AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Chemistry
A six coordinate complex of formula
\( \boldsymbol{C r} \boldsymbol{C l}_{3} \cdot \boldsymbol{6} \boldsymbol{H}_{2} \boldsymbol{O} \) has green colour. A \( \boldsymbol{0 . 1} \boldsymbol{M} \)
solution of the complex when treated
with excess of \( A g N O_{3} \) gave \( 28.7 g \) of white precipitate. The formula of the complex would be
\( \mathbf{A} \cdot\left[C r\left(H_{2} O\right)_{6}\right] C l_{3} \)
B . \( \left[\mathrm{Cr}\left(\mathrm{H}_{2} \mathrm{O}\right)_{5} \mathrm{Cl}\right] \mathrm{Cl}_{2} . \mathrm{H}_{2} \mathrm{O} \)
c. \( \left[C r\left(H_{2} O\right)_{4} C l\right] C l_{2} .2 H_{2} O \)
D. \( \left[C r\left(H_{2} O\right)_{3} C l_{3}\right] .3 H_{2} O \)
Subject: Maths
A circle with area \( A_{1} \) is contained in the
interior of a larger circle with area \( \boldsymbol{A}_{\mathbf{1}}+ \)
\( A_{2} . \) If the radius of the larger circle is 3
and \( A_{1}, A_{2}, A_{1}+A_{2} \) are in A.P., what is
the radius of the smaller circle?
A \( \cdot \frac{\sqrt{3}}{2} \)
B. \( \frac{2}{\sqrt{3}} \)
\( c \cdot \sqrt{3} \)
D. \( \frac{3}{2} \)
Subject: Chemistry
Compound \( A \) when reacted with \( P C l_{5} \)
and then with ammonia gave \( \boldsymbol{B} . \boldsymbol{B} \)
when treated with bromine and caustic
potash produced \( C . C \) on treatment
with \( H C l \) and \( N a N O_{2} \) at \( 0^{\circ} C \) and then
on boiling produced ortho-cresol. Compound \( \boldsymbol{A} \) is :
A . \( o \) -Toluic acid
B. \( o \) -Chlorotoluene
c. \( o \) -Bromotoluene
D. m-Toluic acid
Subject: Maths
ABCD is a parallelogram with sides \( A B= \) \( 12 \mathrm{cm} \mathrm{BC}=10 \mathrm{cm} \) and diagonal \( \mathrm{AC}=16 \)
\( \mathrm{cm} \) The area of the parallelogram and
the distance between the shorter sides
are respectively
A \( \cdot 120.5 \mathrm{cm}^{2} ; 12.05 \mathrm{cm} \)
B . \( 119.8 \mathrm{cm}^{2} ; 11.98 \mathrm{cm} \)
c. \( 118.71 \mathrm{cm}^{2} ; 11.87 \mathrm{cm} \)
D. \( 117.9 \mathrm{cm}^{2} ; 11.79 \mathrm{cm} \)
Subject: Chemistry
Given standard \( E^{\ominus}: \)
\( F e^{3+}+3 e^{-} \rightarrow F e ; E^{\ominus}=-0.036 V \)
\( F e^{2+}+2 e^{-} \rightarrow F e ; E^{\ominus}=-0.440 V \)
The \( E^{\ominus} \) of \( F e^{3+}+e^{-} \rightarrow F e^{2+} \) is:
A. \( 0.476 V \)
\( V \)
в. \( 0.404 V \)
c. \( 0.604 V \)
D. \( 0.772 V \)
Subject: Physics
A solid sphere of mass \( \mathrm{M} \) and radius \( \mathrm{R} \)
is divided into two unequal parts. The first part has a mass of \( \frac{\mathbf{7} M}{\mathbf{8}} \) and is converted into a uniform disc of radius
\( 2 R . \) The second part is converted into a
uniform solid sphere. Let \( \boldsymbol{I}_{\mathbf{1}} \) be the moment of inertia of the disc about its
axis and \( I_{2} \) be the moment of inertia of
the new sphere about its axis. The ratio
\( \boldsymbol{I}_{1} / \boldsymbol{I}_{2} \) is given by :
A . 185
B. 65
c. 285
D. 140
Subject: Physics
A uniform rule is pivoted at its mid point. A weight of \( 50 g f \) is suspended at one end of it. Where should a weight of
\( 100 g f \) be suspended, to keep the rule horizontal?
