AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Chemistry
Statement I: Aniline on reaction with
\( \mathrm{NaNO}_{2} / \mathrm{HCl} \) at \( 0^{\circ} \mathrm{C} \) followed by
coupling with \( \beta \) -naphthol gives a dark blue coloured precipitate. Statement II: The colour of the
compound formed in the reaction of
aniline with \( \mathrm{NaNO}_{2} / \mathrm{HCl} \) at \( 0^{\circ} \mathrm{C} \)
followed by coupling with \( \beta \) -naphthol.
A. Statement I and statement II are true and statement is the correct explanation of statement
B. Statement I and statement II are true and state is not the correct explanation of statement
c. statementl is true and the statement ll is false
D. statement I is false and the statement II is true
Subject: Chemistry
Dalton's atomic theory successfully explained:
(i) Law of conservation of mass
(ii) Law of constant composition
(iii) Law of radioactivity
(iv) Law of multiple proportions
A. (i), (ii) and (iii)
B. (i), (iii) and (iv)
c. (ii), (iii) and (iv)
D. (i), (ii) and (iv)
Subject: Maths
If \( f(x) \) is a differentiable function in the
interval \( (0, \infty) \) such that \( f(1)= \) 1 \( \operatorname{and} \lim _{t \rightarrow x} \frac{t^{2} f(x)-x^{2} f(t)}{t-x}=1, \) for eacch
\( \boldsymbol{x}>0, \) then \( \boldsymbol{f}(\mathbf{3} / 2) \) is equal to:
\( \mathbf{A} \cdot \frac{13}{6} \)
B . \( \frac{23}{18} \)
c. \( \frac{25}{9} \)
D. \( \frac{31}{18} \)
Subject: Physics
What is the de-broglie wavelength for the electron of third class of hydrogen?
\( \mathbf{A} \cdot 9.96 \times 10^{-10} \mathrm{cm} \)
В. \( 9.96 \times 10^{-8} \mathrm{cm} \)
\( \mathbf{c} .9 .96 \times 10^{4} \mathrm{cm} \)
D. \( 9.96 \times 10^{8} \mathrm{cm} \)
Subject: Maths
If \( m \& M \) denotes the minimum and
maximum value of \( |2 z+1| \) where \( \mid z- \)
\( \mathbf{2} i \mid \leq \mathbf{1} \) then \( (\boldsymbol{m}+\boldsymbol{M})^{2} \) is equal to
A . 17
B. 34
c. 51
D. 68
Subject: Maths
If \( \tan \theta_{1}=k \cot \theta_{2}, \) then \( \frac{\cos \left(\theta_{1}+\theta_{2}\right)}{\cos \left(\theta_{1}-\theta_{2}\right)}= \)
A. \( \frac{1+k}{1-k} \)
B \( \cdot \frac{1-k}{1+k} \)
c. \( \frac{k+1}{k-1} \)
D. \( \frac{k-1}{k+1} \)
Subject: Maths
If \( y=\sqrt{\frac{\sec x-1}{\sec x+1}} \) then \( \frac{d y}{d x}= \)
A. \( \frac{1}{2} \sec ^{2} \frac{x}{2} \)
B. \( \sec ^{2} \frac{x}{2} \)
c. \( \frac{1}{2} \tan \frac{x}{2} \)
D. \( \tan \frac{x}{2} \)
Subject: Maths
Two types of boxes \( A, B \) are to be
placed in a truck having capacity of 10
tons. When 150 boxes of type \( A \) and 100 boxes of type \( B \) are loaded in the truck, it weighs 10 tons. But when 260 boxes
of type \( A \) are loaded in the truck, it can
still accommodate 40 boxes of type \( B \)
so that it is fully loaded. Find the weight of each type of box.
