AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Maths
ff \( \boldsymbol{y}=\sec ^{2} \boldsymbol{\Theta}+\cos ^{2} \boldsymbol{\Theta}, \boldsymbol{0} \neq \boldsymbol{0}, \) then
A. \( y=0 \)
B. \( y \leq 0 \)
\( \mathbf{c} \cdot y>2 \)
D. \( y \neq 2 \)
Subject: Maths
Points \( X \& Y \) are taken on the sides QR
\& RS respectively of a parallelogram \( \mathrm{PQRS}, \) so that \( \boldsymbol{Q} \overrightarrow{\boldsymbol{X}}=4 \overrightarrow{\boldsymbol{X}} \boldsymbol{R} \& \overrightarrow{\boldsymbol{R} \boldsymbol{Y}}= \)
\( 4 \vec{Y} \) S. The line \( X Y \) cuts the line \( P R \) at \( Z \) Prove that \( \overrightarrow{P Z}=\left(\frac{21}{25}\right) \overrightarrow{P R} \)
Subject: Physics
If the vector \( 6 \hat{i}-3 \hat{j}-6 \hat{k} \) is decomposed into vectors parallel and perpendicular to the vector \( \hat{i}+\hat{j}+\hat{k} \)
then the vectors are
A \( .-(\hat{i}+\hat{j}+\hat{k}) \& 7 \hat{i}-2 \hat{j}-5 \hat{k} \)
B. \( -2(\hat{i}+\hat{j}+\hat{k}) \& 8 \hat{i}-\hat{j}-4 \hat{k} \)
\( \mathbf{c} \cdot+2(\hat{i}+\hat{j}+\hat{k}) \& 8 \hat{i}-\hat{j}-4 \hat{k} \)
D. none
Subject: Chemistry
Total number of electrons involved per
molecule in the oxidation of \( F e C_{2} O_{4} \) to
\( F e^{3+} \) and \( C O_{2} \) is :
\( \mathbf{A} \cdot \mathbf{3} \)
B. 2
\( c \cdot 4 \)
D. none of these
Subject: Maths
If a hexagon of perimeter \( 24 \mathrm{cm} \) has
equal side lengths, then the length of its
side is
\( A \cdot 2 \mathrm{cm} \)
B. \( 4 \mathrm{cm} \)
\( c \cdot 6 \mathrm{cm} \)
\( \mathbf{D} \cdot 8 \mathrm{cm} \)
Subject: Chemistry
\( 4.5 g \) of aluminium (At. mass \( =27 \) atm
is deposited at cathode from \( \boldsymbol{A} \boldsymbol{l}^{\mathbf{3}+} \)
solution by a certain quantity of electric charge. The volume of hydrogen
produced at STP from \( \boldsymbol{H}^{+} \) ions in solution by the same quantity of electric charge will be
A . \( 44.8 L \)
B. 22.4 L
c. \( 11.2 L \)
D. \( 5.6 L \)
Subject: Maths
If \( \boldsymbol{y}=\boldsymbol{a}+\frac{\boldsymbol{b}}{\boldsymbol{x}}, \) where \( \boldsymbol{a} \) and \( \boldsymbol{b} \) are
constants, and if \( \boldsymbol{y}=\mathbf{1} \) when \( \boldsymbol{x}=-\mathbf{1} \)
and \( y=5 \) when \( x=-5, \) then \( a+b \)
equals.
A . -1
B.
c.
D. 10
E. 11
Subject: Chemistry
Which does not represent correct
method?
