AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Maths
If \( a_{1}, a_{2}, a_{3}, \dots, a_{n} \) are positive real
numbers whose product is a fixed number \( c \), then the minimum value of
\( \boldsymbol{a}_{1}+\boldsymbol{a}_{2}+\boldsymbol{a}_{3}+\ldots \ldots+\boldsymbol{a}_{n-1}+\boldsymbol{a}_{n} \) is
A \( \cdot n(c)^{1 / n} \)
B \cdot \( (n+1) c^{1 / n} \)
\( \mathbf{c} \cdot 2 n c^{1 / n} \)
D \cdot \( (n+1)(2 c)^{1 / n} \)
Subject: Maths
\( \frac{1-\frac{9}{y^{2}}}{1-\frac{3}{y}}-\frac{3}{y}, \) where \( (y \neq 0)= \)
A. \( \frac{y-3}{y} \)
в. \( \frac{y+3}{y} \)
\( c \cdot 3 \)
D.
E \( .3 y-1 \)
Subject: Physics
The resultant of two vectors acting at an
angle of \( 150^{\circ} \) is of magnitude 10 units and is perpendicular to one of the vectors. The magnitude of the other vector is :
A \( \cdot \frac{20}{\sqrt{3}} N \)
в. \( 10 \sqrt{3} \) N
\( c \cdot 20 N \)
D. \( 20 \sqrt{3} N \)
Subject: Chemistry
The acid which gives only primary phosphites and secondary phosphites is :
\( A \cdot H_{3} P O_{3} \)
в. \( \mathrm{H}_{3} \mathrm{PO}_{4} \)
\( \mathrm{c} \cdot \mathrm{HPO}_{3} \)
D. \( \mathrm{H}_{3} \mathrm{PO}_{5} \)
Subject: Chemistry
Which of the following statements
regarding sulphur dioxide is not true?
\( A \cdot S O_{2} \) is an angular molecule
B. \( S O_{2} \) may be regarded as the resonance hybrid of two canonical structures
\( \mathrm{C} \cdot S \mathrm{O}_{2} \) is an anhydride of sulphuric acid
D. \( S O_{2} \) is an anhydride of sulphurous acid
Subject: Physics
A charge \( Q \) is placed on to two opposite corner of a square. A charge q is placed at each of other two corners. Given that
resultant electric force on \( Q \) is zero,
then \( Q \) is equal to :
A \( \cdot(2 \sqrt{2}) / q \)
B . \( -q /(2 \sqrt{2}) \)
c. \( (2 \sqrt{2}) q \)
D. \( (-2 \sqrt{2}) q \)
Subject: Physics
A house is fitted with 4 lamps 60 w each, 2 fans rated 100 w each, an electric kettle rated 2KW. If the energy
\( \operatorname{costs} \) Rs. 5.50 per \( \mathrm{KWh} \), calculate the monthly bill (of 30 days) for running the appliances for 5 hours a day.
Subject: Maths
For \( \boldsymbol{x} \in \boldsymbol{R} \) let \( \boldsymbol{f}(\boldsymbol{x})=|\sin \boldsymbol{x}| \) and
\( g(x)=\int_{0}^{x} f(t) d t . \) Let \( p(x)=g(x)-\frac{2}{\pi} x \)
Then
A. \( p(x+\pi)=p(x) \) for all \( x \)
B . \( p(x+\pi) \neq p(x) \) for all least one but finitely many \( x \)
c. \( p(x+\pi) \neq p(x) \) for infinitely many \( x \)
D. \( p \) is a one-one function
Subject: Chemistry
Starting with elemental phosphorus, \( \boldsymbol{P}_{4} \)
phosphoric acid can be prepared as
shown \( \boldsymbol{P}_{4}(s)+\mathbf{5} O_{2}(\boldsymbol{g}) \longrightarrow \boldsymbol{P}_{4} \boldsymbol{O}_{10}(s) \stackrel{\boldsymbol{H}_{2} O}{\longrightarrow} \)
\( \boldsymbol{H}_{3} \boldsymbol{P} \boldsymbol{O}_{4} \)
A. True
B. False
Subject: Physics
Two particles \( A \) and \( B \) are moving as
shown in the figure. At this moment
of time, the angular speed of A with
respect to B is:
A \( \cdot \frac{v_{a}+v_{b}}{r} \)
в. \( \frac{v_{a}-v_{b}}{r} \)
\( \frac{v_{a} \sin \theta-v_{b} \sin \theta}{r} \) in anticlockwise direction
D. \( \frac{v_{a} \sin \theta+v_{b} \sin \theta}{r} \) in anticlockwise direction
Subject: Maths
For \( a, b \in R-\{0\}, \) let \( f(x)=a x^{2}+ \)
\( b x+a \) satisfies \( f\left(x+\frac{7}{4}\right)= \)
\( f\left(\frac{7}{4}-x\right) \forall x \epsilon R \)
Also the equation \( f(x)=7 x+a \) has
only one real distinct solution.