Subject: Maths
Which of the following expressions is the simplified form of the given
expression, given that \( m \) and \( n \) are positive? \( \sqrt{9 m^{5} n^{2}-m^{4} n^{2}} \)
A. \( 3 \sqrt{m} \)
в. \( 3 m n \)
c. \( 3 n \sqrt{m} \)
D. \( m^{2} n \sqrt{9 m-1} \)
Subject: Maths
Let \( \vec{a}=\hat{i}+\hat{j}+\hat{k}, \vec{b}=\hat{i}+3 \hat{j}+5 \hat{k} \) and
\( \vec{c}=7 \hat{i}+9 \hat{j}+11 \hat{k} . \) Then the area of the
parallelogram with diagonals \( \vec{a}+\vec{b} \) and \( \vec{b}+\vec{c} \) is
A \( .4 \sqrt{6} \)
в. \( \frac{1}{2} \sqrt{21} \)
c. \( \frac{\sqrt{6}}{2} \)
D. \( \sqrt{6} \)
E \( \cdot \frac{1}{\sqrt{6}} \)
Subject: Physics
A block of mass \( m_{1} \) is resting on a
rough horizontal plane, coefficient of kinetic friction between block and
surface is \( \mu . \) If \( m_{1} \) is connected to
another mass \( m_{2} \) with the help of string
and pulley as shown in figure, then the common acceleration when the system
is released from rest will be:
A \( \cdot \frac{m_{2} g}{m_{1}+m_{2}} \)
B. \( \left[\frac{m_{2}-m_{1}}{m_{1}+\mu m_{2}}\right] g \)
C. \( \frac{\mu\left(m_{2}+m_{1}\right)}{m_{1}+m_{2}} g \)
\( \mathbf{D} \cdot\left[\begin{array}{l}\frac{m_{2}-\mu m_{1}}{m_{1}+m_{2}} \\ g\end{array}\right] \)
Subject: Maths
If \( 2 \tan h^{-1} x=\log y, \) then the value of \( y \)
in the terms of \( x \) is
A \( .2 x \)
в. \( \frac{2 x}{1-x^{2}} \)
c. \( x^{2} \)
D. \( \left(\frac{1+x}{1-x}\right) \)
Subject: Physics
A particle moves along a parabolic path \( \boldsymbol{x}=\boldsymbol{y}^{2}+\boldsymbol{y}+1 \) in such a way that the \( y \)
component of the velocity vector remain \( 4 m s^{-1} \) during the motion. The magnitude of the acceleration of the prtile is
\( \mathbf{A} \cdot 4 m s^{-2} \)
B \( \cdot m s^{-2} \)
\( \mathrm{c} \cdot 32 m s^{-2} \)
D. \( 50 m s^{2} \)
Subject: Physics
A mass of \( \mathrm{M} \) kg is suspended by a weightless string. The horizontal force required to displace it until the string
makes an angle of \( 45^{\circ} \) with the initial vertical is :
A. \( \mathrm{Mg}(\sqrt{2}-1) \)
B. \( \mathrm{Mg}(\sqrt{2}+1) \)
c. \( \mathrm{Mg} \sqrt{2} \)
D. \( \frac{\mathrm{Mg}}{\sqrt{2}} \)
Subject: Chemistry
Which of the following statements is/are correct? \( \boldsymbol{C S}_{2}+\boldsymbol{3 C l}_{2} \stackrel{\boldsymbol{\Delta}}{\longrightarrow} \boldsymbol{C C l}_{4}+\boldsymbol{S}_{2} \boldsymbol{C l}_{2} \)
1.0 \( g \) of \( C S_{2} \) and 2.0 g of \( C l_{2} \) reacts. This question has multiple correct options
A \( \cdot 0.714 \mathrm{g} C S_{2} \) is used in the reaction
B. \( 0.286 \mathrm{g} \mathrm{CS}_{2} \) is in excess.
c. \( 1.45 \mathrm{g} \) of \( C C l_{4} \) is formed.
D. \( 0.8 \mathrm{g} / \mathrm{Cl}_{2} \) is in excess.
Subject: Maths
Given that \( r=0.4 \sum(x-\bar{x})(y-\bar{y})= \)
\( \mathbf{1 0 8}, \boldsymbol{\sigma}_{\boldsymbol{y}}=\mathbf{3} \) and \( \sum(\boldsymbol{x}-\overline{\boldsymbol{x}})^{2}=\mathbf{9 0 0} . \) Find
the number of pairs of observations.
Subject: Maths
A plane passes through (1,-2,1) and is
perpendicular to two planes \( 2 x-2 y+ \)
\( z=0 \) and \( x-y+2 z=4 . \) The distance
of the plane from the point is (1,2,2)
\( A \cdot 0 \)
B.