A. \( 10 \mathrm{cm} \) from mid point
B. \( 25 \mathrm{cm} \) from mid point
c. \( 20 \mathrm{cm} \) from mid point
D. \( 15 \mathrm{cm} \) from mid point
Subject: Biology
In which one of the following, the set of
items are wrongly paired?
A. Lysine, glycine, thiamine - Amino acids
B. Myosin, oxytocin and gastrin - Hormones
c. Rennin, nuclease and hyaluronidase - Proteolytic enzymes
D. The nerves that carry signals away from the central nervous system - Afferent neurons
Subject: Maths
The equation of plane containing the lines \( \vec{\gamma}=\vec{\alpha}+\overrightarrow{\lambda \beta} \) and \( \vec{\gamma}=\vec{\beta}+\mu \vec{\alpha} \)
\( \mathbf{A} \cdot\left[\begin{array}{lll}\vec{\gamma} & \vec{\alpha} & \vec{\beta}\end{array}\right]=\vec{\alpha} \cdot \vec{\beta} \)
B \( \cdot\left[\begin{array}{lll}\vec{\gamma} & \vec{\alpha} & \vec{\beta}\end{array}\right]=0 \)
\( \mathbf{c} \cdot\left[\begin{array}{lll}\vec{\alpha} & \vec{\beta} & \vec{\gamma}\end{array}\right]=\vec{\alpha} \cdot \vec{\beta} \)
D. None of these
Subject: Chemistry
Select the correct statement(s).
This question has multiple correct options
A. In hydrometallurgy, \( Z n \) is used as oxidizing agent in the purification of \( A g \) from \( \left[A g(C N)_{2}\right]^{\circ} \)
B. When pine oil or eucalyptus oil is added into the water, it lowers down the surface tunsion by which froth is formed
C. Sodium ethyl xanthate is used as collector
D. Basic copper carbonate or \( P b S O_{4} \) is concentrated by froth floatation method by using an activator
Subject: Physics
A charged spherical drop of mercury is in equilibrium in a plane horizontal air capacitor and the intensity of the
electric field is \( 6 \times 10^{4} V m^{-1} . \) If the
charge on the drop is \( 8 \times 10^{-18} C, \) the
radius of the drop is :
\( \left[\rho_{a i r}=1.29 k g / m^{3} ; \rho_{H g}=13.6 \times 10^{3}\right. \)
A \( \cdot 0.95 \times 10^{-8} m \)
n
в. \( 2.7 \times 10^{-10} \mathrm{m} \)
c. \( 2.7 \times 10^{-8} \mathrm{m} \)
D. \( 0.95 \times 10^{-6} \mathrm{m} \)
Subject: Maths
If the range of \( 5 \cos \theta+3 \cos \left(\theta+\frac{\pi}{3}\right)+ \)
\( \mathbf{3} \) is \( [\boldsymbol{a}, \boldsymbol{b}], \forall \boldsymbol{\theta} \in \mathbf{R} \) then \( \boldsymbol{a}+\boldsymbol{b} \) is equal to
\( \mathbf{A} \cdot \mathbf{6} \)
B. 2
c. 8
D. 4
Subject: Maths
If \( f(x) \) and \( g(x) \) are two polynomials with integral coefficients which vanish at \( x=\frac{1}{2}, \) then what is the factor of HCF
of \( \boldsymbol{f}(\boldsymbol{x}) \) and \( \boldsymbol{g}(\boldsymbol{x}) ? \)
\( \mathbf{A} \cdot x-1 \)
B. \( x-2 \)