The value of \( (a+b) \) is equal to
A . 4
B. 5
c. 6
\( D \)
Subject: Maths
Let \( \Delta(x)= \)
\( \left|\begin{array}{ccc}(\boldsymbol{x}-\mathbf{2}) & (\boldsymbol{x}-\mathbf{1})^{2} & \boldsymbol{x}^{\mathbf{3}} \\ (\boldsymbol{x}-\mathbf{1}) & \boldsymbol{x}^{2} & (\boldsymbol{x}+\mathbf{1})^{3} \\ \boldsymbol{x} & (\boldsymbol{x}+\mathbf{1})^{2} & (\boldsymbol{x}+\mathbf{2})^{3}\end{array}\right| \) Then the
coefficient of \( x \) in \( \Delta(x) \) is \( -k . \) Find \( k \)
\( A \cdot-1 \)
B. 2
\( c \cdot-2 \)
\( D \)
Subject: Physics
In \( 1 g \) of a solid, there are \( 5 \times 10^{21} \)
atoms. If one electron is removed from
energy of \( 0.01 \% \) atoms of the solid, the charge gained by the solid is :
(electronic charge is \( \left.1.6 \times 10^{19} C\right) \)
\( \mathbf{A} \cdot+0.08 C \)
B. \( +0.8 C \)
\( c .-0.08 C \)
D. \( -0.8 C \)
Subject: Physics
The moment of inertia of a uniform
semi circular disc about an axis
passing through its centre of mass and perpendicular to its plane is (Mass of this disc is \( M \) and radius is \( R \) )
\( ^{\mathbf{A}} \cdot \frac{M R^{2}}{2}+M\left(\frac{4 R}{3 \pi}\right)^{2} \)
\( ^{\text {В }} \cdot \frac{M R^{2}}{2}-M\left(\frac{4 R}{3 \pi}\right)^{2} \)
\( ^{\mathrm{c}} \cdot \frac{M R^{2}}{2}-M\left(\frac{2 R}{\pi}\right)^{2} \)
\( ^{\mathrm{D}} \cdot \frac{M R^{2}}{2}+M\left(\frac{2 R}{\pi}\right)^{2} \)
Subject: Maths
For a collection of data, if \( \sum x= \)
\( \mathbf{3 5}, \boldsymbol{n}=\mathbf{5}, \sum(\boldsymbol{x}-\mathbf{9})^{2}=\mathbf{8 2}, \) then find
\( \sum x^{2} \) and \( \sum(x-\bar{x})^{2} \)
Subject: Biology
Find the correct match
\( A \)
\( A-3, B-6, C-2, D-5, E-4 \)
, E -
B. \( A-5, B-2, C-3, D-6 \)
\( C \cdot A-3, B-1, C-2, D-5, E-4 \)
D. \( A-4, B-6, C-5, D-2 \)
Subject: Physics
A crane pulls up a car of mass \( 500 \mathrm{kg} \) to a vertical height of \( 4 m . \) So, work done by
the crane is:
A. \( 19.6 J \)
в. \( 19.6 k J \)
c. \( 19600 k J \)
D. \( 4900 J \)
Subject: Chemistry
Which set contains no ionic species?