\( c \cdot \sqrt{2} \)
D. \( 2 \sqrt{2} \)
Subject: Physics
Two motorcycles \( M_{1} \) and \( M_{2} \) are heading towards each other with a speed of \( 30 k m h^{-1} \) each. A bird flies off
\( M_{1} \) at \( 60 k m h^{-1} \) when distance
between the motorcycles is \( 60 k m \). It
heads towards \( M_{2} \) and then back to \( M_{1} \)
and so on. The total distance the bird
moves till the motorcycles meet is
\( A \cdot 60 k m \)
в. \( 40 \mathrm{km} \)
\( c .50 k m \)
D. 30 km
E. non
Subject: Maths
"If Deb and Sam go to the mall then it is
snowing" Which statement below is logically equivalent?
A. If Deb and Sam do not go to the mall then it is not snowing
B. If Deb and Sam do not go to the mall them it is snowing
C. If it is snowing then Deb and Sam go to the mall
D. If it is not snowing then Deb and Sam do not go to the mal
Subject: Physics
A particle at \( x=0 \) and \( t=0 \) starts
moving along +ve X-direction with velocity v then x varies with time as?
\( \mathbf{A} \cdot \mathbf{t} \)
в. \( t^{3} \)
\( c \cdot t^{2} \)
D. \( t^{1 / 2} \)
Subject: Physics
A force \( \boldsymbol{F}=(\mathbf{1 0}+\mathbf{0 . 5} \boldsymbol{x}) \boldsymbol{N} \) acts on a
particle in \( X \) direction, where \( x \) is in meters. Find the work done by this force during a displacement from \( \boldsymbol{x}=\mathbf{0} \) to
\( \boldsymbol{x}=\mathbf{2} \)
Subject: Maths
If \( x \) is real, \( x+\frac{1}{x} \neq 0 \) and \( x^{3}+\frac{1}{x^{3}}=0 \)
then the value of \( \left(\boldsymbol{x}+\frac{\mathbf{1}}{\boldsymbol{x}}\right)^{\mathbf{4}} \) is
\( \mathbf{A} \cdot \mathbf{4} \)
B. 9
c. 16
D. 25
Subject: Maths
Two sides of a rhombus are along the
lines, \( \boldsymbol{x}-\boldsymbol{y}+\mathbf{1}=\mathbf{0} \) and \( \mathbf{7} \boldsymbol{x}-\boldsymbol{y}-\mathbf{5}= \)
0. If its diagonals intersect at (-1,-2)
then which one of the following is a
vertex of this rhombus??
\( ^{\mathrm{A}} \cdot\left(-\frac{10}{3},-\frac{7}{3}\right) \)
в. (-3,-9)
c. (-3,-8)
D. \( \left(\frac{1}{3},-\frac{8}{3}\right) \)
Subject: Physics
Assertion
The equation \( V=R i \). does not apply to
those conducting devices which do not obey Ohm's law.
Reason
\( V=R i \) is a statement of Ohm's law.
A. Both Assertion and Reason are correct and Reason is the correct explanation of Assertion
B. Both Assertion and Reason are correct, but Reason is not the correct explanation of Assertion
c. Assertion is correct but Reason is incorrect
D. Assertion is incorrect but Reason is correct
Subject: Chemistry
The correct sequence of match for List-
from List-II is:
\( \begin{array}{ll}\text { List-I } & \text { List-II } \\ A) \mathrm{O}_{2} & 1 \text { ) Monoatomic } \\ B \text { Po } & 2 \text { ) Bent molecule } \\ C / \mathrm{S}_{8} & \text { 3) Paramagnetic } \\ D) \mathrm{O}_{3} & \text { 4) Puckered ring }\end{array} \)
B. A-3, B-1, C-4, D-2
c. \( A-4, B-2, C-3, D-1 \)
D. A-2, B-4, C-1, D-3
Subject: Chemistry
In the equilibrium
\( \boldsymbol{C H}_{3} \boldsymbol{C O O H}+\boldsymbol{H} \boldsymbol{F} \rightleftharpoons \)
\( \boldsymbol{C H}_{3} \boldsymbol{C O O H}_{2}^{+}+\boldsymbol{F}^{-} \)
A \( \cdot F^{-} \) is the conjugate acid of \( C H_{3} C O O H \)
B. \( F^{-} \) is the conjugate base of \( H F \)
C. \( C H_{3} C O O H \) is the conjugate acid of \( C H_{3} C O O H_{2}^{+} \)
D. \( C H_{3} C O O H_{2}^{+} \) is the conjugate base of \( C H_{3} C O O H \)
Subject: Physics
n the circuit shown in figure, the \( A C \)
source gives a voltage \( V= \)
\( 20 \cos (2000 t) . \) Neglecting source
resistance, the voltmeter and ammeter
readings will be
A. \( 0 V .2 .0 \)
В. \( 0 V, 1.4 A \)
\( c .5 .6 V, 1.4 \)
) \( .8 V, 2.0 A \)
Subject: Chemistry
Incorrect order of the value of \( \Delta_{0} \) for the
given complexes?
