AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Chemistry
A compound 'X' gives brisk
effervescence of \( C O_{2} \) on treatment with
Na H \( C O_{3} \) and when treated with

Li \( A l H_{4} \) gives ethyl alcohol. Therefore 'X
may be:
A. \( C H_{3} C O C H_{3} \)
в. \( C H_{3} C H_{2} C H O \)
c. \( C H_{3} C H O \)
D. \( C H_{3} C O O H \)
Subject: Physics
A sonar device on a submarine send out
a signal and receives an echo 5 seconds later. Calculate the speed of sound in water, if the distance of the object from the submarine is \( 3625 \mathrm{m} \)
A. \( 1440 \mathrm{ms}^{1} \)
B. \( 1460 \mathrm{ms}^{1} \)
c. \( 1450 m s^{1} \)
D. \( 1470 \mathrm{ms}^{1} \)
Subject: Chemistry
Which among the following sets of atomic numbers is/are associated with
the increasing order of the number of
unpaired electrons?
\( (a) z=29 ; z=20 ; Z=25 ; Z=27 ; Z=24 \)
\( (b) z=20 ; z=29 ; z=22 ; z=27 ; z=25 \)
\( (c) z=19 ; z=22 ; z=24 ; z=26 ; z=25 \)
\( (d) Z=19 ; Z=22 ; Z=26 ; Z=25 ; Z=24 \)
\( A \cdot \) a and \( c \)
B. b and
\( c \cdot a \) and \( d \)
D. b and c
Subject: Maths
A girl walks \( 4 k m \) towards West, then
she walks \( 3 k m \) in a direction \( 30^{\circ} \) East
of North and stops. Then, the girl's displacement from her initial point of departure is
A \( -\frac{5}{2} \hat{i}+\frac{3 \sqrt{3}}{2} \)
B. \( \frac{1}{2} \hat{i}+\frac{\sqrt{3}}{2} \hat{j} \)
c. \( -\frac{1}{2} \hat{i}+\frac{3 \sqrt{3}}{2} \)
D. None of these
Subject: Physics
Which of the following reactions is
impossible?
\( \mathbf{A} \cdot_{2} \mathrm{He}^{4}+_{4} \mathrm{Be}^{9}=_{0} \mathrm{n}^{1}+_{6} \mathrm{C}^{12} \)
\( \mathbf{B} \cdot_{2} \mathrm{He}^{4}+_{7} \mathrm{N}^{14}=_{1} \mathrm{H}^{1}+_{8} \mathrm{O}^{17} \)
\( \mathbf{C} \cdot 4\left(_{1} \mathrm{H}^{1}\right)=_{2} \mathrm{He}^{4}+2\left(_{1} \mathrm{e}^{0}\right) \)
\( \mathbf{D} \cdot_{3} \mathrm{Li}^{4}+_{1} \mathrm{H}^{1}=_{4} \mathrm{Be}^{8} \)
Subject: Physics
The wavefront of a lightbeam is given by the equation \( x+2 y+3 z=c, \) (where \( c \)
is arbitary constant) the angle made by the direction of light with the y-axis is:
A \( \cdot \cos ^{-1} \frac{1}{\sqrt{14}} \)
B. \( \cos ^{-1} \frac{2}{\sqrt{14}} \)
c. \( \sin ^{-1} \frac{1}{\sqrt{14}} \)
D. \( \sin ^{-1} \frac{2}{\sqrt{14}} \)
Subject: Maths
If \( p \) and \( q \) are non-collinear unit vectors
and \( |\boldsymbol{p}+\boldsymbol{q}|=\sqrt{\mathbf{3}}, \) then \( (\mathbf{2} \boldsymbol{p}-\boldsymbol{3} \boldsymbol{q}) \)
\( (3 p+q) \) is equal to
\( \mathbf{A} \cdot \mathbf{0} \)
в. \( \frac{1}{3} \)
\( c \cdot-\frac{1}{3} \)
D. \( \frac{1}{2} \)
\( E \cdot-\frac{1}{2} \)
Subject: Physics
One end of a spring of natural length
\( \ell_{0}=0.1 \mathrm{m} \) and spring constant \( \mathrm{k}=80 \)
N/m is fixed to the ground and other
end is fitted with a smooth ring of mass \( \mathbf{m}=2 \mathrm{gm}, \) which is allowed to slide on a
horizontal rod fixed at a height \( h= \) \( 0.1 \mathrm{m} . \) Initially, the spring makes an
angle of \( 37^{\circ} \) with vertical when the
system is released from rest.

