AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Chemistry
Match the following.
A. Homeostasis
1) Insulin
B. Emergency hormone
2) Structure
of insulin
C. Metabolism
3) Adrenaline
D. Peptide hormones
4) Thyroxine
E. Pancreatic islets
5)
Maintenance of constant internal
environment
F. Sanger
6) Affect
the properties of Plasma membrane
\( A \cdot A-1 ; B-5 ; C-3 ; D-4 ; E-6 ; F-2 \)
B. \( A-2 ; B-4 ; C-3 ; D-1 ; E-6 ; F-2 \)
\( \mathrm{C} \cdot \mathrm{A}-3 ; \mathrm{B}-5 ; \mathrm{C}-3 ; \mathrm{D}-4 ; \mathrm{E}-6 ; \mathrm{F}-1 \)
D. \( A-5 ; B-3 ; C-4 ; D-1,6 ; E-1 ; F-2 \)
Subject: Chemistry
When \( H C O_{3}^{-} \) acts as a Bronsted base,
which of the following is formed?
A \( \cdot C O_{2} \)
в. \( C O_{3} \)
\( \mathrm{c} \cdot \mathrm{CO}_{3}^{2-} \)
D. \( H_{2} C O_{3} \)
Subject: Physics
An electron having charge \( 1.6 \times 10^{-19} \mathrm{C} \)
and mass \( 9 \times 10^{-31} \mathrm{kg} \) is moving with
\( 4 \times 10^{6} \mathrm{m} / \mathrm{s} \) speed in a magnetic field
of \( 2 \times 10^{-1} \) tesla in a circular orbit. The
force acting on an electron and the radius of circular orbit will be:
A \( \cdot 1.28 \times 10^{-14} N, 1.1 \times 10^{-3} m \)
B . \( 1.28 \times 10^{15} N, 1.2 \times 10^{-12} m \)
C . \( 1.28 \times 10^{-13} N, 1.2 \times 10^{-4} \mathrm{m} \)
D. none of these
Subject: Chemistry
A solution has \( p H \) 2. It contains:
A. \( C H_{3} \) СООН
в. \( H_{2} C O_{3} \)
c. \( H N O_{3} \)
\( \mathrm{D} \cdot \mathrm{H}_{2} \mathrm{C}_{2} \mathrm{O}_{4} \)
Subject: Chemistry
The nitrogen containing compound
produced in the reaction of \( \boldsymbol{H} \boldsymbol{N} \boldsymbol{O}_{3} \) with
\( P_{4} O_{10} \) is :
This question has multiple correct options
A . can also be prepared by reaction of \( P_{4} \) and \( H N O_{3} \)
B. is diamagnetic
c. contains one \( N-N \) bond
D. reacts with \( N a \) metal producing a brown gas
Subject: Maths
Cantres of the three circles
\( x^{2}+y^{2}-4 x-6 y-14=0 \)
\( \boldsymbol{x}^{2}+\boldsymbol{y}^{2}+\boldsymbol{2} \boldsymbol{x}+\boldsymbol{4} \boldsymbol{y}-\boldsymbol{5}=\mathbf{0} \)
and \( x^{2}+y^{2}-10 x-16 y+7=0 \)
A. Are the vertices of a right triangle
B. The vertices of an isosceles triangle which is not regular
c. vertices of a regular triangle
D. Are collinear
Subject: Chemistry
The orbital angular momentum of an electron corresponding to \( n=4 \) and
\( \boldsymbol{m}=-\mathbf{3} \) is:
A . 0
в. \( \frac{h}{\sqrt{2} \pi} \)
c. \( \frac{\sqrt{6} h}{2 \pi} \)
D. \( \frac{\sqrt{3} h}{\pi} \)
Subject: Maths
The value of integral \( \int_{\pi / 4}^{3 \pi / 4} \frac{x}{1+\sin x} d x \)
is :
A \( \cdot \pi \sqrt{2} \)
B . \( \frac{\pi}{2}(\sqrt{2}+1) \)
c. \( \pi(\sqrt{2}-1) \)
D. \( 2 \pi(\sqrt{2}-1) \)
Subject: Chemistry
Anhydrous \( A l C l_{3} \) is a covalent
compound. From the data given below,
predict whether it would remain covalent or become ionic in an aqueous
solution.