\( \mathbf{A} \cdot\left[\operatorname{Cr}\left(N H_{3}\right)_{6}\right]^{3+}<\left[\operatorname{Cr}(\operatorname{en})_{3}\right]_{3+} \)
B . \( \left[C o(e n)_{3}\right]^{+3}>\left[R h(e n)_{3}\right]^{+} \)
C \( \cdot\left[C o\left(H_{2} O\right)_{6}\right]^{+2}<\left[\operatorname{Co}\left(H_{2} O\right)_{6}\right]^{+} \)
D. \( \left[N i c l_{6}\right]^{4}-<\left[N i\left(H_{2} O\right)_{6}\right]^{+2} \)
Subject: Chemistry
The value of \( \Delta H \) and \( \Delta S \) for a reaction
are respectively \( 30 k J \) mol \( ^{-1} \) and \( 100 J K^{-1} \) mol \( ^{-1} . \) Then temperature above which the reaction will become
spontaneous is:
\( \mathbf{A} \cdot 300 K \)
в. \( 30 K \)
c. \( 100 K \)
D. \( 300^{\circ} \mathrm{C} \)
Subject: Maths
\( \Delta A M T \sim \Delta A H E \cdot \ln \Delta A M T, M A= \)
\( 6.3 c m, \angle M A T=120^{\circ}, A T=4.9 \mathrm{cm} \)
\( \frac{M A}{H A}=\frac{7}{5} \) Construct \( \Delta A H E \)
Subject: Maths
Let \( \boldsymbol{A}=(\mathbf{1}, \mathbf{2}, \mathbf{3}) \boldsymbol{B}= \)
\( (-1,-2,-1) C=(2,3,2) \) and \( D= \)
\( (4,7,6) . \) Then \( A B C D \) is a
A. rectangle
B. square
c. parallelogram
D. none of these
Subject: Maths
is derivable and has a continuous
derivative at \( \boldsymbol{x}=\mathbf{0} \)
A \( . m \in(1, \infty) \)
B. \( m \in[2, \infty) \)
c. \( m \in(2, \infty) \)
D. \( m \in(-\infty, 2) \)
Subject: Physics
The resistance of a wire at room
temperature \( 30^{\circ} \mathrm{C} \) is found to be \( 10 \Omega \)
Now to increase the resistance by \( 10 \% \) the temperature of the wire must be [The temperature coefficient of resistance of the material of the wire is
\( \left.\mathbf{0 . 0 0 2} \text { per }^{\circ} \boldsymbol{C}\right] \)
A \( \cdot 36^{\circ} \mathrm{C} \)
в. \( 83^{\circ} \) С
\( \mathbf{c} \cdot 63^{\circ} C \)
D. \( 33^{\circ} \mathrm{C} \)
Subject: Physics
The following four wires are made of the same material. Which of these will have
the largest extension when the same tension is applied?
A. Length \( =50 \mathrm{cm}, \) diameter \( =0.5 \mathrm{mm} \)
B. Length = 100 cm, diameter = 1 mm
c. Length\( =200 \mathrm{cm}, \) diameter \( =2 \mathrm{mm} \)
D. Length \( =300 \mathrm{cm}, \) diameter \( =3 \mathrm{mm} \)
Subject: Chemistry
At \( 444^{\circ} C, \) the equilibrium constant \( (K) \) for the reaction \( 2 A B \rightleftharpoons A_{2}+B_{2} \) is \( \frac{1}{64} \) The degree of dissociation of \( A B \) is
A . \( 10 \% \)
B. 20\%
c. \( 30 \% \)
D. \( 50 \% \)
Subject: Maths
From a pack of 52 playing cards, face
cards and tens are removed and kept aside then a card is drawn at random
from the remaining cards. If
A : The event that the card drawn is an
ace
\( \mathrm{H}: \) The event that the card drawn is a
heart
S : The event that the card drawn is a
spade then which of the following holds?