When the spring becomes vertical,
speed of ring is ' \( v^{\prime} \mathrm{m} / \mathrm{s}, \) find ' \( v \) '. \( \left(\cos 37^{\circ}=\frac{4}{5}\right) \)
Subject: Chemistry
Given \( : \boldsymbol{H}_{2} \boldsymbol{O}_{2} \rightarrow \boldsymbol{O}_{2}+\boldsymbol{2} \boldsymbol{H}^{\oplus}+\boldsymbol{2} \boldsymbol{e}^{-} \)
\( \boldsymbol{E}^{\ominus}=-\mathbf{0 . 6 9} \boldsymbol{V} \)
\( \boldsymbol{H}_{2} \boldsymbol{O}_{2}+\boldsymbol{2} \boldsymbol{H}^{\oplus}+\boldsymbol{2} \boldsymbol{e}^{-} \rightarrow \boldsymbol{2} \boldsymbol{H}_{2} \boldsymbol{O} \)
\( \boldsymbol{E}^{\ominus}=\mathbf{1 . 7 7} \boldsymbol{V} \)
\( \boldsymbol{I}^{\ominus} \rightarrow+\mathbf{2} e^{-} \)
\( \boldsymbol{E}^{\ominus}=-\mathbf{0 . 5 3 5} \boldsymbol{V} \)
Which of the following statements is / (are) correct?
This question has multiple correct options
\( \mathbf{A} \cdot H_{2} O_{2} \) behaves as an oxidant for \( I_{2} / I^{\ominus} \)
B. \( H_{2} O_{2} \) behaves as an reductant for \( I_{2} / I^{\ominus} \)
C \( \cdot I^{\ominus} / I_{2} \) behaves as an reductant for \( H_{2} O_{2} \)
D. None of these is correct.
Subject: Physics
The charge on a particle is 100 times that of electron. It is revolving in a circular path of radius \( 0.8 \mathrm{m} \) at a frequency of \( 10^{t h} \) revolutions per second. The magnetic field at the centre of path will be -
A \( \cdot 10^{-16} b_{0} \)
0
B. \( \frac{10^{-7}}{\mu} \)
\( \mathbf{c} \cdot 10^{-17} \mu \)
D. \( 10^{-6} \mu \)
Subject: Maths
The value of \( \left(9 x^{2}+18 x+27\right) \div 9 \) is
equal to
\( \mathbf{A} \cdot x+2 \)
B. \( x^{2}+2 x+2 \)
c. \( x^{2}+2 x+3 \)
D. \( x^{2}+2 x+1 \)
Subject: Maths
The perimeter of a triangle formed by points \( (\mathbf{0}, \mathbf{0}),(\mathbf{6}, \mathbf{0}),(\mathbf{0}, \mathbf{6}) \) is
A. \( 6(2+\sqrt{2}) \) units
B. \( 2+\sqrt{2} \) units
c. \( 6 \sqrt{2} \) units
D. None of the above
Subject: Chemistry
Compounds \( (C) \) and \( (D) \) are:
\( A \)
\[
\begin{array}{l}
\text { сно } \\
\text { соон }
\end{array}
\]
в.
сно \( _{\text {апа }} \) соон СООН \( ^{\text {СН }} \) он
\( c \)
\[
\begin{array}{l}
\mathrm{COOH} \\
\mathrm{COOH}
\end{array}
\]
D.
\[
\begin{array}{l}
\text { соон соон } \\
\text { соон }^{\text {апа }} \text { СН }_{2} \text { он }
\end{array}
\]
Subject: Physics
A conductor carries a current of \( 50 \mu A \) If the area of cross-section of the
conductor is \( 50 \mathrm{mm}^{2} \), then value of the
current density in \( A m^{-2} \) is
A . 0.5
B.