(lonisation energy of \( \boldsymbol{A} \boldsymbol{L}= \) \( \mathbf{5 1 3 7} \boldsymbol{K J} \quad \boldsymbol{m o l}^{-1} \mathbf{)} \)
\( \Delta \boldsymbol{H} \) hydration for \( \boldsymbol{A} \boldsymbol{l}^{3+}= \)
\( -4665 K J m o l^{-1} \)
\( \Delta H \) hydration for \( C l^{-}= \)
\( -381 K J m o l^{-1} \)
A. lonic
B. Covalent
c. Partially ionic
D. Partially covalent
Subject: Physics
Two particles \( A \) and \( B \) start
simultaneously from the same point
and move in a horizontal plane. \( A \) has
an initial velocity \( u_{1} \) due east and
acceleration \( a_{1} \) due north. \( B \) has an
initial velocity \( u_{2} \) due north and
acceleration \( a_{2} \) due east. Which of the
following statements is(are) correct? This question has multiple correct options
A. Their paths must intersect at some point
B. They must collide at some point.
C. They will collide only if \( a_{1} u_{1}=a_{2} u_{2} \)
D. If \( u_{1}>u_{2} \) and \( a_{1}<a_{2} \), the particles will have the same speed at some point of time.
Subject: Chemistry
An amphoteric substance is:
A. a substance that can act as both acids and base by being both proton acceptor and proton donor
B. a substance that acts as an acid by being both a proton acceptor and a proton donor
C. a substance that acts as a base by being both a proton acceptor and a proton donor
D. when a hydronium ion from a base reacts with a hydroxide ion from an acid to make water and a salt
E. a base that forms when an acid loses a proton
Subject: Maths
Calculate the standard deviation of the
following data:
18 \( \quad \) 23 \( \begin{array}{lllll}x & 3 & 8 & 13 & 18\end{array} \) A a \( f \quad \) 7 \( \quad 10 \quad \) 15 \( \quad 10 \quad 8 \)
Subject: Maths
The number of points on the line \( x+ \)
\( \boldsymbol{y}=\mathbf{4} \) which are unit distance apart
from the line \( 2 x+2 y=5 \) is
\( \mathbf{A} \cdot \mathbf{0} \)
B. 1
c. 2
D. \( \infty \)
Subject: Physics
Express 0.006006 into scientific
notation in three significant digits:
A \( \cdot 6.01 \times 10^{-3} \)
B . \( 6.0006 \times 10^{-3} \)
c. \( 6.00 \times 10^{-3} \)
D. \( 6.0 \times 10^{-3} \)
Subject: Physics
A liquid of specific heat 0.3 at \( 90^{\circ} \mathrm{C} \) is
mixed with another liquid of specific
heat 0.5 at \( 15^{\circ} \mathrm{C} \). If the final
temperature of the mixture is \( 60^{\circ} \mathrm{C} \)
then find the ratio of masses of the two
liquids mixed.
