it is a rainy day?
A. The comb does not get charged and it will not attract small bits of paper
B. The comb does not get charged but it will attract small bits of paper.
C. The comb does gets charged and it will attract small bits of paper.
D. The comb does gets charged but it will not attract small bits of paper.
Subject: Chemistry
Which of the following statements is
not correct from the view point of
molecular orbital theory?
\( \mathbf{A} \cdot B e_{2} \) is not a stable molecule.
B. \( H e_{2} \) is not stable but \( H e_{2}^{+} \) is expected to exist.
C. Bond strength of \( N_{2} \) is maximum amongst the homonuclear diatomic molecules belonging to the second period.
D. The order of energies of molecular orbitals in \( N_{2} \) molecule is \( \sigma 2 s<\sigma * 2 s<\sigma 2 p_{z}<\left(\pi 2 p_{x}=\pi 2 p_{y}\right)< \)
\( \left(\pi * 2 p_{x}=\pi 2 p_{y}\right)<\sigma * 2 p_{z} \)
Subject: Maths
Let \( \boldsymbol{f}: \boldsymbol{R}-\{\boldsymbol{n}\} \rightarrow \boldsymbol{R} \) be a function
defined by \( f(x)=\frac{x-m}{x-n} \) such that
\( \boldsymbol{m} \neq \boldsymbol{n}, \) then
A. \( f \) is one one into function
B. \( f \) is one one onto function
c. \( f \) is many one into function
D. \( f \) is many one onto function
Subject: Maths
If \( G \) is centroid and \( A D, B E, C F \) are three
medians of ABC with area \( 72 \mathrm{cm}^{2} \), then
the area of BDG is
A \( \cdot 12 ~ c m^{2} \)
B. \( 16 \mathrm{cm}^{2} \)
c. \( 24 \mathrm{cm}^{2} \)
D. \( 8 \mathrm{cm}^{2} \)
Subject: Maths
frue Enter \( ^{\prime} 1^{\prime} \) else \( ^{\prime} 0^{\prime} \)
\( \left|\begin{array}{ccc}\boldsymbol{x} & \boldsymbol{y} & \boldsymbol{x}+\boldsymbol{y} \\ \boldsymbol{y} & \boldsymbol{x}+\boldsymbol{y} & \boldsymbol{x} \\ \boldsymbol{x}+\boldsymbol{y} & \boldsymbol{x} & \boldsymbol{y}\end{array}\right|=-\boldsymbol{2}(\boldsymbol{x}+ \)
\( \boldsymbol{y})\left(\boldsymbol{x}^{2}+\boldsymbol{y}^{2}-\boldsymbol{x} \boldsymbol{y}\right) \)
Subject: Maths
\( f A=\left[\begin{array}{lll}1 & 1 & 1 \\ 1 & 1 & 1 \\ 1 & 1 & 1\end{array}\right], \) prove that
\( \boldsymbol{A}^{n}=\left[\begin{array}{ccc}\mathbf{3}^{n-1} & \mathbf{3}^{n-1} & \mathbf{3}^{n-1} \\ \mathbf{3}^{n-1} & \mathbf{3}^{n-1} & \mathbf{3}^{n-1} \\ \mathbf{3}^{n-\mathbf{1}} & \mathbf{3}^{n-\mathbf{1}} & \mathbf{3}^{n-1}\end{array}\right], \boldsymbol{n} \in N \)
Subject: Chemistry
From the graph pick out the correct one:
\( \mathbf{A} \cdot \Delta E \) for forward reaction is \( B-A \)
\( \mathrm{B} \cdot \Delta E \) for the forward reaction \( C-A \)
\( \mathrm{C} \cdot \Delta E \) reverse is greater than forward
\( \mathbf{D} \cdot \Delta E \) for forward reaction is \( A+B \)
Subject: Maths
\( \boldsymbol{f}:(\boldsymbol{0}, \infty) \rightarrow(\boldsymbol{0}, \infty) \) defined by
\( \boldsymbol{f}(\boldsymbol{x})=\left\{\begin{array}{ll}2^{x} & \boldsymbol{x} \in(\mathbf{0}, \mathbf{1}) \\ \mathbf{5}^{\boldsymbol{x}} & \boldsymbol{x} \in[\mathbf{1}, \infty)\end{array}\right. \)
