Prove that \( e^{x}-x>1, \) if \( x>0 \)


A uniform magnetic field of 5000 gauss is established along the positive zdirection. A rectangular loop of side \( 20 \mathrm{cm} \) and \( 5 \mathrm{cm} \) carries a current of
\( 10 A \) is suspended in this magnetic
field. What is the torque on the loop in the different cases shown in the
following figures? What is the force in
each case? Which case corresponds to stable equilibrium?


Drift speed of electrons, when \( 1.5 A \) of
current flows in a copper wire of cross section \( 5 m m 2, \) is \( v . \) If the electron
density in copper is \( 9 \times 10^{28} / m^{3} \) the
value of \( v \) in \( m m / s \) is close to
(Take charge of electron to be \( =1.6 \times \)
\( \left.10^{-19} C\right) \)
A . 0.2
B. 3
\( c \cdot 2 \)
D. 0.02


Lanthanoids are:
A. 14 elements in the seventh period(At. no. 90 to 103 ) that are filling \( 5 f \) sublevel
B. 14 elements in the sixth period(At. No. 58 to 71 ) that are filling 4f sublevel.
C. 14 elements in the seventh period(At. No.58 to 71 ) that are filling 4f sublevel
D. 14 elements in the sixth period (At.No.90 to103)


If \( f(x)=\left\{\begin{array}{ll}2 x+3 & x \leq 1 \\ a^{2} x+1 & x>1\end{array}, \) then the \right.
values of \( a \) for which \( f(x) \) is injective.
A . -3
B.
c. 0
D. none of these


A hammer weighing \( 3 \mathrm{kg}, \) moving with a velocity of \( 10 \mathrm{m} / \mathrm{s}, \) strikes against the head of a spike and drives it into a block of wood. If the hammer comes to rest in
\( 0.025 s, \) the impulse associated with the ball will be
A. 30 N s
B. -30 N s
c. \( 15 \mathrm{N} \) s
D. -15 N s


I.P values of post lanthanides \( (\boldsymbol{A} \boldsymbol{g}, \boldsymbol{A} \boldsymbol{u}) \)
have higher values down the group. Explain.


Give the best reagent for the following reaction:
\( C_{2} H_{4}(\text {ethene}) \rightarrow C_{2} H_{6}(\text {ethane}) \)
A \( . H_{2} \)
B. \( H^{+} / H_{2} O \)
c. \( H_{2} / P d \)
D. None of these


The lanthanides and actinides are a
group of closely-related elements which are often found in the products of nuclear fission of heavy elements. They can be separated from one another and from other nuclear products by:
A. distillation
B. ion-exchange chromatography
c. evaporation on a metal foil
D. slow melting


The acidic nature of hydrogen in acetylene cannot be explained by the reaction with:
A. sodium metal
B. ammonical cuprous chloride solution
c. ammonical silver nitrate solution
D. hydrogen cyanide


The displacement of a particle
executing SHM at any instant \( t \) is \( x= \)
\( 7 \cos 0.5 \pi t . \) The time taken by the
particle in reaching from mean position to extreme position will be
A . \( 4 s \)
B . \( 2 s \)
c. \( 1 s \)
D. \( 1 / 2 s \)


Surface area covered by each molecule
of \( \boldsymbol{N} \boldsymbol{H}_{3} \) is :
A \( \cdot 7.065 \times 10^{-20} m^{2} \)
B . 2.8 \( \times 10^{-20} \mathrm{m}^{2} \)
D. 2.8 \( \times 10^{-19} \mathrm{m}^{2} \)


The element which is a liquid above
\( 30^{\circ} C \) is:
A. cesium
B. Lithium
\( c . \) sodium
D. Magnesium


The oxidation state of sulphur in the
anions \( S O_{3}^{2-}, S_{2} O_{4}^{2-} \) and \( S_{2} O_{6}^{2-} \) follows the order:
A \( \cdot S_{2} O_{6}^{2-}<S_{2} O_{4}^{2-}<S O_{3}^{2} \)
B. \( S O_{3}^{2-}<S_{2} O_{4}^{2-}<S_{2} O_{6}^{2} \)
c. \( S_{2} O_{4}^{2-}<S O_{3}^{2-}<S_{2} O_{6}^{2-} \)
D. \( S_{2} O_{4}^{2-}<S_{2} O_{6}^{2-}<S O_{3}^{2} \)


A bag contains Rs. 112 in the form of 1 rupee, 50-paise and 10-paise coins in
the ratio \( 3: 8: 10 . \) What is the number
of 50 -paise coins?
A .112
в. 128
c. 96
D . 24


Assertion
Electorcardiogram is record of electrical activity of the heart which shows certain waves called \( P, Q, R, S \)
and T waves.
Reason
It gives important information concerning the spread of excitation to the different parts of heart and it is of value in the diagnosis of cases of abnormal cardiac rhythm and myocardial damage
A. If both the assertion and the reason are true and the reason is a correct explanation of the assertion
B. If both the assertion and reason are true but the reason is not a correct explanation of the assertion
c. If the assertion is true but the reason is false
D. If both the assertion and reason are false


Write the compound statement of the following compound statement and check whether the compound statement is true or false : "Zero is less
than every positive integer and every negative integer"


Five capacitors of \( 10 \mu F \) capacity each
are connected to a d.c. potential of 100
volts as shown in the adjoining figure.
The equivalent low capacitance
between the points \( A \) and \( B \) will be
equal to:
\( \mathbf{A} \cdot 40 \mu F \)
B. \( 20 \mu F \)
c. \( 30 \mu F \)
\( \mathbf{D} \cdot 10 \mu F \)


Breathing is affected by
A. Expansion of lungs
B. Contraction of lungs
c. Both A and B
D. Heart beat


The process associated with sodium carbonate manufacture is known as
A. Chamber
B. Haber
c. LeBlanc
D. castner


What will the ratio of the wavelength of
the first line to that of the second line of
Paschen series of H atom?
A .256: 175
B. 175: 256
c. 15: 16
D. 24: 27


Light is incident on a prism with an
equilateral triangular cross-section
making an angle of \( \theta \) w.r.t the normal as
shown in the figure. The index of
refraction of the prism is \( \frac{2}{\sqrt{3}} . \) If the
angle \( \theta \) starts at \( 60^{\circ} \) and is gradually made smaller until no light exist from side BC, the final value of \( \theta \) in degrees is


Find the intersection of \( \boldsymbol{A} \) and \( \boldsymbol{B}, \) and
represent it by Venn diagram:
\( \boldsymbol{A}=\{\mathbf{1}, \mathbf{2}, \mathbf{3}\}, \boldsymbol{B}=\{\mathbf{5}, \boldsymbol{4}, \mathbf{7}\} \)


Which of the following is/are true about force
A. Force will always change the magnitude of velocity
B. Force will always change the direction of velocity
c. s.l unit of force is Newton
D. All the above


\( p H \) of a \( 0.1 \mathrm{M} \) monobasic acid is
measured to be \( 2 . \) Its osmotic pressure
at a given temperature of \( \boldsymbol{T} \) Kis:
A . 0.1 RT
в. 0.11 RТ
c. \( 1.1 \mathrm{RT} \)
D. 0.01 RT


If \( i z^{3}+z^{2}-z+i=0 \) then the value of
\( \mathbf{7}|\boldsymbol{z}| \) is
\( A \cdot 7 \)
B. 14
\( c \cdot 21 \)
D. 28


Assertion
The enthalpy of both graphite and diamond is taken to be zero, being elementry substances.
Reason
The enthalpy of formation of an elementary substance in any state is
taken as zero
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


What is the population of these states?
(i) Sikkim
(ii) Lakshadweep


If Rolle's theorem holds for the function
\( \boldsymbol{f}(\boldsymbol{x})=\mathbf{2} \boldsymbol{x}^{\mathbf{3}}+\boldsymbol{b} \boldsymbol{x}^{2}+\boldsymbol{c} \boldsymbol{x}, \boldsymbol{x} \in[-\mathbf{1}, \mathbf{1}], \) at
the point \( x=\frac{1}{2}, \) then \( 2 b+c \) equals:
A . -1
B.
c. -3
D.


"The magnification produced by a spherical mirror is - \( 3 " \). List four informations you obtain from this statement about the mirror/image.


Compare the modal ages of two groups
of students appearing for an entrance
test:
\( \begin{array}{llll}\text { Age } & \mathbf{1 6}- & \mathbf{1 8}- & \mathbf{2 0}- & \mathbf{2 2}- \\ \text { (in } & \mathbf{1 8} & \mathbf{2 0} & \mathbf{2 2} & \mathbf{2 4} \\ \text { years) } & & & \end{array} \)
\begin{tabular}{lcccc}
Group A: & 50 & 78 & 46 & 28 \\
Group B: & 54 & 89 & 40 & 25 \\
\hline
\end{tabular}


What are congruent triangles?


n this diagram, the potential difference
\( A \) and \( B \) is \( 60 V . \) The potential
difference across \( 6 \mu F \) capacitor is:
\( 4.4 V \)
3. \( 10 V \)
\( c .5 V \)
\( 20 V \)


Assertion
In an elastic collision between two bodies, the relative speed of the bodies after collision is equal to the relative speed before the collision.
Reason
In an elastic, the linear momenta of the system is conserved.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Assertion is incorrect and Reason correct


Which can prevent, premature fruit fall?
\( \mathbf{A} \cdot G A_{3} \)
B. Zeatin
c. Ethylene
D. NAA


Find the degrees of the following polynomial
\( 3-4 a b+5 b^{3}+2 a b^{2} \)


The correct order of increasing acidic strength of the following compounds is:
\( \boldsymbol{a}) \boldsymbol{C H}_{3} \boldsymbol{C O O H} \)
\( \boldsymbol{b}) \boldsymbol{C H}_{3} \boldsymbol{O C H}_{2} \boldsymbol{C O O H} \)
\( \boldsymbol{c}) \boldsymbol{C F}_{3} \boldsymbol{C O O H} \)
\( \mathbf{A} \cdot a<b<c \)
В. \( b<c<a \)
c. \( b<a<c \)
D . \( a<c<b \)


The voltage of the cell given below is
\( -0.46 V \)
\( \boldsymbol{P t}\left|\begin{array}{cc}\boldsymbol{N a H} \boldsymbol{S O}_{3} & \boldsymbol{N a}_{2} \boldsymbol{S O}_{3} \\ \boldsymbol{0 . 4} \boldsymbol{M} & \boldsymbol{6 . 4 4} \times \mathbf{1 0}^{-3} \boldsymbol{M}\end{array}\right|\left|\begin{array}{c}\boldsymbol{Z} \boldsymbol{n}^{2+} \\ \boldsymbol{0} . \boldsymbol{3} \boldsymbol{M}\end{array}\right| \)
Also, \( Z n^{2+}+2 e \rightarrow Z n(s) ; E^{o}= \)
\( -0.763 V \)
The value of \( \boldsymbol{K}_{2} \) where \( \boldsymbol{K}_{2}= \) \( \frac{\left[\boldsymbol{H}^{+}\right]\left[\boldsymbol{S O}_{3}^{2-}\right]}{\left[\boldsymbol{H} \boldsymbol{S O}_{3}^{-}\right]} \mathbf{i s} \)
A . \( 6.44 \times 10^{-8} \)
B. \( 5.43 \times 10^{-8} \)
c. \( 7.34 \times 10^{-8} \)
D. None of these


Infinite charges are lying at \( \boldsymbol{x}= \)
\( 1,2,4,8 \dots \) meter on \( X \) -axis and the
value of each charge is \( Q . \) The value of
intensity of electric field at point \( \boldsymbol{x}=\mathbf{0} \) due to these charges will be respectively
\( \mathbf{A} \cdot 12 \times 10^{8} Q N / C \)
в. zero
c. \( 69 \times 10^{9} Q N / C \)
D. \( 4 \times 10^{9} Q N / C \)


Collect information of experiments done by Faraday.


A solid disc rolls clockwise without
slipping over a horizontal path with a
constant speed \( v, \) Then the magnitude
of the velocities of points \( A, B \) and \( C \) with
respect to a standing observer are
respectively


\( A D, B E \) and \( C F, \) the altitude of
\( \Delta A B C \) are equal. Then
\( \mathbf{A} \cdot A C=B C \)
B . \( A D=A B \)
c. \( A B=C F \)
D. None of these


Which of the following oxides is/are
neutral?
This question has multiple correct options
в. \( C O \)
c. \( A l_{2}, o_{3} \)
D. \( N O \)


For a single object, how many images are formed by a single plane mirror?
\( A \)
B. 2
\( c \cdot 3 \)
\( D \)


Find the number of parallelogram
formed if 10 parallel lines in a plane are
intersected by a family of 12 parallel lines.


\( \operatorname{Let} \boldsymbol{F}(\boldsymbol{k})= \)
\( \left(1+\sin \frac{\pi}{2 k}\right)\left(1+\sin (k-1) \frac{\pi}{2 k}\right)(1+\sin \)
The value of \( \boldsymbol{F}(\mathbf{1})+\boldsymbol{F}(\mathbf{2})+\boldsymbol{F}(\mathbf{3}) \) is
equal to
A \( \cdot \frac{3}{16} \)
B.
\( c \cdot \frac{5}{16} \)
D. \( \frac{7}{16} \)


A radioactive nucleus undergoes a series of decays according to the
sequence \( \boldsymbol{A} \stackrel{\boldsymbol{\beta}}{\rightarrow} \boldsymbol{A}_{\mathbf{1}} \stackrel{\boldsymbol{\alpha}}{\rightarrow} \boldsymbol{A}_{2} \stackrel{\boldsymbol{\alpha}}{\rightarrow} \boldsymbol{A}_{\mathbf{3}} \)
If the mass number and atomic number
of \( A_{3} \) are 172 and 69 respectively, then
the mass number and atomic number
of A is
A. 56,23
B. 180,72
c. 120,52
D. 84,38


In a trapezium \( A B C D \) with \( A B \| C D \), it
is given that \( A D \) is not parallel to \( B C \).
Is \( \triangle A B C \cong \triangle A D C ? \) Given reasons


\( \boldsymbol{A} \stackrel{\boldsymbol{K O B r}}{\boldsymbol{C}} \boldsymbol{H} \boldsymbol{B r}_{3} \)
Reactant A is:
A. isopropyl alcohol
B. methanol
c. ethanoic acid
D. n-butyl alcohol


The flow of the electric current through a metallic conductor is:
A. Only due to electrons
B. Only due to +ve charges
c. Due to both nuclei and electrons.
D. Can not be predicted.