A. \( N H_{4} C l, O F_{2}, H_{2} S \)
в. \( C O_{2}, C C l_{4}, C l_{2} \)
c. \( B F_{3}, A l F_{3}, T l F_{3} \)
D. \( I_{2}, C a O, C H_{3} C l \)
Subject: Maths
Find the nature of the roots of the
following quadratic equations. If the real roots exist, find them:
(i) \( 2 x^{2}-3 x+5=0 \)
(ii) \( 3 x^{2}-4 \sqrt{3} x+4=0 \)
(iii) \( 2 x^{2}-6 x+3=0 \)
Subject: Physics
Determine the electric potential at point P due to two point charges each of charge \( +Q, \) with one point charge being at a distance \( \mathrm{R} \) and the other being at a distance \( 2 R \)
\( A \)
\[
\frac{3 Q}{8 \pi_{6} R}
\]
в.
\[
\frac{2 Q}{12 \pi \epsilon_{0} R}
\]
\( c \)
\[
\frac{3 Q}{12 \pi \epsilon_{0} R}
\]
D.
\[
\frac{2 Q}{8 \pi \epsilon_{0} R}
\]
Subject: Chemistry
The work done in adiabatic
compression of 2 mole of an ideal monoatomic gas by constant external
pressure of 2 atm starting from initia pressure of 1 atm and initial
temperature of \( 300 K(R=2 \mathrm{cal} / \mathrm{mol}- \)
degree celsius) is :
A . 360 cal
B. 720 call
c. 800 cal
D. 1000 call
Subject: Maths
\( \lim _{x \rightarrow 0}\left(x^{-3} \sin 3 x+a x^{-2}+b\right) \) exists and
is equal to \( 0, \) then
A \( \cdot a=-3 \) and \( b=\frac{9}{2} \)
B. \( a=3 \) and \( b=\frac{9}{2} \)
c. \( _{a=-3 \text { and } b=-\frac{9}{2}} \)
D. \( a=3 \) and \( b=-\frac{9}{2} \)
Subject: Chemistry
Assertion
Pb \( C l_{2} \) is more stable than \( P b C l_{4} \)
Reason

PbCl \( _{4} \) is powerful oxidising agent.
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
The minimum integral value of the sum of real numbers \( x^{11}, x^{3}, x^{7}, 1,4 x^{-5} \) and
\( x^{-1}, \) where \( x \) can take only those values for which \( f(x)=\ln (x) \) is well defined is
\( \mathbf{A} \cdot \mathbf{8} \)
B. 9
c. 10
D. 11
Subject: Maths
In the given figure \( A B \| C D . \) Find \( x+y \) if
all measurements are indicated in
centimeter.
A. \( 4.5 \mathrm{cm} \)
B. 7.5 \( \mathrm{cm} \)
\( c .6 .5 \mathrm{cm} \)
D. \( 2.75 \mathrm{cm} \)
Subject: Physics
A frame made of metallic wire
enclosing a surface area \( A \) is covered with a soap film. If the area of the frame of metallic wire is reduced by \( 50 \% \), the energy of the soap film will be changed by
A. \( 100 \% \)
B. \( 75 \% \)
\( c .50 \% \)
D. \( 25 \% \)
Subject: Chemistry
\( 0.25 M \) solution of pyridium chloride
\( C_{5} H_{6} N^{+} C l^{-} \) was found to have a \( p H \)
of \( 2.699 . \) What is \( p K_{b} \) for pyridine,
\( \boldsymbol{C}_{\mathbf{5}} \boldsymbol{H}_{\mathbf{5}} \boldsymbol{N} ? \)
Subject: Physics
How may sub-atomic particles are present in an a-particles used in Rutherford's scattering experiment?