c. \( 2 x-1 \)
D. \( 2 x+1 \)
Subject: Chemistry
For an electron with \( n=3 \) has only one
radial node. The orbital angular momentum of the electron will be :
A. 0
B. \( \sqrt{6} \frac{h}{2 \pi} \)
c. \( \sqrt{2} \frac{h}{2 \pi} \)
D \( \cdot 3\left(\frac{h}{2 \pi}\right) \)
Subject: Maths
If \( \boldsymbol{A}=[-\mathbf{1}, \mathbf{1}] \) then \( \boldsymbol{f}: \boldsymbol{A} \rightarrow \boldsymbol{A} \) defined
by \( f(x)=\sin \pi x \) is
A. one-one but not onto
B. onto but not one-one
c. neither one - one nor onto
D. bijective
Subject: Maths
The value of \( \int \frac{x^{2}+1}{x^{4}-x^{2}+1} d x \) is
A \( \cdot \tan ^{-1}\left(2 x^{2}-1\right)+C \)
B. \( \tan ^{-1}\left(\frac{x^{2}-1}{x}\right)+C \)
\( ^{\mathrm{c}} \cdot \sin ^{-1}\left(x-\frac{1}{x}\right)+C \)
D. \( \tan ^{-1} x^{2}+C \)
Subject: Maths
The solution of the given D.E \( \frac{\boldsymbol{d} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}}= \)
\( \frac{\boldsymbol{y}+\sqrt{\boldsymbol{x}^{2}+\boldsymbol{y}^{2}}}{\boldsymbol{x}} \) is
A \( \cdot y+\sqrt{x^{2}+y^{2}}=c x^{2} \)
B . \( x+\sqrt{x^{2}+y^{2}}=c y^{2} \)
c. \( y+\sqrt{x^{2}+y^{2}}=c x \)
D. \( x+\sqrt{x^{2}+y^{2}}=c y \)
Subject: Maths
State true or false.
Given universal set= \( = \) \( \left\{-6,-5 \frac{3}{4},-\sqrt{4},-\frac{3}{5},-\frac{3}{8}, 0, \frac{4}{5}, 1,1 \frac{2}{3}, v\right. \)
From the given set, the set of integers is \( \{-6,-\sqrt{4}, 0,1\} \)
A. True
B. False
Subject: Maths
According to Euclid's division algorithm, HCF of any two positive integers a and b with \( a>b \) is obtained by applying Euclid's division lemma to a and b to find \( q \) and \( r \) such that \( a=b q+ \)
\( r, \) where \( r \) must satisfy
A. \( 1<r<b \)
В. \( 0<r<b \)
c. \( 0 \leq r<b \)
D. \( 0<r \leq b \)
Subject: Maths
If \( f(x+1)=3 x-9, \) then what will be
the value of \( \boldsymbol{f}\left(\boldsymbol{x}^{2}-\mathbf{1}\right) ? \)
A \( \cdot 3 x^{2}-9 \)
B. \( 3 x^{2}-15 \)
c. \( x^{2}-10 \)
D. \( 3 x^{2}-10 \)
Subject: Maths
A cylindrical vessel of height \( 24 \mathrm{cm} \) and
diamater \( 40 \mathrm{cm} \) is full of water. Find the
exact number of small cylindrical bottles, each of height \( 10 \mathrm{cm} \) and diameter \( 8 \mathrm{cm}, \) which can be filled with this water.
Subject: Physics
The input of \( A \) and \( B \) for the Boolean
expression \( (\overline{\boldsymbol{A}+\boldsymbol{B}}) \cdot(\overline{\boldsymbol{A} \cdot \boldsymbol{B}})=\mathbf{1} \) is
A . 0,0
в. 0,1
\( c .1,0 \)
D. 1,1
Subject: Physics
If the scalar and vector products of two vector are \( 4 \sqrt{3} \) and 144 respectively, what is the angle between the two
vectors?