A. one-one but not onto
B. onto but not one-one
c. neither one - one nor onto
D. bijective
Subject: Chemistry
For the reaction \( 4 N H_{3}+5 O_{2} \rightarrow \)
\( 4 N O+6 H_{2} O, \) the rate of reaction with
respect to \( N H_{3} \) is \( 2 x 10^{-3} M s^{-1} . . \) Find
the rate of the reaction with respect to
oxygen in \( M s^{-1} \)
Subject: Chemistry
The main reason for larger number of oxidation state exhibited by the actinides than that corresponding lanthanide, is:
A. lesser energy difference between \( 5 f \) and \( 6 d \) orbital than between \( 4 f \) and \( 5 d \) -orbital
B. larger atomic size of actinides than the lanthanides
C. more energy differenc between 5f and 6d orbitals than between 4f and 5d-orbitals
D. greater reactive nature of the actinides than the lanthanides
Subject: Maths
Let \( A B C D \) is a square with sides of
unit length.Points E and F are taken on
\( \operatorname{sides} A B \) and \( A D \) respectively so that
\( A E=A F \).Let \( P \) be a point inside the
\( \square A B C D \)
Let a line passing through point \( \boldsymbol{A} \) divides the square \( \square A B C D \) into two
parts so that area of one portion is double the other, then the length of portion of line inside the square is
A. \( \frac{\sqrt{10}}{3} \)
B. \( \frac{\sqrt{13}}{3} \)
c. \( \frac{\sqrt{11}}{3} \)
D. \( \frac{2}{\sqrt{3}} \)
Subject: Physics
\( n \) drops of water, each of radius \( 2 m m \)
fall through air at a terminal velocity of
\( 8 \mathrm{cm} / \mathrm{s} \). If they coalesce to form a single drop, then the terminal velocity of the combined drop is \( 32 \mathrm{cm} / \mathrm{s} \). The value of
\( n \) is
Subject: Chemistry
The largest value of Henry's law
constant for the liquid solvent \( \mathrm{H}_{2} \mathrm{O} \) will
be obtained with ............... gas as the solute
and a temperature of \( \ldots \)
A. \( C_{2} H_{4}, 45 \)
B. \( A r, 11 \)
с. \( H C l, 49 \)
D. \( C O_{2}, 32 \)
Subject: Maths
If \( \vec{a} \) and \( \vec{b} \) are not perpendicular and \( \vec{c} \) and \( \vec{d} \) are such that \( \vec{b} \times \vec{c}=\vec{b} \times \vec{a} \) and \( \vec{a} \cdot \vec{d}=0 \) then \( \bar{d} \)
is equal to
A \( \cdot \vec{c}-\left(\frac{\vec{a} \cdot \vec{c}}{\vec{a} \cdot \vec{b}}\right) \cdot \vec{b} \)
B \( \cdot \frac{\vec{a}}{p}-\frac{(\vec{c} \vec{c} \vec{a})}{p^{2}} \vec{b} \)
C \( \cdot \frac{\vec{b}}{p}-\frac{(\vec{a} \cdot \vec{\alpha}) \bar{c}}{\bar{p}^{2}} \bar{c} \)
D. \( \frac{\vec{p}}{p^{2}}-\frac{(\vec{b} \cdot \vec{c})}{\vec{p}} \vec{a} \)
Subject: Physics
Assertion
During change of state specific heat of the substance zero.
Reason
Specific heat of a substance is directly proportional to change of heat and inversely proportional to change in temperature
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