\( \mathbf{A} \cdot T i C l_{2}+2 M g \rightarrow T i+2 M g C l_{2}: K r o l \)
B. \( N i(C O)_{4} \rightarrow N i+4 C O: \) Mond
c. \( _{A g_{2}} C O_{3} \rightarrow 2 A g+C O_{2}+\frac{1}{2} O_{2}: \) van Arkel
\( \mathbf{D} \cdot Z r l_{4} \rightarrow Z r+2 I_{2}: \) van Arkel
Subject: Maths
If \( x=\frac{1-t^{2}}{1+t^{2}} \) and \( y=\frac{2 t}{1+t^{2}} \) at then \( \frac{\boldsymbol{d} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}}=? \)
A \( \cdot \frac{-1}{x^{3}} \)
в. \( \frac{y}{x} \)
c. \( \frac{-x}{y} \)
D. \( \frac{x}{y} \)
Subject: Physics
On the axis and on the equator of an electric dipole for all points
A. On both of them \( V \neq 0 \)
B. On both of them \( V=0 \)
c. on the axis \( V=04 \$ a n d o \)nequatorv Vneq o\$s
D. on the axis \( V \neq 0 \) and on equator \( V=0 \)
Subject: Maths
\( A \) and \( B \) are two events on a sample
space \( S \) such that \( P(A)=0.8, P(B)= \)
\( \mathbf{0 . 6} \) and \( \boldsymbol{P}(\boldsymbol{A} \cup \boldsymbol{B})=\mathbf{0 . 9} \) find \( (\boldsymbol{A} \cap \boldsymbol{B}) \)
A . 0.3
B. 0.4
\( c \cdot 0.5 \)
D. 0.6
Subject: Physics
\( \ln \) an ac circuit, the resistance of \( \mathrm{R} \Omega \) is connected in series with an inductance
I. If phase angle between voltage and
current be \( 45^{\circ}, \) the value of inductive
reactance will be:
A. \( R / 2 \)
B. \( R / \sqrt{2} \)
\( c . R \)
D. Insufficient data
Subject: Physics
Assertion: A resistance is connected to
an ac source. Now a capacitor is included in the series circuit. The
average power absorbed by the resistance will remain same.
Reason: By including a capacitor or an inductor in the circuit average power
across resistor does not change.
A. A and R both are true and R is correct explanation of
B. A and R both are true but R is not the correct explanation of
c. A is true R is false
D. A is false and R is true
Subject: Maths
Let \( \boldsymbol{f}(\boldsymbol{x}) \) be defined \( \forall \boldsymbol{x} \in \boldsymbol{R} \) and
continuous.
\( \operatorname{Let} \boldsymbol{f}(\boldsymbol{x}+\boldsymbol{y})-\boldsymbol{f}(\boldsymbol{x}-\boldsymbol{y})=\boldsymbol{4} \boldsymbol{x} \boldsymbol{y} \forall \boldsymbol{x}, \boldsymbol{y} \in \)
\( \boldsymbol{R} \) and \( \boldsymbol{f}(\mathbf{0})=\mathbf{0}, \) then \( \boldsymbol{f}(\boldsymbol{x})<\mathbf{2} \boldsymbol{x}+\mathbf{3} \) will
have solution:
A. (-1,3)
B . \( (1-\sqrt{5}, 1+\sqrt{5}) \)
c. \( (1-\sqrt{5},-1) \cup(3,1+\sqrt{5}) \)
D. \( (3,1+\sqrt{5}) \)
Subject: Maths
In a trapezium \( A B C D, \) side \( A B \) is parallel to side \( \mathrm{DC} ; \) and the diagonals \( \mathrm{AC} \) and \( \mathrm{BD} \)
intersect each other at a point
Such that:
\( \boldsymbol{P A} \times \boldsymbol{P D}=\boldsymbol{P B} \times \boldsymbol{P C} \)
A. True
B. False
Subject: Maths
Solution of differential equation \( \frac{\boldsymbol{d} \boldsymbol{x}}{\boldsymbol{d} \boldsymbol{y}}= \)
\( \tan x(1+y \sin x) \) is given by
A \( \cdot \operatorname{cosec} x=-y+1+C e^{-y} \)
B. \( y=\tan x+C e^{X} \)
c. \( \sin x e^{y}=1+y+C \)
D. \( \operatorname{cosec} x=y+C e^{y} \)
Subject: Physics
A vessel is filled with water and
kerosene oil. The vessel has a small hole
in the bottom. Neglecting viscosity if
the thickness of water layer is \( h_{1} \)
and kerosene layer is \( h_{2} \) then the
velocity \( v \) of flow of water will be (Given:
density of water is \( \rho_{1} \) g/ \( c c \) and that of
kerosene is \( \rho_{2} \) g/cc, neglecting viscosity):
A \( . v=\sqrt{2 g\left(h_{1}+h_{2}\right)} \)
B. \( v=\sqrt{2 g\left[h_{1}+h_{2}\left(\frac{\rho_{2}}{\rho_{1}}\right)\right]} \)
C. \( v=\sqrt{2 g\left(h_{1} \rho_{1}+h_{2} \rho_{2}\right)} \)
D \( v=\sqrt{2 g\left[h_{1}\left(\frac{\rho_{1}}{\rho_{2}}\right)+h_{2}\right]} \)
Subject: Chemistry
Which of the following order is wrong?
