The time taken by a particle performing \( \boldsymbol{S H} \boldsymbol{M} \) to pass from point \( \boldsymbol{A} \) to \( \boldsymbol{B} \) where its velocities are same is 2
seconds.After another 2 seconds it
returns to \( B \). The time period of oscillation is (in seconds)
A \( .2 s \)
B. 8 s
\( c \cdot 6 s \)
D. \( 4 s \)


A thin semicircular conducting the ring
\( (P Q R) \) of radius \( ^{\prime} r^{\prime} \) is falling with its
plane vertical in a horizontal magnetic
field \( B \), as shown in figure. The potentia difference developed across the ring
when its speed is \( v \), is
A. Zero
B. \( B v \pi r^{2} / 2 \) and \( P \) is at higher potential
\( \mathrm{c} . \pi r B v \) and \( R \) is at higher potential
D. \( 2 r B v \) and \( R \) is at higher potential


The value of \( \int_{0}^{\frac{\pi}{2}} \frac{\cos 3 x+1}{2 \cos x-1} d x \) is
\( A \cdot 2 \)
B.
\( c \cdot \frac{1}{2} \)
D.


The two gases making the highest relative contribution to the greenhouse
gases are:
A \( \cdot C O_{2} \) and \( C H_{4} \)
B. \( C H_{4} \) and \( N_{2} O \)
c. \( C F C s \) and \( N_{2} O \)
D. \( C O_{2} \) and \( N_{2} O \)


\( \int \frac{1}{\left(1+x^{2}\right) \sqrt{\left[p^{2}+q^{2}\left(\tan ^{-1} x\right)^{2}\right]}} d x \)
A \( \cdot \frac{1}{q} \log [t-\sqrt{p^{2}+t^{2}}] \) where \( t=q \tan ^{-1} x \)
B. \( \frac{1}{t} \log [t+\sqrt{p^{2}+t^{2}}] \) where \( t=q \tan ^{-1} x \)
c. \( \frac{1}{q} \log [t+\sqrt{p^{2}+t^{2}}] \) where \( t=q \tan ^{-1} x \)
D. \( \frac{1}{q} \log [t+\sqrt{p^{2}-t^{2}}] \) where \( t=q \tan ^{-1} x \)


\[
\mathbf{f} \boldsymbol{a}_{\mathbf{1}} \boldsymbol{f}_{\mathbf{1}}(\boldsymbol{x})+\boldsymbol{a}_{\mathbf{2}} \boldsymbol{f}_{\mathbf{2}}(\boldsymbol{x})+\boldsymbol{a}_{\mathbf{3}} \boldsymbol{f}_{\mathbf{3}}(\boldsymbol{x})=\mathbf{0}
\]
where \( a_{1}, a_{2}, a_{3} \) are constants (not all
zero) and \( f_{1}, f_{2}, f_{3} \) are twice
differentiable functions.Then \( D= \)
\( \left|\begin{array}{ccc}\boldsymbol{f}_{1}(\boldsymbol{x}) & \boldsymbol{f}_{2}(\boldsymbol{x}) & \boldsymbol{f}_{3}(\boldsymbol{x}) \\ \boldsymbol{D} \boldsymbol{f}_{1}(\boldsymbol{x}) & \boldsymbol{D} \boldsymbol{f}_{2}(\boldsymbol{x}) & \boldsymbol{D} \boldsymbol{f}_{3}(\boldsymbol{x}) \\ \boldsymbol{D}^{2} \boldsymbol{f}_{1}(\boldsymbol{x}) & \boldsymbol{D}^{2} \boldsymbol{f}_{2}(\boldsymbol{x}) & \boldsymbol{D}^{2} \boldsymbol{f}_{3}(\boldsymbol{x})\end{array}\right| \) qual to \( D f_{1}(x)=\frac{d}{d x} f_{1} \)


The equivalent resistance between \( A \)
and B is:
A \( \frac{8 R}{5} \)
в. \( \frac{5 R}{8} \)
\( c \cdot \frac{3 R}{8} \)
D. \( \frac{7 R}{8} \)


Magnetic flux \( \phi \), in weber, in a closed
circuit of resistance \( 10 \Omega \) varies with
time \( t \) in seconds as \( \phi=6 t^{2}-5 t+1 \)
The magnitude of induced current at
\( t=0.25 s \) is :
A. \( 0.2 \mathrm{A} \)
B. 0.6 \( A \)
\( c \cdot 1.2 A \)
D. \( 0.8 \mathrm{A} \)


\( f \sin \left(7 \phi+9^{\circ}\right)=\cos 2 \phi, \) find a value of
\( \phi \)


A horizontal pipe line carries water in a streamline flow. At a point along the tube where the cross-sectional area is
\( 10^{-2} m^{2}, \) the water velocity is \( 2 m s^{-1} \)
and the pressure is 8000 Pa. The
pressure of water at another point where the cross-sectional area is \( 0.5 \times \)
\( 10^{-2} m^{2} \) is?