Subject: Maths
If \( \boldsymbol{A}=\left[\begin{array}{cc}2 & \boldsymbol{4} \\ -\mathbf{1} & \boldsymbol{k}\end{array}\right] \) and \( \boldsymbol{A}^{2}=\mathbf{0}, \) find \( \boldsymbol{k} \)
Subject: Physics
The volume of a colloidal particle \( V_{c} \) as
compared to the volume of a solute
particle in atrue solution \( V_{s} \) could be
A \( \cdot \frac{V_{c}}{V_{s}}=1 \)
B. \( \frac{V_{c}}{V_{s}}=10^{23} \)
c. \( \frac{V_{c}}{V_{s}}=10^{-3} \)
D. \( \frac{V_{c}}{V_{s}}=10^{3} \)
Subject: Maths
Determine whether or not each of the
definition of \( * \) given below gives a
binary operation. In the event that \( * \) is not a binary operation, given justification for this
(i) \( \operatorname{On} Z^{+}, \) define \( * \) by \( a * b=a-b \)
(ii) \( \operatorname{On} Z^{+}, \) define \( * \) by \( a * b=a b \)
(iii) On \( R, \) define \( * \) by \( a * b=a b^{2} \)
(iv) On \( Z^{+}, \) define \( * \) by \( a * b=|a-b| \)
On \( Z^{+}, \) define \( * \) by \( a * b=a \)
Subject: Chemistry
During the electrolysis of the aqueous solution of copper sulphate using Pt electrodes, the reaction taking place at
anode electrode is:
A \( \cdot C u^{2+}+2 e^{-} \rightarrow C u \)
в. \( C u \rightarrow C u^{2+}+2 e^{-} \)
\( \mathbf{c} \cdot 2 H_{2} O \rightarrow 4 H^{+}+O_{2}+4 e^{-} \)
" \( \quad H_{2} O+e^{-} \rightarrow O H^{-}+\frac{1}{2} H_{2} \)
Subject: Maths
The area of the parallelogram constructed on the vectors \( \overrightarrow{\boldsymbol{a}}=\overrightarrow{\boldsymbol{p}}+ \) \( \mathbf{3} \overrightarrow{\boldsymbol{q}} \) and \( \overrightarrow{\boldsymbol{b}}=\boldsymbol{3} \overrightarrow{\boldsymbol{p}}+\overrightarrow{\boldsymbol{q}} \) where \( \overrightarrow{\boldsymbol{p}}, \overrightarrow{\boldsymbol{q}} \) are
unit vectors enclosing an angle of \( 30^{\circ} \) is
A . 4
B. \( \frac{7}{2} \)
\( c \cdot \frac{3}{2} \)
D. None of these
Subject: Maths
Assertion
\( P(n)=n^{2}+n+1 \) is an odd natural
number \( \forall n \in N \)
Reason
If 1 is added to an even number then it
becomes an odd number
A. Both (A) \& (R) are individually true \& (R) is correct explanation of (A),
B. Both (A) \& (R) are individually true but (R) is not the correct (proper) explanation of (A)
c. (A)is true but (R) is false
D. (A)is false but (R) is true
Subject: Maths
If the probability distribution of a random variable x is
\( \boldsymbol{X}=\boldsymbol{x}_{1}: \quad-2 \quad-1 \quad \mathbf{0} \quad \mathbf{1} \quad \mathbf{2} \quad \mathbf{3} \)
\( \boldsymbol{p}\left(\boldsymbol{X}=\boldsymbol{x}_{1}\right): \mathbf{0 . 1} \quad \boldsymbol{k} \quad \mathbf{0 . 2} \quad \mathbf{2 k} \mathbf{0 . 3} \boldsymbol{k} \)
then the mean of \( x \) is
A . 0.6
B. 0.8
\( c .1 .0 \)
D. 0.3
Subject: Physics
Flux through the rectangular piece of area \( 10 \mathrm{cm} \) by \( 20 \mathrm{cm} \) when placed \( (\mathrm{as} \) shown in an uniform electric field of
\( 200 \mathrm{N} / \mathrm{C}, \) ) is
A \( \cdot \) 4.0 \( N m^{2} / C \)
B . 3.5 \( N m^{2} / C \)
c. \( 2.5 \mathrm{Nm}^{2} / \mathrm{C} \)
D. zer
Subject: Maths
The D.E. obtained from \( y=c x^{2}+c^{3} \) is
\( ^{\mathbf{A}} \cdot\left(\frac{d y}{d x}\right)^{3}+4 x^{4} \frac{d y}{d x}=8 x^{3} y \)
\( ^{\mathbf{B}}\left(\frac{d y}{d x}\right)^{3}-4 x^{4} \frac{d y}{d x}=8 x^{3} y \)
\( ^{\mathrm{c}}-\left(\frac{d y}{d x}\right)^{3}-4 x^{4} \frac{d y}{d x}=8 x^{3} y \)
\( \left(\frac{d y}{d x}\right)^{3}-4 x^{4} \frac{d y}{d x}=-8 x^{3} y \)
Subject: Maths
Assertion
Inverse of an orthogonal matrix is
orthogonal.
Reason
The inverse of an identity matrix is the
matrix itself.
