AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Chemistry
When \( P b S \) is treated with warm dilute
\( \boldsymbol{H} \boldsymbol{N} \boldsymbol{O}_{3}, \) the products most likely will be
\( \mathbf{A} \cdot P b^{2+}, S, N O_{2} \)
B . \( P b^{2+}, S, \) NO
c. \( P b O, S, N O \)
D. \( P b O_{2}, S O_{4}^{2-}, N_{2} \)
Subject: Chemistry
What is Henry's constant for neon
dissolved in water given \( C_{N e}= \) \( 23.5 m L / L \) solution and STP volume
\( 22,414 \mathrm{mL} / \text { mole gas }) \) and pressure \( \operatorname{atm}) ? \)
A. 0.00105
5
В. 0.11004
\begin{tabular}{l}
\( c .0 .00115 \) \\
\hline
\end{tabular}
D. 0.00015
Subject: Maths
\( A \) and \( B \) each throw a die. The probability that \( A^{\prime} \) 's throw is not greater than B's is
A \( \cdot \frac{21}{36} \)
в. \( \frac{12}{35} \)
c. \( \frac{7}{12} \)
D. \( \frac{5}{12} \)
Subject: Maths
The height of a room is 'a' and the areas of the two adjacent walls of a room are
b' and 'c'. The area of the roof will be
A \( \cdot \frac{b c}{a} \)
B. \( b c \)
c. \( \frac{a c}{b^{2}} \)
D. \( \frac{b c}{a^{2} c} \)
Subject: Biology
Assertion
The atmospheric concentration of \( \boldsymbol{C O}_{2} \)
at which photosynthesis just compensates for respiration is referred
to as \( C O_{2} \) compensation point.
Reason
The \( C O_{2} \) compensation point is reached
when the amount of \( C O_{2} \) uptake is less
than that generated through
respiration, because the level of \( C O_{2} \) in
the atmosphere is more than that
required for achieving \( C O_{2} \)
compensation point.
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
Compute \( \boldsymbol{P}(\boldsymbol{A} \mid \boldsymbol{B}), \) if \( \boldsymbol{P}(\boldsymbol{B})=\mathbf{0 . 2 5} \) and
\( \boldsymbol{P}(\boldsymbol{A} \cap \boldsymbol{B})=\mathbf{0 . 1 8} \)
Subject: Maths
If \( \boldsymbol{x}=\sin ^{-1}(\sin 10) \) and \( \boldsymbol{y}= \)
\( \cos ^{-1}(\cos 10), \) then \( y-x \) is equal to:
\( A \cdot \pi \)
в. \( 7 \pi \)
\( c \cdot 0 \)
D. 10
Subject: Physics
When plate voltage in diode valve is increased from \( 100 \mathrm{V} \) to \( 150 \mathrm{V} \). Then, plate
increases from \( 7.5 \mathrm{mA} \) to \( 12 \mathrm{mA} \), then dynamic plate resistance will be
\( \mathbf{A} \cdot 10 k \Omega \)
B. \( 11 k \Omega \)
\( \mathbf{c} \cdot 15 k \Omega \)
D. \( 11.1 k . \Omega \)
Subject: Maths
A pack of coffee powder contains a mixture of \( x \) gms of coffee and \( y \) gms of choco. The amount of coffee powder is greater than that of chocolate and each
pack weights at least 10 g. Which of the following inequalities describe the given condition? This question has multiple correct options
A. \( x<y \)
в. \( x+y \geq 10 \)
c. \( x+y \leq 10 \)
D. \( x>y \)
Subject: Chemistry
The products for the following reactions
are:
(i) \( C H_{3}-C_{H}^{B r}-C H_{2}-C H_{3}+ \)
alc. \( \boldsymbol{K O H} \rightarrow \boldsymbol{X} \)
(ii) \( \boldsymbol{C H}_{3}-\underset{_{\mathrm{I}}^{\mathrm{CH}}}{\boldsymbol{H}}-\boldsymbol{C H}=\boldsymbol{C H}_{2} \stackrel{\boldsymbol{O}_{3}}{\longrightarrow} \)