How can you determine direction of magnetic field lines around a current
carrying conductor
A. Left hand Thumb Rule
B. Right Hand Thumb Rule
c. By rotating the conductor
D. Using sonometer


Radiation of \( \lambda=155 \) nm was
irradiated to \( L i \text { (work function }=5 e v) \)
plate. The stopping potential.


Let \( g:[1,3] \rightarrow Y \) be a function defined
\( \operatorname{as} g(x)=\ln \left(x^{2}+3 x+1\right) . \) Then
(a) Determine whether \( g(x) \) one-one or
many-one.
(b) Find the set \( Y \), so that \( g(x) \) is onto.
(c) Find \( g^{-1}(x) \), if it exists.


A potentiometer having a wire of \( 4 m \) length is connected to the terminals of a battery with a steady voltage. \( A \)
leclanche cell has a null point at 1 m. If
the length of the potentiometer wire is increased by 1 m, the position of the null point is
\( \mathbf{A} \cdot 1.5 m \)
B. \( 1.25 \mathrm{m} \)
c. 10.05 m
D. \( 1.31 m \)


Find teh adjoint of the matrix \( \boldsymbol{A}= \) \( \left(\begin{array}{ccc}1 & 0 & -1 \\ 3 & 4 & 5 \\ 0 & -6 & -7\end{array}\right) \) and hence find the
matrix \( \boldsymbol{A}^{-1} \)


\( \left(\frac{1}{4}\right)^{\frac{-1}{2}}-3(8)^{\frac{2}{3}}+\left(\frac{9}{16}\right)^{\frac{-1}{2}} \)


Evaluate the following limits. \( \lim _{x \rightarrow 0} \frac{a x+b}{c x+d}, d \neq 0 \)
A \( \cdot \frac{a}{c} \)
B. \( a \)
\( c \cdot \frac{b}{d} \)
D. None of these


Factorise:
\( 4 x+12 \)
\( \mathbf{A} \cdot 4(x+2) \)
B . \( 4(x+3) \)
\( \mathbf{c} \cdot 3(x+4) \)
D. none of these


The unit of conductance is
and that of specific
conductance is
\( \mathbf{A} \cdot \operatorname{oh} m^{-1} ; o h m^{-1} c m^{2} \)
B . \( o h m^{-1} c m^{2} ; \) ohm \( ^{-1} c m^{-1} \)
\( \mathbf{c} \cdot o h m^{-1} c m^{-1} ; o h m^{-1} c m^{2} \)
D. \( o h m^{-1} ; o h m^{-1} c m^{-1} \)


The volume of 3 M \( H C l \) required to
completely react with 1.431 g of sodium carbonate :
\( \mathbf{A} \cdot 10 \mathrm{ml} \)
B. 9 m
\( c \cdot 8 m \)
D. 7 m


The projection of the line \( x+y=0 \)
\( z=0 \) on the plane \( x-y+z=1 \) is
\begin{tabular}{l}
A \( \cdot \frac{3 x-1}{3}=\frac{3 y+1}{-3}=\frac{3 z-1}{-2} \) \\
\hline
\end{tabular}
B. \( \frac{4 x-1}{3}=\frac{2 y+1}{-3}=\frac{4 z+1}{-6} \)
\begin{tabular}{l}
C. \( \frac{3 x-1}{-3}=\frac{3 y+1}{3}=\frac{3 z-1}{6} \) \\
\hline
\end{tabular}
D. \( \frac{4 x-1}{2}=\frac{2 y+1}{1}=\frac{4 z+1}{-2} \)