\( \mathbf{A} \cdot \) Both \( (\mathrm{A}) \&(\mathrm{R}) \) are individually true \( \&(\mathrm{R}) \) is correct explanation of \( (A) \)
B. Both (A) \& (R) are individually true but (R) is not the correct (proper) explanation of (A).
C. (A)is true but (R) is false,
D. (A)is false but (R) is true.
Subject: Chemistry
Consider following statements.
\( (I) \) The size of the lanthanide ions
\( \left(M^{3+}\right) \) decreases as the atomic
number of \( M \) increases.
\( (I I) \) Electronic spectra of lanthanides show very broad bands.
\( (I I I) \) As with transition metals, coordination number six is very
common in lanthanide complexes.
Which of the statements given above
is/are correct?
A. \( I \) only
B. \( I \) and \( I I \)
c. \( I \) and \( I I I \)
D. III only
Subject: Maths
A unit vector \( \boldsymbol{d} \) is equally inclined at an angle \( \alpha \) with the vectors \( a=\cos \theta . i+ \)
\( \sin \theta . j, b=-\sin \theta . i+\cos =\theta . j \) and
\( c=k . \) Then \( \alpha \) is equal to
A \( \cdot \cos ^{-1}\left(\frac{1}{\sqrt{2}}\right) \)
B. \( \cos ^{-1}\left(\frac{1}{\sqrt{3}}\right) \)
c. \( \cos ^{-1} \frac{1}{3} \)
D.
Subject: Maths
If the line \( y-m x+m-1=0 \) cuts the
\( \operatorname{circle} x^{2}+y^{2}-4 x-4 y+4=0 \) at two
real points, then \( m \) belongs to
A . [1,1]
B . [-2,2]
\( c \cdot(-\infty, \infty) \)
D. [-4,4]
Subject: Maths
\( \boldsymbol{I}=\int \frac{x+2}{(x+1)^{2}} \boldsymbol{d} \boldsymbol{x} ; \) then I is equal to
\( \mathbf{A} \cdot \log (x+1)+\frac{1}{x+1}+c \)
B. \( \log (x+2)-\frac{1}{x+1}+c \)
c. \( \log (1+x)-\frac{1}{x+1}+c \)
D. \( \log (x+2)+\frac{1}{x+1}+c \)
Subject: Physics
In finding the electric field using Gauss law the formula \( |\overrightarrow{\boldsymbol{E}}|=\frac{\boldsymbol{q}_{e n c}}{\in_{\mathbf{0}}|\boldsymbol{A}|} \) is
applicable. In the formula \( \in_{0} \) is
permittivity of free space, \( \boldsymbol{A} \) is the area
of Gaussian surface and \( q_{e n c} \) is charge enclosed by the Gaussian surface. This
equation can be used in which of the
following situation?
A. For any choice of Gaussian surface.
B. Only when the Gaussian surface is an equipotential surface and \( |\vec{E}| \) is constant on the surface.
C. Only when \( |\vec{E}|= \) constant on the surface
D. Only when the Gaussian surface is an equipotential surface.
Subject: Maths
\( \frac{x^{2}+1}{\left(x^{2}+2\right)\left(2 x^{2}+1\right)}= \)
\( k\left[\frac{1}{x^{2}+2}+\frac{1}{2 x^{2}+1}\right] \Rightarrow k= \)
\( A \cdot \frac{1}{4} \)
B. 3
\( c \cdot \frac{1}{5} \)
D.