A. No. of Protons - 4
No. of Neutrons - 0,
No. of Electrons - 0
B. No. of Protons - 2.
No. of Neutrons - 0,
No. of Electrons - 2
c. No. of Protons - 2 ,
No. of Neutrons - 2,
No. of Electrons - 0
D. No. of Protons - 2
No. of Neutrons - 2,
No. of Electrons -
Subject: Chemistry
For the equilibrium \( S O_{2} C l_{2}(g) \rightleftharpoons \)
\( \boldsymbol{S} \boldsymbol{O}_{2}(\boldsymbol{g})+\boldsymbol{C l}_{2}(\boldsymbol{g}), \) what is the
temperature at which \( \frac{\boldsymbol{K}_{\boldsymbol{p}}(\boldsymbol{a} \boldsymbol{t m})}{\boldsymbol{K}_{c}(\boldsymbol{M})}=\mathbf{3} ? \)
в. \( 0.36 K \)
c. 36.54
D. 273 K
Subject: Physics
Assertion
When a bus starts suddenly, a person standing in it falls backwards.
Reason
It is due to inertia of rest.
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
Identify the equations involved in
bleaching action of \( \boldsymbol{S O}_{2} \)
A. \( S O_{2}+H_{2} O \rightarrow H_{2} S O_{3} \)
в. \( S O_{2}+O_{2} \rightarrow S O_{3} \)
c. \( S O_{2}+2 H_{2} O \rightarrow H_{2} S O_{4}+2[H] \)
D. \( S O_{3}+H_{2} O \rightarrow H_{2} S O_{4} \)
Subject: Physics
A wave of angular frequency \( \omega \) propagates so that a certain phase of oscillation moves along x-axis, y-axis
and z-axis with speeds \( c_{1}, c_{2} \) and \( c_{3} \)
respectively. The propagation constant \( \boldsymbol{k} \) is
A \( \cdot \frac{\omega}{\sqrt{c_{1}^{2}+c_{2}^{2}+c_{3}^{2}}}(\hat{i}+\hat{j}+\hat{k}) \)
B. \( \frac{\omega_{\hat{i}}}{c_{1}}+\frac{\omega_{\hat{\jmath}}}{c_{2}}+\frac{\omega}{c_{3}} \hat{k} \)
c. \( (\omega \hat{i}+\omega \hat{j}+\omega \hat{k}) \frac{1}{c} \)
D. \( \frac{\omega}{\left(c_{1}+c_{2}+c_{3}\right)}(\hat{i}+\hat{j}+\hat{k}) \)
Subject: Physics
Two north poles of pole strengths \( 4 A- \)
\( m \) and \( 16 A-m \) are separated by a
distance of \( 20 \mathrm{cm} . \) The position of the neutral point from \( 4 A-m \) pole is :
\( \mathbf{A} \cdot 20 \mathrm{cm} \)
B. \( 18 \mathrm{cm} \)
c. \( 10 \mathrm{cm} \)
D. \( 6.67 \mathrm{cm} \)
Subject: Chemistry
In a hydrogen atom, the electronjumps from 3 to 2 energy level, the energy released is:
A \( \cdot 3.03 \times 10^{-19} \) Jatom \( ^{-1} \)
В. \( 1.03 \times 10^{-19} \) Jatom\( ^{-1} \)
c. \( 3.03 \times 10^{-18} \) Jatom \( ^{-1} \)
D. \( 6.06 \times 10^{-19} \) Jatom \( ^{-1} \)
Subject: Maths
Two probability distributions of the discrete random variable \( X \) and \( Y \) are
given below.
\( \boldsymbol{X} \quad \mathbf{0} \) 3 \( \mathbf{2} \)
\( P(X) \quad \frac{1}{5} \quad \frac{2}{5} \quad \frac{1}{5} \quad \frac{1}{5} \)
\[
\begin{array}{ccccc}
\boldsymbol{Y} & \mathbf{0} & \mathbf{1} & \mathbf{2} & \mathbf{3} \\
P(Y) & \frac{1}{5} & \frac{3}{10} & \frac{2}{5} & \frac{1}{10}
\end{array}
\]
Then
A.
\[
E\left(Y^{2}\right)=2 E(X)
\]
B.