\( \vec{B}=\hat{i}-3 \hat{j}+\hat{k} . \) Find the
a. Area of the triangle whose two sides are representedby the vectors \( \overrightarrow{\boldsymbol{A}} \) and \( \overrightarrow{\boldsymbol{B}} \)
b. Area of the parallelogram whose two adjacent sidesare represented by the vectors \( \vec{A} \) and \( \vec{B} \)
c. Area of the parallelogram whose
diagonals are represented by the vectors \( \vec{A} \) and \( \vec{B} \)
A \( \cdot \) a. \( \frac{1}{2}|\vec{A} \times \vec{B}| \)
b. \( |\vec{A} \times \vec{B}| \)
c. \( \frac{1}{3}|\vec{A} \times \vec{B}| \)
B. a. \( \frac{1}{2}|\vec{A} \times \vec{B}| \)
b. \( |\vec{A} \times \vec{B}| \)
c. \( \frac{1}{2}|\vec{A} \times \vec{B}| \)
c. \( _{\text {a. }} \frac{1}{2}|\vec{A} \times \vec{B}| \)
b. \( |\vec{A} \times \vec{B}| \)
c. \( \frac{1}{4}|\vec{A} \times \vec{B}| \)
D. \( _{\text {a. }} \frac{1}{3}|\vec{A} \times \vec{B}| \)
b. \( \mid \vec{A} \times \vec{B} \)
c. \( \frac{1}{2}|\vec{A} \times \vec{B}| \)


When \( x^{3}-6 x^{2}+12 x-4 \) is divided by
\( x-2, \) the remainder is
A .4
B. 0
\( c .5 \)
D. 6


Emf of the cell
\( \boldsymbol{P t . H}_{2}(\boldsymbol{1} \boldsymbol{a t m})\left|\boldsymbol{H}^{+}(\boldsymbol{a q} \cdot) \| \boldsymbol{A} \boldsymbol{g} \boldsymbol{C l}\right| \boldsymbol{A} \boldsymbol{g} \) is
\( 0.27 V \) and \( 0.26 V \) at \( 25^{\circ} C \) and \( 35^{\circ} C \)
Heat of reaction occuring inside the cell
\( \operatorname{at} 25^{\circ} \mathrm{C} \) is:
A \( .-54.8 k J \)
B . \( 26.05 k J \)
c. \( -26.05 k J \)
D. \( +54.8 k J \)


Sketch and label Malpighian body.


For a glass plate as a polariser with
refractive index 1.633 , calculate the
angle of incidence at which light is polarised.


In
[0,1] Lagrange's Mean Value theorem is NOT applicable to
A \( \cdot(\mathrm{x})=\left\{\begin{array}{ll}\frac{1}{2}-\mathrm{x}, & \mathrm{x}<\frac{1}{2} \\ \left(\frac{1}{2}-\mathrm{x}\right)^{2} & \mathrm{x} \geq \frac{1}{2}\end{array}\right. \)
B. \( f(x)=\left\{\begin{array}{ll}\frac{\sin x}{x}, & x \neq 0 \\ 1, & x=0\end{array}\right. \)
c. \( f(x)=x|x| \)
D. \( f(x)=|x| \)


To \( A g_{2} C r O_{4} \) solution over its own precipitate, \( C r O_{4}^{2-} \) ions are added. This results in:
A . Increase in \( A g^{+} \) concentration
B. Decrease in \( A g^{+} \) concentration
c. Increase in solubility product
D. shifting of \( A g^{+} \) ions from the precipitate into the solution


\( \Delta A B D \) and \( \Delta E C D \) are congruent.
State whether the above statement is
true or false.
A . True
B. False


Find the principal value of \( \tan ^{-1} \sqrt{3}- \)
\( \sec ^{-1}(-2) \)


A circle is described with minor axis of
the ellipse as diameter. If the foci lie on the circle, then the eccentricty of the ellipse is
A \( \cdot \frac{1}{\sqrt{3}} \)
в. \( \frac{1}{\sqrt{2}} \)
\( c \cdot \frac{1}{2} \)
D. \( \frac{1}{\sqrt{5}} \)


\( A 3^{o} \) alcohol as given can be obtained by
the reaction of \( P h M g B r \) and:
This question has multiple correct options
A. ethyl carbonate
B. benzophenone
c. ethyl benzoate
D. benzamide


The process in which the internal energy of the system remains constant is :
A. adiabatic
B. isobaric
c. isochoric
D. isothermal


Which of the following statement(s) is/are correct?
This question has multiple correct options
A. \( O_{3} \) molecule is bent.
B. Ozone is violet-black in solid state.
c. Ozone is diamagnetic gas.
D. oNCl and ONO- are not isoelectronic