\( \mathbf{A} \cdot N H_{3}<P H_{3}<A s H_{3}: \) Acidic strength
B . \( L i<B e<B<C: I E_{1} \)
c. \( A l_{2} O_{3}<M g O<N a_{2} O<K_{2} O: \) Basic strength
D \( \cdot L i^{+}<N a^{+}<K^{+}<C s^{+}: \) Ionic character
Subject: Chemistry
Assertion
An electrochemical cell can be set-up
only if the redox reaction is
spontaneous.
Reason
A reaction is spontaneous if free energy change is negative.
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: Physics
Two particles of mass \( m_{1} \) and \( m_{2} \) in projectile motion have velocities \( \vec{v}_{1}< \)
\( \vec{v}_{2} \) respectively at tine \( t=0 . \) They collide at time \( t_{0} . \) Their velocities become \( \overrightarrow{v_{1}^{\prime}} \) and \( \vec{v}_{2}^{\prime} \) at time \( 2 t_{0^{\prime}} \) while still moving in
air. The value of
\( \left|\left(m_{1} \vec{v}_{1}^{\prime}+m_{2} \overrightarrow{v_{2}^{\prime}}\right)-\left(m_{1} \vec{v}_{1}+m_{2} \vec{v}_{2}\right)\right| \)
Subject: Physics
\( (n-1) \) equal point masses each of
mass \( \mathrm{m} \) are placed at the vertices of a regular n-polygon. The vacant vertex has a position vector a with respect to the centre of the polygon. Find the positive
vector of centre of mass:
A \( \cdot \frac{1}{n-1} a \)
в. \( -\frac{1}{(n-1)} a \)
c. \( (n-1) a \)
D. \( -\left(\frac{n-1}{a}\right) \)
Subject: Physics
Rex Things throws his mother's crystal vase vertically upwards with an initia velocity of \( 26.2 m / s . \) Determine the height to which the vase will rise above its initial height.
A . \( 34.0 m \)
B. \( 39.0 m \)
c. \( 35.0 m \)
D. \( 37.0 m \)
Subject: Biology
In which of the following, scientific
name, family and common name are correctly mentioned?
A. Scientific name-Batrachospermum, FamilyRhodophyceae, Common name-Frog's spawn algae
B. Scientific name-Spirogyra, Family-Chlorophyceae, Common name-Water net
c. Scientific name-Lycopodium, Family-Lycopodiaceae, Common name-sanjeevani
D. scientific name-Selaginella, Family-Lycopodiaceae, Common name-Little club moss
Subject: Chemistry
Match the List-I with List-II and choose
the correct answer from the code.
\( \begin{array}{ll}\begin{array}{l}\text { List-I } \\ \text { (Electrolyte) }\end{array} & \begin{array}{l}\text { List-II } \\ \text { (Solubility product) }\end{array} \\ \text { A. } B i_{2} S_{3} & \text { 1. } 4 s^{3} \\ \text { B. } A l(O H)_{3} & \text { 2. } 27 s^{4} \\ \text { C. CdS } & \text { 3. } 108 s^{5} \\ \text { D. } C a F_{2} & \text { 4. } s^{2}\end{array} \)
\( \mathbf{A} \)
\( A-1, B-2, C-3, D-4 \)
B. \( A-2, B-3, C-1, D-4 \)
C \( . A-4, B-3, C-2, D-1 \)
D . \( A-3, B-2, C-4, D-1 \)
Subject: Chemistry
A physician wishes to prepare a buffer solution at \( p H=3.58 \) that efficiently
resists a change in \( p H \) yet contains only small conc. of the buffereing agents. Which one of the following weak acid together with its sodium salt would be best to use?