This question has multiple correct options
\( \mathbf{A} \cdot 9 P(A)=4 P(H) \)
B . \( P(S)=4 P(A \cap H) \)
c. \( 3 P(H)=3 P(A \cup S) \)
D. None of these
Subject: Physics
A metal sphere of radius a is having
charge \( +Q \) on it Now it is connected with
a metal wire to a concentric spherica
shell of radius 2 a Then the net potential
at the surface of outer shell is
\( ^{A} \cdot \frac{K Q}{a} \)
в. \( \frac{K Q}{2 a} \)
c. \( \frac{3}{2} \frac{K Q}{a} \)
D. \( \frac{2 K Q}{a} \)
Subject: Chemistry
In a closed cylinder of capacity \( 24.6 L \)
the following reaction occurs at \( 27^{\circ} \mathrm{C} \)
\( \boldsymbol{A}_{2}(s) \rightleftharpoons \boldsymbol{B}_{2}(s)+2 C(\boldsymbol{g}) \)
At equilibrium, \( 1 g \) of \( B_{2}(s) \) (molar
mass \( =50 g m o l^{-1} \) ) is present. The
equilibrium constant \( \boldsymbol{K}_{\boldsymbol{p}} \) for the
equilibrium in \( a t m^{2} \) unit is:
\( \left[\boldsymbol{R}=\mathbf{0 . 0 8 2} \boldsymbol{L} \boldsymbol{a t m} \boldsymbol{K}^{-1} \boldsymbol{m o l}^{-1}\right] \)
A \( \cdot 1.6 \times 10^{-2} \)
в. \( 1.6 \times 10^{-5} \)
c. \( 1.6 \times 10^{-3} \)
D. \( 1.6 \times 10^{-4} \)
E . \( 1.6 \times 10^{-1} \)
Subject: Chemistry
Heptane and octane form an ideal
solution. At \( 373 K \), the vapour
pressures of the two liquid components are \( 105.2 k P a \) and \( 46.8 k P a \)
respectively. What will be the vapour pressure of a mixture of \( 26.0 \mathrm{g} \) of
heptane and \( 35 g \) of octane?
Subject: Chemistry
In electrolysis of \( A l_{2} O_{3} \) by Hall-
Heroult process,
A. cryolite \( N a_{3}\left[A l F_{6}\right] \) lowers the \( m . p . \) of \( A l_{2} O_{3} \) and increases its electrical conductivity
B. Al is obtained at cathode and probably \( C O_{2} \) at anode
c. Both (a) and
(b) are correct
D. None of the above
Subject: Maths
The value of the determinant \( \mid \begin{array}{ccc}1+a^{2}-b^{2} & 2 a b & -2 b \\ 2 a b & 1-a^{2}+b^{2} & 2 a \\ 2 b & -2 a & 1+a^{2}-b^{2}\end{array} \)
is equal to
\( A \)
B \( \cdot\left(1+a^{2}+b^{2}\right) \)
c. \( \left(1+a^{2}+b^{2}\right)^{2} \)
D. \( \left(1+a^{2}+b^{2}\right)^{3} \)
Subject: Physics
Diameter of plano-convex lens is \( 6 \mathrm{cm} \)
and thickness at the centre is \( 3 \mathrm{mm} \). If
speed of light in material of lens is \( 2 x \)
\( 10^{8} m / s, \) the focal length of the lens is:
A. \( 20 \mathrm{cm} \)
B. 30 cm
c. \( 10 \mathrm{cm} \)
D. \( 15 \mathrm{cm} \)
Subject: Maths
A survey was conducted by a group of students as a part of their environment
awareness programme, in which they collected the following data regarding the number of plants in 20 houses in a locality.
Find the mean number of plants per house.
Number
\[
\begin{array}{lll}
\mathbf{0}- & \mathbf{2}- & \mathbf{4}- \\
\mathbf{2} & \mathbf{4} & \mathbf{6}
\end{array}
\]
of plants
Number
of
houses
Which method did you use for finding
the mean, and why?