A \( \cdot \tan ^{-1}(12 \sqrt{3}) \)
B \( \cdot \tan ^{-1}\left(\frac{38}{\sqrt{3}}\right) \)
c. \( \tan ^{-1}\left(\frac{\sqrt{3}}{12}\right) \)
D. \( \tan ^{-1}(36) \)
Subject: Chemistry
Equilibrium constant \( \left(\boldsymbol{K}_{C}\right) \) of
\( \mathbf{2} \boldsymbol{H} \boldsymbol{I}_{(\boldsymbol{g})} \rightleftharpoons \boldsymbol{H}_{2(\boldsymbol{g})}+\boldsymbol{I}_{2(\boldsymbol{g})} \) is \( \boldsymbol{2} \times \mathbf{1 0}^{-4} \)
What is the equilibrium concentration
of \( \boldsymbol{H} \boldsymbol{I}, \) if concentration of \( \boldsymbol{H}_{2(\boldsymbol{g})} \) and \( \boldsymbol{I}_{2}(\boldsymbol{g}) \)
respectively are \( 2.2 \times 10^{-2} M \) and
\( \mathbf{2} . \mathbf{2} \times \mathbf{1 0}^{-\mathbf{4}} \mathbf{M} ? \)
A \( \cdot 1.55 \times 10^{-1} M \)
В. \( 2.22 \times 10^{-5} \) М
c. \( 3.11 \times 10^{-5} M \)
D. \( 6.66 \times 10^{-5} M \)
Subject: Maths
If four points are \( \boldsymbol{A}(\boldsymbol{6}, \boldsymbol{3}), \boldsymbol{B}(-\boldsymbol{3}, \boldsymbol{5}), \boldsymbol{C}(\boldsymbol{4},-\boldsymbol{2}) \) and \( \boldsymbol{P}(\boldsymbol{x}, \boldsymbol{y}) \)
then the ratio of the areas of \( \triangle P B C \)
and \( \triangle A B C \) is
A \( \cdot \frac{x+y-2}{7} \)
в. \( \frac{x-y-2}{7} \)
c. \( \frac{x-y+2}{2} \)
D. \( \frac{x+y+2}{2} \)
Subject: Chemistry
The compound in which the number of
\( d \pi-p \pi \) bonds are equal to those
present in \( C l O_{4}^{-} \) is:
A. \( X e F_{4} \)
в. \( X e O_{3} \)
\( \mathrm{c} \cdot \mathrm{XeO}_{4} \)
D. \( X e F_{6} \)
Subject: Physics
If charge on left plate of the \( 5 \mu F \)
capacitor in the circuit segment shown
in the figure is \( -20 \mu C \), the charge on
the right plate of \( 3 \mu F \) capacitor is :
\( \mathbf{A} \cdot+8.57 \mu C \)
B. \( -8.57 \mu C \)
c. \( +11.42 \mu C \)
D. \( -11.42 \mu C \)
Subject: Physics
A black body is at a temperature of \( 2880 K . \) The radiation energy emitted by this object with wavelength in between
\( 499 n m \) and \( 500 n m \) is \( U_{1}, \) between 999
nm and 1000 nm is \( U_{2} \) and between
\( 1499 \mathrm{nm} \) and \( 1500 \mathrm{nm} \) is \( U_{3} . \) If Wein
constant is \( 2.8 \times 10^{6} \mathrm{nmK} \), then
A \( \cdot U_{1}=0 \)
в. \( U_{3}=0 \)
\( \mathbf{c} \cdot U_{1}>U_{2} \)
D. \( U_{2}>U_{1} \)
Subject: Chemistry
For the reaction \( 2 \mathrm{A}+\mathrm{B} \rightarrow \mathrm{C}+3 \mathrm{D} \) which of
the following is / are correct? This question has multiple correct options
\( ^{\mathbf{A}} \cdot+\frac{\Delta[D]}{\Delta t}=-\frac{1}{3} \frac{\Delta[C]}{\Delta t} \)
B. \( +\frac{\Delta[C]}{\Delta t}=-\frac{1}{2} \frac{\Delta[A]}{\Delta t} \)
c. \( -\frac{1}{2} \frac{\Delta[B]}{\Delta t}=-\frac{1}{3} \frac{\Delta[D]}{\Delta t} \)
D. \( \frac{\Delta[C]}{\Delta t}=+\frac{1}{3} \frac{\Delta[D]}{\Delta t} \)
Subject: Physics
A body is thrown vertically upwards with
an initial velocity \( u \). The expression for the maximum height attained by the body is
A \( \cdot \frac{u}{2 g g} \)
в. \( \frac{g^{2}}{2 u} \)
c. \( \frac{u^{2}}{g} \)
D. \( \frac{u^{2}}{2 g} \)
Subject: Maths