A. \( m \) -chloro benzoic acid \( \left(p K_{a}=3.98\right) \)
B. \( p \) -chlorocinnamic acid \( \left(p K_{a}=4.41\right) \)
C. 2,5-dihydroxy benzoic acid ( \( p K_{a}=2.97 \) )
D. Acetoacetic aced ( \( p K_{a}=3.58 \) )
Subject: Chemistry
Hexaamminenickel(II)
hexanitrocobaltate(III) can be written
as?
\( \mathbf{A} \cdot\left[N i\left(N H_{3}\right)_{6}\right]_{2}\left[C o\left(N O_{2}\right)_{6}\right]_{3} \)
\( \mathbf{B} \cdot\left[N i\left(N H_{3}\right)_{6}\right]_{3}\left[C o\left(N O_{2}\right)_{6}\right]_{2} \)
\( \mathbf{c} \cdot\left[N i\left(N H_{3}\right)_{6}\right]\left[C o\left(N O_{2}\right)_{6}\right] \)
D. \( \left[N i\left(N H_{3}\right)_{6}\left(N O_{2}\right)_{6}\right] C o \)
Subject: Chemistry
A compound which can be used in
space vehicles both to a absorb \( C O_{2} \)
and liberate \( \boldsymbol{O}_{2} \) is:
A . \( N a O H \)
в. \( N a_{2} O \)
c. \( N a_{2} O_{2} \)
\( \mathbf{D} \cdot C a O+N a O H \)
Subject: Maths
Exhaustive set of values of parameter \( \boldsymbol{a} \)
so that \( \sin ^{-1} x-\tan ^{-1} x=a \quad \) has a
solution is
A. \( \left[-\frac{\pi}{6}, \frac{\pi}{6}\right] \)
B. \( \left[-\frac{\pi}{4}, \frac{\pi}{4}\right] \)
\( \mathbf{c} \cdot\left[-\frac{\pi}{2}, \frac{\pi}{2}\right] \)
D. none of these
Subject: Physics
Two electric charges \( 12 \mu C \) and \( -6 \mu \)
electric field intensity at zero potentia
and outside the region between them
A \( \cdot 1.25 \times 10^{6} N / C \)
В. \( 3.75 \times 10^{5} N / C \)
c. \( 4.5 \times 10^{6} N / C \)
D. \( 6.75 \times 10^{5} N+C \)
Subject: Physics
(a) State Ampere's circuital law. Use this law to obtain the expression for the magnetic field inside an air cored toroid of average radius r having 'n' turns per unit length and carrying a steady current I
(b) An observer to the left of a solenoid of N terms each of cross section area \( A \)
observes that a steady current lin it flows in the clockwise direction. Depict the magnetic field lines due to the solenoid specifying its polarity and show that it acts as a bar magnet of
magnetic momentum \( \boldsymbol{m}=\boldsymbol{N} \boldsymbol{I} \boldsymbol{A} \)
Subject: Physics
A heavy chain with a mass per unit
length \( p \) is pulled by the constant force \( F \) along a horizontal surface consisting
of a smooth section and rough section.
The chain is initially at rest on the
rough surface with \( \boldsymbol{x}=\mathbf{0} . \) If the coefficient of kinetic friction between
the chain and the rough surface is \( \mu_{k} \)
determine the velocity \( v \) of the chain when \( x=L . \) The force \( F \) is greater than
\( \mu_{k}, p g L \) in order to initiate the motion.