Subject: Maths
Evaluate: \( \int \frac{\sin ^{2} x}{\cos ^{4} x} d x \)
A \( \cdot \frac{1}{2} \tan ^{2} x+c \)
B \( \cdot \frac{1}{2} \cot ^{2} x+c \)
c. \( \frac{1}{3} \cot ^{3} x+c \)
D. \( \frac{1}{3} \tan ^{3} x+c \)
Subject: Chemistry
The number of \( s p^{2} \) hybridized carbon
atoms in the given compound is:
\[
\mathbf{H C} \equiv \mathbf{C}-\mathbf{C H}_{2}-\mathbf{U}-\mathbf{C H}_{2}-\mathbf{C H}=\mathbf{C H}_{2}
\]
\( A \cdot 3 \)
B. 4
\( c \cdot 5 \)
\( D \)
Subject: Maths
Let \( \bar{a} \) and \( \bar{b} \) be two unit vectors and let \( \theta \)
be angle between them then \( (\bar{a}+\bar{b})^{2}- \) \( (\bar{a}-\bar{b})^{2}= \)
A \( \cdot \cos \theta \)
B . \( 2 \cos \theta \)
\( c \cdot 3 \cos \theta \)
D. \( 4 \cos \theta \)
Subject: Chemistry
Consider the reactions:
\( \mathbf{2} S_{2} O_{3}^{2-}(\boldsymbol{a} \boldsymbol{q})+\boldsymbol{I}_{2}(\boldsymbol{s}) \rightarrow \boldsymbol{S}_{4} \boldsymbol{O}_{6}^{2-}(\boldsymbol{a} \boldsymbol{q})+ \)
\( 2 I^{-}(a q) \)
\( \boldsymbol{S}_{2} \boldsymbol{O}_{3}^{2-}(\boldsymbol{a} \boldsymbol{q})+\boldsymbol{2} \boldsymbol{B} \boldsymbol{r}_{2}(\boldsymbol{l})+\boldsymbol{5} \boldsymbol{H}_{2} \boldsymbol{O}(\boldsymbol{l}) \rightarrow \)
\( \mathbf{2} \boldsymbol{S} \boldsymbol{O}_{\mathbf{4}}^{\mathbf{2}-}(\boldsymbol{a} \boldsymbol{q})+\boldsymbol{4} \boldsymbol{B} \boldsymbol{r}^{-}(\boldsymbol{a} \boldsymbol{q})+\mathbf{1 0} \boldsymbol{H}^{+}(\boldsymbol{a} \boldsymbol{q}) \)
Why does the same reductant,
thiosulphate react differently with iodine and bromine?
Subject: Maths
\( \left|\begin{array}{ccc}\boldsymbol{a} & \boldsymbol{a}+\boldsymbol{b} & \boldsymbol{a}+\boldsymbol{b}+\boldsymbol{c} \\ \mathbf{2} \boldsymbol{a} & \mathbf{3} \boldsymbol{a}+\mathbf{2} \boldsymbol{b} & \boldsymbol{4} \boldsymbol{a}+\boldsymbol{3} \boldsymbol{b}+\boldsymbol{2} \boldsymbol{c} \\ \boldsymbol{3} \boldsymbol{a} & \boldsymbol{6} \boldsymbol{a}+\boldsymbol{3} \boldsymbol{b} & \boldsymbol{1 0} \boldsymbol{a}+\boldsymbol{6 b}+\boldsymbol{3} \boldsymbol{a}\end{array}\right|=\boldsymbol{a}^{3} \)
Subject: Maths
\( A B C \) is an isosceles triangle with
vertex at \( A \) and \( P \) is any point inside
the triangle. If the rectangle contained by perpendicular from \( \boldsymbol{P} \) to sides \( \boldsymbol{A B} \) and \( A C \) is equal to square of the perpendicular from \( \boldsymbol{P} \) to base \( \boldsymbol{B} \boldsymbol{C}, \) then prove that the locus of \( \boldsymbol{P} \) is a circle.
Subject: Chemistry
Which of the following contains maximum number of atoms?
A. \( 0.16 g \) СН\( _{3} \)
В. \( 0.28 g N_{2} \)
\( \mathbf{c} \cdot 0.36 g C_{6} H_{12} O_{6} \)
D. \( 1.1 g C O_{2} \)
Subject: Chemistry
Which of the following is the most effective in causing coagulation of ferric hydroxide solution?