\( c \cdot 10^{-3} \)
D. \( 10^{-6} \)
Subject: Maths
\( \boldsymbol{g}(\boldsymbol{x})=\left\{\begin{array}{ll}\mathbf{1} & \boldsymbol{x} \leq-\boldsymbol{2} \\ \frac{\mathbf{1}}{\mathbf{2}} \boldsymbol{x} & -\boldsymbol{2}<\boldsymbol{x}<\mathbf{4} \text { .then } \\ \sqrt{\boldsymbol{x}} & , \boldsymbol{x} \geq \mathbf{4}\end{array}\right. \)
A. \( g \) is a continuous function
B. all the discontinuities are removable discontinuities
c. all the discontinuities are jump
D. all the discontinuities are infinitt
Subject: Chemistry
Two moles of gas \( A_{2} \) are mixed with two
moles of gas \( B_{2} \) in a flask of volume 1 lit.
If at equilibrium 0.5 moles of \( A_{2} \) is obtained. Then find out Kp for reaction
\( \boldsymbol{A}_{2}(\boldsymbol{g})+\boldsymbol{B}_{2}(\boldsymbol{g}) \rightarrow \boldsymbol{2} \boldsymbol{A} \boldsymbol{B}(\boldsymbol{g}) \)
\( A \cdot 12 \)
B. 9
\( c \cdot 4 \)
D. 36
Subject: Physics
A circular disc of radius 0.2 meter is placed in a uniform magnetic field of \( \frac{1}{\pi} \) \( \boldsymbol{w} \boldsymbol{b} / \boldsymbol{m}^{2} \) in such way that its axis makes an angle of \( 60^{\circ} \) with \( \vec{B} \). The magnetic flux linked with the disc is?
A. 0.08 wb
B. 0.01 wb
\( c .0 .02 \mathrm{wb} \)
D. 0.06 wb
Subject: Maths
The internal and external diameters of a
hollow hemispherical vessel are \( 24 \mathrm{cm} \)
and \( 25 c m, \) respectively. The cost to paint \( 1 \mathrm{cm}^{2} \) surface is \( R s .0 .05 . \) Find the
total cost to paint the vessel all over.
(use \( \left.\pi=\frac{22}{7}\right) \)
A . Rs.2100
B. \( R s .1867 \)
c. \( R s .1245 \)
D. None of the above
Subject: Maths
Find \( \frac{\boldsymbol{d} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}} \) of \( \boldsymbol{x}^{2}+\boldsymbol{x} \boldsymbol{y}+\boldsymbol{y}^{2}=\mathbf{1 0 0} \)
Subject: Biology
toppr ow
Q Type your question
Choose the correct body plan from \( A \) to \( G \)
and fill in the table.
Column I Column II
Name of the animal \( \quad \) Body Plan
(i) Silverfish
(ii) Planaria
(iii) Jellyfish
(iv) Lizard
(v) Ascaris
Ectoderm
I Fndodern
\( \therefore \therefore \). mesoderm
cavity
Subject: Physics
A coil having 500 square loops each of side \( 10 \mathrm{cm} \) is placed normal to a magnetic field which increases at the rate of \( 1 T s^{-1} . \) The induced e.m.f. is
A . 0.1
B. 5.0 V
\( c \cdot 0.5 v \)
D. 1.0
Subject: Chemistry
Statement 1: Elemental iodine has a
higher boiling point than elemental bromine.

Statement 2 : lodine forms stronger covalent bonds than bromine.