\( ^{\text {A }} \cdot \sqrt{\frac{2 F}{P}-\mu_{k} g L} \)
в. \( \sqrt{\frac{F}{P}-\mu_{k} g L} \)
\( c \)
Subject: Maths
Rajdhani Express stops at six intermediate stations between Kota
and Mumbai.Five passengers board at Kota. Each passengers can get down at any station till Mumbai. The probability that all five passengers will get down at different stations, is
\( ^{A} \cdot \frac{^{6} P_{5}}{6^{5}} \)
в. \( \frac{^{6} C_{5}}{6^{5}} \)
c. \( \frac{7}{7^{5}} \)
D. \( \frac{7}{7^{5}} \)
Subject: Biology
Assertion
In \( C_{4} \) cycle, first stable product has 4
carbon compound
Reason
In \( C_{4} \) plants, \( C_{3} \) cycle is absent
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
The resistance of a coi is \( 4.2 \Omega \) at
\( 100^{\circ} \mathrm{C} \) and the temperature coefficient
of resistance of its material is
\( 0.004 /^{\circ} \mathrm{C} . \) Its resistance at \( 0^{\circ} \mathrm{C} \)
A . \( 6.5 \Omega \)
B. 3\Omega
\( c .5 \Omega \)
D. 4\Omega
Subject: Physics
A force of \( 20 \mathrm{N} \) acting on a body of mass
\( 10 \mathrm{kg} \) is found to double its velocity in 8
s. Find its initial velocity?
\( A \cdot 6 m s^{-1} \)
B . \( 16 \mathrm{m} \mathrm{s}^{-1} \)
\( c \cdot 8 m s^{-1} \)
D. \( 10 \mathrm{m} \mathrm{s}^{-1} \)
Subject: Physics
A bullet on penetrating \( 30 \mathrm{cm} \) into its target loses its velocity by \( 50 \% . \) What additional distance will it penetrate
into the target before it comes to rest?
\( \mathbf{A} \cdot 30 \mathrm{cm} \)
B. \( 20 \mathrm{cm} \)
c. \( 10 \mathrm{cm} \)
D. \( 5 \mathrm{cm} \)
Subject: Biology
Identify the correct statement regarding
enzyme inhibition.
A. Non-competitive inhibition of an enzyme can be overcomed by adding large amount of substrate.
B. Competitive inhibition is seen when a substrate competes with an enzyme for binding to an inhibitor protein.
C. Competitive inhibition is seen when the substrate and the inhibitor compete for the active site on the
enzyme.
D. Non-competitive inhibitors often bind to the enzyme irreversibly.
Subject: Chemistry
In the reaction of \( \boldsymbol{H} \boldsymbol{I} \) with \( \boldsymbol{H}_{2} \boldsymbol{S} \boldsymbol{O}_{4} \) the
oxidation state of sulphur is changed to
\( -2 . \) Identify the correct balanced
equation:
A \( \cdot H_{2} S O_{4}+2 H I \rightarrow S O_{2}+2 H_{2} O+I_{2} \)
B . \( H_{2} S O_{4}+6 H I \rightarrow S+4 H_{2} O+3 I_{2} \)
\( \mathrm{c} \cdot \mathrm{H}_{2} \mathrm{SO}_{4}+8 \mathrm{HI} \rightarrow \mathrm{H}_{2} \mathrm{S}+4 \mathrm{H}_{2} \mathrm{O}+4 \mathrm{I}_{2} \)
D. All of these
Subject: Maths
Factorize the following using appropriate identities:
\( (\mathrm{i}) 9 x^{2}+6 x y+y^{2} \)
\( (\mathrm{ii}) 4 \boldsymbol{y}^{2}-\mathbf{4} \boldsymbol{y}+\mathbf{1} \)
\( (i i i) x^{2}-\frac{y^{2}}{100} \)
Subject: Maths
If a relation \( ^{\prime} \boldsymbol{R}^{\prime} \) is defined by \( \boldsymbol{R}= \)
\( \left\{(x, y) / 2 x^{2}+3 y^{2} \leq 6\right\}, \) then the
domain of \( \boldsymbol{R}(\boldsymbol{x}, \boldsymbol{y}) \) is
This question has multiple correct options
A \( \cdot x \in[-3,3] \)
B . \( x \in[-\sqrt{3}, \sqrt{3}] \)
c. \( y \in[-\sqrt{2}, \sqrt{2}] \)
D \( \cdot y \in[-2,2] \)
Subject: Maths
Five ordinary dies are rolled at random and the sum of numbers shown is 16
What is the probability that the number
shown on each is any one from 2,3,4 or
\( \mathbf{5} ? \)
A \( \cdot \frac{9}{49} \)
B. \( \frac{3}{49} \)
c. \( \frac{2}{49} \)
D. None of these
Subject: Chemistry
The position of \( B r \) in the compound in
\( \boldsymbol{C H}_{3} \boldsymbol{C H}=\boldsymbol{C H C}(\boldsymbol{B r})\left(\boldsymbol{C H}_{3}\right)_{2} \) can be
classified as:
A . ally!