Assertion
Conc. \( H_{2} S O_{4} \) can not be used to
prepare pure HBr from NaBr.
Reason
It reacts slowly with NaBr
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 certain weak acid has dissociation
constant of \( 1.0 \times 10^{-4} . \) The equilibrium
constant for its reaction with a strong
base is:
A \( \cdot 1.0 \times 10^{-4} \)
B . \( 1.0 \times 10^{-10} \)
c. \( 1.0 \times 10^{10} \)
D. \( 1.0 \times 10^{-14} \)


Consider the following diagram:
\( A, B, C \& D \) is :
A. Root hair, Cortex Endodermis \& Pericycle, stelar system respectively
B. Root hair, Cortex Endodermis \& Nodule, vescular tissue xylem respectirely
C. Root hair, Root nodule, Stelar system, xylem respectively.
D. Root hair, Epiblema, Cortex, Endodermis respectively


The equation of the plane passing through the straight line \( \frac{x-1}{2}= \) \( \frac{\boldsymbol{y}+\mathbf{1}}{\mathbf{- 1}}=\frac{\boldsymbol{z}-\mathbf{3}}{\mathbf{4}} \) and perpendicular to
plane \( \boldsymbol{x}+\mathbf{2} \boldsymbol{y}+\boldsymbol{z}=\mathbf{1 2} \) is:
A. \( 9 x+2 y-5 z+8=0 \)
в. \( 9 x+2 y-5 z+10=0 \)
c. \( 9 x-2 y+5 z+6=0 \)
D. \( 9 x-2 y-5 z+4=0 \)


Find the value of a given \( \mathbf{3}+\frac{\mathbf{1}}{\mathbf{4}}(\mathbf{3}+\boldsymbol{p})+\frac{\mathbf{1}}{\mathbf{4}^{2}}(\mathbf{3}+\mathbf{2} \boldsymbol{p})+\frac{\mathbf{1}}{\mathbf{4}^{3}}(\mathbf{3}+ \)
\( \mathbf{3} \boldsymbol{p})+\ldots=? \)


Decreasing order of enol content of the following compound in liquid phase:
\( \mathbf{A} \cdot a>b>c>d \)
В \( . c>b>a>d \)
\( c \cdot c>b>d>a \)
D. \( b>c>a>d \)


Let \( z \) be a complex number and \( c \) be a
real number \( \geq 1 \) such that \( z+ \)
\( \boldsymbol{c}|\boldsymbol{z}+\mathbf{1}|+\boldsymbol{i}=\mathbf{0}, \) then \( c \) belongs to
A . [2,3]
B. (3,4)
c. \( [1, \sqrt{2}] \)
D. None of these


A point object is placed at a distance of \( 25 \mathrm{cm} \) from a convex lens. Its focal
length is \( 22 \mathrm{cm} . \) A glass slab of
refractive index 1.5 is inserted between
the lens and the object, then the image is formed at infinity. Find the thickness of the glass slab (in cm).


In \( \triangle A B C, \angle B \) is a right angle. The median AD and BE are at right angles. Then angle \( C \) is
A . 60
B. \( \tan ^{-1}\left(\frac{1}{\sqrt{2}}\right) \)
c. \( \tan ^{-1} \sqrt{2} \)
D. 90


The equilibrium constant for the
following reactions is \( 1.6 \times 10^{5} \) at
\( 1024 K \)
\( \boldsymbol{H}_{2(g)}+\boldsymbol{B} \boldsymbol{r}_{2(g)} \rightleftharpoons \mathbf{2} \boldsymbol{H} \boldsymbol{B} \boldsymbol{r}_{(\boldsymbol{g})} \)
Find the equilibrium pressure of all gases if 10.0 bar of \( H B r \) is introduced
into a sealed container at \( 1024 K \)


The nerve that carries the signals from the ear to the brains is called:
A. auditory nerve
B. optic nerve
c. motor nerve
D. spinal cord


When a mixture of carbon monoxide
and chlorine is exposed to sunlight the product formed is:
A. carbon tetrachloride
B. phosgene
c. phosphine
D. carbon chloride


The sum of the series \( \frac{1}{(1 \times 2)}+ \) \( \frac{1}{(2 \times 3)}+\frac{1}{(3 \times 4)}+\ldots \ldots+ \)
\( \frac{1}{(100 \times 101)} \) is equal to
A \( \cdot \frac{20}{1010} \)
в. \( \frac{100}{1010} \)
c. \( \frac{50}{101} \)
D. \( \frac{25}{101} \)