A. Both Statement 1 and Statement 2 are correct and Statement 2 is the correct explanation of Statement 1.
B. Both Statement 1 and Statement 2 are correct and Statement 2 is not the correct explanation of Statement 1.
c. Statement 1 is correct but Statement 2 is not correct
D. Statement 1 is not correct but statement 2 is correct
E. Both the Statement 1 and Statement 2 are not correct
Subject: Physics
A bullet of mass \( \mathrm{m} \) is fired from a gun of mass M. The recoiling gun compresses a spring of force constant k by a distance d. Then the velocity of the bullet is :
A. \( k d \sqrt{M / m} \)
в. \( \frac{d}{M} \sqrt{k m} \)
c. \( \frac{d}{m} \sqrt{k M} \)
D. \( \frac{k M}{m} \sqrt{d} \)
Subject: Chemistry
A student conducted an experiment and obtained three values during three repetitive trials: \( 1.65,1.68,1.71 . \) Later, the student discovered that the true value
was \( 2.37 . \) In contrast to the real value,
the experimental results should be characterized as:
A. not accurate and not precise
B. accurate but not precise
c. not accurate but precise
D. accurate and precise
E. accurate, precise, but unrealiable
Subject: Physics
The rate of change of velocity gives acceleration. If the acceleration of a
particle is \( a=3 t^{2} m s^{-2} \) and velocity of
particle at \( t=0 \) is \( 1 m s^{-1}, \) then velocity
of the particle at \( t=2 s \) will be
A \( \cdot 12 m s^{-1} \)
B. \( 13 m s^{-1} \)
\( \mathrm{c} \cdot 11 \mathrm{ms}^{-1} \)
\( \mathbf{D} \cdot 9 m s^{-1} \)
Subject: Maths
If \( f \) and \( g \) are differentiable functions
then \( D *(f g) \) is equal to
A. \( f D * g+g D * f \)
В. \( D * f D * g \)
C \( \cdot f^{2} D * g+g^{2} D * f \)
D \( \cdot f(D * g)^{2}+g(D * f)^{2} \)
Subject: Maths
\[
\begin{aligned}
\boldsymbol{f}(\boldsymbol{x})=& \frac{|\boldsymbol{x}|}{\boldsymbol{x}} \boldsymbol{x} \neq \mathbf{0} \\
\mathbf{0} \boldsymbol{x}=\mathbf{0}
\end{aligned}
\]
Check whether \( f(x) \) is continous or not
at \( x=0 \)
Subject: Biology
Which of the following statements are
correct?
(i) When a fruit develops from the inflorescence, it is composite.
(ii) Mesocarp is the edible part in apple.
(iii) Gynobasic style is seen in Ocimum.
(iv) Hypanthodium is a special type of inflorescence found in Euphorbia species.
A. (i) and (iv) are correct
B. (i) and (iii) are correct
C \( . \) (i) and (ii) are correct
D. (ii), (iii) and (iv) are correct
E. (ii) and (iv) are correct
Subject: Physics
A uniform rod of length \( l \) is placed
symmetrically on two walls as shown in figure. The rod is in equilibrium. If
\( N_{1} \) and \( N_{2} \) are the normal forces
exerted by the walls on the rod then:
\( \mathbf{A} \cdot N_{1}>N_{2} \)
В. \( N_{1}<N_{2} \)
\( \mathbf{c} \cdot N_{1}=N_{2} \)
D. \( N_{1} \) and \( N_{2} \) would be in the vertical directions
Subject: Physics
Find the moments of time when the
particle is at the distance \( 10.0 \mathrm{cm} \) from the origin.