A balloonist is ascending at a velocity of
\( 12 m s^{-1} . A \) packet is dropped from it
when it is at height of \( 65 m \) from the ground, it drops a packet. Time taken by the packet to reach the ground is
\( \mathbf{A} \cdot 5 s \)
B. \( -5 s \)
c. \( 7 s \)
D. \( \frac{13}{5} s \)


The value of \( K_{c} \) for the reaction
\( \mathbf{3} \boldsymbol{O}_{\mathbf{2}}(\boldsymbol{g}) \rightleftharpoons \mathbf{2} \boldsymbol{O}_{\mathbf{3}}(\boldsymbol{g}) \) is \( \mathbf{2} . \mathbf{0} \times \mathbf{1 0}^{-\mathbf{5 0}} \mathbf{a} \mathbf{t} \)
\( 25^{\circ} \mathrm{C} . \) If the equilibrium concentration
of \( O_{2} \) in air at \( 25^{\circ} C \) is \( 1.6 \times 10^{-2} \mathrm{M} \)
what is the concentration of \( O_{3} \) ?


A graph is plotted by taking \( ^{\circ} \boldsymbol{C} \) along
the Y-axis and \( ^{\circ} \boldsymbol{F} \) along the X-axis. It is
a/an
A. parabola
B. straight line
c. ellipse
D. circle


In the given reaction,
\( \mathbf{2} \boldsymbol{K}_{\mathbf{4}}\left[\boldsymbol{F} \boldsymbol{e}(\boldsymbol{C} \boldsymbol{N})_{6}\right](\boldsymbol{a} \boldsymbol{q})+\boldsymbol{H}_{2} \boldsymbol{O}_{2}(\boldsymbol{a} \boldsymbol{q}) \longrightarrow \)
\( \mathbf{2} \boldsymbol{K}_{\mathbf{3}}\left[\boldsymbol{F} \boldsymbol{e}(\boldsymbol{C} \boldsymbol{N})_{\boldsymbol{6}}\right](\boldsymbol{a} \boldsymbol{q})+\boldsymbol{2} \boldsymbol{K} \boldsymbol{O} \boldsymbol{H}(\boldsymbol{a} \boldsymbol{q}) \)
Which of the following processes takes place?
A. Oxidation due to removal of potassiummm
B. Oxidation due to removal of iron
c. Reduction due to removal of potassium
D. Oxidation due to removal of electronegative element


Six vectors, a through f have the magnitudes and directions indicated in
the figure. Which of the following
statements is true?
A. \( b+e=f \)
B. \( b+c=f \)
c. \( d+c=f \)
D. \( d+e=f \)


Two men hit at a target with probabilities \( \frac{1}{2} \) and \( \frac{1}{3} \) respectively. What is the probability that exactly one of them hits the target?
A \( \cdot \frac{1}{2} \)
B. \( \frac{1}{3} \)
\( c \cdot \frac{1}{6} \)
D. \( \frac{2}{3} \)


A conducting slider of resistance
\( R(10 \Omega), \) mass \( 50 g \& \) length10cm is
kept on a U-shaped frame as shown in
figure. There is uniform magnetic field
\( (B=0.1 T) \) perpendicular to plane of
frame. The slider is attached to a spring \( (K=0.5 N / m) . \) The slider is displaced
by an amount \( A_{0} \& \) released. Time in
which its amplitude become \( A_{0} / e \) is
A . \( 9000 s \)
B. 10000 s
c. \( 12000 s \)
D. 15000 s


\( 500 \mathrm{mL} \) of chlorine contaminated water
is treated with \( K I \) and mixture
required \( 100 \mathrm{mL} \) of \( 0.01 \mathrm{M} \) hypo. What is
concentration of \( C l_{2} \) in millimoles per
litre?


For the reaction, \( 2 N O(g)+2 H_{2}(g) \rightarrow \)
\( N_{2}(g)+2 H_{2} O(g) \) the rate expression
can be written in the following ways:
\( \left\{\boldsymbol{d t}\left[\boldsymbol{N}_{2}\right] / \boldsymbol{d} t\right\}= \)
\( \boldsymbol{k}_{1}[\boldsymbol{N} \boldsymbol{O}]\left[\boldsymbol{H}_{2}\right] ;\left\{\boldsymbol{d}\left[\boldsymbol{H}_{2} \boldsymbol{O}\right] / \boldsymbol{d} \boldsymbol{t}\right)= \)
\( \boldsymbol{k}[\boldsymbol{N} \boldsymbol{O}]\left[\boldsymbol{H}_{2}\right] \)
\( \{-\boldsymbol{d}[\boldsymbol{N} \boldsymbol{O}] / \boldsymbol{d} \boldsymbol{t}\}= \)
\( \boldsymbol{k}_{\mathbf{1}}^{\prime}[\boldsymbol{N} \boldsymbol{O}]\left[\boldsymbol{H}_{2}\right] ;\left\{-\boldsymbol{d}\left[\boldsymbol{H}_{2}\right] / \boldsymbol{d} t\right\}= \)
\( k_{1}^{\prime \prime}[N O]\left[H_{2}\right] \)
The relation ship between \( k, k_{1}, k_{1}^{\prime} \) and
\( k_{1}^{\prime \prime} \) is:


A body moves \( 6 \mathrm{m} \) north. \( 8 \mathrm{m} \) east and 10m vertically upwards, what is its resultant displacement from initial position (only magnitude)
A \( \cdot 10 \sqrt{2} m \)
the
в. \( 10 m \)
c. \( \frac{10}{\sqrt{2}} m \)
D. \( 10 \times 2 m \)


What makes diazonium ion one of the
best leaving group of organic chemistry?
A. Half filled electronic configuration of nitrogen atom
B. High electronegativity of nitrogen atom
c. very high stability of dinitrogen molecule in the atmosphere
D. Weaker \( C-N \) bond


The pressure of a certain mass of gas at \( 27^{0} \mathrm{Cis} 84 \mathrm{cm} \) of Hg. If \( 25 \% \) of the gas is
now introduced into the same vessel at
the same temperature, the final pressure of the gas will be in cm of Hg
A . 105
B. 100
\( c \cdot 95 \)
D. 90


Which of the following is not an air pollutant?
A. \( N_{2} \)
в. \( N_{2} \),
c. \( N O \)
D. \( C O \)


Which of the following expressions does not represent simple harmonic motion?
A \( . x= \) Acoswt \( + \) Bsinwt
В. \( F=\sqrt{k y} \)
c. \( F=k y \)
D. none of these


If co-ordinates of a point \( P \) is (1,2,2) then unit vector along the position vector of the point \( P \) will be
A \( \cdot \frac{1}{3}(\hat{i}+2 \hat{j}+2 \hat{k}) \)
B . \( \hat{i}+2 \hat{j}+2 \hat{k} \)
c \( \cdot \frac{1}{3}(\hat{i}-2 \hat{j}-2 \hat{k}) \)
D. \( \frac{1}{\sqrt{3}}(\hat{i}+\hat{j}+\hat{k}) \)


Which of the following structure
produces digestive enzymes?
A. I, III and
B. II, III and
c. \( \| \) । \( , \) IV, \( v \), and vıl
D. I, III, V, and VI
E . II, III, and IV


\( f(x)=3 x^{4}+17 x^{3}+9 x^{2}-7 x- \)
\( 10 ; g(x)=x+5 \)


\( \tan \left(\cot ^{-1} x\right)=\cot \left(\tan ^{-1} x\right) \)


The most common oxidation states of
cerium are
\( A \cdot+2 \) and +4
B. +3 and +4
\( c \cdot+3 \) and +5
D. +2 and +3


The change in internal energy of two moles of a gas during adiabatic expansion is found to be -100 . \( J \). The
work done during the process is
\begin{tabular}{l}
A. \( -100 \mathrm{J} \) \\
\hline
\end{tabular}
B. \( 0 J \)
c. \( 100 J \)
D. 200 J


Given,
\( N H_{3}(g)+3 C l_{2}(g) \rightleftharpoons N C l_{3}(g)+ \)
\( 3 H C l(g) ;-\Delta H_{1} \)
\( N_{2}(g)+3 H_{2}(g) \rightleftharpoons 2 N H_{3}(g) ;-\Delta H_{2} \)
\( H_{2}(g)+C l_{2}(g) \rightleftharpoons 2 H C l(g) ; \Delta H_{3} \)
The heat formation of \( N C l_{3}(g) \) in terms
of \( \Delta H_{1}, \Delta H_{2} \) and \( \Delta H_{3} \) is:
\( ^{\mathbf{A}} \cdot \Delta H_{f}=-\Delta H_{1}+\frac{1}{2} \Delta H_{2}+\frac{3}{2} \Delta H_{3} \)
B. \( \Delta H_{f}=-\Delta H_{1}+\frac{1}{2} \Delta H_{2}-\frac{3}{2} \Delta H_{3} \)
\( \mathrm{c} \cdot_{\Delta H_{f}=\Delta H_{1}-\frac{1}{2} \Delta H_{2}-\frac{3}{2} \Delta H_{3}} \)
D. none of these


State True or False.
\( \ln C O_{2} \) molecule, \( C O \) bond is polar but
\( C O_{2} \) molecule is non-polar because the
vector sum of Dipole moment of the two
CO bond is zero.
A. True
B. False


Let \( R \) be the set of all real numbers and
\( \boldsymbol{f}:[-\mathbf{1}, \mathbf{1}] \rightarrow \boldsymbol{R} \) be defined by \( \quad \boldsymbol{f}(\boldsymbol{x})= \)
\( \left\{\begin{array}{c}x \sin \frac{1}{x}, x \neq 0 \\ 0, x=0\end{array} . \) Then \right.
A. \( f \) satisfies the conditions of Rolle's theorem on [-1,1]
B. \( f \) satisfies conditions of Lagrange's Mean Value Theorem on [-1,1]
c. \( f \) satisfies the conditions of Rolle's theorem on [0,1]
D. \( f \) satisfies the conditions of Lagrange's Mean Value Theorem on [0,1


Which of the following is basic compound present in coal tar?
A. Quinoline
B. Benzene
c. Toluene
D. Pheno


Evaluate the given integral. \( \int \sin ^{-1}\left(\frac{2 x}{1+x^{2}}\right) d x \)


An atom of an element has two
electrons in the M shell. Identify its atomic number.
A . 10
B. 12
\( c \cdot 14 \)
D. 15


If \( \mathrm{BC} \) and \( \mathrm{AD} \) are equal perpendiculars
to line segment \( A B, \) then \( \Delta O B C \cong \)
\( \Delta O A D \) by which of the following tests
of congruence? What can be said about
\( A B \) and \( C D ? \)
A. \( A S A \) test, CD bisects AB
B. \( S A S \) test, AB bisects \( c \) D
c. \( A S A \) test, AB bisects \( c \) D
D. \( S A S \) test, CD bisects AB


A prism is made of glass of unknown refractive index. A parallel beam of light is incident on a face of the prism. The angle of minimum deviation is
measured to be \( 40^{\circ} . \) What is the
refractive index of the material of the
prism? The refracting angle of the prism
is \( 60^{\circ} . \) If the prism is placed in water (refractive index 1.33 ), predict the new angle of minimum deviation of a parallel beam of light.


State whether true or false.
Copper is a poor conductor of electricity as compared to glass.
A. True
B. False


A pair of long, straight current-carrying
wires and four marked points are shown
in above figure. Find out the points at
which net magnetic field is zero?
A. Point 1 only
B. Points 1 and 2 only
c. Point 2 only
D. Points 3 and 4 only
E. Point 3 only


Which one of the following spherical lenses does not exhibit dispersion? The
radii of curvature of the surfaces of the
lenses are as given in the diagram.
\( A \)
B.
\( c \)
\( D \)


A uniform charged solid sphere of radius \( R \) has potential \( V_{0} \) (measure with respect to \( \infty \) ) on its surface. For this sphere the equipotential surfaces with potentials \( \frac{3 V_{0}}{2}, \frac{5 V_{0}}{4}, \frac{3 V_{0}}{4}, \frac{V_{0}}{4} \) have
radius \( R_{1}, R_{2}, R_{3} \) and \( R_{4} \) respectively.
Then
A. \( R_{1}=0 \) and \( R_{2}>\left(R_{4} R_{3}\right) \)
B. \( R_{1} \neq 0 \) and \( \left(R_{2} R_{1}\right)>\left(R_{4} R_{3}\right) \)
c. \( R_{1}=0 \) and \( R_{2}<\left(R_{4} R_{3}\right) \)
D . \( 2 R<R_{4} \)


Total number of lone pair of electrons in
\( I_{3}- \) ion is :
A . 9
B. 12
\( c .3 \)
D. 6


Discuss the continuity of
\[
\boldsymbol{f}(\boldsymbol{x})=
\]
\( \left\{\begin{array}{l}\frac{\sin 2 x}{\sqrt{1-\cos 2 x}} \text { for } 0<x \leq \pi / 2 \\ \frac{\cos }{\pi-2 x} \quad \text { for } \frac{\pi}{2}<x<\pi\end{array} \) at \right.
\( \boldsymbol{x}=\boldsymbol{\pi} / 2 \)


Which of the following are isomeric
amines of the formula \( C_{3} H_{9} N ? \)
A \( \cdot C H_{3} C H_{2} C H_{2} N H_{2} \)
B. \( \left(C H_{3}\right)_{3} N \)
c. \( C H_{3} C H_{2} N H C H_{3} \)
D. All of the above


A particle of mass \( \mathrm{m} \) is executing oscillations about the origin on the \( x \) axis. Its potential energy is \( V(x)= \)
\( k|x|^{3} \) where \( k \) is a positive constant. If
the amplitude of oscillation is a, them its time period T is?
A. proportional to \( \frac{1}{\sqrt{a}} \)
B. Independent of a
c. Proportional to \( \sqrt{a} \)
D. Proportional to \( a^{3 / 2} / 2 \)


represents the passage of white light
through a prism?
\( A \)
3
\( c \)
\( D \)


In a step up transformer
A. \( N_{s}=N_{p} \)
B. \( N_{s}<N_{p} \)
\( \mathbf{c} \cdot N_{s}>N_{p} \)
D. nothing can be said.


Two satellites \( A \) and \( B \) revolve around a
planet in two coplanar circular orbits in
the same sense with radii \( 10^{4} \mathrm{km} \) and
\( 2 \times 104 \mathrm{km} \) respectively. Time period of
\( A \) is 28 hours. What is time period of
another
satellite?


Two parallel chords are drawn in a circle
of diameter \( 30.0 \mathrm{cm} . \) The length of one
chord is \( 24.0 \mathrm{cm} \) and the distance
between the two chords is \( 21.0 \mathrm{cm} . \) find
the length of the other chord.