The diameter of the sun is \( 1.4 \times 10^{9} m \)
and its distance from the earth is \( 1.5 \times \)
\( 10^{11} \) m. Find the radius of the image of
the sun formed by a lens of focal length
\( \mathbf{2 0 c m} \)


Sometimes the behaviour of a
compound is explained by assuming that it exists in between two or more
different possible structures. This phenomenon is called
A. isomerism
B. resonance
c. mutarotation
D. allotropism


Condensation of chromosome with
visible centromere occurs during
A. \( G_{1}- \) phase
B. \( G_{2}- \) phase
c. \( S \) - phase
D. \( M- \) phase


The converse of the contrapositive of the
conditional \( \boldsymbol{p} \rightarrow \sim \boldsymbol{q} \) is.
A \( . p \rightarrow q \)
в. \( p \rightarrow \sim q \)
\( \mathbf{c} . \sim q \rightarrow p \)
\( \mathbf{D} \cdot \sim p \rightarrow q \)


If \( \boldsymbol{y}=\frac{1}{4}(\boldsymbol{x} \pm \boldsymbol{A})^{2} \)
Hence prove: \( \boldsymbol{y}_{1}^{2}=\boldsymbol{y} \)


Agar is obtained from
A. Red algae
B. Brown algae
c. Blue green algae
D. Green algae


Name the octants in which the following
points lie: \( (\mathbf{5}, \mathbf{2}, \mathbf{3}) \)


The direction of the force on a current-
carrying wire placed in a magnetic field depends on
A. the direction of the current
B. the direction of the field
c. the direction of the current as well as field
D. neither the direction of current nor the direction of field


The process of turning and loosening of soil is called
A. Tilling
B. Harvesting
c. Threshing
D. Irrigation


Two pieces of resistance wire, \( A \) and \( B \) are cut from the same coil. A is twice as
long as B. The difference between the total resistance of the combination of
wires \( A \) and \( B \), when connected in series
and in parallel is \( 21 \Omega \). The resistance of
A will be.
A . \( 18 \Omega \)
B . \( 16.5 \Omega \)
c. \( 14 \Omega \)
D. \( 18.6 \Omega \)


The light reflected back into the denser medium when a ray of light passes from a denser to a rarer medium, is said to
be \( \ldots \)
A. Totally relfected
B. Totally refracted
c. Internally reflected
D. Internally refracted


The condition for observing Fraunhoffer diffraction from a single slit is that the light wavefront incident on the slit
should be
A. spherical
B. cylindrical
c. plane
D. elliptical


Which of the following could be a substance found in waste water that
floats on the top and is removed in the
Primary Treatment of water?
A. Oil and grease
B. Human faeces
c. Hair
D. Plastic


The maximum value attained by the tension in the string of a swinging pendulum is four times the minimum value it attains. There is no slack in the
string. The angular amplitude of the pendulum is?
A \( \cdot 90^{\circ} \)
B. \( 60^{\circ} \)
\( c \cdot 45^{\circ} \)
D. \( 30^{\circ} \)


Evaluate integral of \( \int \frac{d x}{\sqrt[4]{1+x^{4}}}, \) the
ans is
\( A \)
\[
-\frac{1}{4}\left[\log \frac{\sqrt[4]{1+1 / x^{4}}-1}{\sqrt[4]{\left(1+1 / x^{4}\right)}+1}-2 \tan ^{-1}\left(1+\frac{1}{x^{4}}\right)^{\frac{1}{4}}\right]
\]
B.
\[
-\frac{1}{4}\left[\log \frac{\sqrt[4]{1+1 / x^{4}}-1}{\sqrt[4]{\left(1+1 / x^{4}\right)}+1}+2 \tan ^{-1}\left(1+\frac{1}{x^{4}}\right)^{\frac{1}{4}}\right]+C
\]
\( c \)
\[
\frac{1}{4}\left[\log \frac{\sqrt[4]{1+1 / x^{4}}-1}{\sqrt[4]{\left(1+1 / x^{4}\right)}+1}+2 \tan ^{-1}\left(1+\frac{1}{x^{4}}\right)^{\frac{1}{4}}\right]
\]
\( D \)
\[
\frac{1}{4}\left[\log \frac{\sqrt[4]{1+1 / x^{4}}-1}{\sqrt[4]{\left(1+1 / x^{4}\right)}+1}-2 \tan ^{-1}\left(1+\frac{1}{x^{4}}\right)^{\frac{1}{4}}\right]+C
\]