\[
E\left(Y^{2}\right)=E(X)
\]
\( \mathbf{c} \cdot E(Y)=E(X) \)
\( D \)
\[
E\left(X^{2}\right)=2 E(Y)
\]
Subject: Maths
\( f x, Y, z \) are the three sums of money such that \( Y \) is a simple interest on \( x \) and \( z \) is a simple interest on \( Y \) for same time and rate, then
\( \mathbf{A} \cdot X^{2}=Y Z \)
B . \( Y^{2}=Z X \)
\( \mathbf{c} \cdot Z^{2}=X Y \)
D. \( X Y Z=1 \)
Subject: Physics
A stone is dropped from the \( 16^{t h} \) storey
of a multi-storeyed building and it
reaches the ground in 4 s. In the first second, it passes through how many
storeys of the building \( \left(\boldsymbol{g}=\mathbf{1 0 m s}^{-2}\right) \) ?
\( \mathbf{A} \cdot \mathbf{1} \)
B. 2
\( c \cdot 3 \)
D. None
Subject: Maths
Let then \( \boldsymbol{f}(\boldsymbol{x})= \)
\( (x-4)(x-5)(x-6)(x-7) \) then
A \( \cdot f^{\prime}(x)=0 \) has four real roots
\( \mathbf{B} \cdot \) three roots of \( f^{\prime}(x)=0 \) lie in (4,5)\( \cup(5,6) \cup(6,7) \)
C \( \cdot \) the euation \( f^{\prime}(x)= \) has only two roots \( >d \). three roots
of \( f^{\prime}(x)=0(3,4) \cup(4,5) \cup(5,6) \)
D. three roots of \( f^{\prime}(x)=0(3,4) \cup(4,5) \cup(5,6) \)
Subject: Maths
Evaluate \( \int x^{2} \log x d x \)
A. \( \frac{x^{2}}{2} \log x-\frac{1}{9} x^{2}+c \)
B \( \cdot \frac{x^{3}}{3} \log x-\frac{1}{9} x^{2}+c \)
c. \( \frac{x^{3}}{3} \log x-\frac{1}{9} x^{3}+c \)
D. \( \frac{x^{3}}{3} \log x+\frac{1}{9} x^{3}+c \)
Subject: Physics
Two small particles of equal masses
start moving in opposite directions
from a point \( A \) in a horizontal circular
orbit. Their tangential velocities are \( \boldsymbol{v} \)
and \( 2 v \) respectively, as shown in the
figure. Between collisions, the particles
move with constant speeds. After making how many elastic collisions, other than that at \( A \), these two
particles will again reach the point \( A \) ?
A . 4
B. 3
\( c \cdot 2 \)
D.
Subject: Chemistry
Q Type your question-
\( s p^{2} \) hybridized carbon atom of an aromatic ring. It is more acidic than an alcohol, but less acidic than
a carboxylic acid. It is even less acidic
than carbonic acid but more acidic
than water. Thus, phenol is unable to
protonate \( H C O_{3}^{-} \) anion but easily
protonates \( \boldsymbol{O H}^{-} \) anion. The \( \boldsymbol{O H}^{-} \) group activates the benzene ring so much that electrophilic substitution takes place readily.
The correct order of acidity of the
following substituted phenols is:
A \( . I>I I>I I I>I V \)
в. \( I>I I I>I V>I I \)
с. \( I>I I>I V>I I I \)
I I \( I>I I I>I I>I V \)
\( V \)
Subject: Maths
Points \( X \) and \( Y \) are taken on the sides
QR and RS, respectively of a parallelogram PQRS, so that \( Q X=4 X R \) sand \( \mathrm{RY}=4 \mathrm{YS} \). The line \( \mathrm{XY} \) cuts the line
PR at Z. Find the ratio PZ:ZR.