\( \boldsymbol{Y}+\boldsymbol{Z} \)
A. \( X=\left(C H_{3}\right)_{2} C=C H_{2}, Y=C H_{3} C H_{2} C H O, Z= \)
\( C H_{3} C H_{2} C H O \)
B. \( X=C H_{2}=C H_{2}, Y=C H_{3} C H O, Z=C H_{3} C O O H \)
c. \( X=C H_{3}-C H=C H-C H_{3}, Y=C H_{3}-C H \)
D. \( X=C H_{3}-C H=C\left(C H_{3}\right)_{2}, Y=H C H O, Z= \)
\( C H_{3} C H O \)
Subject: Physics
The area of cross-section of a large tank
is \( 0.5 m^{2} \) It has an opeoing near the
bottom having area ofcross-section
\( 1 c m^{2}, A \) load of \( 20 \mathrm{kg} \) is applied on the water at the top. Find the velocity of the
water coming out of the opening at the time when the height of water level is
\( 50 \mathrm{cm} \) above the bottom. (Takeg=
\( \left.10 m / s^{2}\right) \)
Subject: Maths
Find the ranges of the following
functions:
\( f(x)=1-x-x^{2} \)
\( f(x)=\frac{3 x+7}{x-8} \)
\( \boldsymbol{f}(\boldsymbol{x})=\boldsymbol{x}^{2}+\boldsymbol{2} \boldsymbol{x}+\boldsymbol{8} \)
\( f(x)=\frac{4 x-7}{x-3} \)
Subject: Maths
Liquid kerosene fills a conical vessel of
base radius \( 2 \mathrm{cm} \). and height \( 3 \mathrm{cm} . \) This liquid leaks through a hole in the bottom and collects in a cylindrical jar of radius \( 2 \mathrm{cm} . \) The total height of kerosene after all of it is collected in the
cylindrical jar is -
\( \mathbf{A} \cdot \pi \mathrm{cm} \)
B. \( 2 \pi \mathrm{cm} \)
\( c \cdot 1 \mathrm{cm} \)
\( D \cdot 2 \mathrm{cm} \)
Subject: Physics
Two mirrors \( A \) and \( B \) are placed at right
angles to each other as shown in figure. A ray of light incident on mirror \( A \) at an
angle of \( 25^{\circ} \) falls on mirror \( \mathrm{B} \) after
reflection. The angle of reflection for the ray reflected from mirror B would be:
\( \mathbf{A} \cdot 25^{\circ} \)
B. \( 50^{\circ} \)
\( \mathbf{c} \cdot 65^{\circ} \)
D. \( 115^{\circ} \)
Subject: Maths
If \( \theta=\sin ^{-1} x+\cos ^{-1} x-\tan ^{-1} x, x \geq \)
\( 0, \) then the smallest interval in which \( \theta \)
lies is-
\( ^{\mathrm{A}} \cdot \frac{\pi}{2} \leq \theta \leq \frac{3 \pi}{4} \)
В. \( \quad 0 \leq \theta \leq \frac{\pi}{4} \)
\( ^{\mathrm{c}}-\frac{\pi}{4} \leq \theta \leq 0 \)
\( \stackrel{\pi}{4} \leq \theta \leq \frac{\pi}{2} \)
Subject: Maths
The middle term in the expansion of
\( \left(\frac{x}{y}+\frac{y}{x}\right)^{8} \) is
\( A \cdot^{8} C_{5} \)
в. \( ^{8} \mathrm{C}_{6} \)
\( \mathrm{c} \cdot^{8} \mathrm{C}_{4} \)
D. \( ^{8} \mathrm{C}_{2} \)
Subject: Chemistry
Each question below consists of two statements. I in the left-hand column
and II in the right-hand For each
question. determine whether statement is true or false and whether statement
II is true or false.
I: Potassium permanganate is a colored compound.
Il: Both potassium and manganese are
metals.
A. Both statements are true
B. Statement I is true and Statement II is false
c. Statement II is true and Statement I is false
D. Both Statements are false
Subject: Biology
Identify the incorrectly matched pair.