The essential requirements for a good heating element are
A. High resistivity and low melting point
B. High resistivity and high melting point
C. Low resistivity and low melting point
D. Low resistivity and high melting point


Which one of the following is a catabolic
process?
A. Regulation
B. Photosynthesis
c. Digestion
D. Secretion


The bases that are common in both RNA
and DNA are:
A. adenine, guanine, thymine
B. adenine, uraci, cytosine
c. adenine, guanine, cytosine
D. guanine, uracil, thymine


In froth floatation process for the
purification of ores, the particles of ore float because:
A. their surface is not easily wetted by water
B. they are light
c. they are insoluble
D. they bear electrostatic charge


If \( 2 x+3 y+4=0 \) is the perpendicular
bisector of the segment joining the points \( \boldsymbol{A}(\mathbf{1}, \mathbf{2}) \) and \( \boldsymbol{B}(\boldsymbol{a}, \boldsymbol{b}), \) then the
value of \( a+b \) is
A \( \cdot-\frac{81}{13} \)
B. \( -\frac{136}{13} \)
c. \( -\frac{135}{13} \)
D. \( -\frac{134}{5} \)


Thermal decomposition of a \( M n \) compound \( (X) \) at \( 513 K \) results in
compound \( Y, M n O_{2} \) and a gaseous
product. \( M n O_{2} \) reacts with \( N a C l \) and
concentrated \( H_{2} S O_{4} \) to give a pungent
\( \operatorname{gas} Z \)
\( X, Y \) and \( Z, \) respectively.
\( \mathbf{A} \cdot K_{2} M n O_{4}, K M n O_{4} \) and \( S O_{2} \)
B . \( K_{2} M n O_{4}, K M n O_{4} \) and \( C l_{2} \)
c. \( K_{3} M n O_{4}, K_{2} M n O_{4} \) and \( C l_{2} \)
D. \( K M n O_{4}, K_{2} M n O_{4} \) and \( C l_{2} \)


A man can swim in still water at a
speed of \( 3 k m / h \). He wants to cross a
river that flows at \( 2 k m / h \) and reach the point directly opposite to his starting point.
(a) In which direction should he try to
swim (that is, find the angle his body makes with the river flow)?
(b) How much time will he take to cross
the river if the river is \( 500 m \) wide?


Assertion
All small oscillations are simple harmonic in nature.
Reason
Oscillations of spring block system are always simple harmonic whether amplitude is small or large.
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


A taxon derived from a single ancestral population is a
A. Phenetic
c. Phylogenetic
D. Polyphyletic


Who performed the gold foil experiment?
A. Thomson
B. Goldstein
c. chadwick
D. Rutherford


Explain with examples:
macronutrients, micronutrients,
beneficial nutrients, toxic elements and essential elements.


A pair of dice is thrown 4 times. If
getting a total of 9 in a single throw is considered as a success then find the
mean and variance of successes.


Find the mean deviation about the
mean for the data.
\( \begin{array}{cccccc}x_{i} & 5 & 10 & 15 & 20 & 25 \\ f_{i} & 7 & 4 & 6 & 3 & 5\end{array} \)


The nuclear radius of \( _{4} B e^{8} \) nucleus is :
A \( \cdot 1.3 \times 10^{-15} \mathrm{m} \)
B . 2.6 \( \times 10^{-15} \mathrm{m} \)
c. \( 1.3 \times 10^{-13} \) и
D. 2.6 \( \times 10^{-13} \mathrm{m} \)


From a tower of height \( \boldsymbol{H}, \) a particle is thrown vertically upwards with a speed
\( u . \) The time taken by the particle, to hit the ground, is \( n \) times that taken by it to reach the highest point of its path.
The relation between \( \boldsymbol{H}, \boldsymbol{u} \) and \( \boldsymbol{n} \) is:
A \( \cdot 2 g H=n u^{2}(n-2) \)
B . \( g H=(n-2) u^{2} \)
C \( \cdot 2 g H=n^{2} u^{2} \)
D. \( g H=(n-2)^{2} u^{2} \)


What change in volume will be observed
when temperature of water gradually
increases from \( 0^{\circ} \mathrm{C} \) to \( 15^{\circ} \mathrm{C} \) ?
A. Increase steadily
B. Decreases steadily
c. At first decreases then increases
D. At first increases then decreases


Number of \( \sigma \) and \( \pi \) bonds present in
\( \boldsymbol{C H}_{3}-\boldsymbol{C H}=\boldsymbol{C H}-\boldsymbol{C} \equiv \boldsymbol{C H} \) are:
A. \( 10 \sigma, 3 \pi \)
B. \( 10 \sigma, 2 \pi \)
\( \mathrm{c} .9 \sigma, 2 \pi \)
D. \( 8 \sigma, 3 \pi \)


Draw a circle with centre \( C \) and radius
\( 3 \mathrm{cm} . \) Take a point \( \boldsymbol{P} \) outside the circle
such that \( C P=6 \mathrm{cm} . \) Construct
tangents \( \boldsymbol{P} \boldsymbol{A} \) and \( \boldsymbol{P} \boldsymbol{B} \) from this point to
the circle, where \( A \) and \( B \) are the
intersection points of the tangents. Then \( \boldsymbol{m} \angle \boldsymbol{A} \boldsymbol{C B}=? \)
\( \mathbf{A} \cdot 60 \)
B. \( 120^{\circ} \)
\( c \cdot 30^{\circ} \)
D. \( 90^{\circ} \)


In a double-slit experiment, instead of taking slits of equal width, one slit is made twice as wide as the other. Then,
in the interference pattern?
A. The intensities of both maxima and the minima increase
B. The intensity of the maxima increases and the minima has zero intensity
c. The intensity of the maxima decreases and that of the minima increases
D. The intensity of the maxima decreases and the minima has zero intensity


Growth curve shows
A. Increase in the length of the animal with age.
B. Increase in the mass of the animal with time.
C. Increase in the number of cells with age.
D. Increase in the mass of the animal with temperature


Photosynthetic yield is reduced due to
A. Plasmolysis of cell
B. Glycolysis of glucose
c. Photolysis of water
D. Photorespiration


The sum of 5 digit numbers such that the sum of their digit is even is :
\( \mathbf{A} .50000 \)
B. 45000
c. 60000
\( D \cdot \) none


Heat absorbed or lost by a substance is
proportional to and


Identify the correct lewis symbol from the following:
\( A \cdot \cdot C \cdot \)
B. \( \dot{O} \)
c. \( \dot{B} \bullet \)
D. \( \dot{N} \)


When a single anticodon can recognize more than one codon of mRNA it is called as
A. Template hypothesis
B. Degeneracy
c. Gene flow hypothesis
D. collinearity hypothesis


A monkey of mass \( 40 \mathrm{kg} \) climbs on a massless rope of breaking strength 600
N. The rope will break if the monkey
\( \left(\boldsymbol{g}=\mathbf{1 0 m} / \boldsymbol{s}^{\mathbf{2}}\right) \)
A. climbs up with a uniform speed of \( 5 \mathrm{m} / \mathrm{s} \)
B. climbs up with an acceleration of \( 6 m / s^{2} \)
C . climbs down with an acceleration of \( 4 \mathrm{m} / \mathrm{s}^{2} \)
D. Moves down with a uniform speed of \( 5 \mathrm{m} / \mathrm{s} \)


Which among the following is the correct order of melting point?
\( A \)
B.
\( c \)
\( D \)


A car has two horns having a difference in frequency of 180 Hz. The car is approaching a stationary observer with a speed of \( 60 \mathrm{ms}^{-1} \). Calculate the
difference in frequencies of the notes as heard by the observer, if velocity of sound in air is \( 330 m s^{-1} \)


The number of moles of \( \boldsymbol{K} \boldsymbol{M} \boldsymbol{n} \boldsymbol{O}_{4} \)
reduced by one mole of KI in alkaline medium is:
A. one
B. two
c. five
D. one fifth


The radius of a sphere is \( 28 \mathrm{cm} . \) Find its
curved surface area
\[
\left(\boldsymbol{\pi}=\frac{\mathbf{2 2}}{\mathbf{7}}\right)
\]


Which of the following is the mode of asexual reproduction?
A. Budding
B. Spore formation
c. Binary fission
D. All of the above


Which is the correct increasing order of boiling points of the following compounds?
1 - lodobutane,
1 - Bromobutane, 1 -
Chlorobutane, Butane
A. Butane <1 - Chlorobutane <1- Bromobutane <1 lodobutane
B. 1 - lodobutane <1 - Bromobutane <1 - Chlorobutane Butane
c. Butane \( <1 \) - lodobutane \( <1 \) - Bromobutane \( <1- \) Chlorobutane
D. Butane <1 - Chlorobutane <1 - lodobutane <1 Bromobutane


By increase in temperature by \( 10 K \), the rate of reaction becomes double. How
many times the rate of reaction will be
if the temperature is increased from
\( 303 K \) to \( 353 K ? \)
A . 4
B. 8
c. 16
D. 32


Student \( A \) and student \( B \) sit in identical
office chairs facing each other, as
shown in figure. Student A is heavier than student B. Student A suddenly pushes with his feet. Which of the
following occurs?
A. Neither student applies a force on each other
B. A exerts a force that is applied to B, but A experiences no force
c. Each student applies a force to the other, but A exerts the larger force
D. The students exert the same amount of force on each
other


Draw the circuit diagram of a full wave
rectifier and state how it works.


Show that the relation 'a \( R \) b if and only
if \( a-b \) is an even integer defined on the
\( Z \) of integers is an equivalence relation.


Find the value of \( \theta \) if \( \frac{(3+2 i \sin \theta)}{(1-2 i \sin \theta)} \) is
purely real or purely imaginary.
A \( \cdot \theta=n \pi \pm \frac{\pi}{6}, n \in Z \)
в. \( \theta=n \pi \pm \frac{\pi}{2}, n \in Z \)
c. \( \theta=n \pi \pm \frac{\pi}{3}, n \in Z \)
D. \( \theta=n \pi \pm \frac{\pi}{4}, n \in Z \)


A ball after falling a distance of 5 meter
from rest hits floor of a lift and
rebounds. At the time of impact the lift was moving up with a velocity of 1 \( m / \) sec. The velocity with which the ball rebounds just after impact is- \( (g= \) \( \mathbf{1 0} \boldsymbol{m} / \boldsymbol{s e c}^{2} \)
A. \( 10 \mathrm{m} / \mathrm{sec} \)
B. \( 11 \mathrm{m} / \mathrm{sec} \)
c. \( 12 \mathrm{m} / \mathrm{sec} \)
D. \( 13 \mathrm{m} / \mathrm{sec} \)


A particle of mass ' \( m^{\prime} \) is rigidly
attached at \( ^{\prime} A^{\prime} \) to a ring of mass \( ^{\prime} 3 m^{\prime} \)
and radius ' \( r .^{\prime} \) The system is released
from rest and rolls without sliding. The angular acceleration of ring just after
release is
\( ^{A} \cdot \frac{g}{4 r} \)
в. \( \frac{g}{6 r} \)
\( c \)
\( \frac{g}{2 r} \)


Assertion
A dam for water reservoir is built
thicker at bottom than at the top.
Reason
Pressure of water is very large at the
bottom.
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


Which of the following instrument is used for measuring gauge pressure?
A. Thermometer
B. Barometer
c. Manometer
D. Hydrometer


Two point charges, each of charge \( q, \) are
placed at a separation of \( 2 a \). The
electric potential at their midpoint will
be :
A. zero
в. \( \frac{q}{2 \pi \varepsilon_{0} a} \)
c. \( \frac{q}{8 \pi \varepsilon_{0} a} \)
D. \( \frac{q}{2 \pi \varepsilon_{0} a^{2}} \)


Construct \( \Delta L M N \) in which \( \angle N= \)
\( \mathbf{7 3}^{\circ}, \boldsymbol{L} \boldsymbol{N}=\mathbf{5 . 7} \mathbf{c m}, \boldsymbol{M} \mathbf{N}=\mathbf{6 . 8 c m} \)


The excess pressure inside a sperical drop of water is four times that of
another drop. Then their respective mass ratio is :
A .1: 6
B. 8: 1
\( c \cdot 1: 4 \)
D. 1: 64


Zero of the zero polynomial is
\( \mathbf{A} \cdot \mathbf{0} \)
B. 1
C . Any real number
D. Not defined


If \( |z|=1, \) then \( |z-1| \) is
\( \mathbf{A} \cdot<|a r g(z)| \)
B \( \cdot>|a r g(z)| \)
\( \mathbf{C} \cdot=|\arg (z)| \)
D. None of these


Under condition of constant
¡Illumination, the compensation period
for a whole aquarium would be of
infinite length when
A. The biomass of animals equals the biomass of plants.
B. The respiratory exchanges of the animals are equal to the photosynthesis exchanges of the plants.
C. The oxygen intake of the animals equal of oxygen outputs of photosynthesis
D. The carbon dioxide output of the animals and plants is equal to the photosynthetic intake of the plants.


In an electromagnetic wave, the electric magnetising fields are \( 100 V / m \) and
0.265 A. The maximum energy flow is?
\( \mathbf{A} \cdot 26.5 W / m^{2} \)
B. \( 36.5 W / m^{2} \)
\( \mathbf{c} \cdot 46.7 W / m^{2} \)
\( \mathbf{D} \cdot 765 W / m^{2} \)


Which one from the following is used to measure heat?
A. Pipette
B. Manometer
c. Balance
D. Calorimeter


12 farmers harvest the crops in the field
in 20 hours. How many workers will be
required to do the same work in 15 hours


Assertion
Walking is more easier on the ground
than on sand.
Reason
In the former case reaction comes into
play more quickly.
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


The electronic configuration of
potassium is 2,8,8,1 and not 2,8,9


Which one of the following constitutes a group of the isoelectronic species?
A. \( \mathrm{CN}^{-}, \mathrm{N}_{2}, \mathrm{O}_{2}^{2-}, \mathrm{C}_{2}^{2-} \)
в. \( \mathrm{N}_{2}, \mathrm{O}_{2}^{-}, \mathrm{NO}^{+}, \mathrm{CO} \)
\( \mathrm{c} \cdot \mathrm{C}_{2}^{2-}, \mathrm{O}_{2}^{-}, \mathrm{CO}, \mathrm{NO} \)
D. \( \mathrm{NO}^{+}, \mathrm{C}_{2}^{2-}, \mathrm{CN}^{-}, \mathrm{N}_{2} \)


State whether the statement
\( p: \) If \( x \) is a real number such that \( x^{3}+ \)
\( 19 x=0, \) then \( x \) is 0 is true / False
A. True
B. False


True structure is predicted by :
A. valence bond approach
B. Sidgwick approach
c. hybrid orbital formation
D. None of the above


Out of the following, which is the most stable compound?
A \( \cdot\left[B e\left(H_{2} O\right)_{4}\right]^{2+} \)
В \( \cdot\left[M g\left(H_{2} O\right)_{4}\right]^{2+} \)
\( ^{\mathrm{c}} \cdot\left[C a\left(H_{2} O\right)_{4}\right]^{2+} \)
D. \( \left[\operatorname{Sr}\left(H_{2} O\right)_{4}\right]^{2+} \)


Sun is the ultimate source of energy for
the earth.
A. True
B. False
c. Ambiguous
D. Data insufficient


The value of resistance of the coil
calculated by the student is :
A . \( 3 \Omega \)
в. \( 4 \Omega \)
\( c .5 \Omega \)
D. 8\Omega


A cylinder of mass \( M_{c} \) and sphere of
\( \operatorname{mass} M_{s} \) are placed at points \( A \) and \( B \)
of two inclines, respectively. (See

Figure). If they roll on the incline without
slipping such that their accelerations are the same, then the ratio \( \frac{\sin \theta_{c}}{\sin \theta_{s}} \) is :
\( A \cdot \sqrt{\frac{8}{7}} \)
B. \( \sqrt{\frac{15}{14}} \)
\( c \)
7
D. 15
14


The lines of force of a bar magnet are:
A. Parallel and straight
B. Concentric circles
c. Curved lines
D. Curved closed loops


Compare and contrast the arrangement of elements in Mendeleev's periodic
table and the Modern periodic table.