In the following sequence of reaction, all stereoisomers of (X) have been taken. \( \boldsymbol{C H}_{3}-\boldsymbol{C H}-\boldsymbol{C H}=\boldsymbol{C H}-\boldsymbol{C}_{D} \boldsymbol{H}-\boldsymbol{C} \boldsymbol{I} \)
\( (x) \)
\( (\boldsymbol{Y}) \stackrel{N \boldsymbol{H}_{2} \boldsymbol{O} \boldsymbol{H}}{\longrightarrow}(\boldsymbol{Z}) \)
Here,
\( \mathrm{Q}= \) Total number of stereoisomers of \( \mathrm{Y} \)
\( \mathrm{R}= \) Total number of stereoisomers of \( \mathrm{Z} \).
Find out \( Q \) and \( R \)
A \( . \mathrm{Q}=1, \mathrm{R}=2 \)
B . Q=2, R=3
c. \( Q=2, R=4 \)
D. \( Q=3, R=1 \)


Which electronic configuration of an element has abnormally high difference between second and third ionisation
energy?
A \( \cdot 1 s^{2}, 2 s^{2}, 2 p^{6}, 3 s^{1} \)
B . \( 1 s^{2}, 2 s^{2}, 2 p^{6}, 3 s^{2}, 3 p^{1} \)
c. \( 1 s^{2}, 2 s^{2}, 2 p^{6} \)
D. \( 1 s^{2}, 2 s^{2}, 2 p^{6}, 3 s^{2} \)


Complex forming ability will be minimum in :
A. actinides
B. lanthanides
c. transition metals
D. it will be almost same in all the three


Answer the following question:
Calculate the effective atomic
number(e.a.n.) of copper in
\( \left[\boldsymbol{C u}\left(\boldsymbol{N} \boldsymbol{H}_{3}\right)_{4}\right]^{2+}[\boldsymbol{Z} \text { of } \boldsymbol{C u}=\boldsymbol{2 9}] \)
2. Explain ionisation isomerism in coordination compounds with a suitable example.


Define hydrogen bond. Explain different types of hydrogen bond giving examples.


RNA is not found in
A . Cytoplasm
B. Nucleus
c. cell sap
D. All of the above


Which one of the following is the correct
statement?
\( \mathbf{A} \cdot H C O_{3}^{-} \) is the conjugate base of \( C O_{3}^{2-} \)
B. \( N H_{2}^{-} \) is the conjugate acid of \( N H_{3} \)
\( \mathrm{C} \cdot \mathrm{H}_{2} \mathrm{SO}_{4} \) is the conjugate acid of \( \mathrm{HSO}_{4}^{-} \)
D. \( N H_{3} \) is the conjugate base of \( N H_{2}^{-} \)
\( \mathrm{E} \cdot \mathrm{H}_{2} \mathrm{CO}_{3} \) is the conjugate base of \( \mathrm{HCO}_{3}^{-} \)


If \( n \) is the number density of free electrons in a metallic wire, then the
resistance is proportional to
A \( . n \)
B \( \cdot n^{2} \)
\( c \cdot \frac{1}{n} \)
D. \( \frac{1}{n^{2}} \)


The most appropriate reagent for the
following stereoselective reduction is:
\( \mathbf{A} \cdot \mathrm{NaBH}_{4} \)
\( \mathbf{B} \cdot \mathrm{Et}_{2} \mathrm{BOMe}, \mathrm{NaBH}_{4}, \mathrm{H}_{2} \mathrm{O}_{2} \)
\( \mathbf{C} \cdot \mathrm{LiAlH}_{4} \)
\( \mathrm{D} \cdot \mathrm{Me}_{4} \mathrm{NBH}(\mathrm{OAc})_{3} \)


A point source \( S \) is placed at a distance
of \( 15 \mathrm{cm} \) from a converging lens of focal
length \( 10 \mathrm{cm} \) on its principal axis. Where should a diverging mirror of focal length \( 12 c m \) be placed so that a real image is formed on the source itself?


If \( y=\ln \sqrt{\frac{1-\sin x}{1+\sin x}} \) then \( \frac{d y}{d x} \) equals-
\( A \cdot \sec x \)
B. - sec \( x \)
\( c \cdot \csc x \)
\( \mathbf{D} \cdot \sec x \tan x \)


Assertion
Cathode rays get deflected towards the
negative plate of electric field.
Reason
Cathode rays are negatively charged.
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.