A. Pair of skeletal parts - Sternum and ribs
Category - Axial skeleton
B. Pair of skeletal parts - Clavicle and glenoid cavity
Category - Pelvic girdle
C. Pair of skeletal parts - Humerus and ulna
Category - Appendicular skeleton
D. Pair of skeletal parts - Malleus and stapes
Category - Ear ossicles
Subject: Physics
A gun of mass M fires a bullet of mass \( \mathrm{m} \) with a velocity v relative to the gun. The average force required to bring the gun to rest in 0.5 sec. is
A \( \cdot \frac{2 \mathrm{Mmv}}{\mathrm{M}+\mathrm{m}} \)
в. \( \frac{M m v}{2(M+m)} \)
c. \( \frac{3 \mathrm{Mmv}}{2(\mathrm{M}+\mathrm{m})} \)
D. \( \frac{\mathrm{Mmv}}{(\mathrm{M}+\mathrm{m})} \)
Subject: Maths
A line makes an angle \( \theta \) with each of the
\( x- \) and \( z^{-} \) axes. If the angle \( \beta, \) which it makes with the \( y \) -axis, is such that
\( \sin ^{2} \beta=3 \sin ^{2} \theta, \) then \( \cos ^{2} \theta \) equals-
A \( \cdot \frac{2}{3} \)
B. \( \frac{1}{5} \)
\( c \cdot \frac{3}{5} \)
D. \( \frac{2}{5} \)
Subject: Maths
\( \int e^{x \sec x} \cdot \sec x(1+x \tan x) d x= \)
A \( \cdot e^{x \sec x}+c \)
B. \( -e^{x \sec x}+c \)
c. \( \frac{1}{e^{x \sec x}}+c \)
D. \( -e^{x \tan x}+c \)
Subject: Chemistry
Nitrogen reacts with a metal \( M \) to
produce a compound \( X . \) This compound
\( X, \) when dissolved in water forms
pungent gas \( Y \) which can be identified
easily by the formation of white fumes in the presence of \( \boldsymbol{H} \boldsymbol{C l} \)
Identify \( \boldsymbol{Y} \)
A. Nitrogen dioxide
B. Ammonia
c. Nitrous oxide
D. Nitric oxide
Subject: Chemistry
The correct relationship between free energy change in a reaction and the corresponding equilibrium constant \( \boldsymbol{K} \)
is:
A \( .-\Delta G^{\circ}= \) RTin \( K \)
в. \( \Delta G= \) RT in \( K \)
c. \( -\Delta G=R T \) in \( K \)
D. \( \Delta G^{\circ}=R T \) in \( K \)
Subject: Physics
Assertion
The time period of a simple pendulum is independent of its length.
Reason
The length of a pendulum is the distance between point of suspension
and centre of the bob
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
Find \( \boldsymbol{K} \)
If \( \boldsymbol{K}^{2}+\boldsymbol{4} \boldsymbol{K}+\mathbf{8}, \boldsymbol{2} \boldsymbol{K}^{2}+\mathbf{3} \boldsymbol{K}+\boldsymbol{6} \) and
\( 3 K^{2}+4 K+4 \) are any 3 consecutive
terms of \( \boldsymbol{A} \cdot \boldsymbol{P} \)
Subject: Maths
The probabilites of three events \( \boldsymbol{A}, \boldsymbol{B} \)
and \( C \) are \( P(A)=0.6, P(B)=0.4 \) and
\( \boldsymbol{P}(\boldsymbol{C})=\mathbf{0 . 5 .} \). If \( \boldsymbol{P}(\boldsymbol{A} \cup \boldsymbol{B})= \)
\( \mathbf{0 . 8}, \boldsymbol{P}(\boldsymbol{A} \cap \boldsymbol{C})=\mathbf{0 . 3}, \boldsymbol{P}(\boldsymbol{A} \cap \boldsymbol{B} \cap \boldsymbol{C})= \)
0.2 and \( P(A \cup B \cup C) \geq 0.85, \) then
A \( \cdot 0.2 \leq P(B \cap C) \leq 0.35 \)
B . \( 0.5 \leq P(B \cap C) \leq 0.85 \)
c. \( 0.1 \leq P(B \cap C) \leq 0.35 \)
D. None of these
Subject: Chemistry
Which of the following reactions does
not show the acidic nature of ethyne?