The price of the diesel is Rs. 70 per litre and the price of the petrol is Rs. 40 per litre. If the profit after selling the mixture at Rs. 75 per litre be \( 25 \% \). Find the ratio of the diesel and petrol in the mixture


Given that \( \sqrt{3} \) and \( \sqrt{5} \) are irrational numbers, prove that \( \sqrt{3}+\sqrt{5} \) is an
irrational number.


A string of length \( ^{\prime} l^{\prime} \) is fixed at both
ends. It is vibrating in its \( 3^{r d} \) overtone
with maximum amplitude \( ^{\prime} a^{\prime} . \) The amplitude at a distance \( \frac{l}{3} \) from one end is:
\( A \)
B. 0
c. \( \frac{\sqrt{3} a}{2} \)
D. \( \frac{a}{2} \)


Number of shell in which valence
electrons of iodine lies:


Explain why AI(OH)3AI(OH)3 is
amphoteric in nature.


Which of the following mixture does not obey Daltons law of partial pressures.
A \( \cdot C O_{2} \) and \( O_{2} \) at room temperature
B. \( N H_{3} \) and \( H C l \) at \( 0^{\circ} C \)
C. \( N H_{3} \) and \( H C l \) at room temperature
D. Excess of \( C l_{2} \) and \( N H_{3} \)


In vacuum, to travel distance 'd', light takes time 't' and in a medium to travel
distances '5 \( d \), it takes time 'T'. The
critical angle of the medium is
A \( \cdot \sin ^{-1}\left(\frac{5 T}{t}\right) \)
B. \( \sin ^{-1}\left(\frac{5 t}{3 T}\right) \)
c. \( \sin ^{-1}\left(\frac{5 t}{T}\right) \)
D. \( \sin ^{-1}\left(\frac{3 t}{5 T}\right) \)


Assertion
All the stoichiometric calculations are
based on law of conservation of mass.
Reason

In redox reactions, both oxidation and
reduction takes place simultaneously.
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


Oxide of nitrogen formed in the atmosphere during the lightenings is :
A. NO
в. \( \mathrm{N}_{2} \mathrm{O} \)
c. \( \mathrm{NO}_{2} \)
D. None


Which of the following effects could not be explained by Maxwell's electromagnetic wave theory?
A. Photoelectric effect
B. Compton effect
c. Raman effect
D. All of these


\( \operatorname{Let} \frac{\mathbf{d}}{\mathbf{d} x} \boldsymbol{F}(\boldsymbol{x})=\frac{e^{\sin x}}{\boldsymbol{x}}, \boldsymbol{x}>\mathbf{0} \)
\( \int_{1}^{4} \frac{2 e^{\sin x^{2}}}{x} d x=F(k)-F(1) \) then one
of the possible value of k is


Phellogen and phellem respectively denote
A. cork and cork cambium
B. cork cambium and cork
c. secondary cortex and cork
D. cork and secondary cortex


The output impedance of a transistor connected in the.................arrangement is the highest,
A. common emitter
B. common collector
c. common base
D. none of the above


Which gas is essential constituent of
almost all fuel gases?
A. \( C O_{2} \)
в. \( N_{2} \)
\( c \cdot c o \)
D. \( H_{2} O \)


The National Capital Territory of India is
A. Kolkata
B. Chennai
c. New Delhi
D. Mumbai


Assertion
Malonic acid \( \left(\boldsymbol{H} \boldsymbol{O} \boldsymbol{O} \boldsymbol{C}-\boldsymbol{C} \boldsymbol{H}_{2}-\right. \)
COOH ) does not form cyclic anhydride
on heating.
Reason
It is like \( \beta \) - keto acid, on heating it
prefer to decarboxylate.
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


Find the \( n^{t h} \) term and the sum of first \( n \)
terms of the sequence 0.3,0.33,0.333
\( 0.3333, \)


Give the possible products formed by the oxidation of 1,2 -dimethyl cyclobutene by hot \( K M n O_{4} \)
A. butan-1,4-dione and formic acid
B. 1,2-dihydroxy-1,2-dimethyl cyclobutane
c. hexan-2,5-dione
D. none of these


fixed resistors of resistance \( 2.0 \Omega \) and
\( 4.0 \Omega \) connected in series with a \( 3.0 \Omega \)
resistor fitted with a sliding contact.
These are connected across a battery of
e.m.f \( 9.0 \mathrm{V} \) and zero internal resistance,
as shown
What are the maximum and the
minimum output voltages of this
potential divider circuit?
A. maximum voltage/V : \( 4.0 ; \) minimum voltage \( / V: 2.0 \)
B. maximum voltage/V : 5.0 ; minimum voltage/V : 2.0
C. maximum voltage/V : \( 9.0 ; \) minimum voltage \( / V: 0 \)
D. maximum voltage/V : 9.0 ; minimum voltage/ \( V: 2.0 \)


Which one of the following reagents can not be used to oxidise primary alcohols to aldehydes?
\( \mathbf{A} \cdot C r O_{3} \) in anhydrous medium
B. \( K M n O_{4} \) in acidic medium
c. Pyridinium chlorochromate
D. Heat in presence of Cu at 573 k


Electrolytes which allow large current to pass through them are known as:
A. weak electrolytes
B. strong electrolytes
c. non-electrolytes
D. none of the above


Show that:
\( \left|\begin{array}{lll}\boldsymbol{a} & \boldsymbol{b} & \boldsymbol{c} \\ \boldsymbol{b} & \boldsymbol{c} & \boldsymbol{a} \\ \boldsymbol{c} & \boldsymbol{a} & \boldsymbol{b}\end{array}\right|^{2}= \)
\[
\left|\begin{array}{ccc}
2 b c-a^{2} & c^{2} & b^{2} \\
c^{2} & 2 a c-b^{2} & a^{2} \\
b^{2} & a^{2} & 2 a b-c^{2}
\end{array}\right|=
\]
\( \left(a^{3}+b^{3}+c^{3}-3 a b c\right)^{2} \)


Assertion (A) : A wheel may be rotated
with uniform angular velocity even though the tangential forces are applied
on it.
Reason (R) : Angular acceleration of wheel is zero when tangential force and frictional force produce torques equal in magnitude and opposite in direction
A. Both A and R are true and R is correct explanation of A
B. Both A and R are true and R is not correct explanation of A
C. A is true and R is false
D. A is false and R is true


A single electron orbits around a stationary nucleus of charge +Ze where \( \mathrm{Z} \) is atomic number and 'e' is the
magnitude of the electric charge. The hydrogen like species required 47.2eV to excite the electron from the second Boh
orbit to the third Bohr orbit. Find
(i) the value of \( Z \) and give the hydrogen like species formed.
(ii) the kinetic energy and potential energy of the electron in the first Bohr
orbit.


The maximum kinetic energy of a particle of mass 100 g and time period lpi secs, executing SHM at its mean position is given as 50 J. The amplitude of oscillation is
A \( . A=50 \sqrt{10} \mathrm{m} \)
В. \( A=5 \sqrt{10} m \)
c. \( A=50 m \)
D. \( A=25 m \)


Is \( \pi \) an irrational number? Why?


State true or false.
If an isosceles triangle has more than one line of symmetry, then it must be an equilateral triangle.
A. True
B. False


Match the following and choose the
correct option given below.
Compound / Type
A. Dry ice
I. Anti-knocking compound
B. \( \quad \) II. Electronic diode or triode Semiconductor
C. Solder
III. Joining circuits
IV. Refrigerant for preserving
D. TEL \( \quad \) food
A. \( A-I, B-11, C-1 V, D-111 \)
B. \( A-11, B-111, C-1, D-1 V \)
C. \( A-I V, B-I I I, C-11, D-1 \)
D. \( A-I V, B-11, C-111, D-1 \)


Which is a secant?
\( A \cdot \) ми
B. on
\( c . P Q \)
D. None


The speed of propagation of a wave in a medium is \( 300 \mathrm{m} / \mathrm{s} \). The equation of
motion of point at \( x=0 \) is given by \( y= \) \( 0.04 \sin 600 \pi t(\text { metre }) . \) The
displacement of a point \( x=75 \mathrm{cm} \) at \( t= \) \( 0.01 \mathrm{s} \) is
A . \( 0.02 \mathrm{m} \)
B. 0.04 \( m \)
c. zero
D. \( 0.028 \mathrm{m} \)


Which of the following indicates tetany?
A. spasm
B. Muscular cramps
c. Tremors
D. All of the above


Consider the following ligands \( N H_{2}^{-} \)
acac (Acetylacetone), \( O H^{-}, \) Gly, \( O_{2}^{-} \) Phen, DMG, \( N O_{2}^{-}, C O_{3}^{2-}, C l^{-}, C H_{3} C O O^{-}, e n, S O_{4}^{2} \)
Then calculate value of " \( \boldsymbol{P}+\boldsymbol{Q}-\boldsymbol{R}- \)
\( \boldsymbol{S}^{\prime \prime} . \) Here
P: Total number of ligands which act as bridging as well as monodentate only.
Q: Total number of flexidentate ligands.
R: Total number of bidentate ligands only.
S: Total number of unsymmetrical bidentate ligands.
\( A \)
B. 2
\( c .5 \)
D. 6


The function \( \mathbf{f}: \mathbf{R} \rightarrow \mathbf{R} \) defined by
\( \mathbf{f}(\mathbf{x})=\sin \mathbf{x} \) is
This question has multiple correct options
A. neither one one nor onto
B. onto
c. one-one
D. many one


Find the value of \( f(2), \) so that the function \( \boldsymbol{f}(\boldsymbol{x})=\frac{12 \boldsymbol{x}-\mathbf{2 4}}{(\mathbf{4}+\mathbf{2} \boldsymbol{x})^{1 / 3}-\mathbf{2}}, \boldsymbol{x} \neq \mathbf{2} \)
is continuous everywhere


The weight of glucose present in \( 500 g \) of 0.5 molal aqueous solution is:
A . \( 22.5 g \)
в. \( 37.8 g \)
c. \( 41.2 g \)
D. \( 45 g \)


The points of intersection of the line \( 4 x-3 y-10=0 \) and the circle
\( x^{2}+y^{2}-2 x+4 y-20=0 \)
are....................and.
This question has multiple correct options
A \( .(4,2) \)
в. (-2,-6)
D. (-2,-4)


Which of the following processes
results in the formation of a new
compound?
A. Dissolving common salt in water
B. Heating water
c. Heating platinum rod
D. Heating iron rod


Explain the principle and working of a nuclear reactor with the help of a
labelled diagram.


The black shapes in the figure are closed surfaces. The electric field lines
are in red. For which case the net flux through the surfaces is non-zero?
(b)
\( (c) \)
A. In all cases net flux is non-zero
B. Only (c) and (d)
c. only (a) and (b)
D. only (b), (c) and (d)


Which of the following does not possess the ability to do work not because of motion?
A. A sparrow flying in the sky.
B. A sparrow moving slowly on the ground.
c. A sparrow in the nest on a tree
D. A squirrel going up a tree


Two magnets are kept one above the other and made to oscillate in
horizontal plane. The period combination is 6 second. When one of
the magnets is reversed pole to pole, the period of oscillations of combination is
3 second. Compare the magnetic pole moments of the two magnets.


How to find area of circle?


An electron microscope is operated at
\( 40 K v . \) The ratio of resolving power of this microscope and another one which uses yellow light of wavelength \( 6 \times 10^{7} \)
is :
\( \mathbf{A} \cdot 7 \times 10^{-25} \)
B . \( 9.78 \times 10^{4} \)
c. \( 9.78 \times 10^{-4} \)
D. \( 9.78 \times 10^{-6} \)


\( I=\int e^{x} \frac{(2+\sin 2 x)}{(1+\cos 2 x)} d x \)
A \( \cdot e^{x} \sin x \)
B. \( e^{x} \cos x \)
\( \mathbf{c} \cdot e^{x} \tan x \)
D. \( e^{x} \cos 2 x \)


Write the degree of the following polynomial. \( 12-x+4 x^{3} \)


The distance between the vertex and the
center of mass of a uniform solid planar
circular segment of angular size \( \boldsymbol{\theta} \) and
radius R is given by
A \( \cdot \frac{4}{3} R \frac{\sin (\theta / 2)}{\theta} \)
B. \( R \frac{\sin (\theta / 2)}{\theta} \)
c. \( \frac{4}{3} R \cos \left(\frac{(\theta)}{2}\right) \)
D \( \cdot \frac{2}{3} R \cos (\theta) \)


The I.U.P.A.C name for \( \boldsymbol{K}_{\mathbf{3}}\left[\boldsymbol{C o}\left(\boldsymbol{N} \boldsymbol{O}_{2}\right)_{\boldsymbol{6}}\right] \) is
A. Potassium(I) hexanitrocobaltate (II)
B. Potassium(I) hexanitrocobaltate (IV)
c. Potassium hexanitrocobalt (0)
D. Potassium hexanitritocobaltate (III)


Let \( \boldsymbol{f}=\left\{\left(\boldsymbol{x}, \frac{\boldsymbol{x}^{2}}{\mathbf{1}+\boldsymbol{x}^{2}}\right): \boldsymbol{x} \in \boldsymbol{R}\right\} \) be a
function from \( R \) into \( R \) Determine the
range of \( \boldsymbol{f} \)


Find the value of \( k \) for which each of the
following systems of equations have infinitely many solution:
\( \boldsymbol{x}+(\boldsymbol{k}+\mathbf{1}) \boldsymbol{y}=\boldsymbol{4} \)
\( (k+1) x+9 y=5 k+2 \)


How is ethyl amine prepared from methyl iodide?