\( \mathbf{A} \cdot 4: 21 \)
в. 3: 4
c. 21: 4
D. 4: 3
Subject: Chemistry
In which of the following \( K_{p} \) is less than
\( \boldsymbol{K}_{c} ? \)
A \( \cdot N_{2} O_{4}(g) \rightleftharpoons 2 N O_{2}(g) \)
B . \( 2 H I(g) \rightleftharpoons H_{2}(g)+I_{2}(g) \)
c. \( 2 S O_{2}(g)+O_{2}(g) \rightleftharpoons 2 S O_{3}(g) \)
D. \( P C l_{5}(g) \rightleftharpoons P C l_{3}(g)+C l_{2}(g) \)
Subject: Physics
The angle between \( \vec{P}+\vec{Q} \) and \( \vec{P}-\vec{Q} \)
will be:
A. \( 90^{\circ} \) only
B. between \( 0^{\circ} \) and \( 180^{\circ} \)
c. \( 180^{\circ} \) only
D. None of these
Subject: Physics
A circular metal plate of radius \( \boldsymbol{R} \) is rotating with a uniform angular velocity \( \omega \) with its plane perpendicular to a uniform magnetic field \( B \). Then the emf developed between the centre and the
rim of the plate is
A \( \cdot \pi \omega B R^{2} \)
B. \( \omega B R^{2} \)
\( \mathbf{c} \cdot \pi \omega B R^{2} / 2 \)
D. \( \omega B R^{2} / 2 \)
Subject: Maths
Calculate the values of the
determinants:
\( \left|\begin{array}{ccc}\boldsymbol{b}+\boldsymbol{c} & \boldsymbol{a} & \boldsymbol{a} \\ \boldsymbol{b} & \boldsymbol{c}+\boldsymbol{a} & \boldsymbol{b} \\ \boldsymbol{c} & \boldsymbol{c} & \boldsymbol{a}+\boldsymbol{b}\end{array}\right| \)
Subject: Chemistry
Which of the following reaction is used
to make a fuel cell?
\( \mathbf{A} \cdot C d(s)+2 N i(O H)_{3}(s)+H_{2} O(l) \longrightarrow C d O(s)+ \)
\[
2 N i(O H)_{3}(s)+H_{2}(g)
\]
B \( .2 \mathrm{Fe}(s)+\mathrm{O}_{2}(g)+4 H^{+}(a q) \longrightarrow 2 \mathrm{Fe}^{2+}(a q)+2 \mathrm{H}_{2} \mathrm{O}(l) \)
\( \mathbf{c} \cdot P b(s)+P b O_{2}(g)+2 H_{2} S O_{4}(a q) \longrightarrow 2 P b S O_{4}(s)+ \)
\( 2 H_{2} O(l) \)
D. \( 2 H_{2}(g)+O_{2}(g) \longrightarrow 2 H_{2} O(l) \)
Subject: Maths
\( i \log \left(\frac{x-i}{x+i}\right) \) is equal to
\( \mathbf{A} \cdot 2 i \log (x-i)-i \log \left(x^{2}+1\right) \)
B. \( 2 i \log (x-i)+i \log \left(x^{2}+1\right) \)
\( \mathbf{c} \cdot 2 i \log (x+i)-3 i \log \left(x^{2}+1\right) \)
D. \( 2 i \log (x-i)-i \log \left(x^{2}+i\right) \)
Subject: Physics
The accuracy in the measurement of the diameter of hydrogen atom measured as \( 1.06 \times 10^{-10} \mathrm{m} \) is :
A .0 .01
В. \( 106 \times 10^{-10} \)
c. \( \frac{1}{106} \)
D. \( 0.01 \times 10^{-10} \)
Subject: Physics
A concave spherical surface of radius of
curvature \( 10 \mathrm{cm} \) separates two
medium \( \boldsymbol{x} \) \& \( \boldsymbol{y} \) of refractive index \( 4 / 3 \& \)
\( 3 / 2 \) respectively. If the object is placed
along principal axis in medium \( X \) then:
A. image is always real
B. image is real if the object distance is greater than 90 \( \mathrm{cm} \)
C. image is always virtual
D. image is virtual if the object distance is less than 90 \( \mathrm{cm} \)
Subject: Physics
What does a neutron decays to?
\( \mathbf{A} \cdot \) one \( p, \) one \( v \) one \( \beta^{+} \)
B. one \( \beta+, \) one \( \beta- \) and \( v \)
C . one \( p \), one \( \beta^{-} \) and one \( \bar{v} \)
D. all the above
Subject: Biology
Assertion
Deforestation is one main factor
contributing to global warming.