Solution of the differential equation \( \boldsymbol{y}^{\prime}+\boldsymbol{y} \sec ^{2} \boldsymbol{x}=\sec ^{2} \boldsymbol{x} \cdot \boldsymbol{\operatorname { t a n }} \boldsymbol{x} \) is
A \( \cdot y=(\tan x+1)+c e^{-\tan x} \)
B . \( y=(\tan x-1)+c e^{-t a n x} \)
C \( \cdot y=(\tan x+1)+c e^{\tan x} \)
D. None of these
Subject: Maths
Factorise:
\( x^{2}-6 x-135 \)
\( \mathbf{A} \cdot(5 x)(13 x+9) \)
B. \( (x-15)(13 x+9) \)
\( \mathbf{C} \cdot(5 x)(x+9) \)
D. \( (x-15)(x+9) \)
Subject: Chemistry
\( N a O H+P_{4}+H_{2} O \rightarrow \)
\( \mathbf{A} \cdot P H_{3}+N a H_{2} P O_{2} \)
в. \( P H_{3}+N a_{2} P O_{4} \)
c. \( P H_{3}+N a_{2} H P O \)
D. \( H_{3} P O_{4}+N a O \)
Subject: Maths
\( \ln \) a \( \Delta A B C, E \) and \( F \) are the mid-points
of \( A C \) and \( A B \) respectively. The altitude
AP to BC intersects FE at Q. Prove that
\( \boldsymbol{A} \boldsymbol{Q}=\boldsymbol{Q} \boldsymbol{P} \)
Subject: Chemistry
There is no ring strain in cyclohexane, but cyclobutane has an angle strin of
\( 9^{\circ} 44^{\prime} . \) If \( \Delta H_{c}^{\circ} \) of cyclohexane per
\( \left(C H_{2}\right) \) group is 660 kJ \( m o l^{-1} \) and \( \Delta H_{c}^{\circ} \)
of cyclobutane is \( 2744 \mathrm{kJ} \) mol\( ^{-1} \),what
is the ring strain in \( \mathrm{kJ} \) mol\( ^{-1} \) of
cyclobutane?
A \( .-104 \)
B. 104
\( c \cdot-2084 \)
D. 2084
Subject: Physics
Statement 1: There can be
displacement of an object even in the absence of any force acting on it. Statement 2: An object in uniform motion in a straight line shows
displacement even when the net force acting on it is zero.
A. Both statement 1 and statement 2 are true and statement 2 is correct explanation of statement
B. Both statement 1 and statement 2 are true, but statement 2 is not correct explanation of statement
c. statement 1 is true but statement 2 is false
D. Statement 1 is false but statement 2 is true
Subject: Physics
Two plane mirrors are inclined at \( 70^{0} . \) A
ray incident on one mirror at an angle \( \theta \) after reflection falls on the second
mirror and is reflected from there
parallel to the first mirror \( \boldsymbol{\theta} \) is
A \( .50^{\circ} \)
В . \( 45^{\circ} \)
\( c \cdot 30^{0} \)
D. 55
Subject: Maths
For any two complex numbers \( z_{1} \) and \( z_{2} \) with \( \left|z_{1}\right| \neq\left|z_{2}\right|,\left|\sqrt{2} z_{1}+i \sqrt{3} \overline{z_{2}}\right|^{2}+ \)
\( \left|\sqrt{3} \overline{z_{1}}+i \sqrt{2} z_{2}\right|^{2} \) is
A \( \cdot \) less than \( 5\left(\left|z_{1}\right|^{2}+\left|z_{2}\right|^{2}\right) \)
B. greater than \( 10 \mid z_{1} z_{2} \)
C . equal to \( 2\left|z_{1}\right|^{2}+3\left|z_{2}\right|^{2} \)
D. zero
Subject: Physics
Q Type your question.
perween I nomson's model ana
Rutherford's model better.
(a) Is the average angle of deflection of \( \alpha \) -particles by a thin gold foil predicted by Thomson's model much less, about
the same, or much greater than that predicted by Rutherford's model?
(b) Is the probability of backward scattering (i.e., scattering of \( \alpha \) -particles
at angles greater than \( 90^{\circ} \) ) predicted by
Thomsons model much less, about the
same, or much greater than that predicted by Rutherfords model?