A. \( 1.1,9, \) and \( 11 s \)
B. \( 1,10, \) and \( 11 s \)
c. \( 1.1,10, \) and \( 11 s \)
D. \( 1.1,9, \) and \( 13 s \)
Subject: Physics
The diameter of the eye ball of a normal
eye is about \( 2.5 \mathrm{cm} . \) The power of the eye lens varies from
\( \mathbf{A} \cdot 9 D \) to \( 8 D \)
B. \( 40 D \) to \( 32 D \)
c. \( 44 D \) to \( 40 D \)
D. None of these
Subject: Chemistry
Complete the following reaction, \( P_{4}+ \)
\( N a O H+H_{2} O \rightarrow ? \)
A. \( P H_{3}+N a_{2} H P O_{2} \)
в. \( P H_{3}+N a H_{2} P O_{2} \)
c. \( H_{3} P O_{4}+N a O \)
D. \( P H_{3}+N a_{2} P O_{4} \)
Subject: Physics
A boat travels from south bank to north
bank of a with a maximum speed of 8
km/h. To arrive at a opposite to the point of start, the boat should start angle :
\( \mathbf{A} \cdot \tan ^{-1}(1 / 2) W \) of \( \mathrm{N} \)
B. \( \tan ^{-1}(1 / 2) N \) of \( w \)
c. \( 30^{\circ} \mathrm{WofN} \)
D. \( 30^{\circ} \) Nof \( W \)
Subject: Physics
Two magnetic poles of strengths \( 40 A m \) and \( 10 A m \) are separated by a distance
of \( 20 \mathrm{cm} \) in air. The force between them
if the distance is reduced to \( 10 \mathrm{cm} \) is
A \( \cdot 4 \times 10^{-3} N, 10^{-3} N \)
B . \( 10^{-3} N, 4 \times 10^{-3} N \)
c. \( 2 \times 10^{-3} N, 10^{-3} N \)
D. \( 10^{-3} N, 2 \times 10^{-3} N \)
Subject: Physics
Figure shows the position-time graph of
a particle of mass 4 kg. Let the force on
the particle for \( t<0,0 F_{1}, F_{2} \) and \( F_{3} \)
respectively. Then
A \( \cdot F_{1}=F_{2}=F_{3}=0 \)
B. \( F_{1}>F_{2}=F_{3} \)
\( \mathrm{c} \cdot F_{1}>F_{2}>F_{3} \)
\( F_{1}<F_{2}<F_{3} \)
Subject: Maths
Fill in the boxes with the symbols '<' or
'>' to make the given statements true:
\( \frac{5}{11} \square \frac{3}{7} \)
\( \frac{8}{15} \square \frac{3}{5} \)
\( \frac{11}{14} \square \frac{29}{35} \)
\( \frac{13}{27} \square \frac{15}{48} \)
Subject: Maths
Determine the domain and range of the relation R defined by \( \boldsymbol{R}=\{(\boldsymbol{x}, \boldsymbol{x}+\mathbf{5}) \)
\( \boldsymbol{x} \in\{\mathbf{0}, \mathbf{1}, \mathbf{2}, \mathbf{3}, \mathbf{4}, \mathbf{5}\}\} \)
Subject: Physics
Light of two different frequencies whose
protons have energies \( 1 e V \) and \( 2.5 e V \)
respectively, successively illuminate a metallic surface whose work function is
\( 0.5 e V . \) Ratio of maximum speeds of
emitted electrons will be
A .1: 5
B. 1: 4
c. 1: 2
D. 1: 1
Subject: Maths
Prove the following by using principle of mathematical induction for all \( \boldsymbol{n} \in \boldsymbol{N} \)
\( \mathbf{1} . \mathbf{3}+\mathbf{3 . 5}+\mathbf{5 . 7}+\ldots \ldots .+(\mathbf{2 n}- \)
\( \mathbf{1})(\mathbf{2 n}+\mathbf{1})=\frac{\boldsymbol{n}\left(\mathbf{4} \boldsymbol{n}^{2}+\mathbf{6} \boldsymbol{n}-\mathbf{1}\right)}{\mathbf{3}} \)
Subject: Maths
Let \( \boldsymbol{f}:(-1,1) \rightarrow(-1,1) \) be continuous
\( \boldsymbol{f}(\boldsymbol{x})=\boldsymbol{f}\left(\boldsymbol{x}^{2}\right) \) for all \( \boldsymbol{x} \in(-1,1) \) and
\( f(0)=\frac{1}{2}, \) then the value of \( 4 f\left(\frac{1}{4}\right) \) is
A . 1
B. 2
\( c \cdot 3 \)
D. 4
E . 5
Subject: Chemistry
The compound \( N a_{2} I r C l_{6} \) reacts with triphenylphosphine in diethyleneglycol
in an atmosphere of \( C O \) to give
\( \left[\operatorname{Ir} C l(C O)\left(P P h_{3}\right)_{2}\right], \) known as 'Vaska's
compound'. The number of unpaired electrons and oxidation state of iridium
in the complex respectively is:
[Atomic number of \( \boldsymbol{I r}=\mathbf{7 7}] \)
\( A \cdot 0,0 \)
B. \( 0, \)
\( c \cdot 1, \)
D. 1,2
Subject: Biology
conversion of glucose into ethanol, a
key process of anaerobic energy
transformation in some organisms.