A. \( K C l \)
в. \( K N O_{3} \)
\( \mathrm{c} \cdot K_{2} \mathrm{SO}_{4} \)
D \( \cdot_{K_{3}}\left[F e(C N)_{6}\right] \)
Subject: Maths
The value of \( \sin h^{-1}(3) \)
\( A \cdot \log (1+\sqrt{2}) \)
B \( \cdot \log (2+\sqrt{3}) \)
\( \mathbf{c} \cdot \log (3+\sqrt{5}) \)
D \( \cdot \log (3+\sqrt{10}) \)
Subject: Chemistry
A solution contains 200 g ppm \( C a C O_{3} \) If there is \( \frac{\boldsymbol{x} \times \boldsymbol{N}_{\boldsymbol{A}}}{\mathbf{1 0}^{\boldsymbol{6}}} \boldsymbol{C a C} \boldsymbol{O}_{3} \) molecules
per gram, what is the value of \( x ? \)
Subject: Physics
A wire of length L and radius r fixed at
one end and a force \( F \) applied to the other end produces and extension \( l \). The
extension produced in another wire of the same material of length 2Land radius \( 2 r \) by a force \( 2 F \) is:
\( \mathbf{A} \cdot l \)
в. \( 2 l \)
\( c \cdot \frac{l}{2} \)
D. 4
Subject: Biology
If one litre of water at \( 25^{\circ} C \) is mixed
with one litre of water at \( 45^{\circ} \mathrm{C} \) the
temperature of the water will be
\( \mathbf{A} \cdot 70^{\circ} \mathrm{C} \)
B \( \cdot 20^{\circ} \mathrm{C} \)
\( \mathrm{c} \cdot<25^{\circ} \mathrm{C} \)
\( \mathrm{D} \cdot>25^{\circ} \mathrm{C\&}<45^{\circ} \mathrm{C} \)
Subject: Maths
Inverse circular functions,Principal
values of \( \sin ^{-1} x, \cos ^{-1} x, \tan ^{-1} x \)
\[
\tan ^{-1} x+\tan ^{-1} y=\tan ^{-1} \frac{x+y}{1-x y}
\]
\( x y<1 \)
\[
\pi+\tan ^{-1} \frac{x+y}{1-x y}, \quad x y>1
\]
Prove
(a) \( \sin ^{-1} \frac{4}{5}+\sin ^{-1} \frac{5}{13}+\sin ^{-1} \frac{16}{65}=\frac{\pi}{2} \)
(b) \( \sin ^{-1} \frac{3}{5}+\sin ^{-1} \frac{8}{17}=\cos ^{-1} \frac{36}{85} \)
\( (c) \sin ^{-1} \frac{3}{5}+\cos ^{-1} \frac{12}{13}=\cos ^{-1} \frac{33}{65} \)
Subject: Biology
Which of the following is true for the inheritance of sex chromosomes in
humans?
A. The gametes from each parent have either an \( x \) or a chromosome.
B. The gamete from the mother has either an \( x \) or a \( y \) chromosome.
c. The gamete from the father has either an \( x \) or a chromosome.
D. The gamete from the father only has an \( x \) chromosome.
E. The gamete from the mother only has a \( Y \) chromosome.
Subject: Chemistry
\( K_{c} \) for the reaction of decomposition of
\( \mathrm{CaCO}_{3} \) can be written as
в. \( \left[\mathrm{CO}_{3}\right] \)
\( \mathrm{c} \cdot[\mathrm{CaO}]\left[\mathrm{CO}_{2}\right] \)
D. None of these
Subject: Maths
The value of \( \frac{1^{2}}{1.3}+\frac{2^{2}}{3.5}+\cdots+ \)
\( \frac{n^{2}}{(2 n-1)(2 n+1)} \) is
A \( \cdot \frac{n(n+1)}{2(2 n+1)} \)
B. \( \frac{n(n-1)}{2(2 n-1)} \)
c. \( \frac{n^{2}(n-1)^{2}}{2(2 n+1)} \)
D. none of these
Subject: Physics
The relation between force ' \( F \) ' and
density ' \( d \) ' is \( F=\frac{x}{\sqrt{d}} . \) The dimensions
of \( x \) are:
\( \mathbf{A} \cdot\left[L^{-1 / 2} M^{3 / 2} T^{-2}\right] \)
B \( \cdot\left[L^{-1 / 2} M^{1 / 2} T^{-2}\right] \)
\( \mathbf{C} \cdot\left[L^{-1} M^{3 / 2} T^{-2}\right] \)
D・ \( \left[L^{-1} M^{1 / 2} T^{-2}\right] \)
Subject: Physics
Assertion
(A): Steel is more elastic than
rubber.