A. Acetylene reacts with sodamide to form sodium acetylides.
B. When passed through ammoniacal cuprous chloride solution, a red precipitate is formed.
C. Acetylene reacts with chlorine in the dark to form di or tetrachlorides.
D. Acetylene when passed through ammoniacal silver nitrate gives a white precipitate.
Subject: Physics
A piezo - electric quartz plate is vibrating to produce wavelength of \( 10^{-2} m . \) Find the frequency, if for quartz,
\( \boldsymbol{E}=\mathbf{8} \times \mathbf{1 0}^{\mathbf{1 0}} \mathbf{N m}^{-\mathbf{2}} \) and \( \boldsymbol{\rho}=\mathbf{2 . 6 5} \times \)
\( 10^{3} k g m^{-3} \)
Subject: Physics
Energy required to move a body of mass
\( \mathrm{m} \) from an orbit of radius \( 2 \mathrm{R} \) to \( 3 \mathrm{R} \) is:
\( ^{\mathbf{A}} \cdot \frac{G M m}{12 R^{2}} \)
в. \( \frac{G M m}{3 R^{2}} \)
c. \( \frac{G M m}{8 R} \)
D. \( \frac{G M m}{6 R} \)
Subject: Physics
In a transformer number of turns in
primary circuit is 500 and in secondary circuit number of turns is 10 and load
resistance is \( 10 \Omega \) and voltage of secondary coil is \( 50 \mathrm{V} \) then find the
current in primary circuit.
A . \( 0.2 \mathrm{A} \)
B. \( 0.3 \mathrm{A} \)
c. 0.4 A
D. 0.1A
Subject: Physics
The magnitude of the earths magnetic
field at a place is \( B_{0} \) and the angle of
dip is \( \delta . A \) horizontal conductor of length
lying along the magnetic north-south moves eastwards with a velocity \( v . \) The emf induced across the conductor is:
A . zero
B. \( B_{0} v l \sin \delta \)
c. \( B_{0} l v \)
D. \( B_{0} l \cos \delta \)
Subject: Physics
If the mass of a body is \( 12.1 \mathrm{g} \) and its density is \( 2.2 \mathrm{g} / \mathrm{cc}, \) its volume is.
\( \mathbf{A} \cdot 5.5 \mathrm{cm}^{3} \)
B. 8 сс
c. 11 сс
D. 55 сс
Subject: Maths
\( f\left|\begin{array}{ccc}\mathbf{6} i & -\mathbf{3} i & \mathbf{1} \\ \mathbf{4} & \mathbf{3} i & -\mathbf{1} \\ \mathbf{2 0} & \mathbf{3} & \boldsymbol{i}\end{array}\right|=\boldsymbol{x}+\boldsymbol{i} \boldsymbol{y}, \) then
A \( . x=3, y=1 \)
B. \( x=1, y=3 \)
c. \( x=0, y=3 \)
D. \( x=0, y=0 \)
Subject: Maths
The adjoint of the matric \( \boldsymbol{A}= \) \( \left[\begin{array}{lll}1 & 0 & 2 \\ 2 & 1 & 0 \\ 0 & 3 & 1\end{array}\right] \) is
A. \( \left[\begin{array}{ccc}-1 & 6 & 2 \\ -2 & 1 & -4 \\ 6 & 3 & 1\end{array}\right] \)
B.
\[
\left[\begin{array}{ccc}
1 & 6 & -2 \\
-2 & 1 & 4 \\
6 & -3 & 1
\end{array}\right]
\]
\( c \)
\[
\left[\begin{array}{ccc}
6 & 1 & 2 \\
4 & -1 & 2 \\
6 & 3 & -1
\end{array}\right]
\]
D.