Subject: Maths
If \( \mathbf{A}+\left|\begin{array}{cc}\mathbf{4} & \mathbf{2} \\ \mathbf{1} & \mathbf{3}\end{array}\right|=\left|\begin{array}{cc}\mathbf{6} & \mathbf{9} \\ \mathbf{1} & \mathbf{4}\end{array}\right| \) then \( \mathbf{A}= \)
\( \mathbf{A} \cdot\left|\begin{array}{ll}2 & 7 \\ 0 & 1\end{array}\right| \)
\( \mathbf{B} \cdot\left|\begin{array}{ll}0 & 1 \\ 2 & 7\end{array}\right| \)
\( \mathbf{C} \cdot\left|\begin{array}{ll}1 & 0 \\ 2 & 7\end{array}\right| \)
\( \mathbf{D} \cdot\left|\begin{array}{ll}2 & 1 \\ 0 & 7\end{array}\right| \)
Subject: Chemistry
In the equilibrium \( 4 H_{2} O(g)+ \)
\( \mathbf{3} F e(s) \leftrightharpoons F e_{3} O_{4}(s)+4 H_{2}(g), \) the yield
of \( H_{2} \) can be increased by:
A. increasing the pressure
B. passing more steam
c. increasing the mass of iron
D. decreasing the pressure
Subject: Maths
\( \int x \sqrt{\frac{a^{2}-x^{2}}{a^{2}+x^{2}}} d x= \)
A \( \cdot \frac{1}{2} a^{2} \cos ^{-1}\left(\frac{x^{2}}{a^{2}}\right)+\frac{1}{2} \sqrt{a^{4}+x^{4}}+c \)
B \( \cdot \frac{1}{2} \sin ^{-1}\left(\frac{x^{2}}{a^{2}}\right)+\frac{1}{2} \sqrt{a^{4}+x^{4}}+c \)
c. \( \frac{1}{2} a^{2} \sin ^{-1}\left(\frac{x^{2}}{a^{2}}\right)+\frac{1}{2} \sqrt{a^{4}-x^{4}}+c \)
D. \( \frac{1}{2} \cos ^{-1}\left(\frac{x^{2}}{a^{2}}\right)+\frac{1}{2} \sqrt{a^{4}+x^{4}}+c \)
Subject: Physics
If \( S \) is stress and \( Y \) is Young's modulus
of material of wire, then energy stored in the wire per unit volume is:
\( \mathbf{A} \cdot 2 S^{2} Y \)
в. \( \frac{s}{Y x} \)
c. \( \frac{2 Y}{S^{2}} \)
D. \( \frac{s^{2}}{2 Y} \)
Subject: Chemistry
For the manufacture of ammonia by the
reaction \( \boldsymbol{N}_{2}+\boldsymbol{3} \boldsymbol{H}_{2} \rightleftharpoons \mathbf{2} \boldsymbol{N} \boldsymbol{H}_{3}+ \)
21.9 \( K c a l \), the favorable conditions are:
A. low temperature, , low pressure \& catalyst
B. low temperature, high pressure \& catalyst
c. high temperature, low pressure \( \& \) catalyst
D. low temperature, high pressure
Subject: Maths
If \( \boldsymbol{A}=\left(\begin{array}{ll}2 & 2 \\ 9 & 4\end{array}\right) ; I=\left(\begin{array}{ll}1 & 0 \\ 0 & 1\end{array}\right), \) then
\( 10 A^{-1} \) is equal to
A \( .4 I-A \)
B. \( 6 I-A \)
c. \( A-4 I \)
D. \( A-6 I \)
Subject: Maths
The D.E whose signature is \( y= \)
\( C_{1} e^{3 x}+C_{2} e^{5 x} \) is:
A \( \cdot y_{2}+2 y_{1}+15 y=0 \)
в. \( y_{2}+8 y_{1}+15 y=0 \)
c. \( y_{2}+8 y_{1}-15 y=0 \)
D. \( y_{2}-8 y_{1}+15 y=0 \)
Subject: Chemistry
Select the correct order of ionic
conductance of the following cations in
an aqueous solution.
A \( . L i^{+}<N a^{+}<K^{+}<R b^{+} \)
B . \( L i^{+}>N a^{+}>K^{+}>R b^{+} \)
c. \( L i^{+}<N a^{+}>K^{+}>R b^{+} \)
D. \( L i^{+}=N a^{+}<K^{+}<R b^{+} \)
Subject: Chemistry
Which of the following statements is
not true about sucrose?
A. On hydrolysis, it produces glucose and fructose.
B. The glycosidic linkage is present between \( C_{1} \) of \( \alpha \) glucose and \( C_{1} \) of \( \beta \) - fructose.