(c) Keeping other factors fixed, it is found experimentally that for small thickness \( t, \) the number of \( \alpha \) -particles
scattered at moderate angles is proportional to t. What clue does this linear dependence on t provide?
(d) In which model is it completely wrong to ignore multiple scattering for the calculation of average angle of
scattering of \( \alpha \) -particles by a thin foil?
Subject: Maths
Nick surveyed a random sample of the freshman class of his high school to determine whether the Fall Festival
should be held in October or November.
Of the 90 students surveyed, \( 25.6 \% \) preferred October. Based on this information, about how many students in the entire 225 -person class would be expected to prefer having the Fall Festival in October?
A. 50
в. 60
\( c \cdot 75 \)
D. 80
Subject: Maths
\( \frac{\boldsymbol{d}}{\boldsymbol{d} \boldsymbol{x}}\left[\log _{e}\left\{\left(\boldsymbol{e}^{\boldsymbol{x}}+\boldsymbol{2}\right)+\right.\right. \)
\( \sqrt{\boldsymbol{e}^{2 \boldsymbol{x}}+\boldsymbol{4} \boldsymbol{e}^{\boldsymbol{x}}+\boldsymbol{5}}\}]= \)
A. \( \frac{1}{\sqrt{e^{2 x}+4 e^{x}+5}} \) C. \( \frac{e^{x}}{\sqrt{e^{2 x}+4 e^{x}+5}} \)
D. \( \frac{e^{x}}{\sqrt{e^{2 x}+4 e^{x}+3}} \)
\( \sqrt{e^{2 x}+4 e^{x}+3} \)
Subject: Chemistry
\( \boldsymbol{S} \boldsymbol{i} \boldsymbol{C l}_{4} \stackrel{\boldsymbol{H}_{2} \boldsymbol{O}}{\longrightarrow} \boldsymbol{X} \stackrel{\mathbf{1 0 0} \boldsymbol{0}}{\longrightarrow} \boldsymbol{Y} \)
In the above reaction, how many oxygen atom(s) is/are present in \( \mathrm{X} \) and \( \mathrm{Y} \) ? [f answer is \( 6 \text { and } 4, \text { represent as } 64] \)
Subject: Biology
Assertion
Slime moulds show alternation of
generation.
Reason
The sporangia bearing slime moulds
represent haplophase.
A. Both the assertion and the reason are true and the
reason is a correct explanation of the assertion
B. Both the assertion and reason are true but the reason
is not a correct explanation of the assertion
C. The assertion is true but the reason is false
D. Both the assertion and reason are false
Subject: Maths
Let \( f, g \) and \( h \) are differentiable functions. If \( \boldsymbol{f}(\mathbf{0})=\mathbf{1} ; \boldsymbol{g}(\mathbf{0})=\mathbf{2} ; \boldsymbol{h}(\mathbf{0})= \)
3 and the derivative of their pair wise
products at \( x=0 \) are \( (f g)^{\prime}(0)= \)
\( \mathbf{6} ;(\boldsymbol{g} \boldsymbol{h})^{\prime}(\mathbf{0})=\mathbf{4} \) and \( (\boldsymbol{h} \boldsymbol{f})^{\prime}(\mathbf{0})=\mathbf{5} \) then
compute the value of \( (f g h)^{\prime}(0) \)
A . 12
B . 15
c. 16
D. None of these
Subject: Maths
When \( 4 g^{3}-3 g^{2}+g+k \) is divided by
\( g-2, \) the remainder is \( 27 . \) Find the
value of \( k \)
\( \mathbf{A} \cdot \mathbf{3} \)
B. 5
c. 8
D. 12
E . 10
Subject: Physics
Two coils have mutual inductance
\( 0.005 H . \) The current changes in the form coil according to equation, \( \boldsymbol{I}= \)
\( I_{0} \sin \omega t . \) Where \( I_{0}=10 A . \) and \( \omega= \)
\( 100 \pi \) rads/s. The maximum value of
emf in the second coil is :
A . \( 12 \pi \)
B. \( 8 \pi \)
\( c .5 \pi \)
D. \( 2 \pi \)
Subject: Maths
\( \sin ^{-1} x+\sin ^{-1} \frac{1}{x}+\cos ^{-1} x+ \)
\( \cos ^{-1} \frac{1}{x}= \)
A . \( \pi \)
в.