Reason
Besides \( C O_{2}, \) two other gases, methane and CFCs, are also included under green
house gases.
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
\( A B C D \) is a parallelogram of area
162 sq.cm. \( P \) is a point on \( A B \) such
that \( \boldsymbol{A P}: \boldsymbol{P B}=\mathbf{1}: \mathbf{2} \)
Calculate the ratio \( \boldsymbol{P} \boldsymbol{A}: \boldsymbol{D} \boldsymbol{C} \)
A . 1: 3
B. 3: 1
\( c .3: 2 \)
D. 2: 3
Subject: Maths
If \( \vec{a}=\hat{i}+\hat{j}+2 \hat{k} \) and \( \vec{b}=3 \hat{i}+2 \hat{j}-\hat{k} \)
find the value of \( (\vec{a}+3 \vec{b}) \cdot(2 \vec{a}-\vec{b}) \)
Subject: Maths
Let \( \boldsymbol{f}(\boldsymbol{x})=\frac{2}{\pi} \operatorname{cosec}^{-1} \frac{x+1}{2} \) Then
\( \mathbf{A} \cdot \lim _{x \rightarrow 1^{+}} f(x)=0 \)
\( \mathbf{B} \cdot \lim _{x \rightarrow 1} f(x)=\frac{\pi}{2} \)
\( \mathbf{C} \cdot \lim _{x \rightarrow-3^{-}} f(x)=-1 \)
\( \mathbf{D} \cdot \lim _{x \rightarrow-3} f(x)=1 \)
E \( \cdot \lim _{x \rightarrow-3} f(x)=-\frac{\pi}{2} \)
Subject: Physics
Assertion
The temperature coefficient of resistance is always positive.
Reason
On increasing the temperature the resistance of metals and alloys
increase.
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
Prove the following by using the principle of mathematical induction for
all \( \boldsymbol{n} \in \boldsymbol{N}: \frac{\mathbf{1}}{\mathbf{2 . 5}}+\frac{\mathbf{1}}{\mathbf{5 . 8}}+\frac{\mathbf{1}}{\mathbf{8 . 1 1}}+\dots \dots+ \)
\( \frac{1}{(3 n-1)(3 n+2)}=\frac{n}{(6 n+4)} \)
Subject: Chemistry
The correct combination is:
\( \mathbf{A} \cdot\left[N i(C N)_{4}\right]^{2-} \) -tetrahedral; \( \left[N i(C O)_{4}\right] \) -paramagnetic
B. \( \left[N i C l_{4}\right]^{2-} \) -paramagnetic; \( \left[N i(C O)_{4}\right] \) -tetrahedral
\( \mathbf{c} \cdot\left[N i C l_{4}\right]^{2-} \) -diamagnetic; \( \left[N i(C O)_{4}\right] \) -square-planar
D. \( \left[N i C l_{4}\right]^{2-} \) -square-planar; \( \left[N i(C N)_{4}\right]^{2-} \) -paramagnetic
Subject: Physics
The ratio of magnetic dipole moment of
an electron of charge \( e \) and mass \( m \) in Bohr's orbit in hydrogen atom to its
angular momentum is
A \( \cdot \frac{e}{m} \)
B. \( \frac{m}{e} \)
c. \( \frac{2 m}{e} \)
D. \( \frac{e}{2 m} \)
Subject: Biology
Assertion
Prothrombin is essential for blood
clotting
Reason
Prothrombin is synthesised in the liver
in the presence of \( C a^{++} \)
A. Both statements 1 and 2 are correct
B. Statement 1 is correct but statement 2 is incorrect
c. statement 1 is incorrect but statement 2 is correct
D. Both statements 1 and 2 are incorrect
Subject: Chemistry
In aqueous solutions, amino acids mostly exist as:
A \( . N H_{2}-C H R-C O O H \)
в. \( N H_{2}-C H R-C O O^{-} \)
c. \( _{N H_{3} C H R C O O H}^{+} \).