B. ary!
c. viny!
D. secondary
Subject: Physics
An emf of \( 15 V \) is applied in a circuit of inductance \( 5 H \) and resistance \( 10 \Omega \)
The ratio of currents flowing at \( t=\infty \)
and \( t=1 s \) will be
A \( \cdot 1-e^{-1} \)
B \( \cdot e^{-1} \)
c. \( \frac{e^{2}}{e^{2}-1} \)
D. \( \frac{e^{1 / 2}}{e^{1 / 2}-1} \)
Subject: Chemistry
Number of sigma and pi bonds in \( \mathrm{ClO}_{3}^{-} \)
ion are:
\( \mathbf{A} \cdot 2 \sigma \) and \( 2 \pi \)
B. \( 3 \sigma \) and \( 3 \pi \)
\( \mathbf{c} \cdot 3 \sigma \) and \( 2 \pi \)
D. \( 2 \sigma \) and \( 3 \pi \)
Subject: Physics
A steel wire of mass \( 3.16 K g \) is
stretched to a tensile strain of \( 1 \times 10^{-3} \) What is the elastic deformation energy
if density \( \rho=7.9 g / c c \) and \( Y=2 \times 10^{11} \)
\( \mathrm{N} / \mathrm{m}^{2} ? \)
A. \( 4 K J \)
в. \( 0.4 K J \)
c. \( 0.04 K J \)
D. \( 4 J \)
Subject: Maths
Find \( S_{n}, \) the sum of the first \( n \) terms, for
the following geometric series. \( a_{1}= \)
\( \mathbf{1 2 0}, \boldsymbol{a}_{5}=\mathbf{1}, \boldsymbol{r}=-\mathbf{2} \)
A .20 .66
B. 40.66
c. 80.66
D. 100.66
Subject: Physics
Two point charges \( +q \) and \( -q \) are placed at a distance \( x \) apart. A third charge is placed in such a way so that all the three charges are in equilibrium.
Then :
A. unknown charge is \( -4 q / 9 \)
B. unknown charge is \( -9 q / 4 \)
c. it should be at \( (x / 3) \) from smaller charge between them
D. none of the above
Subject: Physics
Find the static friction force acting on
the cone \( A, \) if \( \omega=1.0 \) rad/s.
\( \mathbf{A} \cdot F_{f r}=12 N \)
\( \mathbf{B} \cdot F_{f r}=6 N \)
\( \mathbf{C} \cdot F_{f r}=18 N \)
\( \mathbf{D} \cdot F_{f r}=3 N \)
Subject: Chemistry
The solubility product of \( A g C l \) is \( 1.8 \times \)
\( 10^{-10} . \) Precipitation of \( A g C l \) will occur
only when equal volumes of solutions of
A \( \cdot 10^{-4} M A g^{+} \) and \( 10^{-4} M C l^{-} \) are mixed
B . \( 10^{-7} M A g^{+} \) and \( 10^{-7} M C l^{-} \) are mixed
C \( \cdot 10^{-5} M A g^{+} \) and \( 10^{-5} M C l^{-} \) are mixed
D. \( 10^{-10} M A g^{+} \) and \( 10^{-10} M C l^{-} \) are mixed
Subject: Maths
If \( P \) and \( Q \) are the sum and product
respectively of all integral values of \( x \)
satisfying the equation \( |\mathbf{3}[\boldsymbol{x}]-\mathbf{4} \boldsymbol{x}|=\mathbf{4} \)
then
(where [.] denotes represents greatest integer function \( ) \) This question has multiple correct options
\( \mathbf{A} \cdot P=0 \)
B . \( P=8 \)
c. \( Q=-16 \)
D. \( Q=-9 \)
Subject: Maths
Of 28 people in a park, 12 are children and the rest are adults. 8 people have to leave at \( 3 \mathrm{pm} ; \) the rest do not. If, after 3
\( \mathrm{pm}, \) there are 6 children still in the park, how many adults are still in the park?