\[
\left[\begin{array}{ccc}
-6 & 2 & 1 \\
4 & -2 & 1 \\
3 & 1 & -6
\end{array}\right]
\]
Subject: Physics
A metal rod of length \( 1 \mathrm{m} \) is clamped at
two points as shown in the figure. Distance of the lamp from the two ends
are \( 5 c m \) and \( 15 c m \) respectively. Find the minimum and next higher
frequency of natural longitudinal oscillation of the rod. Given that Young's modulus of elasticity and density of aluminium are \( \boldsymbol{Y}=\mathbf{1 . 6} \times \mathbf{1 0}^{\mathbf{1 1}} \mathbf{N m}^{-\mathbf{2}} \)
and \( p=2500 k g m^{-3} \) respectively.
\( A \cdot 40 \mathrm{kHz}, 120 \mathrm{kHz} \)
B. 120 kHz, 40 kHz
c. \( 40 \mathrm{kHz}, 40 \mathrm{kHz} \)
D. 1200 kHz, 120 kHz
Subject: Biology
Assertion
Auxins were the first growth hormones
discovered in plants.
Reason
In most of plant tip movements in
seedling stages led to the discovery of
auxins.
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
An iron scale is calibrated at \( 0^{\circ} C . \) The
length of a zinc rod is measured to be
\( 100 \mathrm{cm} \) by the scale when the rod and
the scale both are at \( 0^{0} C . \) What will be
the length of the rod as measured by the
scale when both are at \( 100^{\circ} \mathrm{C} \). Given :
\( \boldsymbol{\alpha}_{i r o n}=1.2 \times 10^{-5}^{\circ} \boldsymbol{C}^{-1} \) and \( \boldsymbol{\alpha}_{z i n c}= \)
\( \mathbf{2 . 6} \times \mathbf{1 0}^{-\mathbf{4} \circ} \mathbf{C}_{-\mathbf{1}} \)
Subject: Maths
State true or false:
\( \boldsymbol{F}(\boldsymbol{x}, \boldsymbol{y})=\boldsymbol{e}^{\boldsymbol{y} / \boldsymbol{x}}+\ln \boldsymbol{x}-\ln \boldsymbol{y} \) is
homogeneous function of degree zero.
A . True
B. False
Subject: Chemistry
(i) Write the structural formula of
acetic acid.
(ii) Write the electron dot structure of
ethane.
(iii) Explain odd atom by an example.
(iv) Select unsaturated hydrocarbon in
\( \boldsymbol{C}_{2} \boldsymbol{H}_{6}, \boldsymbol{C}_{3} \boldsymbol{H}_{4}, \boldsymbol{C}_{3} \boldsymbol{H}_{8} \) and \( \boldsymbol{C}_{2} \boldsymbol{H}_{4} \)
(v) Write a difference between soap and
detergents.