D. \( H_{3} \stackrel{+}{N C H R C O O} \)
Subject: Physics
Two trains start a distance of \( 2000 m \)
apart. Train one is moving with a constant speed of \( 30 m / s \) directly
towards train 2 which starts from rest
and accelerates with a constant acceleration of \( 5 m / s^{2} \) directly towards train 1. When do the trains meet?
\( \mathbf{A} \cdot 22.9 s \)
в. \( 34.9 s \)
\( c .30 s \)
D. \( 40 s \)
Subject: Chemistry
The correct IUPAC name of the alkyl
group, \( \begin{array}{cc}c_{2} H_{5} & c_{2} H_{5} \\ C H_{3}-C H-C H_{2}-C H^{\prime}-C H_{3} & \end{array} \)
A. 2-ethyl-3-sec-butyl propyl
B. 2,4-diethyl pentane
c. 2-ethyl-4-methylhexyl
D. 2-methyl-4-ethylexyl
Subject: Maths
Let \( l \) be the length of each equal side of
an isosceles triangle. If the length of each equal side is doubled, keeping its height unchanged, then the difference of the squares of bases of the new triangle and the given triangle is
\( \mathbf{A} \cdot \mathbf{0} \)
B. \( 4 l^{2} \)
\( \mathrm{c} \cdot 9 l^{2} \)
D. \( 12 l^{2} \)
Subject: Chemistry
What is an example of a single replacement reaction?
A. \( A+X \rightarrow A X \)
в. \( A X \rightarrow A+X \)
c. \( A+B X \rightarrow A X+B \)
D. \( A X+B Y \rightarrow A Y+B X \)
E . \( A+X \rightarrow B+Y \)
Subject: Chemistry
The percentage degree of hydrolysis of a salt of weak acid \( (\boldsymbol{H} \boldsymbol{A}) \) and weak base \( (B O H) \) in its \( 0.1 ~ M \) solution is found
to be \( 10 \% \). If the molarity of the solution is \( 0.05 M, \) the percentage hydrolysis of
the salt should be:
A . \( 5 \% \)
B. \( 10 \% \)
\( c \cdot 20 \% \)
D. none of the above
Subject: Physics
A sinusoidal wave of frequency \( 500 H z \)
has a speed of \( 350 m / s \). The phase difference between two displacements at a certain point at times 1 ms apart is
A \( \cdot \frac{\Pi}{4} \)
в. \( \frac{\text { П }}{2} \)
\( c . \Pi \)
D. \( \frac{3 \Pi}{2} \)
Subject: Maths
\( \lim _{x \rightarrow 0} \frac{1-\cos \left(x^{2}\right)}{x^{3}\left(4^{x}-1\right)} \) is equal to
This question has multiple correct options
A \( \frac{1}{4 \log 2} \)
B. \( \frac{1}{2 \log 4} \)
\( \mathbf{c} \cdot \log 4 \)
D \( \quad 1-\frac{1}{2} \log \left(\frac{e^{2}}{4}\right) \)
Subject: Chemistry
Assertion
Carbon shows tetravalency in all hydrocarbons.
Reason
Carbon shares its four valence electrons
with other atoms and forms four single covalent bonds to get nearest noble gas
formation.
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
Which of the following is not changed for the observations
\( \mathbf{3 1}, \mathbf{4 8}, \mathbf{5 0}, \mathbf{6 0}, \mathbf{2 5}, \mathbf{8}, \mathbf{3 x}, \mathbf{2 6}, \mathbf{3 2} ? \) (where \( \boldsymbol{x} \)
lies between \( 10 \text { and } 15) \)
A . A.M
B. Range
c. Median
D. Q.D
Subject: Biology
Assertion
The driving force for passive absorption is non metabolic in origin.
Reason
The driving force for active absorption is energy derived from metabolic
processes.
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
Evaluate: \( \int \frac{\cos x-\sin x}{1+\sin 2 x} d x \)
A \( \cdot \frac{1}{\sin x+\cos x}+C \)
в. \( -\frac{1}{\sin x+\cos x}+C \)
c. \( \frac{2}{\sin 2 x+\cos x}+C \)
D. \( -\frac{2}{\sin 2 x+\cos x}+C \)