A . 14
B . 18
c. 15
D. 16
Subject: Chemistry
If first dissociation of \( \boldsymbol{X}(\boldsymbol{O} \boldsymbol{H})_{3} \) is \( \mathbf{1 0 0 \%} \)
whereas second dissociation is \( 50 \% \)
and third dissociation is negligible then the \( p H \) of \( 4 \times 10^{-3} M X(O H)_{3} \) is :
A. 11.78
B. 10.78
c. 2.5
D. 2.22
Subject: Chemistry
Which is true according to the Faraday
Law of electrolysis? Here \( m \) is the mass
deposited at an electrode, \( Q \) is the
charge at the electrode and \( I \) is the
current passed.
\( A \cdot m \propto I^{2} \)
в. \( m \propto Q \)
\( \mathrm{c} \cdot m \propto Q^{2} \)
D. \( m \) does not depend on \( Q \)
Subject: Chemistry
Show with balanced equations what happens when the following are mixed:
potassium permanganate interacts with manganese dioxide in the
presence of potassium hydroxide.
\( \mathbf{A} \cdot 2 K M n O_{4}+4 K O H+M n O_{2} \rightarrow 3 K_{2} M n O_{4}+2 H_{2} O \)
B. \( 3 K M n O_{4}+4 K O H+M n O_{2} \rightarrow 4 K_{2} M n O_{4}+2 H_{2} O \)
c. \( 3 K M n O_{4}+3 K O H+M n O_{2} \rightarrow 3 K_{2} M n O_{4}+2 H_{2} O \)
D. None of these
Subject: Maths
A thin rod of length \( l \) in the shape of a semicircle is pivoted at one of its ends such that it is free to oscillate in its own
plane. The frequency \( \boldsymbol{f} \) of small oscillations of the semicircular rod is :
A \( \cdot \frac{1}{2 \pi} \sqrt{\frac{g \pi}{2 l}} \)
в. \( \frac{1}{2 \pi} \sqrt{\frac{g \sqrt{\pi^{2}+4}}{2 l}} \)
c. \( \frac{1}{2 \pi} \sqrt{\frac{g \sqrt{\pi+2}}{l}} \)
D. \( \frac{1}{2 \pi} \sqrt{\frac{g \sqrt{\pi^{2}+1}}{2 \pi l}} \)
Subject: Physics
Given that \( T \) stands for time period and stands for the length of simple pendulum. If \( g \) is the acceleration due to gravity, then which of the following
statements about the relation \( \boldsymbol{T}^{2}= \)
\( (l / g) \) is correct?
A. It is correct both dimensionally as well as numerically y
B. It is neither dimensionally correct nor numerically.
c. It is dimensionally correct but not numerically.
D. It is numerically correct but not dimensionally.
Subject: Physics
A square plate of mass \( M \) and edge \( L \)
is shown in the fig. The moment of
inertia of the plate about the axis in the
plane of plate and passing through one
of its vertex making an angle \( 15^{0} \) with the horizontal is
A. \( \frac{M L^{2}}{12} \)
B. \( \frac{11 M L^{2}}{24} \)
\( c \cdot \frac{7 M L^{2}}{12} \)
D. none of these
Subject: Physics
A hollow spherical conducting shell of
inner radius \( r_{1} \) and other radius \( r_{2} \) has
a charge \( Q . A \) charge \( -q \) is placed at the centre of the sphere. The surface charge densities on the inner and outer
surfaces of the sphere will be
respectively:-
\( ^{\mathbf{A}} \cdot \frac{q}{4 \pi r_{1}^{2}} \) and \( \frac{q}{4 \pi r_{2}^{2}} \)