Subject: Chemistry
The volume of water required to make \( 0.20 \mathrm{M} \) solution from \( 16 \mathrm{ml} \) of \( 0.5 \mathrm{M} \) solution is:
A . \( 40 \mathrm{ml} \)
B. 16 \( \mathrm{ml} \)
c. \( 50 \mathrm{ml} \)
D. 24 m
Subject: Physics
Moment of inertia of a hollow sphere of
mass \( \mathrm{M} \) and diameter \( \mathrm{D} \) about its
diameter
A \( . M D^{2} / 5 \)
В. \( 2 M D^{2} / 5 \)
c. \( M D^{2} / 6 \)
D. \( 5 M D^{2} / 2 \)
Subject: Physics
\( \vec{B}=\hat{i}-3 \hat{j}+\hat{k} . \) Find the
a. Area of the triangle whose two sides are representedby the vectors \( \overrightarrow{\boldsymbol{A}} \) and \( \overrightarrow{\boldsymbol{B}} \)
b. Area of the parallelogram whose two adjacent sidesare represented by the vectors \( \vec{A} \) and \( \vec{B} \)
c. Area of the parallelogram whose
diagonals are represented by the vectors \( \vec{A} \) and \( \vec{B} \)
A \( \cdot \) a. \( \frac{1}{2}|\vec{A} \times \vec{B}| \)
b. \( |\vec{A} \times \vec{B}| \)
c. \( \frac{1}{3}|\vec{A} \times \vec{B}| \)
B. a. \( \frac{1}{2}|\vec{A} \times \vec{B}| \)
b. \( |\vec{A} \times \vec{B}| \)
c. \( \frac{1}{2}|\vec{A} \times \vec{B}| \)
c. \( _{\text {a. }} \frac{1}{2}|\vec{A} \times \vec{B}| \)
b. \( |\vec{A} \times \vec{B}| \)
c. \( \frac{1}{4}|\vec{A} \times \vec{B}| \)
D. \( _{\text {a. }} \frac{1}{3}|\vec{A} \times \vec{B}| \)
b. \( \mid \vec{A} \times \vec{B} \)
c. \( \frac{1}{2}|\vec{A} \times \vec{B}| \)
Subject: Physics
A sheet of \( 15.0 g \) of gold at \( 25.0 C \) is
placed on a \( 30.0 g \) sheet of copper at \( 45.0 C . \) What is the final temperature of
the two metals assuming that no heat is lost to the surroundings. The specific heats of gold and copper are
\( 0.129 J / g C \) and \( 0.385 J / g C \)
respectively.
Subject: Physics
A metallic rod of length 'L' and crosssection 'A' has Young's modulus 'Y' and coefficient of linear expansion \( \alpha \). If the
rod is heated to a temperature 'T', then the energy stored per unit volume is:
A \( \cdot \frac{1}{2} Y \alpha^{2} T^{2} \)
B. \( \frac{1}{2} Y A \alpha^{2} T^{2} \)
c. \( \frac{1}{2} Y A \alpha T \)
D. \( \frac{1}{2} Y A^{2} \alpha^{2} T^{2} \)
Subject: Physics
A body projected vertically up travels a
height \( h \) in the \( n^{t h} \) second. The distance
travelled by it in the next two seconds is
\( A \cdot h+2 g \)
в. \( 2 h+g \)
c. \( 2 h+2 g \)
D. \( 2 h+3 g \)
Subject: Maths
The point \( P \) is the intersection of the
straight line joining the points \( Q(2,3,5) \) and \( R(1,-1,4) \) with the plane
\( 5 x-4 y-z=1 . \) If \( S \) is the foot of the
perpendicular drawn from the point
\( T(2,1,4) \) to \( Q R, \) then the length of the
line segment \( P S \) is
A \( \cdot \frac{1}{\sqrt{2}} \)
B. \( \sqrt{2} \)
\( c \cdot 2 \)
D. \( 2 \sqrt{2} \)
Subject: Maths
Find the equation of directrix and
length of latus rectum of the parabola \( x^{2}=16 y \)
A. \( y-4=0 \) and 16
B. \( y+4=0 \) and 16
c. \( y-4=0 \) and 4
D. \( y+4=0 \) and 4
Subject: Physics
The time, in which a force of \( 2 \mathrm{N} \) produces a change in momentum of \( 0.4 k g m s^{-1} \) in a body whose mass is 1
kg is:
A. \( 0.2 \mathrm{s} \)
B. 0.02 \( s \)
\( c .0 .5 \mathrm{s} \)
D. \( 0.05 \mathrm{s} \)
Subject: Maths
\( \boldsymbol{A}=\left[\begin{array}{ccc}\mathbf{1} & \mathbf{- 3} & \mathbf{- 4} \\ \mathbf{- 1} & \mathbf{3} & \mathbf{4} \\ \mathbf{1} & \mathbf{- 3} & \mathbf{- 4}\end{array}\right] \) and \( \mathbf{A}^{2}=\boldsymbol{\lambda} \boldsymbol{I} \) then
\( \boldsymbol{\lambda}= \)
\( A \cdot 0 \)
B.
\( c \cdot \frac{1}{2} \)
D. -
Subject: Biology
Complete the following sentences by selecting the correct option.