C. It is also named as invert sugar.
D. It is a non reducing sugar.
Subject: Maths
Let \( \omega \neq 1 \) be a cube root of unity and \( S \)
be the set of all non-singular matrices of the form \( \left[\begin{array}{ccc}\mathbf{1} & \boldsymbol{a} & \boldsymbol{b} \\ \boldsymbol{\omega} & \boldsymbol{1} & \boldsymbol{c} \\ \boldsymbol{\omega}^{2} & \boldsymbol{\omega} & \boldsymbol{1}\end{array}\right] \) Where each of
\( a, b \) and \( c \) is either \( \omega \) or \( \omega^{2} \). Then the
number of distinct matrices in the set
\( \boldsymbol{S} \) is
\( A \cdot 2 \)
B. 6
\( c \cdot 4 \)
D. 8
Subject: Maths
The area bounded by \( y^{2}=4 x \) and \( x^{2}= \)
\( 4 y \) is
A \( -\frac{20}{3} \) sq. units
B. \( \frac{16}{3} \) sq. units
\( ^{\mathrm{c}} \cdot \frac{14}{3} \mathrm{sq} . \) units
D. \( \frac{10}{3} \) sq. units
Subject: Physics
A sphere of coefficient of linear
expansion \( \alpha, \) mass \( \mathrm{m} \) and radius \( \mathrm{r} \) is spinning about an axis through its diameter with an angular velocity \( \omega \)
when it is heated such that its
temperature increases by \( \Delta t, \) the
angular velocity becomes.
\( A \)
\[
\omega(1+\alpha \Delta t)^{2}
\]
B.
\[
\frac{\omega}{(1+\alpha \Delta t)^{2}}
\]
c.
\[
\omega(1+\alpha \Delta t)
\]
D. \( \omega \alpha \Delta t \)
Subject: Physics
A stone is dropped from a height equal to \( n R(R \) is the radius of the Earth)
from the surface of the Earth. The
velocity of the stone on reaching the surface of the Earth is :
A \( \cdot \sqrt{\frac{2 g(n+1) R}{n}} \)
в. \( \sqrt{\frac{2 g R}{n+1}} \)
c. \( \sqrt{\frac{2 g n R}{n+1}} \)
D. \( \sqrt{2 g n R} \)
Subject: Physics
A stationary body explodes into two
fragments of masses \( \boldsymbol{m}_{1} \) and \( \boldsymbol{m}_{2} . \) If momentum of one fragments \( \mathrm{p} \), the minimum energy of explosion is
\( ^{\mathbf{A}} \cdot \frac{p^{2}}{2\left(m_{1}+m_{2}\right)} \)
В. \( \frac{p^{2}}{2 \sqrt{m_{1} m_{2}}} \)
c. \( \frac{p^{2}\left(m_{1}+m_{2}\right)}{4 m_{1} m_{2}} \)
D. \( \frac{p^{2}}{2\left(m_{1}-m_{2}\right)} \)
Subject: Maths
Inverse of the statement "If the triangle
with side lengths \( a, b, c \) is a right
triangle, then \( a^{2}+b^{2}=c^{2} \)
A \( \cdot \) If \( a^{2}+b^{2} \neq c^{2} \) then the triangle with side lengths \( a, b, c \) is not a right triangle.
B. If \( a^{2}+b^{2}=c^{2} \) then the triangle with side lengths \( a, b, c \) is a right triangle
C. If the triangle with side lengths \( a, b, c \) is a not right triangle, then \( a^{2}+b^{2} \neq c^{2} \)
D. None of the above.
Subject: Maths
\( \int \frac{1}{x \log x[\log (\log x)]} d x= \)
\( \mathbf{A} \cdot \log |\log (\log x)|+c \)
\( \mathbf{B} \cdot \log |\log x|+c \)
\( \mathbf{c} \cdot-\log |\log x|+c \)
\( \mathbf{D} \cdot-\log |\log (\log x)|+c \)
Subject: Physics
In an experiment of single slit diffraction pattern, first minimum for red light coincides with first maximum
of some other wavelength. If wavelength
of red light is \( 6000 A^{\circ} \), then wavelength
of first maximum will be
A \( .3000 A^{\circ} \)
B . \( 4000 A^{\circ} \)
c. \( 5000 A^{\circ} \)
D. \( 6000 A^{\circ} \)
Subject: Physics
Consider two vectors \( \vec{A} \) and \( \vec{B} \). Let
these two vectors represent two
adjacent sides of a parallelogram. We construct a parallelogram OACB as shown in the diagram. Which of the following represent the resultant
vector?