В \( \cdot \frac{-q}{4 \pi r_{1}^{2}} \) and \( \frac{Q+q}{4 \pi r_{2}^{2}} \)
c. \( \frac{q}{4 \pi r_{1}^{2}} \) and \( \frac{Q-q}{4 \pi r_{2}^{2}} \)
D. \( _{\text {O and }} \frac{Q-q}{4 \pi r_{2}^{2}} \)
Subject: Chemistry
Product \( (A) \) is:
Снз \( -c \equiv c- \) сн \( _{3} \) Соыа КМпо \( _{4}(t) \)
\( \mathbf{C H}_{3}-\mathbf{C H}_{2}-\mathbf{U}-\mathbf{C}-\mathbf{H} \)
\( \mathbf{C H}_{3}-\mathbf{U}-\| \)
\( \mathbf{O H} \mathbf{~ O H} \)
\( \mathbf{C H}_{3}-\mathbf{C H}-\mathbf{C H}-\mathbf{C H}_{3} \)
\( o=C H-C H \)
\( h \)
Subject: Maths
If three consecuting vertices of a
parallelogram are \( \boldsymbol{A}(\mathbf{4}, \mathbf{3}, \mathbf{5}), \boldsymbol{B}(\mathbf{0}, \mathbf{6}, \mathbf{0}), \boldsymbol{C}(-\mathbf{8}, \mathbf{1}, \mathbf{4}) \) and \( \boldsymbol{D} \)
is the fourth vertex then the anlge between \( \overline{A C} \) and \( \overline{B D} \) is
\( ^{\mathbf{A}} \cdot \cos ^{-1}\left[\frac{55}{\sqrt{149} \sqrt{161}}\right] \)
\( ^{\mathbf{B}} \cdot \cos ^{-1}\left[\frac{65}{\sqrt{149} \sqrt{161}}\right] \)
\( ^{\mathbf{c}} \cdot \cos ^{-1}\left[\frac{15}{\sqrt{149} \sqrt{161}}\right] \)
D. \( \cos ^{-1}\left[\frac{3}{\sqrt{149} \sqrt{161}}\right] \)
Subject: Physics
The radius of a coil decreases steadily
at the rate of \( 10^{2} \mathrm{m} / \mathrm{s} \). A constant and
uniform magnetic field of induction \( 10^{3} W b / m^{2} \) acts perpendicular to the plane of the coil. The radius of the coil when the induced e.m.f. in the coil is \( 1 \mu \)
\( v, \) is
\( ^{A} \cdot \frac{2}{\pi} \mathrm{cm} \)
в. \( \frac{3}{\pi} \mathrm{cm} \)
c. \( \frac{4}{\pi} \mathrm{cm} \)
D. \( \frac{5}{\pi} \mathrm{cm} \)
Subject: Physics
Match List-1 with list-2
\( \begin{array}{ll}\text { List-1 } & \text { List-2 } \\ \text { A. Emitter } & \text { E. Transistor } \\ \text { B. Base } & \text { F. Moderately doped } \\ \text { C. Collector } & \text { G. Lightly doped } \\ \text { D. Transfer of resistance } & \text { H. Heavily doped } \\ \text { I. largest physical size }\end{array} \)
A. A-F B-E C-H,I D-G
B. A-G B-F.I C-E D-H
c. A-HB-G C-F,I D-E
D. A-E B-H,I C-G D-F
Subject: Maths
The sum of \( \frac{1}{x+y} \) and \( \frac{1}{x-y} \) is
A \( \cdot \frac{2 y}{x^{2}-y^{2}} \)
в. \( \frac{2 x}{x^{2}-y^{2}} \)
c. \( \frac{2 x}{y^{2}-x^{2}} \)
D. \( -\frac{2 y}{x^{2}-y^{2}} \)
Subject: Maths
If India FDI from OPEC countries was
proportionately the same in 1992 and
1997 as the total FDI from all over the
world and if the FDI in 1992 from the
OPEC countries was Euro 2 million.
What was the amount of FDI from the
OPEC countries in \( 1997 ? \)
Trends of FDI in India
A . 1
в. 10.72
\( c \cdot 11.28 \)
D. 11.
Subject: Maths
If \( \tan ^{-1} \frac{a+x}{a}+\tan ^{-1} \frac{a-x}{a}=\frac{\pi}{6} \)
then \( x^{2}=? \)
A \( \cdot 2 \sqrt{3} a \)
an
B. \( \sqrt{3} a \)
\( c \cdot 2 \sqrt{3} a^{2} \)
\( ^{2} \)
D. None of these