Tissue plasmin activator
A. Helps in wound healing
B. Dissolves clot in blood vessels of heart
c. Allergy response
D. None of the above


Which of the following waves do not require any kind of medium to
propagate?
A. Sound
B. Earthquake Waves
c. Light waves
D. water surface waves


Find out the following squares by using the identities:
\( \left(x-\frac{1}{x}\right)^{2} \)


Which of the quantities are different in
\( \boldsymbol{H}^{+}, \boldsymbol{D}^{+}, \boldsymbol{T}^{+} ? \)
This question has multiple correct options
A. No.of electrons
B. No.of neutrons
c. Electron configuration
D. Ionic mass


A chord of a circle of radius \( 12 \mathrm{cm} \)
subtends an angle of \( 120^{\circ} \) at the centre.
Find the area of the corresponding
segment of the circle. (Use \( \pi=3.14 \text { and } \sqrt{3}=1.73) \)


The value of the determinant
\( \Delta=\left|\begin{array}{lll}\log x & \log y & \log z \\ \log 2 x & \log 2 y & \log 2 z \\ \log 3 x & \log 3 y & \log 3 z\end{array}\right| \)
\( A \cdot 0 \)
\( \mathbf{B} \cdot \log (x y z) \)
\( \mathbf{C} \cdot \log (6 x y z) \)
\( \mathbf{D} \cdot 6 \log (x y z) \)


Supposing that it is 9 to 7 against a person A who is now 35 years of age living till he is \( 65, \) and 3 to 2 against a person B now 45 living till he is \( 75 ; \) find the chance that one at least of these
persons will be alive 30 years hence.


Bond angle in \( \mathbf{P}_{4} \) molecule is
A \( \cdot 60^{\circ} \)
В. \( 90^{\circ} \)
\( c \cdot 120^{\circ} \)
D. \( 109^{0} 28^{\prime} \)


In plants the translocation of organic solutes take place through
A. Epidermis
B. Xylem
c. Phloem
D. Pith


For which of the following cases, \( \Delta S= \)
\( \frac{\Delta H}{T} ? \)
A. Process of which \( \Delta C_{P}=0, \) but \( \Delta C_{V}=0 \)
B. An isothermal process
C. An isobaric process
D. An isothermal reversible phase transition process


Assertion: Physical adsorption of molecules on the surface requires
activation energy. Reason: The bonds of adsorbed
molecules are broken.
A. Both Assertion and Reason are correct and Reason is the correct explanation of Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation of Assertion
c. Assertion is correct but reason is incorrect
D. Assertion is incorrect but reason is correct
E. Both Assertion and Reason are incorrect


A gas is enclosed in a vessel of volume
\( \boldsymbol{V} \) at temperature \( \boldsymbol{T}_{1} \) and pressure \( \boldsymbol{P} \) the vessel is connected to another
vessel of volume \( V / 2 \) by a tube and a stopcock. The second vessel is initially evacuated. If the stopcock is opened, the temperature of the second vessel
becomes \( T_{2} \). The first vessel is
maintained at a temperature of \( T_{1} \)
What is the final pressure \( P_{1} \) in the
apparatus?
A \( \frac{2 P T_{2}}{2 T_{2}+T_{1}} \)
в. \( \frac{2 P T_{2}}{T_{2}+T_{1}} \)
c. \( \frac{P T_{2}}{2 T_{2}+T_{1}} \)
D. \( \frac{2 P T_{2}}{T_{1}+T_{2}} \)


Find the value of \( x \) for which
\( \left(\frac{3}{4}\right)^{6} \times\left(\frac{16}{9}\right)^{5}=\left(\frac{4}{3}\right)^{x+2} \)


What is acid rain? Mention two of its
effects.


In the diagram \( \square A B C D \) is the
rectangular paper. If \( A B=20 \mathrm{cm} \) and
\( B C=14 \mathrm{cm} \) then what is the area of
the shaded region if the semicircle
with diameter \( B C \) is cut from the
paper.


Cholesterol is a component found in the phospholipid bilayer of the cell
membrane and
A. Makes the membrane more permeable to watersoluble substances such as ions and monosaccharides
B. Maintains the fluidity of the cell membrane
C. Builds and maintains membrane channels
D. Dissolves in large quantities and travels through the bloodstream


Pyramid of energy is always...........