Find \( Q M \)
\( A \cdot 13 c m \)
3. \( 12 \mathrm{cm} \)
\( c .5 \mathrm{cm} \)
D. \( 8 \mathrm{cm} \)


For any integers \( a \) and 3 , there exists
unique integers \( q \) and \( r \) such that \( a= \)
\( 3 q+r . \) Find the possible value of \( r \)


Which of the following reactions correctly represent(s) the preparation of
\( M g C O_{3} ? \)
This question has multiple correct options
\( \mathbf{A} \cdot M g\left(H C O_{3}\right)_{2} \stackrel{\text {heat}}{\rightarrow} M g C O_{3}+H_{2} O+C O_{2} \)
B. \( M g\left(H C O_{3}\right)_{2}+M g O \rightarrow 2 M g C O_{3}+H_{2} O \)
\( \mathbf{c} \cdot M g S O_{4}+2 N a H C O_{3} \rightarrow M g C O_{3}+N a_{2} S O_{4}+ \)
\( H_{2} O+C O_{2} \)
D. None of these


A particle moves uniformly in a circle of radius \( 25 \mathrm{cm} \) at two revolution per
second. Find the acceleration of the
particle in \( \boldsymbol{m} / \boldsymbol{s}^{2} \)


A sum of Rs. 11000 was taken as a loan.
This is to be repaid in two equal instalments. If the rate of interest be
\( 20 \% \) compounded annually, then the value of each instalment is
A. Rs. 8420
B. Rs. 7920
c. Rs. 7200
D. Rs. 7000


If a body moves with uniform velocity, the velocity-time graph
A. makes a positive slope with time axis
B. is a straight line parallel to velocity axis
c. is a straight line parallel to time axiss
D. is a curve


Statement-I : Energy is released when heavy nuclei undergo fission or light nuclei undergo fusion and Statement-11: For heavy nuclei, binding energy per nucleon increases with increasing Z. while for light nuclei it decreases with increasing Z.
A. Both the statements are true and Statement 2 is the correct explanation for Statement
B. Both the statements are true but Statement 2 is not the correct explanation for Statement 1
c. statement 1 is true but Statement 2 is false
D. Statement1 is false but Statement 2 is true


The internal energy of compressed real
gas, as compared to that of the ideal gas at the same temperature is
A . less
B. more
c. sometimes less, sometimes more
D. maximum


Which of the following reactions occurs
at cathode during charging of storage
battery?
\( \mathbf{A} \cdot P b^{2+}+2 e^{-} \rightarrow P b \)
B \( \cdot P b \rightarrow P b^{2+}+2 e^{-} \)
\( \mathbf{c} \cdot P b^{2+}+S O_{4}^{2-} \rightarrow P b S O_{4} \)
D \( \cdot P b S O_{4}+2 H_{2} O \rightarrow P b O_{2}+4 H^{+}+S O_{2}^{2-}+2 e^{-} \)


Why is friction greater between rough surfaces than between smooth ones?


Q Type your question
A population study of plants was done
in an abandoned field. Each year for 3
years the vegetation was sampled. The chart indicates the results of the body.
\( \begin{array}{ll}\text { Number } \\ \text { of } \\ \text { Year } & \text { Plants } \\ \text { per Acre }\end{array} \)
Ragweed \( \quad \) Timothy
Grass Sandspur \begin{tabular}{llll}
1 & 3,800 & 4,900 & 600 \\
2 & 1,500 & 2,209 & 1,185 \\
\hline
\end{tabular} 752 2,234
Which of the following are initially most successful in succession?
A. Sandspur and ragweedd
B. Sandspur and timothy grass
c. Ragweed and timothy grass
D. Ragweed and wire grass
E. Sandspur and goldenroo


The ion that always keeps the cardiac muscle unit in contracting state is
A. Sodium
B. Potassium
c. Calcium
D. Magnesium


Photochromic glass, used for sunglasses, darkens when exposed to bright light and becomes more transparent again when the light is less bright. The darkness of the glass is related to the
concentration of silver atoms.
The following reactions are involved. reaction \( 1 A g^{+}+C l^{-} \rightleftharpoons A g+C l \)
reaction 2 \( \boldsymbol{C u}^{+}+\boldsymbol{C l} \rightarrow \boldsymbol{C u}^{2+}+\boldsymbol{C l}^{-} \)
reaction 3 \( C u^{2+}+A g \rightarrow C u^{+}+A g^{+} \)
Which statement about these reactions
is correct?
A \( \cdot C u^{+} \) and \( C u^{2+} \) ions act as catalysts
B. \( C u^{+} \) ions act as an oxidising agent in reaction 2
c. Reaction 3 increases the darkness of the glass
D. silver atoms are reduced in reaction 3


All of our cells contain protooncogenes that may turn into oncogenes, which are cancer genes. Which statement best describes the protooncogenes?
A. Came into our cells from a viral infection of our ancestors
B. Arose from plasmids that have been inserted into bacteria and now reside in us
C. Are DNA "junk" with no known function
D. Turn into oncogenes as we age
E. Help regulate cell division


If \( f(x) \) is a polynomial in \( x(>0) \)
satisfying the equation \( \boldsymbol{f}(\boldsymbol{x})+ \) \( f\left(\frac{1}{x}\right)=f(x) \cdot f\left(\frac{1}{x}\right) \) and \( f(2)=-7 \)
then \( f(3) \) is equal to
A . -26
в. -27
c. -28
D. -29


The value of \( \left|\begin{array}{ll}\cos 15^{\circ} & \sin 15^{\circ} \\ \sin 75^{\circ} & \cos 75^{\circ}\end{array}\right| \)


ff \( z=-5+2 \sqrt{-4}, \) then the value of
\( z^{2}+10 z+41 \) is equal to
\( A \cdot 2 \)
B . - -
\( c \cdot 0 \)
D. None of these


An alternating voltage source is connected in an \( A C \) circuit whose
maximum value is 170 volt. The value
of potential at a phase angle of \( 45^{\circ} \) will
be
A . 120.56 volt
B. 110.12 Volt
c. 240 volt
D. zero


Let \( A, B, C, D, E \) be the interior angles of
convex pentagon and \( \boldsymbol{\Delta}=\left|\begin{array}{ccc}\cos \boldsymbol{A} & \sin \boldsymbol{A} & \sin (\boldsymbol{A}+\boldsymbol{D}+\boldsymbol{E}) \\ \cos \boldsymbol{B} & \sin \boldsymbol{B} & \sin (\boldsymbol{B}+\boldsymbol{D}+\boldsymbol{E}) \\ \cos \boldsymbol{C} & \sin \boldsymbol{C} & \sin (\boldsymbol{C}+\boldsymbol{D}+\boldsymbol{E})\end{array}\right| \)
find \( \Delta(\pi / 3)+\Delta^{\prime}(\pi / 6) \)


There are three coins. One is a two-
headed coin another is a biased coin
that comes up heads \( 75 \% \) of the time
and third is an unbiased coin. One of the
three coins is chosen at random and
tossed, it shows heads, what is the probability that it was the two-headed
coin?


A solid conducting sphere having a
charge \( Q \) is surrounded by an
uncharged concentric conducting
hollow spherical shell. Let the potential difference between the surface of the
solid sphere and that of the outer surface of the hollow shell be \( V \). If the
shell is now given a charge \( -3 Q \), the
new potential difference between the
same two surfaces is:
\( \mathbf{A} \cdot V \)
B. \( 2 V \)
c. \( 4 V \)
\( \mathbf{D} \cdot-2 V \)


Assertion
Specialization of cells is advantageous
for
the organism
Reason
It increase the operational efficiency of
an
organism
A. If both the assertion and the reson are true and the
reason
is correct explanation of the assertion.
B. If both the assertion and the reson are true but the
reason
is not correct explanation of the assertion.
C. If the assertion is true but the reason is false
D. If both the assertion and reason are false


Assertion
If the roots of the equations \( x^{2}-b x+ \)
\( c=0 \) and \( x^{2}-c x+b=0 \) differ by the
same quantity, then \( b+c \) is equal to
-4
Reason
If \( \alpha, \beta \) are the roots of the equation \( A x^{2}+B x+C=0, \) then \( \alpha-\beta= \)
\( \frac{\sqrt{\boldsymbol{B}^{2}-\boldsymbol{4} \boldsymbol{A} \boldsymbol{C}}}{\boldsymbol{A}} \)
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Assertion is incorrect but Reason is correct


State the following statement is True or
False
\( C=\{x \mid x \in Q, 3<x<5\} \) is an
example of a finite set.
A. True
B. False


Which of the following does not appear
to involve active transport across
membrane?
A. the movement of mineral nutrients from the apoplast to the symplast
B. the movement of sugar from mesophyll cells into sieve-tube members in corn
c. the movement of sugar from one sieve-tube member to the next
D. \( K^{+} \) uptake by guard cells during stomatal opening


If \( x_{1}, x_{2}, \dots ., x_{n} \) are any real number and
\( \boldsymbol{n} \) is any positive integer, then \( ? \)
B \( \cdot n \sum_{i=1}^{n} x_{i}^{2} \geq\left(\sum_{i=1}^{n} x_{i}\right)^{2} \)
c. \( n \sum_{i=1}^{n} x_{i}^{2} \geq n\left(\sum_{i=1}^{n} x_{i}\right)^{2} \)
D. None of the above


A policeman and a thief are equidistant from the jewel box, upon considering jewel box as origin, the position of the policeman is (0,5) . If the ordinate of the position of the thief is zero, then write the coordinates of the position of the thief.


The standard heat of combustion of
\( A l \) is \( -837.8 k J \) mol \( ^{-1} \) at \( 25^{\circ} \) C. If \( A l \)
reacts with \( O_{2} \) at \( 25^{\circ} C \), the formation of
0.150 mol of \( A l_{2} O_{3} \) release \( x k J \) of
heat. \( x \) is


If a rectangle and a parallelogram are equal in area and have the same base
and are situated on the same side then
the quotient:
is
A. Equal to 1
B. Greater than 1
c. Less than 1
D. Indeterminate


Write the identity relation on \( \operatorname{set} A= \)
\( \{a, b, c\} \)


Two elements \( X \) and \( Y \) have the
following electronic configurations \( X=1 s^{2} 2 s^{2} 2 p^{6} 3 s^{2} 3 p^{6} 4 s^{2} \) and \( Y= \)
\( 1 s^{2} 2 s^{2} 2 p^{6} 3 s^{2} 3 p^{5} . \) The formula of the
compound formed by the combination of \( X \) and \( Y \) is :
A \( . X Y_{2} \)
B . \( X_{5} Y_{2} \)
c. \( X_{2} Y_{5} \)
D. \( X Y_{5} \)


Create a concept map using the following words.

Electromagnetism, Electricity, Magnetism, Solenoid, Electromagnet, Magnet field, Electromagnetic induction, Generators, and
Transformers, motors.


The equation of a line is \( 5 x-3= \)
\( \mathbf{1 5 y}+\mathbf{7}=\mathbf{3}-\mathbf{1 0 z} . \) Write the direction
\( \operatorname{cosines} \) of the line.


The phase angle between the projections of uniform circular motion
on two mutually perpendicular diameter is
A . \( \pi \)
в. \( 3 \pi / 4 \)
c. \( \pi / 2 \)
D. zero


A cylinder and \( a \) cone have equal bases.
The height of the cylinder is \( 3 \mathrm{cm} \) and
the area of its base is \( 100 \mathrm{cm}^{2} \). The cone
is placed upon the cylinder. Volume of
the solid figure so formed is \( 500 \mathrm{cm}^{3} \)
Find the total height (in \( c m \) ) of the
figure.


State Huygen's principle.


Let \( X \) be a set containing n elements.
Two subsets \( A \) and \( B \) of \( X \) are chosen
at random, the probability that \( \boldsymbol{A} \cup \) \( B=X \) is
A \( \cdot \frac{2 n}{2^{2 n}} \)
в. \( \frac{1}{2 n} C_{n} \)
\( \frac{c \cdot \frac{1 \cdot 3 \cdot 5 \cdot \ldots .(2 n-1)}{2^{n} n !}}{(2)} \)
D. \( \left(\frac{3}{4}\right)^{n} \)


Chloragogen cells of earthworm are similar to \( \ldots \ldots . . . . \) vertebrate organ.
A. Spleen
B. Liver
c. Kidney
D. Lung


A mixture of all isomers of pentane is allowed to react with chlorine radicals
(produced by photochemical cleavage
of \( C l_{2} \) ). How many different isomeric alkyl radicals can form by hydrogen abstraction in the following reaction?
Pentane (all isomers) \( +C l^{*} \rightarrow \) Penty
radicals (all isomers) \( +\boldsymbol{H} \boldsymbol{C l} \)
A . 5
B. 6
\( c \cdot 7 \)
\( D \)


Blue litmus turns red when added to
a/an:
A . acid
B. base
c. oil
D. none of the above


Consider the above Lewis Dot structure:
The formal charges on \( S \) and \( O \) are
respectively:
A .0,0
в. +2,0
\( c \cdot 0,-2 \)
\( \mathrm{D} \cdot+1,- \)


Fossil fuels are obtained from:
A. remains of non-living materials
B. dead remains of birds only
C. dead remains of insects only
D. dead remains of living organisms


The Van't Hoff factor for a dilute
aqueous solution of glucose is :
A. Zero
в. 1.0
c. 1.5
D. 2.0


The van't Hoff reaction isotherm is:
\( \mathbf{A} \cdot \Delta G=R T \log _{e} K_{p} \)
в. \( -\Delta G= \) RТlog\( _{e} K_{p} \)
\( \mathbf{c} \cdot \Delta G=R T^{2} I n K_{p} \)
D. none of these


If the average life time of an excited state of hydrogen is of the order of \( 10^{-8} s, \) estimate how many orbits an electron makes when it is in the state
\( n=2 \) before it suffers a transition to
state \( n=2\left(\text { Bohr radius } a_{0}=5.3 \times\right. \)
\( \left.10^{-11} m\right) ? \)


\( \boldsymbol{x}=\mathbf{0}, \boldsymbol{y}=-\mathbf{0 . 5 0 0 m}, \boldsymbol{z}=\mathbf{0} \)


Heat is supplied to a certain
homogeneous sample of matter, at a
uniform rate. Its temperature is plotted against time, as shown.Which of the
following conclusions can be drawn?
A . Its specific heat capacity is greater in the solid state than in the liquid state
B. Its specific heat capacity is smaller in the solid state than in the liquid state.
c. Its latent heat of vaporization is greater than its latent heat of fusion
D. Its latent heat of vaporization is smaller than its latent heat of fusion


The hybridization of iron in
\( \boldsymbol{K}_{4}\left[\boldsymbol{F} \boldsymbol{e}(\boldsymbol{C} \boldsymbol{N})_{6}\right] \) is?
A \( \cdot d s p^{2} \)
B \( \cdot s p^{3} \)
c. \( d^{2} s p^{3} \)
D. \( d^{2} s p^{2} \)


Electric charge can not flow through
A. insulators
B. conductors
c. both insulators and conductors
D. neither insulators nor conductors


An automobile engine propels a \( 1000 \mathrm{kg} \) car \( A \) along a leveled road at a speed of \( 36 k m h^{-1} . \) The frictional force is 100
N. Suppose after traveling a distance of \( 200 \mathrm{m}, \) this car collides with another
stationary car \( \mathrm{B} \) of the same mass and comes to rest. Let Its engine also stop at the same time. Now, car B starts
moving on the same level road without getting its engine started. Find the speed of the car B just after the collision.
A. \( 36 \mathrm{km} / \mathrm{h} \)
B. 72 km/h
\( \mathbf{c} \cdot 18 \mathrm{km} / \mathrm{h} \)
D. \( 100 \mathrm{km} / \mathrm{h} \)


When \( S O_{3} \) treated with \( D_{2} O, \) the
products are:
A. deutero sulphuric acid
B. deuterium sulphuric acid
c. deuterium and sulphuric acid
D. \( D_{2} S O_{3} \)


A matrix has 8 elements. What are the
possible orders it can have?