\( A \cdot O A \)
в. \( O C \)
\( c . O B \)
D. None
Subject: Maths
Differentiation of \( (2 x+3)^{6} \) with respect
to \( x \) is
A \( \cdot 12(2 x+3)^{5} \)
B. \( 6(2 x+3)^{5} \)
c. \( 3(2 x+3)^{5} \)
D. \( 6(2 x+3)^{6} \)
Subject: Maths
A farmer plans to mix two types of food
to make a mix of low cost feed for the
animals in his farm. A bag of food \( \boldsymbol{A} \)
\( \operatorname{costs} \$ 10 \) and contains 40 units of
proteins, 20 units of minerals and 10
units of vitamins. A bag of food \( B \) costs
\( \$ 12 \) contains 30 units of proteins, 20
units of minerals and 30 units of
vitamins. How many bags of food \( A \) and
\( B \) should the consumed by the animals
each day in order to meet the minimum
daily requirements of 150 units of
proteins, 90 units of minerals and 60 units of vitamins at a minimum cost?
Subject: Maths
If \( \boldsymbol{x}<\mathbf{0}, \) then \( \tan ^{-1} \boldsymbol{x} \) is equal to
This question has multiple correct options
A \( \cdot-\pi+\cot ^{-1} \frac{1}{x} \)
B. \( \sin ^{-1} \frac{x}{\sqrt{1+x^{2}}} \)
c. \( -\cos ^{-1} \frac{1}{\sqrt{1+x^{2}}} \)
D. \( -\operatorname{cosec}^{-1} \frac{\sqrt{1+x^{2}}}{x} \)
Subject: Physics
If circular coil with \( N_{1} \) turns is changed
in to a coil of \( N_{2} \) turns. What will be the
ratio of self inductances in both cases.
A \( \cdot \frac{N_{1}}{N_{2}} \)
B. \( \frac{N_{2}}{N_{1}} \)
c. \( \frac{N_{1}^{2}}{N_{2}^{2}} \)
D. \( \sqrt{\frac{N_{1}}{N_{2}}} \)
Subject: Physics
The position vector of \( \boldsymbol{P} \) relative to \( \boldsymbol{Q} \) as
a function of time is \( (\text { in } \boldsymbol{k} \boldsymbol{m}) \)
A \( \cdot \frac{128 t}{10^{3}} \hat{\imath}+\left(\frac{252 t}{10^{3}}-60 t\right) \)
3 \( \frac{252 t}{10^{3}} \hat{\imath}-\left(\frac{128 t}{10^{3}}\right) \)
c. \( \frac{128 t}{10^{3}} \hat{\imath}-\left(\frac{252 t}{10^{3}}\right) \)
D \( \cdot \frac{252 t}{10^{3}} \hat{\imath}+60 t \)
Subject: Chemistry
The standard electrode potential \( \left(E^{\circ}\right) \)
for Daniel cell is \( +1.1 \mathrm{V} \). Calculate \( \Delta G^{\circ} \)
for the reaction.
\( \boldsymbol{Z} \boldsymbol{n}(\boldsymbol{s})+\boldsymbol{C} \boldsymbol{u}_{(a q)}^{2+} \rightarrow \boldsymbol{Z} \boldsymbol{n}_{(a q)}^{2+}+\boldsymbol{C u}(\boldsymbol{s}) \)
\( (1 F=96500 C / m o l) \)
Subject: Physics
The ionisation potential of hydrogen
atom is \( -13.6 \mathrm{eV} \). An electron in the
ground state of a hydrogen atoms absorb a photon of energy \( 12.75 \mathrm{eV} . \) How many different spectral line can one
expect when the electron make a
downward transition?