Reason (R): Under a given deforming force, steel is deformed less than rubber.
A) Both Assertion and Reason are true and the reason is correct explanation of
the assertion
B)Both Assertion and Reason are true,
but reason is not correct explanation of the assertion
C) Assertion is true, but the reason is
false
D) Assertion is false, but the reason is
true
\( A \cdot A \)
B. B
\( c \cdot c \)
\( D \cdot D \)
Subject: Maths
A spherical shape jar has a radius of 2
cm. What is the volume of the jar?
A. \( 30.493 \mathrm{cm}^{3} \)
В. \( 13.493 \mathrm{cm}^{3} \)
c. \( 23.493 \mathrm{cm}^{3} \)
D. \( 33.493 c m^{3} \)
Subject: Maths
What must be added to \( x^{3}-3 x^{2}- \)
\( 12 x+19 \) so that the result is exactly
divisible by \( x^{2}+x-6 ? \)
A \( .2 x-5 \)
B. \( 2 x+5 \)
c. \( -2 x-5 \)
D. \( x+5 \)
Subject: Physics
A steel ball strikes a fixed smooth steel
plate placed on a horizontal surface at an angle \( \theta \) with the vertical. If the
coefficient of restitution is \( e \), the angle
at which the rebound will take place is
\( A \cdot \theta \)
B. \( \tan ^{-1}\left[\frac{\tan \theta}{e}\right] \)
\( c \cdot e \tan \theta \)
D. \( \tan ^{-1}\left[\frac{e}{\tan \theta}\right] \)
Subject: Maths
\( \left|\begin{array}{lll}\mathbf{a}+\mathbf{b} & \mathbf{a} & \mathbf{b} \\ \mathbf{a} & \mathbf{a}+\mathbf{c} & \mathbf{c} \\ \mathbf{b} & \mathbf{c} & \mathbf{b}+\mathbf{c}\end{array}\right|= \)
\( A \cdot 4 \) abc
B. abç
\( c \cdot 2 a^{2} b^{2} c^{2} \)
D. \( 4 a^{2} b^{2} c^{2} \)
Subject: Chemistry
Select the correct statement
regarding hydrides of \( L i \) and \( B e \)
\( \mathbf{A} \cdot \operatorname{Both} L i H \) and \( B e H_{2} \) are ionic.
B. \( L i H \) is ionic while \( B e H_{2} \) is covalent.
C . Both \( L i H \) and \( B e H_{2} \) are covalent.
D. \( L i H \) is covalent while \( B e H_{2} \) is ionic.
Subject: Maths
Find the magnitude of two vectors \( \vec{a} \) and
\( \vec{b}, \) having the same magnitude and such
that the angle between them is \( 60^{\circ} \) and their scalar product is \( \frac{1}{2} \)
A \( .-1,-1 \)
в. 1,1
c. -2,-2
D. 2,2
Subject: Physics
A projectile is fired with a speed \( u \) at an angle \( \theta \) with horizontal. Its speed when
its direction of motion makes an angle
\( \alpha^{\prime} \) with the horizontal is
A . u \( \sec \theta \cos \alpha \)
B. u \( \sec \theta \sin \alpha \)
\( c \cdot u \cos \theta \sec \alpha \)
D. u \( \sin \theta \sec \alpha \)
Subject: Chemistry
Calculate osmotic pressure of a solution (write only integer part) obtained on mixing \( 100 \mathrm{mL} \) of \( 3.4 \% \) (mass/vol) solution of urea (molar
mass 60 ) and \( 50 \mathrm{mL} \) of \( 1.6 \% \) (mass/vol)
solution of cane sugar (molar mass 342
\( \operatorname{at} 27^{\circ} C \)
Subject: Maths
Given positive integers \( i>1, n>2 \) and that the coefficients of \( (3 r)^{t h} \) and \( (r+ \)
2) \( ^{t h} \) terms in the bionomial expansion
of \( (1+x)^{2 n} \) are equal, then
A \( . n=2 r \)
B. n=3r
c. \( n=2 r+1 \)
D. None of these.