Which one of the following has bast fibres?
A. Parenchyma
B. Sclerenchyma
c. Phloem
D. xylem


Statement A : A neutron travelling with a velocity collides head on an atom of
atomic mass number \( A \) at rest. The
fraction of the total energy retained by neutron is \( \left(\frac{A-1}{A+1}\right)^{2} \)
Statement B : The kinetic energy
conserves during an elastic collision
\( A \cdot A \) and \( B \) are true
B. A is true but B is false
c. A is false but B is true
D. A and B are false


The phenomenon of motion of
colloidal particles is known as brownian
movement
A. Linear
B. Zig-Zag
c. circular
D. none


What is mole?


The reaction \( A \stackrel{K}{\longrightarrow} \) Product is zeroorder while the reaction \( B \stackrel{K}{\longrightarrow} \) Product
is first-order reaction. For what initial
concentration of \( A \) is the half lives of the
two reactions equal?
A. 2\operatorname{ln } 2 \text { M }
B. 2 M
\( c \cdot \ln 2 M \)
D. In 4 M


Polyethylene glycols are used in the preparation of which type of detergents?
A. cationic detergents
B. Anionic detergents
c. Non-ionic detergents
D. Soaps


The degree of dissociation \( (\alpha) \) of a weak
electrolyte, \( A_{x} B_{y} \) is related to van't Hoff
factor (i) by the expression:
A \( \cdot \alpha=\frac{i-1}{(x+y-1)} \)
B. \( \alpha=\frac{i-1}{x+y+1} \)
c. \( \alpha=\frac{x+y-1}{i-1} \)
D. \( \alpha=\frac{x+y+1}{i-1} \)


Solve the inequalities for real \( x \) \( \frac{3(x-2)}{5} \leq \frac{5(2-x)}{3} \)


Evaluate the integral \( \int_{0}^{2}\left(x^{2}+2 x+\right. \)
1) \( d x \)


If \( y=\tan ^{-1}\left(\frac{a \cos x-b \sin x}{b \cos x+a \sin x}\right) \) then
\( \frac{\boldsymbol{d} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}}=? \)
\( A \cdot \frac{a}{b} \)
B. \( \frac{-b}{a} \)
c.
D. -


Two roads are represented by the
equations \( \boldsymbol{y}-\boldsymbol{x}=\boldsymbol{6} \) and \( \boldsymbol{x}+\boldsymbol{y}=\mathbf{8} \)
An inspection bungalow has to be so constructed that it is at a distance of
100 from each of the roads. Possible
location of the bungalow is given by :
This question has multiple correct options
A \( \cdot(100 \sqrt{2}+1,7) \)
в. \( (1-100 \sqrt{2}, 7) \)
c. \( (1,7+100 \sqrt{2}) \)
D. \( (1,7-100 \sqrt{2}) \)


The ratio of specific charge of an electron to that of a proton is
A . 1: 1
в. 1837: 1
c. 1: 1836
D. 2: 1


The speed of a train increases at a
constant rate \( \alpha \) from zero to \( v \) and then
remains constant for an interval and
finally decreases to zero at a constant rate \( \beta . \) The total distance travelled by
the train is \( l . \) The time taken to
complete the journey is \( t . \) Then This question has multiple correct options
A \( \cdot t=\frac{l(\alpha+\beta)}{\alpha \beta} \)
B. \( t=\frac{l}{v}+\frac{v}{2}\left(\frac{1}{\alpha}+\frac{1}{\beta}\right) \)
C \( t \) is minimum when \( v=\sqrt{\frac{2 l \alpha \beta}{(\alpha-\beta)}} \)
D. \( t \) is minimum when \( v=\sqrt{\frac{2 l \alpha \beta}{(\alpha+\beta)}} \)


Sulphur reacts with chlorine in 1: 2
ratio and forms \( X . \) hydrolysis of \( X \) gives
a sulphur compound \( Y \). What is the
hybridization state of central atom in the compound?
\( A \cdot s p^{3} \)
B \( \cdot s p^{2} \)
\( c \cdot s p \)
D. \( d s p^{2} \)


For how long and at what temperature an experiment is run to determine the value of \( B O D \) of a water body?
A \( \cdot 10^{\circ} \mathrm{C} \) for 10 days
B. \( 20^{\circ} \mathrm{C} \) for 5 days
c. \( 20^{\circ} \mathrm{C} \) for 2 days
D. \( 5^{\circ} \mathrm{C} \) for 20 days


\( \bar{a}=x \hat{i}+y \hat{j}+z \hat{k}, \bar{b}=\hat{j} \) then the vector
\( \bar{c} \) for which \( \bar{a}, \bar{b}, \bar{c} \) form a right hand triad
A \( . x(\hat{i}-\hat{k}) \)
B. 0
\( \mathbf{c} .-z \hat{i}+x \hat{k} \)
D. \( y \hat{j} \)


Use the mirror equation to deduce that:
(a) an object placed between \( f \) and \( 2 f \) of a concave mirror produces a real
image beyond \( 2 f \)
(b) a convex mirror always produces a virtual image independent of the location of the object.
(c) the virtual image produced by a convex mirror is always diminished in size and is located between the focus
and the pole.
(d) an object placed between the pole and focus of a concave mirror produces a virtual and enlarged image. [Note: This exercise helps you deduce algebraically properties of images that one obtains from explicit ray diagrams.


ff \( f(x)=x^{2}-4 x+5 \) on [0,3] then the
absolute maximum value is:
\( A \cdot 2 \)
B. 3
\( c \cdot 4 \)
D. 5


Assertion
Thin films such as soap bubble or a thin layer of oil on water show beautiful
colors when illuminated by white light.
Reason

It happens due to the interference of light reflected from the upper surface of thin film.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Assertion is incorrect but Reason is correct


Evaluate :
\( \int \frac{1}{\sin ^{2} x \cos ^{2} x} d x \)
A . \( -\tan 2 x+C \)
B. \( -2 \cot 2 x+C \)
\( c \cdot \tan x+\cot 2 x+C \)
D. None of these


A particle execute \( S H M \) from the
mean position. its amplitude is \( A \) its time period \( T . \) At what displacement its
speed is half of its maximum speed?
A \( \cdot \frac{\sqrt{3} \mathrm{A}}{2} \)
B. \( \frac{\sqrt{2}}{3} \mathrm{A} \)
\( c \cdot \frac{2 A}{\sqrt{3}} \)
\( D \cdot \frac{3 A}{\sqrt{2}} \)


A cone, hemisphere and a cylinder stand on the same base and have equal
height. Find the ratio of their:
Volumes.


If \( \vec{a} \) and \( \vec{b} \) are unit vectors and \( \alpha \) is the
angle between them, then \( \vec{a}+\vec{b} \) is a
unit vector when \( \cos \alpha= \)
A \( \cdot-\frac{1}{2} \)
B. \( \frac{1}{2} \)
\( c \cdot-\frac{\sqrt{3}}{2} \)
D. \( \frac{\sqrt{3}}{2} \)


Which one of the following statements
are correct?
\( \mathbf{A} \cdot \) If \( g(x)(\neq 0) \) and \( f(x) \) are two polynomials \( \in F(x) \), then there exists unique polynomials \( q(x) \) and \( r(x) \in F(x) \) such that \( f(x)=g(x) q(x)+r(x) \) where \( \operatorname{deg} . r(x)< \)
\( \operatorname{deg} . g(x) \)
B. If \( g(x)(\neq 0) \) and \( f(x) \) are two polynomials \( \in F(x) \), then there exists unique polynomials \( q(x) \) and \( r(x) \in F(x) \) such that \( f(x)=g(x) q(x)+r(x) \) where \( \operatorname{deg} . r(x) \leq \)
\( \operatorname{deg} . g(x) \)
C \( \cdot \) If \( g(x)(\neq 0) \) and \( f(x) \) are two polynomials \( \in F(x) \), then there exists unique polynomials \( q(x) \) and \( r(x) \in F(x) \)
such that \( f(x)=g(x) q(x)+r(x) \) where either \( r(x)=0 \) or \( \operatorname{deg} . r(x)<\operatorname{deg} . g(x) \)
D. If \( g(x)(\neq 0) \) and \( f(x) \) are two polynomials \( \in F(x) \), then there exists unique polynomials \( q(x) \) and \( r(x) \in F(x) \) such that \( f(x)=g(x) q(x)+r(x) \) where \( f(x)=0 \) or \( \operatorname{deg} . r(x)=\operatorname{deg} . g(x) \)


A current source sends a current \( \boldsymbol{I}- \)
\( i_{0} \cos (\omega t) . \) when connected across an
unknown load, it gives a voltage output
of \( \boldsymbol{v}=\boldsymbol{v}_{0} \sin [\boldsymbol{\omega} \boldsymbol{t}+(\boldsymbol{\pi} / \mathbf{4})] \) across that
load. then the voltage across the current source may be brought in phase with the current through it by
A. Connecting an inductor in series with the load
B. Connecting a capacitor in series with the load
c. connecting an inductor in parallel with the loadd
D. connecting a capacitor in parallel with the load


If \( P(A)=\frac{3}{5} \) and \( P(B)=\frac{1}{5}, \) find
\( \mathbf{1 0 0} \boldsymbol{P}(\boldsymbol{A} \cap \boldsymbol{B}) \) if \( \boldsymbol{A} \) and \( \boldsymbol{B} \) are
independent events.


Whenever practicable, synthetic methods should be designed to use and generate substances that are little or
not toxic to human health and
environment, is an objective of:
A. waste management
B. green chemistry
c. air pollution
D. green revolution


There is increase in blood urea when
there is insufficient filtration in
A. Loop of Henle
B. Distal tubule
c. Bowman's capsule
D. collecting tubule


State whether true or false:
\( \sin 2 x+2 \sin 4 x+\sin 6 x= \)
\( 4 \cos ^{2} x \sin 4 x \)
A. True
B. False


Give the type of isomerism exhibited by each of the following pairs. n-Butyl alcohol and diethyl ether
A. Functional
B. Position
c. Tautomerism
D. None of These


The mass of a lead ball is M. It falls
down in a viscous liquid with terminal velocity V. The terminal velocity of another lead ball of mass \( 8 \mathrm{M} \) in the
same liquid will be:
A . \( 64 V \)
в. \( 4 V \)
\( c .8 V \)
D. \( V \)


The IUPAC name of anisole is:
A. ethoxybenzene
B. methoxybenzene
c. propoxybenzene
D. butoxybenzene


In given diagrams write the direction of
magnetic field produced at point \( \boldsymbol{P} \) in
form of \( \otimes \) and \( \odot \)


In triangle \( A B C ; M \) is mid-point of \( A B, N \) mid-point of \( A C \) and \( D \) is any point in base BC. Then:
\( A . \) MN bisects AD
B. MN divides AD in the ratio 1: 3
c. MN divides AD in the ratio 1: 2
D. MN divides AD in the ratio 1: 4


Three equal cubes are placed adjacently in a row. Find the ratio of
total surface area of the new to that of
the sum of the surface areas of the
three cubes.


Find the ratio in which the yz-plane
divides the join of the points (-2,4,7)
and (3,-5,8) and also find the \( c o \)
ordinates of the point of intersection of
this line with the \( y z \) - plane.
A \( \cdot \lambda=\frac{2}{3} \) and \( \left(0, \frac{2}{5}, \frac{37}{5}\right) \)
B. \( \lambda=\frac{1}{3} \) and \( \left(\frac{-3}{4}, \frac{7}{4}, \frac{29}{4}\right) \)
c. \( \lambda=\frac{2}{3} \) and \( \left(\frac{-3}{4}, \frac{7}{4}, \frac{29}{4}\right) \)
D \( \lambda=\frac{1}{3} \) and \( \left(0, \frac{2}{5}, \frac{37}{5}\right) \)


Let \( \boldsymbol{f}: \boldsymbol{R} \rightarrow \boldsymbol{R} \) and \( \boldsymbol{f}(\boldsymbol{x})=\log _{e} \boldsymbol{x}, \boldsymbol{R} \)
being the set of real numbers then which of the following is not correct?
A. \( f \) is onto
B. \( f \) is one-one
c. \( f \) is invertible
D. \( f \) is into


Change in focal length of an eye-lens to focus the image of object at varying distances is done by the action of :
A. Pupil
B. Ciliary muscles
c. Retina
D. Blind spot


Identify which of the following is NOT a characteristic of electromagnetic
waves?
A. contain electrical properties
B. have crests and troughs
c. contain magnetic properties
D. travel through space
E. have crests but no troughs


Q Type your question
\( \mathbf{A} \)
\( B \)
\( \mathbf{C} \)
\( D \)


The IUPAC name of crotonaldehyde is
A. Butenaldehyde
B. Butanal-1
c. But-2-en-1-al
D. Prop-2-en-1-ol


At resonant frequency the current
amplitude in series LCR circuit is:
A. maximum
B. minimum
c. zero
D. infinity


Find the shortest distance of (3,4) from
origin.