\( A \)
B. 4
\( c \cdot 2 \)
D. 6
Subject: Chemistry
Among the following four compounds the acidity order is:
(a) Phenol
(b) methyl phenol
(c) meta nitrophenol
(d) para-nitrophenol
A \( . c>d>a>b \)
в. \( a>d>c>b \)
c. \( b>a>c>d \)
D. \( d>c>a>b \)
Subject: Chemistry
\( M n O_{2}+4 H C l \rightarrow M n C l_{2}+C l_{2}+ \)
\( 2 H_{2} O \)
If 1 g of \( H C l \) and 1 g of \( M n O_{2} \) is heated together, the maximum weight of \( C l_{2} \) gas evolved will be:
A .2 g
B. 0.975 g
c. \( 0.486 \mathrm{g} \)
D. 0.972 g
Subject: Physics
An inductor coil stores \( U \) energy when \( i \)
current is passed through it and
dissipates energy at the rate of \( P . \) The time constant of the circuit, when this
coil is connected across a battery of
zero internal resistance is :
A \( \cdot \frac{4 U}{P} \)
в. \( \frac{U}{P} \)
c. \( \frac{2 U}{P} \)
D. \( \frac{2 P}{U} \)
Subject: Physics
An immersion heater is rated \( 836 W . \) It
should heat \( 1 l \) of water from \( 20^{0} C \) to \( 40^{0} \)
\( \mathrm{C} \) in about:
A. \( 200 s \)
B. \( 100 s \)
\( \mathbf{c} .836 s \)
D. \( 418 s \)
Subject: Physics
\( \boldsymbol{R}_{1}, \boldsymbol{R}_{2}, \boldsymbol{R}_{3} \) are different values of \( \boldsymbol{R} \)
\( \mathbf{A}, \mathbf{B}, \mathbf{C} \) are the null points obtained
corresponding to \( \boldsymbol{R}_{1}, \boldsymbol{R}_{2} \) and \( \boldsymbol{R}_{3} \)
respectively. For which resistor, the value of \( X \) will be the most accurate and
why?
\( A \cdot R_{1} \)
B. \( R_{2} \)
\( c \cdot R_{3} \)
D. All same
Subject: Maths
The distances of the point \( \boldsymbol{P}(\mathbf{1}, \mathbf{2}, \mathbf{3}) \)
from the coordinates axes are:
A \( \cdot \sqrt{13}, \sqrt{10}, \sqrt{5} \)
в. \( \sqrt{11}, \sqrt{10}, \sqrt{5} \)
c. \( \sqrt{13}, \sqrt{20}, \sqrt{15} \)
D. \( \sqrt{23}, \sqrt{10}, \sqrt{5} \)
Subject: Physics
A jet of a liquid of density \( \rho \) with a cross-sectional area A is incident at an
angle \( \theta \) on a wall with a velocity \( v \) and
bounces with no loss of energy. The angle \( \theta \) is measured with respect to the
wall. The force in a direction normal
to the surface of the wall is:
A \( \cdot 2 \rho A v^{2} \cos \theta \)
B. \( 2 \rho A v^{2} \sin \theta \)
\( \mathbf{c} \cdot 2 \rho A v^{2} \cos ^{2} \theta \)
D. \( 2 \rho A v^{2} \sin ^{2} \theta \)
Subject: Biology
Match the columns
\begin{tabular}{lll|l} 
Column I & \multicolumn{3}{c} { Column II } \\
a & Arachis & 1. & Swollen placenta \\
b & Cichorium & 2. & Epicalyx \\
c & Lilium & 3. & Fasciculate tuberous root \\
d & Physalia & 4. & Geocarpy \\
& 5. & Bulbils
\end{tabular}
\( \mathbf{A} \)
\( a-4, b-3, c-2, d-5 \)
B. \( a-4, b-1, c-2, d-3 \)
\( \mathrm{C} \cdot \mathrm{a}-5, \mathrm{b}-4, \mathrm{c}-3, \mathrm{d}- \)
D. \( a-4, b-3, c-5 \) \( d- \)
Subject: Chemistry
Assertion
An ionic solid is a good conductor of electricity.
Reason
An ionic solid is composed of positive and negative ions joined together by
electrostatic forces.
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 incorrect but Reason is correct
D. Both Assertion and Reason are incorrect
Subject: Chemistry
Carbon can not be used i the reduction
of \( A l_{2} O_{3} \) because:
A. its is expensive.
B. the enthalpy of formation of is \( C O_{2} \) more than that of \( A l_{2} O_{3} \)
c. pure carbon is not easily available.
D. the enthalpy of formation of \( A l_{2} O_{3} \) is too high