c. \( \frac{3 \pi}{2} \)
D. None of these
Subject: Maths
A police cruiser, approaching a rightangled intersection from the north, is chasing a speeding car that has turned the corner and is now moving straight
east. When the cruiser is \( 0.6 \mathrm{km} \) north
of the intersection and the car is \( 0.8 \mathrm{km} \)
to the east, the police determine with radar that the distance of the car is
increasing at \( 20 \mathrm{km} / \mathrm{h} \). Suppose that the cruiser is moving at \( 60 \mathrm{km} / \mathrm{h} \) at the instant of measurement.
The speed of the car is (in \( \mathrm{km} / \mathrm{h}) \)
A . 70
B. 80
c. 75
D. 60
Subject: Biology
In reflex action, the reflex arc is formed
by
A. Brain \( \rightarrow \) spinal cord \( \rightarrow \) muscles
B. Receptor \( \rightarrow \) spinal cord \( \rightarrow \) muscles
c. Muscle \( \rightarrow \) receptor \( \rightarrow \) brain
D. Muscles \( \rightarrow \) spinal cord \( \rightarrow \) receptor
Subject: Maths
The value of the determinant
\( \left|\begin{array}{ccc}\mathbf{1} & \mathbf{1} & \mathbf{1} \\ m_{\mathbf{C}} & m+\mathbf{C}_{1} & m+\mathbf{2} \\ m & \mathbf{C}_{1} \\ m & \boldsymbol{m}+\mathbf{1} & \boldsymbol{C}_{2}\end{array}\right| \mathbf{~ i s ~ e q u a l ~ t o ~} \)
\( \mathbf{A} \cdot \mathbf{1} \)
B. -
\( c \cdot 0 \)
D. None of these
Subject: Chemistry
Which of the following methods can be
used to prepare propanoic acid?
\( \mathbf{A} \)
B.
\( \mathrm{CH}_{2}=\mathrm{CH}_{2}+\mathrm{CO}+\underset{(\text { Steam })}{\mathrm{H}_{2} \mathrm{O}}-\frac{\text { High pressure }}{570-670 \mathrm{K}} \)
C. Reaction of \( E t M g B r \) with dry ice followed by the acidification with diL \( H C l \)
D. Sodium ethoxide is heated with \( C O \) under pressure followed by the acidification with dil, \( H C l \)
Subject: Chemistry
A white solid \( X \) reacts with dil. \( H C l \) to
give colourless gas which is used in fire extinguishers. The solid \( \boldsymbol{X} \) is:
A \( . \) NaCl
в. \( C H_{2} \) СОО \( N a \)
\( \mathbf{c} \cdot N a_{2} C O_{3} \)
D. \( \operatorname{NaH} \mathrm{CO}_{3} \)
Subject: Physics
Five identical cubes each of mass \( m \)
are on a straight line with two adjacent faces in contact on a horizontal surface
as shown in the figure. Suppose the surface is frictionless and a constant
force \( \boldsymbol{P} \) is applied from left to right to the end face of \( A ; \) which of the following statements are correct?