Isobars have:
A. same mass number but different atomic number
B. same number of neutrons but different mass number
C. same difference between number of protons and neutrons
D. same mass number and atomic number


Arrange the following in increasing
order of oxidation state of \( N i \)
\( \boldsymbol{K}_{2}\left[\boldsymbol{N} \boldsymbol{i}(\boldsymbol{C} \boldsymbol{N})_{4}\right], \boldsymbol{K}_{2}\left[\boldsymbol{N} \boldsymbol{i} \boldsymbol{F}_{6}\right], \boldsymbol{N} \boldsymbol{i}(\boldsymbol{C} \boldsymbol{O})_{4} \)
A \( \cdot N i(C O)_{4}, K_{2}\left[N i(C N)_{4}\right], K_{2}\left[N i F_{6}\right] \)
B . \( K_{2}\left[N i(C N)_{4}\right], N i(C O)_{4}, K_{2}\left[N i F_{6}\right] \)
c. \( N i(C O)_{4}, K_{2}\left[N i F_{6}\right], K_{2}\left[N i(C N)_{4}\right] \)
D. \( K_{2}\left[N i F_{6}\right], K_{2}\left[N i(C N)_{4}\right], K_{2}\left[N i(C N)_{4}\right]^{\prime} \)


A spring is stretched by \( 0.20 m \) when a
mass of \( 0.50 \mathrm{kg} \) is suspended. A mass of \( 0.25 \mathrm{kg} \) is suspended, then its period
of oscillation will be \( \left(g=10 m / s^{2}\right) \)
(approximately)
A \( .0 .628 s \)
B. \( 0.251 s \)
\( \mathbf{c} \cdot 6.28 s \)
D. 2.51s


Carboxylic group is present in:
A . ethylene
B. methanoic acid
c. formaldehyde
D. ethanol


An electron is accelerated to one-tenth
the velocity of light. Suppose its velocity can be measured with a precision of \( 1 \% \) what must be the uncertainty in position?
A. \( 2.13 \times 10^{-10} \)
B . \( 1.93 \times 10^{-10} \)
c. \( 3.85 \times 10^{-10} \)
D. \( 1.52 \times 10^{-10} \)


Active uptake of minerals by root mainly depends on the
A. Availability of oxygen
B. Light
c. Temperature
D. Availability of carbon dioxide


The initial speed with which water strikes the ground in \( m s^{-1} \) is:
A . 10
B. 5
\( c \cdot 5 \sqrt{2} \)
D. \( 10 \sqrt{2} \)


A straight line passes through the points (2,4) and \( (5,-2) . \) Taking \( 1 c m= \) 1 units, mark these points on a graph
paper and draw the straight line through these points. If points \( (\boldsymbol{m},-\mathbf{4}) \)
and \( (3, n) \) lie on the drawn line, find the
values of \( m \) and \( n \)
A. \( m=1 \) and \( n=2 \)
B. \( m=3 \) and \( n=2 \)
c. \( m=6 \) and \( n=2 \)
D. \( m=9 \) and \( n=2 \)


The only poisonous lizard of the world is
A. Hemidactylus
B. Phrynosoma
c. Heloderma
D. Uromastix


Of the following which plant hormone
inhibits growth?
A. Cytokynins
B. Gibberelins
c. Auxins
D. Abscisic acid


Keratin, a structural protein is present
in :
A. hair
B. skin
c. wool
D. all


Fill in the blank.
Dams are \( _{---} \) at the base.
A. thicker
B. thinner
c. same
D. can't say


Which of the following gases can result
in the formation of acid rain?
A. Ozone
B. Carbon monoxide
c. Sulphur dioxide
D. chlorofluorocarbon


The work done in adiabatic
compression of 2 mole of an ideal monoatomic gas by constant external
pressure of 2 atm starting from initia pressure of 1 atm and initial
temperature of \( 300 K(R=2 \mathrm{cal} / \mathrm{mol}- \)
degree celsius) is :
A . 360 cal
B. 720 call
c. 800 cal
D. 1000 call


In bullocks,horses,camels pulling carts the effort(force)is caused by
A. The woody carts
B. The muscles of animals
c. Muscles of humans
D. The frictional force between the roads and wheels of the carts


\( A, B \) and \( C \) are the three forces each of
magnitude \( 4 N \) acting in the plane of
paper as shown in the figure. The point
O lies in the same plane. Which force
has the least moment about \( O \) ?
\( A \cdot A \)
в. \( B \)
\( c . C \)
D. all the above


Solve the following differential equation \( \frac{d y}{d x}=\sec ^{2} x \)


Assign oxidation number to the
underlined element in \( N a H \underline{S} O_{4} \)


What is Iymph? Write its function.


Find the number of terms of the A.P.
\( -12,-9,-6,-\ldots, 21 . \) If 1 is added to
each term of this A.P., then find the sum
of all terms of the A.P. thus obtained.


The length of a seconds hand in a watch
is \( 1 \mathrm{cm} . \) The change in its velocity in 15 s is
A. \( 0 \mathrm{cm} / \mathrm{s} \)
B. \( \frac{\pi}{30 \sqrt{2}} \mathrm{cm} / \mathrm{s} \)
c. \( \frac{\pi}{30} \mathrm{cm} / \mathrm{s} \)
D. \( \frac{\pi}{30} \sqrt{2} \mathrm{cm} / \mathrm{s} \)


Synthesis of each molecule of glucose in photosynthesis involves:
A. 6 molecules of ATP
B. 18 molecules of ATP
c. 10 molecules of ATP
D. 8 molecules of ATP


Which of the following is not added the extraction of silver by cyanide process?
A . \( N a C N \)
B. Air
\( c \cdot Z n \)
D. \( N a_{2} S_{2} O_{3} \)


Critical temperature and pressure of a
real gas is \( 27^{\circ} \mathrm{C} \) and 75 atm
respectively. The critical volume of 1 mole of real gas is :
A. 12.47 litre
B. 0.12 litre
c. 1.24 litre
D. data insufficient


The polynomials \( \left(2 x^{3}-5 x^{2}+x+a\right) \)
and \( \left(a x^{3}+2 x^{3}-3\right) \) when divided by
\( (x-2) \) leave the remainders \( R_{1} \) and \( R_{2} \)
respectively. Find the value of \( ^{\prime} a^{\prime} \) in the
following case, if
\( \boldsymbol{R}_{1}-\boldsymbol{2} \boldsymbol{R}_{2}=\mathbf{0} \)


Write five rational numbers greater
than -2


Based on physical similarity, which
skulls appear to be most closely related?
A. 1 and 2
B. 1 and 3
\( c \cdot 2 \) and 3
D. 2 and 4
E. 1 and 4


If true enter 1 , else enter 0
Number of \( \sigma \) -bonds in \( C(C N)_{4} \) are eight
\( A \)


Differentiate the given function


A source \( S \) is kept directly behind the
slit \( S, \) in a double-slit apparatus. Find
the phase difference at a point \( O w h i c h \)
is equidistant from \( s 18 \) s2 What will be
the phase difference at \( P \) if a liquid of refraction index \( \mu \) is filled. (wavelength
of light in air is / due to the source) \( (\lambda<<d, d<<D,\langle>>d) \)
A. between the screen and the slits
B. between the slits \( \& \) the source S. In this case find the minimum distance between the points on the screer where the intensity is half the maximum intensity on the screen
c. Beyond the slits
D. None of these


Which of the following is not oxidised by
\( \boldsymbol{O}_{3} ? \)
A. \( K I \)
в. \( K M n O_{4} \)
c. \( K_{2} \) Мп \( O_{4} \)
D. \( F e S O_{4} \)


Four identical pendulums are made by attaching a small ball of mass 100 g on a \( 20 \mathrm{cm} \) long thread and suspended from the same point. Now each ball is given charge \( Q \) so that balls move away from each other with each thread
making an angle of \( 45^{\circ} \) from the vertical. The value of \( Q \) is close to \( \left.\frac{1}{4 \pi \epsilon_{0}}=9 \times 10^{9} \text { in Sl units }\right) \)
A . \( 1 \mu C \)
в. \( 1.5 \mu \) С
\( c \cdot 2 \mu c \)
D. 2.5 \( \mu \) C


The farthest point, upto which the eye can see objects clearly, is called for a
normal eye.
A. near point, \( 50 \mathrm{cm} \)
B. power of accommodation, \( 100 \mathrm{m} \)
c. far point, infinity
D. range of vision, \( 25 \mathrm{cm} \)


Which of the following is responsible for the relatively high boiling point of
water?
A. Hydrogen bonding
B. lonic bonding
c. Metallic bonding
D. Non-polar covalent bonding
E. Polar covalent bonding


The given graph represent the how much consumers would be willing to
pay for store brand and brand name
products. If a consumer is chosen at
random, then the probability that the
consumer is will to pay at least \( \$ 8 \) for
the product is \( \frac{u}{b}, \) where \( a, b \) are \( c 0 \)
primes. Find the value of \( b-a ? \)

Store Brand \( \square \) Brand Name


When a body is charged, its mass:
A. increases
B. decreases
c. remains same
D. none of these


Evaluate the definite integral \( \int_{0}^{\frac{\pi}{4}} \tan x d x \)


Find the volume of a sphere of radius 3
\( \mathrm{cm} \)


If three terms are in A.P. and there sum
is \( 18 . \) Find the second term.


If \( x=\cos 10^{\circ} \cos 20^{\circ} \cos 40^{\circ}, \) then the
value of \( x \) is
A \( \cdot \frac{1}{4} \tan 10^{\circ} \)
B. \( \frac{1}{8} \cot 10^{\circ} \)
c. \( \frac{1}{8} \cos 10^{\circ} \)
D. \( \frac{1}{8} \sec 10^{\circ} \)


In an experiment to study the properties of ethanoic acid, a student takes about \( 3 \mathrm{mL} \) of ethanoic acid in a dry test tube He adds an equal amount of distilled water to it and shakes the test tube
well. After some time he is likely to observe that:
A. a colloid is formed in the test tube
B. the ethanoic acid dissolves readily in water
c. the solution becomes light orange
D. water floats over the surface of ethanoic acid
E. a homogenous solution of ethanoic acid and water is formed


Which type of addition reaction gives more stable products
A . 1,2 -addition
B. 1, 4-addition
C. Both (a) and (b)
D. None of these


Differentiate the following function with
respect to \( x \) \( \frac{x+\cos x}{\tan x} \)


Find \( \int \frac{\sqrt{\boldsymbol{x}}}{\sqrt{\boldsymbol{a}^{3}-\boldsymbol{x}^{3}}} \boldsymbol{d} \boldsymbol{x} \)


Most of the animals which can be
divided into two equal halves by only two planes included in the phylum
A. Porifera
B. Ctenophora
c. Platyhelminthes
D. All of the above


The universe consists of:
A. Galaxies
B. Planets
c. stars
D. All of the above


If the tube length of astronomical telescope is \( 96 \mathrm{cm} \) and magnifying power is 15 for normal setting, then the focal length of the objective is
\( \mathrm{cm} \)
A . 100
B. 90
\( c .105 \)
D. 92


White phosphorous is more reactive
due to:
A. bond angle strain
B. its polymeric nature
c. both of them
D. less density


Construct a quadrilateral \( P Q R S \) where \( \boldsymbol{P Q}=\mathbf{4} \boldsymbol{c m}, \boldsymbol{Q} \boldsymbol{R}=\boldsymbol{6} \boldsymbol{c m}, \boldsymbol{R} \boldsymbol{S}= \)
\( \mathbf{5} c m \cdot \boldsymbol{P} \boldsymbol{S}=\mathbf{5} . \mathbf{5} \boldsymbol{c m} \) and \( \boldsymbol{P} \boldsymbol{R}=\mathbf{7} \boldsymbol{c m} \)


Write a and b in the given flow chart of neuron through which information
travels as an electrical impulse.
Dendrite \( \rightarrow a \rightarrow b \rightarrow \) End point of neuron


Assertion
Magnetic field interacts with a moving charge and not with a stationary charge.
Reason

A moving charge produces a magnetic field.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Assertion is incorrect but Reason is correct


From which of the following algae, agar is commercially extracted?
a) Gracilaria
b) Fucus
c) Sargassum
d) Gelidium
e) Turbinaria
A. c and e
B. b and c
\( c . \) d and \( e \)
D. a and b
\( E \cdot \) a and \( d \)


f \( p=-2, \) find the value of:
\( -3 p^{2}+4 p+7 \)


Statement-I: For every natural number \( \boldsymbol{n} \geq 2, \frac{1}{\sqrt{1}}+\frac{1}{\sqrt{2}}+\ldots \ldots+\frac{1}{\sqrt{n}}>\sqrt{\boldsymbol{n}} \)
Statement-2: For every natural number \( \boldsymbol{n} \geq \mathbf{2}, \sqrt{\boldsymbol{n}(\boldsymbol{n}+\mathbf{1})}<\boldsymbol{n}+\mathbf{1} \)
A. Statement-1 is true, Statement-2 is true; Statement- is a correct explanation for Statement-
B. Statement-1 is true, Statement-2 is false.
c. Statement- - is false, statement-2 is true
D. Statement-1 is true, Statement-2 is true; Statement- is not a correct explanation for Statement-


The IUPAC name of this given compound
is :
A. pentyl amine
B. methyl-n-propyl amine
\( c . \) diethyl amine
D. Pentan-2-amine


A pulse moves in a string as indicated in the sketch. At the end of astring is a ring that can slide without friction on a
post. On reflection,the pulse would most
nearly be represented by
\( A \)
B. 2
\( c \cdot 3 \)
\( D \)


Let \( \boldsymbol{A}=\{\mathbf{1}, \mathbf{2}, \mathbf{3}, \mathbf{4}\} \)
\( \boldsymbol{S}=\{(\boldsymbol{a}, \boldsymbol{b}) ; \boldsymbol{a}, \boldsymbol{b} \in \boldsymbol{A}, \boldsymbol{a} \text { divides } \boldsymbol{b}\}, \) write
down \( S \) explicitly


Weight \( 50-\quad 56 \)
(in \( \mathrm{kg}) \)
Number
of 15
students
Garima collected the data regarding
weights of students of her class and prepared the above table:
A student is to be selected randomly from her class for some competition.
The probability of selection of the
student is the highest whose weight (in
kg) is in the interval
A. \( 44-49 \)
B. \( 56-61 \)
c. \( 50-55 \)
D. \( 62-67 \)


State True or False.
Setting of cement is an endothermic
process
A. True
B. False


True or False
VI A group elements are known as
chalcogens.