The best explanation for this is that
A. Step 1 illustrates that ATP hydrolysis is an energetically favorable exergonic reaction that couples the free energy released when ATP forms ADP and Pi (inorganic phosphate) with the endergonic conversion of glucose into pyruvate.
B. NADH is oxidized during step 1 and reduced during step
3
c. Step 1 illustrates the phosphorylation of ADP into ATP, which is coupled to the energetically favorable conversion of glucose into pyruvate
D. In step 1 ATP is oxidized and glucose is reduced, and it is this coupling that provides the energy to drive ethanol production
Subject: Maths
The position vectors of \( \boldsymbol{P} \) and \( \boldsymbol{Q} \) are
respectively \( a \) and \( b \). If \( R \) is a point on
\( P Q, P Q \) such that \( P R=5 P Q, \) then the
position vector of \( \boldsymbol{R} \) is
A \( .5 b-4 a \)
B. \( 5 b+4 a \)
c. \( 4 b-5 a \)
D. \( 4 b+5 a \)
Subject: Physics
One half of a convex lens of focal length \( 10 \mathrm{cm} \) is covered with a black paper. Can such a lens produce an image of a complete object placed at a distance of \( 30 \mathrm{cm} \) from the lens? Draw a ray
diagram to justify your answer. A \( 4 \mathrm{cm} \) tall object is placed perpendicular to its principal axis of a convex lens of focal length \( 20 \mathrm{cm} . \) The distance of the object from the lens is 15 cm. Find the nature, position and the size of the image.
Subject: Physics
The graph below represents the motion
of a remote control car back and forth
along a straight line path.

What is the average velocity of the car
during the first 25 seconds of its
motion?
\( \mathbf{A} \cdot 8.0 m / s \)
B. \( 7.0 \mathrm{m} / \mathrm{s} \)
c. \( 5.0 m / s \)
D. \( 4.0 \mathrm{m} / \mathrm{s} \)
E . \( 3.0 \mathrm{m} / \mathrm{s} \)
Subject: Physics
How much time will have elapsed?
A \( .1 .42 \times 10^{-8} \mathrm{s} \)
B . \( 2.84 \times 10^{-8} \mathrm{s} \)
c. \( 3.84 \times 10^{-8} \mathrm{s} \)
D. \( 5.68 \times 10^{-8} \mathrm{s} \)
Subject: Physics
A piece of copper wire has twice the radius of steel wire. One end of the
copper wire is joined to one end of steel wire so that both of them can be
subjected to the same longitudinal force. \( Y \) for steel is twice that of copper.
When the length of copper wire is increased by \( 1 \% \), the steel wire will be stretched by
A . 2\% of its original length
B. 1\% of its original length
c. \( 4 \% \) of its original length
D. 0.5\% of its original length
Subject: Physics
Two short electric dipoles are placed as
shown ( \( r \) is distance between their
centres). The energy of electric interaction between these dipoles will
be:
\( \left(C \text { is centre of dipole of moment } \boldsymbol{P}_{2}\right) \)
\( A \)
B. \( -\frac{2 k P_{1} P_{2} \cos \theta}{r^{3}} \)
c. \( \frac{-2 k P_{1} P_{2} \sin \theta}{r^{3}} \)
D.