(A) Inspiratory capacity (IC) = (i) + IRV
(B) \( (i i)=T V+I R V+E R V \)
(C) Functional residual capacity \( (\mathrm{FRC})= \) ERV \( +(\text { iii }) \)
A. (ii)Vital capacity (ii) Tidal volume (iii)Residual volume
B. (i)Expiratory capacity
(ii) Residual volume (iii) Inspiratory reserve volume
c. (i)Tidal volume (ii) Vital capacity (iii) Residual volume
D. (i)Tidal volume (ii) Total lung capacity (iii) Expiratory capacity
Subject: Maths
If \( \sin ^{-1}(x)+\sin ^{-1}(2 x)=\frac{\pi}{3}, \) then \( x= \)
A \( \cdot \frac{3}{28} \)
B. \( \frac{\sqrt{3}}{28} \)
c. \( \sqrt{\frac{3}{28}} \)
D. \( \frac{3}{\sqrt{28}} \)
Subject: Physics
A block of mass \( m \) and surface area \( A \)
just begins to slide down an inclined plane when the angle of inclination is \( \pi / 5 . \) Keeping the mass of the block
same, if the surface area is doubled, the inclination of the plane at which
the block starts sliding will be:
A \( . \pi / 5 \)
в. \( \pi / 10 \)
c. \( 2 \pi / 5 \)
D. \( \pi / 5 \sqrt{2} \)
Subject: Maths
If \( \boldsymbol{y}=\boldsymbol{s} \boldsymbol{e} \boldsymbol{c}^{-1}\left[\frac{\boldsymbol{x}+\mathbf{1}}{\boldsymbol{x}-\mathbf{1}}\right]+\boldsymbol{s i n}^{-1}\left[\frac{\boldsymbol{x}-\mathbf{1}}{\boldsymbol{x}+\mathbf{1}}\right] \)
\( z=\operatorname{cosec}^{-1}\left[\frac{2 x+3}{3 x+2}\right]+ \)
\( \cos ^{-1}\left[\frac{3 x+2}{2 x+3}\right] \) then
This question has multiple correct options
A. \( y=\pi / 2 \)
2
B. \( z=\pi / 2 \)
\( \mathbf{c} \cdot y+z=\pi \)
D. \( y+z=\pi / 2 \)
Subject: Physics
There are two wires, \( A \) and \( B \), made of same material. Both the wires have the
same length. It is observed that the resistance of wire \( A \) is four times
the resistance of wire \( \mathrm{B} \), then find the
ratio of their cross sectional areas.
A . 4: 1
B. 1: 4
c. 1: 2
D. 2: 1
Subject: Chemistry
In the neighbourhood of your school hard water required for an experiment is not available. Select from the
following grous of salts available in your school, a group each member of which, if dissolved in distilled water, will make
it hard :
A. sodium chloride, calcium chloride
B. potassium chloride, sodium chloride
c. sodium chloride, magnesium chloride
D. calcium chloride, magnesium chloride
Subject: Chemistry
\( \boldsymbol{A l}^{3+}(\boldsymbol{a q})+\boldsymbol{3} \boldsymbol{e}^{-} \rightarrow \boldsymbol{A l}(\boldsymbol{s}) ; \boldsymbol{E}^{\circ}= \)
\( -1.66 V \)
\( \boldsymbol{C u}^{2+}(\boldsymbol{a q})+\boldsymbol{2} \boldsymbol{e}^{-} \rightarrow \boldsymbol{C u}(\boldsymbol{s}) ; \boldsymbol{E}^{\circ}= \)
\( +0.34 V \)
What voltage is produced under standard conditions to give a
spontaneous reactions by combination of these two-half cells?