The number of total product produced upon monochloriation of \( (+) 2 \) chlorobutane is
\( A \cdot 3 \)
B. 4
\( c \cdot 5 \)
D. 6


Ine glven apparatus snows a neavy piston supported by gas trapped in a cylinder. The cross-sectional area of the
piston is \( 4.0 \times 10^{-4} m^{2} . \) The pressure of
the gas inside the cylinder is \( 1.5 \times 10^{5} \)
Pa and atmospheric pressure is \( 1.0 \times \)
\( 10^{5} \) Pa. Find the mass of the piston
(Take \( \left.g=10 \mathrm{m} s^{-2}\right) \)
\( A \cdot 1 \mathrm{kg} \)
в. 2 kg
\( c \cdot 3 k g \)
\( 0.4 \mathrm{kg} \)


The area of the smaller part bounded by the semi-circle \( y=\sqrt{4-x^{2}}, y=x \sqrt{3} \)
and \( x \) -axis is
A \( \cdot \frac{\pi}{3} \)
в. \( \frac{2 \pi}{3} \)
c. \( \frac{4 \pi}{3} \)
D. none of these


The decreasing order of priority for the
following functional groups is:
I. \( \boldsymbol{R}-\boldsymbol{O H} \)
II. \( \boldsymbol{R}-\boldsymbol{C} \equiv \boldsymbol{C}-\boldsymbol{R} \)
III. \( \boldsymbol{R}-\boldsymbol{O}-\boldsymbol{R} \quad \) IV. \( \boldsymbol{R}-\boldsymbol{N} \boldsymbol{H}_{2} \)
\( A \cdot(\mid V)>(\mid)>(||)>(\| \mid) \)
B. (IV) > (I) > (III) > (II)
\( c \cdot(1)>(\mid V)>(|| \mid)>(||) \)
D. (II) > (III) > (IV) > (I)


'Biological Oxygen Demand' (BOD) is a
measure of
A. Industrial wastes poured into water bodies
B. Extent to which water is polluted with organic compounds
c. Amount of carbon monoxide inseparably combined with haemoglobin
D. Amount of oxygen needed by green plants during night


Draw the venn diagram to illustrate \( (\boldsymbol{A} \cup \boldsymbol{B}) \)


Given \( a=7, a_{13}=35, \) find the d
A . 2.33
B. 2.72
\( c . \) 3.89
D. 4.56


If the base of a parallelogram decreases
by \( 20 \% \), and the height increases by, 40 \( \% \) by what percent does the area increase?


If the mean of \( n \) observations \( x_{1}, x_{2}, \ldots \)
\( x_{n} \) is \( \bar{x} \),then the sum of deviations of
observations from mean is
A . 0
B. \( n \bar{x} \)
c. \( \bar{x} \)
D. none of these


A particle moves along the curve \( x^{2}= \)
2y. At what point, ordinate increases at
the same rate as abscissa increases?


Which is logically equivalent to "If today is Sunday Matt cannot play hockey"?
A. Today is Sunday and Matt can play hockey
B. If Matt plays hockey then today is not Sunday
c. Today is Sunday and Matt cannot play hockey
D. Today is not Sunday if and only if Matt plays hockey


When a non-volatile solute is dissolved
in a solvent, the relative lowering of vapour pressure is equal to :
A. mole fraction of solvent
B. mole fraction of solute
c. molarity of solution
D. molality of solution


A disease, in which eye lens become cloudy and the opaque lens is removed and a new artificial lens is inserted, is :
A. hypermetropia
B. astigmatism
c. cataract
D. near-sightedness


Which sulphur has an open chain \( S_{8} \) molecule?
This question has multiple correct options
A. Rhombic sulphur
B. Monoclinic sulphur
c. Plastic sulphur
D. Roll sulphur


The mass of an object is measured by two students (true weight is 12 kg)
Student 1: He measures 12 kg Student 2 : She measures \( 12.5 \mathrm{kg} \) Measurement of which student is more
accurate.
A. Student 1
B. Student 2
c. Both are equally accurate
D. Cannot be compared.


Why are aldehydes and ketones polar
compounds?


According to classical theory, if an electron is moving in a circular orbit around the nucleus:
A. it will continue to do so for sometime
B. its orbit will continuously shrink
c. its orbit will continuously enlarge
D. it will continue to do so for all the time


Auxospores are formed in the life cycle
of diatoms these structure are
A. Vegetuative cells with ploidy level
B. Asexual spores with ploidy level N
c. Statosspores with 2N ploidy Level
D. Sexual spores with ploidy level \( 2 N \)


Given that \( A, B \) and \( C \) are events such
\( \operatorname{that} \boldsymbol{P}(\boldsymbol{A})=\boldsymbol{P}(\boldsymbol{B})=\boldsymbol{P}(\boldsymbol{C})= \)
\( \mathbf{1} / \mathbf{5}, \boldsymbol{P}(\boldsymbol{A} \cap \boldsymbol{B})=\boldsymbol{P}(\boldsymbol{B} \cap \boldsymbol{C})=\mathbf{0} \) and
\( \boldsymbol{P}(\boldsymbol{A} \cap \boldsymbol{C})=1 / 10 . \) The probability that
at least one of the events \( A, B \) or \( C \)
occurs is
A \( .1 / 2 \)
в. \( 2 / 3 \)
\( c \cdot 2 / 5 \)
D. 3/5


The potential energy of a particle of mass m free to move along x-axis is given by \( U=\frac{1}{2} k x^{2} \) for \( x<0 \) and \( U=0 \)
for \( \boldsymbol{x} \geq \mathbf{0} \) (x denotes the x-coordinate of
the particle and \( k \) is a positive constant). If the total mechanical
energy of the particle is \( \mathrm{E} \), then its \( \operatorname{speed} \operatorname{at} x=-\sqrt{\frac{2 E}{k}} \) is :
A. zero
B. \( \sqrt{\frac{2 E}{m}} \)
c. \( \sqrt{\frac{E}{m}} \)
D. \( \sqrt{\frac{E}{2 m}} \)


What are terminating decimals?


Sound
A. needs a material medium for its propagation
B. does not need a material medium for its propagation
C. can travel without any material medium
D. needs light for travelling


Account for the following:
(a) Gabriel phthalimide synthesis is not preferred for preparing aromatic primary amines.
(b) On reaction with benzene sulphonyl chloride, primary amine yields product soluble in alkali whereas secondary amine yields product insoluble in alkali


One of the fuel cells uses the reaction of
hydrogen and oxygen to form water. Write down the cell reaction taking place in the anode and cathode of that fuel cell.


According to the adsorption theory of catalysis, the rate of reaction increases with the use of a catalyst because:
A. the heat liberated during adsorption increases the rate of reaction
B. the kinetic energy of reactants increases which increases the rate of reaction
C. the activation energy of reaction increases which increases the rate of reaction
D. the concentration of reactants at the active centers becomes high due to adsorption the rate of reaction


(A) 1 faraday \( =96,500 \) coulomb. It is a charge of 1 mole electrons.
(R) 1 faraday charge liberates one gram equivalent of substance at an electrode.
A. Both (R) and (A) are true and reason is the. correct explanation of assertion
B. Both (R) and (A) are true but reason is not correct explanation of assertion
c. Assertion
(A) is true but reason
(R) is false
D. Assertion
(A) and reason
(R) both are false
E. Assertion (A) is false but reason (R) is true


The circumference of a circle is
measured as \( 56 \mathrm{cm} \) with an error 0.02
\( \mathrm{cm} . \) The percentage error in its area is
A \( \cdot \frac{1}{7} \)
в. \( \frac{1}{28} \)
c. \( \frac{1}{14} \)
D. \( \frac{1}{56} \)


Study the following lists.
ListList-II
(A) A. G
(I) Classified plant communities tansley
(II) Structure and function of
(B) Wanning
(C) Odum
(III) Term 'Biosphere'
(D) Reiter
(IV) Term' Ecology'
(V) Term'Ecosystem'
Identify the sequence of list II with
respect to list I
A. A- (II), B- (V), C- (I), D- (III)
B. A-(IV),B-(III), C-(V),D- (II)
\( c \cdot A-(1 V), B-(111), C-(V), D-(1) \)
D. \( A-(V), B-(1), C-(11), D-(1 V) \)


Which of the following conditions
correctly describes the manner of
determining the sex in a given
example?
A. \( x \) O condition in humans as found in Klinefelter's
syndrome determines female sex
B. Homozygous sex chromosomes zZ determines female sex in birds
C. \( X O \) type of sex determines male sex in grasshopper
D. Homozygous sex chromosomes \( X X \) produce male in Drosophila


Which of the following will act as cathode when connected to standard
hydrogen electrode which has \( \boldsymbol{E}^{0} \) value
given as zero?
¡) \( Z n / Z n+2, E^{0}=-0.76 V \)
ii) \( \boldsymbol{C u}^{+2} / \boldsymbol{C u}, \boldsymbol{E}^{0}=+\mathbf{0 . 3 4} \boldsymbol{V} \)
iii) \( \boldsymbol{A l} / \boldsymbol{A l}^{+3}, \boldsymbol{E}^{0}=-\mathbf{1 . 6 6} \boldsymbol{V} \)
iv \( \mathbf{H} \boldsymbol{g}^{\mathbf{2}+} / \boldsymbol{H} \boldsymbol{g}, \boldsymbol{E}^{\mathbf{0}}=+\mathbf{0 . 8 8 5} \boldsymbol{V} \)
A . i and i i
B. ii and iv
c. i and iii
D. i,ii,iii and iv


Which of the following sequences is the correct order of naming the sub groups at various levels in the classification of
animal kingdom?
A. Kingdom, Phylum, Order, Family, class
B. Kingdom, Phylum, Class, Family, Order, Genus
c. Kingdom, Phylum, Class, Order, Genus, Family, species
D. Kingdom, Phylum, Class, Order, Family, Genus, Specie


There is a regular polygon whose each
interior angle is \( 145^{\circ} \) State true or false.
A. True
B. False


A wave of amplitude \( 10 \mathrm{cm} \) and frequency 1000 Hz is travelling with a velocity of \( 300 \mathrm{m} / \mathrm{s} \). Calculate the phase difference of a particle at a distance of \( 3 \mathrm{m} \) from the origin after \( 1.001 \mathrm{s} \)


Number of \( \boldsymbol{H} \) atoms \( \left(\text { as } \boldsymbol{N}_{\boldsymbol{o}} \) ) present in \right.
one mole of isopropanol \( C_{3} H_{8} O \) is:


On \( 31 s t \) October the time of setting of
the moon given as \( 12: 03 . \) Have you ever
seen the moon at 12 in the afternoon?
Why dont we easily see the moon or
stars during the day?


In a transformer the output current and
voltage are \( 4 \mathrm{A} \) and \( 20 \mathrm{V} \) respectively. If the ratio of number of turns in the
primary and secondary coil is 2: 1 respectively, what is the input current and voltage?
\( A \cdot 2 A \) and 40
B. 1 A and 20
c. 4 A and \( 10 v \)
D. 8 A and 40 v


Dimension of capacitance is?
A \( \cdot M^{-1} L^{-2} A^{2} T^{4} \)
B. \( M L^{2} A^{-2} T^{-4} \)
c. \( M L A^{-1} T^{4} \)
D. \( M^{-1} L^{-1} A^{2} T^{2} \)


On making a coil of copper wire of length I and coil radius \( r, \) the value of self inductance is obtained as \( L \). If the
coil of same wire, but of coil radius r/2, is made, the value' of self inductance will be- -
A . 2L
B. 4L
\( c \cdot L / 2 \)
\( D \cdot L / 3 \)


An electron is moving towards east in a magnetic field acting vertically downwards. So the electron is deflected
towards:
A. South
B. North
c. East
D. west


State whether the following statement
is True or False.
The product of two even numbers is always even.
A. True
B. False


If \( \vec{P}+\vec{Q}=\vec{P}-\vec{Q} \) and \( q \) is the angle between \( \vec{P} \) and \( \vec{Q}, \) then
A \( \cdot q=0^{\circ} \)
в. \( q=90^{\circ} \)
c. \( P=0 \)
D. \( Q=0 \)


Which of the following noble gas is least polarisable?
A . не
B. Ne
c. \( \mathrm{kr} \)
D. \( x_{e} \)


A cube of side a carries a charge \( q \) each at the corners of a cube.Then the
potential at the centre of cube is then
going to be
A \( \cdot \frac{8 q}{\pi \varepsilon_{0} a} \)
в. \( \frac{4 q}{4 \pi \varepsilon_{0} a} \)
c. \( \frac{4 q}{\sqrt{3} \pi \varepsilon_{0} a} \)
D. \( \frac{2 q}{\pi \varepsilon_{0} a} \)


A current of 2 amp when passed for 5 hours through a molten salt deposits \( 22.2 g \) of metal of atomic mass \( 177 . \) The
oxidation state of the metal in the
metal salt is:
A. +1
B. +2
\( c \cdot+3 \)
D. +4


Give equations of the following reactions:
(i) Oxidation of propan-1-ol with alkaline
\( \boldsymbol{K} \boldsymbol{M} \boldsymbol{n} \boldsymbol{O}_{4} \) solution
(ii) Bromine in \( C S_{2} \) with phenol.
(iii) Dilute \( \boldsymbol{H} \boldsymbol{N} \boldsymbol{O}_{3} \) with phenol
(iv) Treating phenol wih chloroform in
presence of aqueous \( N a O H \)


Assertion
Helium has the highest value of ionisation energy among all the elements known.
Reason
Helium has the highest value of electron affinity among all the elements
known.
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


Verify L.M.V for the function? \( \boldsymbol{f}(\boldsymbol{x})= \) \( \left\{\begin{array}{cc}2+x^{3} & x \leq 1 \\ 3 x & x>1\end{array}\right\} o n[-1,2] \)


The length of hour hand of a wrist watch
is \( 1.5 \mathrm{cm} . \) Find magnitude of radial acceleration?
A \( .3 .175 \times 10^{-4} \mathrm{m} / \mathrm{s}^{2} \)
B . \( 4.175 \times 10^{-4} \mathrm{m} / \mathrm{s}^{2} \)
c. \( 6.754 \times 10^{-4} \mathrm{m} / \mathrm{s}^{2} \)
D. \( 4.754 \times 10^{-4} \mathrm{m} / \mathrm{s}^{2} \)


Evaluate :
\( \int_{0}^{\pi / 2} \frac{\sin x}{1+\cos ^{2} x} d x \)


The S.I. symbol for refractive index is \( r \)
A. True
B. False