Subject: Physics
Assertion
Vibrational energy of diatomic molecule corresponding to each degree of
freedom is \( k_{B} T \)
Reason
For every molecule, vibrational degree of freedom is 2
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: Chemistry
DE \( \boldsymbol{C H}_{3}-\boldsymbol{C H}-\boldsymbol{C H}_{2}-\boldsymbol{C H}_{3} \frac{A l_{2} \boldsymbol{O}_{3}}{573 \boldsymbol{K}} \)
\( \boldsymbol{C H}_{3}-\boldsymbol{C H}=\boldsymbol{C H}-\boldsymbol{C H}_{3} \)
Butane-2-ol
2-ene
Subject: Physics
What is the conductivity of a
semiconductor if electron density \( = \)
\( 5 \times 10^{12} / c m^{3} \) and hole density \( =8 \times \)
\( \mathbf{1 0}^{13} / \mathbf{c m}^{3}\left(\boldsymbol{\mu}_{e}=\mathbf{2 . 3 m}^{2} \boldsymbol{V}^{-1} \boldsymbol{s}^{-1}, \boldsymbol{\mu}_{\boldsymbol{h}}=\right. \)
\( \left.0.01 m^{2} V^{-1} s^{-1}\right) \)
\( \mathbf{A} \cdot 5.634 \)
B. 1.968
c. 3.421
D. 8.964
Subject: Maths
If \( \boldsymbol{x} \boldsymbol{y}+\boldsymbol{y}^{2}=\tan \boldsymbol{x}+\boldsymbol{y}, \) then \( \frac{\boldsymbol{d} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}} \) is equa
to
A \( \frac{\sec ^{2} x-y}{(x+2 y-1)} \)
B. \( \frac{\cos ^{2} x+y}{(x+2 y-1)} \)
C \( \frac{\sec ^{2} x-y}{(2 x+y-1)} \)
D. \( \frac{\cos ^{2} x+y}{(2 x+2 y-1)} \)
Subject: Physics
There exists a non-uniform electric field
along \( x \) -axis as shown in the figure
below. The field increases at a uniform
rate along +ve x-axis. A dipole is placed inside the field as shown.Which one of
the following is correct for the dipole?
A. Dipole moves along positive x-axis and undergoes a clockwise rotation
B. Dipole moves along negative x-axis and undergoes a clockwise rotation
c. Dipole moves along positive x-axis and undergoes a anticlockwise rotation
D. Dipole moves along negative x-axis and undergoes a anticlockwise rotation
Subject: Chemistry
Select the correct order with respect to
boiling point of the given compounds.
A. \( H_{2} O>H_{2} S>H_{2} S e>H_{2} T e \)
в. \( H_{2} O>H_{2} T e>H_{2} S e>H_{2} S \)
c. \( H_{2} T e>H_{2} S e>H_{2} S>H_{2} O \)
D. \( H_{2} S>H_{2} O>H_{2} T e>H_{2} S e \)
Subject: Chemistry
Give the reagent that would best
accomplish the following
transformation:
\( \mathbf{A} \cdot M C P B A \)
в. \( C H_{3} \) СООН
\( \mathbf{c} \cdot\left(C H_{3}\right)_{3} \operatorname{COOC}\left(C H_{3}\right) \)
D. \( B r_{2} / N a O H \)
Subject: Chemistry
The end product 'W' in the following
sequence of reactions is :
\( A \)
\( P h-C H_{2}-C H_{2}-O-C H-P h \)
B. \( P h-C H-O-C H-P h \)
c. \( P h-C H_{2}-O-C H_{2}-C H_{2}-P h \)
\( D \)
Subject: Physics
A \( 5 \mathrm{m} \) long aluminium wire \( (\boldsymbol{Y}=\mathbf{7} \times \)
\( \left.10^{10} N m^{-2}\right) \) of diameter \( 3 \mathrm{mm} \) supports
a \( 40 \mathrm{kg} \) mass. In order to have the same
elongation in the copper wire \( (\boldsymbol{Y}= \)
\( \left.12 \times 10^{10} N m^{-2}\right) \) of the same length
under the same weight, the diameter should now be (in \( \mathrm{mm} \) ).