A \( .1 .32 \mathrm{V} \)
W
в. \( -1.32 v \)
c. \( 2.00 V \)
D. \( -2.00 V \)
Subject: Physics
The ratio of the magnetic field at the
centre of a circular loop to the magnetic field at the centre of the square loop, which is made by a constant length current carrying wire is:
A \( \cdot \frac{\pi^{2}}{16} \)
в. \( \frac{\pi^{2}}{8 \sqrt{2}} \)
c. \( \frac{\pi^{2}}{4 \sqrt{2}} \)
D. \( \frac{\pi^{2}}{2 \sqrt{2}} \)
Subject: Maths
Simplify and express the result in the form of a rational number :
\( \left(\frac{3}{11} \times \frac{2}{9}\right)+\left(\frac{-6}{21} \div \frac{1}{-42}\right)- \)
\( \left(-1 \frac{1}{3} \times \frac{9}{24}\right)-\left(\frac{-2}{7} \times-21\right) \)
Subject: Physics
Interference is produced with two coherent sources of the same intensity If one of the sources is covered with a
thin film so as to reduce the intensity of light coming out of it to half, then:
A. bright fringes will be less bright and dark fringes will be less dark
B. bright fringes will be more bright and the dark fringes will be more dark
c. brightness of both types of the fringes will remain the same
D. dark region will spread completely
Subject: Chemistry
An oxyacid of phosphorus has the following properties: The complex
neutralisation of the acid with sodium
hydroxide solution given an aqueous solution of sodium ions and oxy-acid
anions in the ratio 2:1. When a solution
of the acid is warmed with silver nitrate
solution, metallic silver is deposited.
\( p H 0.01 \mathrm{M} \) solution of the sodium salt of
this acid formed (assume \( \boldsymbol{p} \boldsymbol{K}_{\boldsymbol{a}_{1}}=\boldsymbol{2} \boldsymbol{x} \)
is
\( A \cdot 6+2 x \)
B. \( 6-2 x \)
\( c \cdot 6-x \)
D. \( 6+x \)
Subject: Maths
Differentiate \( \cos ^{-1} x \)
A \( \cdot \frac{-1}{\sqrt{\left(1-x^{2}\right)}} \)
B. \( \frac{1}{\sqrt{\left(1-x^{2}\right)}} \)
c. \( \frac{-1}{\sqrt{\left(1+x^{2}\right)}} \)
D. \( \frac{1}{\sqrt{\left(1+x^{2}\right)}} \)
Subject: Physics
What will be the wavelength of the \( x \) rays which give a diffraction angle \( 2 \theta \)
equal to \( 16.80^{\circ} \) for a crystal, if the inter planner distance in the crystal is 0.200 nm and only first order diffraction is
observed \( \left(\sin 8.40^{\circ}=0.146\right) \)
Subject: Chemistry
10 mL of hydrogen combines with 5 mL
of oxygen to yield water. When 200 mL of hydrogen at STP is passed over heated
\( C u O, \) the \( C u O \) loses 0.144 g of its weight. State the law illustrated by these chemical combinations.
A. Law of multiple proportion
B. Law of constant composition
c. Law of reciprocal proportion
D. None of the above
Subject: Chemistry
What is the unit for the rate constant of
a second order reaction?
A \( \cdot s^{-1} \)
B. mol \( L^{-1} \)
c. mol \( L^{-1} s^{-1} \)
D. \( \mathrm{L} \) mol \( ^{-1} s^{-1} \)
E \( \cdot \operatorname{mol}^{2} L^{-2} s^{-2} \)
Subject: Chemistry
To make \( 50 \mathrm{mL} \) solution of \( K C l \) of \( 1 \mathrm{M} \)
how many grams of \( K C l \) are required to add to this solution?
A \( .1 .00 \mathrm{g} \)
В. \( 1.86 \mathrm{g} \)
c. \( 3.73 \mathrm{g} \)
D. 7.45 g
E . \( 1.49 \mathrm{g} \)
Subject: Physics
\( \ln \operatorname{arclation} F=a \sin k_{1} x+b \sin k_{2} T \)
where \( F, x \) and \( T \) denote the force
distance and time respectively. Units of
\( k_{1} \) and \( k_{2} \) are respectively a
A. meter, \( s \)
B . meter \( ^{-1}, s^{-1} \)
c. meter \( ^{-1}, s \)
D. meter, \( s^{-1} \)