\( \mathbf{P} \rightarrow \)\begin{tabular}{|l|l|l|l|l|}
\hline \( \mathbf{A} \) & \( \mathbf{B} \) & \( \mathbf{C} \) & \( \mathbf{D} \) & \( \mathbf{E} \) \\
\hline
\end{tabular}
A the acceleration of the system is \( \frac{5 P}{m} \)
B. the resultant force acting on each cube is \( \frac{P}{5} \)
c. the force exerted on D due to C is \( \frac{2 P}{5} \)
D. the acceleration of the cube \( D \) is \( \frac{P}{5} \) m
Subject: Chemistry
In the \( A l_{2} C l_{6} \) dimer:
\( \mathbf{A} \cdot \) all the \( A l-C l \) bonds are equivalent
B. three \( A l-C l \) bonds are equivalent and three are not
C. two \( A l-C l \) bonds are equivalent and four are not
D. four \( A l-C l \) bonds are equivalent and two are not
Subject: Chemistry
What will be the melting point of KCl if enthalpy change for the reaction is 7.25
mol \( ^{-1} \) and entropy change is 0.007 \( K^{-1} m o l^{-1} ? \)
\( \mathbf{A} \cdot 1835.2 \mathrm{K} \)
B. 173 К
c. \( 1035.7 \mathrm{K} \)
D. 1285.2 K
Subject: Physics
A body of mass \( m \) is taken from the earth's surface to the height equal to twice the radius (R) of the earth. The
change in potential energy of body will
be
A. \( 3 m g R \)
B. \( \frac{1}{3} m g R \)
c. \( 2 m g R \)
D. \( \frac{2}{3} m g R \)
Subject: Physics
For the situation shown in the figure,
flux through the square loop is
\( \mathbf{A} \cdot\left(\frac{\mu_{0} i a}{2 \pi}\right) \ln \left(\frac{a}{2 a-b}\right) \)
B \( \cdot\left(\frac{\mu_{0} i b}{2 \pi}\right) \ln \left(\frac{a}{2 b-b}\right) \)
\( \left(\frac{\mu_{0} i b}{2 \pi}\right) \ln \left(\frac{a}{b-a}\right) \)
\( \left(\frac{\mu_{0} i a}{2 \pi}\right) \ln \left(\frac{2 a}{b-a}\right) \)
Subject: Maths
The number of solutions of \( [\sin x+ \) \( \cos x]=3+[-\sin x]+[-\cos x] \) in the
interval \( [\mathbf{0}, \mathbf{2} \boldsymbol{\pi}] \) is (where [.] denotes the greatest integer function.)
\( \mathbf{A} \cdot \mathbf{0} \)
B. 4
\( c .3 \)
D. Infinitely many
Subject: Physics
Light of wavelength \( \lambda \) falls on a metal
having work function \( h c / \lambda_{0} \)

Photoelectric effect will take place only if
\( A \cdot \lambda \geq \lambda_{0} \)
в. \( \lambda \geq 2 \lambda_{0} \)
c. \( \lambda \leq \lambda_{0} \)
D. \( \lambda<\lambda_{0} / 2 \)
Subject: Maths
The value of \( \sum_{r=1}^{n} \int_{0}^{1} f(r-1+x) d x \) is equal to (if function has period 1 )
A \( \cdot \int_{0}^{1} f(x) d x \)
B. \( _{n \int_{0}}^{1} f(x) d x \)
c. \( (n-1) \int_{0}^{1} f(x) d x \)
D. \( \int_{0}^{n} f(x) d x \)
Subject: Chemistry
The IUPAC name of the compound is:
\[
\begin{array}{l}
C H_{2}-C H-C H_{2}-C H_{2} \\
N_{2} \quad C H_{3} \quad \quad_{N H_{2}}
\end{array}
\]
A. 2 - Methyl - butane - 1,4 - diamine
B. 3 - Methyl - butane - 1, 4 - diamine
C . 2 - Methyl - butane - 1, 3 - diamine
D. 2 - Methyl pentane - 1, 5 - diamine
Subject: Chemistry
Which of the following is true for
spontaneous adsorption of \( \boldsymbol{H}_{2} \) gas
without dissociation on the solid
surface?
A. Process is exothermic and \( \Delta \mathrm{S}<0 \)
B. Process is endothermic and \( \Delta S>0 \)
c. Process is exothermic and \( \Delta S>0 \)
D. Process is endothermic and \( \Delta S<0 \)
Subject: Chemistry
Circumference of the first orbit of
hydrogen atom is given by the formula:
\( \left[a_{0}=\frac{h^{2}}{4 \pi^{2} m e^{2}}\right] \)
A \( \cdot \frac{22}{7} a \)
в. \( \frac{\pi a_{0}}{2} \)
c. \( \sqrt{4} \pi a_{0} \)
D. \( \pi a_{0} \)
Subject: Physics
The energy taken by system is \( \delta Q, \) work
done by system is \( \delta W \) and increase in
internal energy is \( d U, \) the quantity which does not depend on path is :
\( \mathbf{A} \cdot d U \)
B. \( \delta Q \)
\( \mathbf{c} \cdot \delta Q \& \delta W \)
D. \( \delta W \)