A . 1.75
в. 1.5
c. 2.5
D. 5.0
Subject: Physics
A uniform disc of mass \( M \) and radius \( R \)
is mounted on an axle supported in frictionless bearings. A light cord is wrapped around the rim of the disc and
a steady downward pull \( T \) is exerted on
the cord. If we hang a body of mass \( m \) with the cord, the tangential acceleration of the disc will be
A. \( \frac{m g}{M+m} \)
в. \( \frac{m g}{M+2 m} \)
c. \( \frac{2 m g}{M+2 m} \)
D. \( \frac{M+2 m}{2 m g} \)
Subject: Physics
Three charges each of magnitude q are placed at the corners of an equilateral triangle, the electrostatic force on the
charge placed at the center is(each side of triangle is \( L \) )
A. Zero
\( ^{\mathrm{B}} \frac{1}{4 \pi \varepsilon_{0}} \frac{q^{2}}{L^{2}} \)
c. \( \frac{1}{4 \pi \varepsilon_{0}} \frac{3 q^{2}}{L^{2}} \)
\( D \)
Subject: Maths
If \( A=10 w^{3}+20 w^{2}-55 w+60 \)
\( \mathrm{B}=-25 w^{2}+15 w-10 \) and
\( \mathbf{C}=\mathbf{5} \boldsymbol{w}^{2}-\mathbf{1 0} \boldsymbol{w}+\mathbf{2 0} \)
then \( A+B-C \) is equal to
A \( \cdot 10 w^{3}+10 w^{2}+30 w+30 \)
B. \( 10 w^{3}+10 w^{2}-30 w+30 \)
c. \( 10 w^{3}-10 w^{2}-30 w+30 \)
D. None of these
Subject: Chemistry
What concentration of nitrogen should
be present in a glass of water at room
temperature? Assume a temperature of
\( 25^{\circ} \mathrm{C}, \) a total pressure of 1 atmosphere
and mole fraction of nitrogen in air of \( 0.78 .\left(K_{H} \text { for nitrogen }=8.42 \times 10^{-7}\right. \)
\( \mathrm{M} / \mathrm{mm} \mathrm{Hg} \)
Subject: Maths
The equation of the straight line passing through the point (4,3) and making intercepts on the cordinate axes whose sum is \( -1, \) is :
A \( \cdot \frac{x}{2}+\frac{y}{3}=-1 \) and \( \frac{x}{-2}+\frac{y}{1}=-1 \)
B. \( \frac{x}{2}-\frac{y}{3}=-1 \) and \( \frac{x}{-2}+\frac{y}{1}=-1 \)
c. \( \frac{x}{2}+\frac{y}{3}=-1 \) and \( \frac{x}{-2}+\frac{y}{1}=1 \)
D. \( \frac{x}{2}-\frac{y}{3}=1 \) and \( \frac{x}{-2}+\frac{y}{1}=1 \)
Subject: Chemistry
The correct name for the complex ion
\( \left[\operatorname{CoCl}(O N)(e n)_{2}\right]^{+} \) is :
A. chlorobis(ethylenediamine)nitrito-O-cobaltate (III) ion
B. chlorodiethyldiaminenitrito-O-cobalt (III) ion
C. chloronitrito-O-diethyldiamine cobaltate (III) ion
D. chlorobis(ethylenediamine)nitrito-O-cobalt (III) ion
Subject: Chemistry
In the following reaction,the product 'R' is \( : \boldsymbol{C a} \boldsymbol{C}_{2} \stackrel{\boldsymbol{H}_{2} \boldsymbol{O}}{\longrightarrow} \boldsymbol{P}_{\boldsymbol{t u b e}}^{h o t} \stackrel{i r o n}{\boldsymbol{Q}} \frac{C \boldsymbol{H}_{3} C l}{A \boldsymbol{l} C l_{3}} \boldsymbol{R} \)
A. Chloro benzene
B. benzene
c. toluene
D. anisole
Subject: Physics
The electric current in a circular coil of
two turns produced a magnetic
induction of \( 0.2 \mathrm{T} \) at its centre. The coil
is unwound and then rewound into a
circular coil of four turns. If same
current flows in the coil, the magnetic induction at the centre of the coil now
is:
A. \( 0.2 T \)
в. \( 0.4 \mathrm{T} \)
\( c .0 .65 \)
D. 0.8 T
Subject: Physics
Two superimposing waves are
represented by equation \( \boldsymbol{y}_{1}= \)
\( 2 \sin 2 \pi(10 t-0.4 x) \) and \( y_{2}= \)
\( 4 \sin 2 \pi(20 t-0.8 x) . \) The ratio of \( I_{\max } \) to
\( \boldsymbol{I}_{m i n} \)
\( \mathbf{A} \cdot 36: 4 \)
B. 25: 9
\( c \cdot 1: 4 \)
D. 4: 1