A cell can be balanced against \( 110 \mathrm{cm} \) and \( 100 \mathrm{cm} \) of potentiometer wire, respectively with and without being short circuited through a resistance of 10\Omega. Its internal resistance is
A . \( 1 \Omega \)
B. \( 0.5 \Omega \)
c. \( 2 \Omega \)
D. none


The number of \( \sigma- \) and \( \pi- \) bonds in
peroxodisulphuric acid are, respectively:
A. 9 and 4
B. 11 and 4
c. 4 and 8
D. 4 and 9


\( N a H C O_{3}+C H_{3} C O O H \longrightarrow \)
\( C H_{3} C O O N a+C O_{2}+H_{2} O \)
This reaction is used as a test of
carboxylic acid because :
A. gas is confirmed when it turns lime water black
B. gas is confirmed when it turns lime water milky
c. gas is confirmed when it turns lime water light green
D. gas is confirmed when it turns lime water brown


The relative atomic masses of many
elements are not whole numbers
because:
A. they can't be determined very accurately
B. the atoms ionize during the determination
c. of the existence of isotopes
D. of the presence of impurities


Which of the following has two or more same electronic configuration?
This question has multiple correct options
A. Allotropes
B. Amphiprotic
c. Isoelectronic
D. Isomers
E. Isotopes


Alkali metals impart blue color to:
A. acidic solution
B. ammonia solution
c. nitrate solution
D. none of these


Which of the following quantities is/are positive?
This question has multiple correct options
A \( \cdot \cos \left(\tan ^{-1}(\tan 4)\right) \)
B. \( \sin \left(\cot ^{-1}(\cot 4)\right) \)
c. \( \tan \left(\cos ^{-1}(\cos 5)\right) \)
D. \( \cot \left(\sin ^{-1}(\sin 4)\right) \)


\( \mathbf{f}(\mathbf{x})=\frac{\mathbf{a x}+\mathbf{b}}{\mathbf{c x}+\mathbf{d}}(\boldsymbol{a d}-\boldsymbol{b c} \neq \mathbf{0}) \)
A. Has a maximum
B. Has a minimum
c. Neither max nor min is true
D. Both max and min are true


Let \( N_{\beta} \) be the number of \( \beta \) particles emitted by 1 gram of \( ^{24} N a \) radioactive
nuclei (half life \( =15 h r s \) ) in 7.5 hours,
\( N_{\beta} \) is close to (Avogadro number \( = \)
\( \left.6.023 \times 10^{23} / g \text { mole }\right) \)
A . \( 1.75 \times 10^{22} \)
B. \( 6.2 \times 10^{21} \)
C \( .7 .5 \times 10^{21} \)
D. \( 1.25 \times 10^{22} \)


If \( \boldsymbol{A}=\{\boldsymbol{x}: \boldsymbol{x} \in \boldsymbol{W}, \boldsymbol{3} \leq \boldsymbol{x}<\mathbf{6}\}, \boldsymbol{B}= \)
\( \{\boldsymbol{3}, \boldsymbol{5}, \boldsymbol{7}\} \) and \( \boldsymbol{C}=\{\mathbf{2}, \boldsymbol{4}\} ; \) find :
\( \boldsymbol{B}-\boldsymbol{C} \)


If 2,8 are the roots of \( x^{2}+a x+\beta=0 \)
and 3,3 are the roots of \( x^{2}+\alpha x+b= \)
0 then find the roots of \( x^{2}+a x+b=0 \)
A . -1,-9
в. 1,9
c. -2,-8
D. 2,8


A microscope is focused on a mark, then a glass slab of refractive index 1.5 and thickness of \( 3 \mathrm{cm} \) is placed on the mark to get the mark again in focus, the microscope should be moved
A. \( 4 \mathrm{cm} \)
B. 2cm
\( c .6 \mathrm{cm} \)
D. 8cm


Among reptiles, in which of the following is self mutilation generally
seen?
A. Snakes
B. Lizards
c. crocodiles
D. Tortoises


The given table shows the rank of three different minerals on the scale of
hardness.
\begin{tabular}{ll}
Mineral & Rank of hardness \\
\( \mathrm{x} \) & 5 \\
\( \mathrm{Y} \) & 3 \\
\hline
\end{tabular} \( z \) Based on the data, which of the
following results of scratch test will be
obtained?
\( A \)
\( =\sqrt{12} \)
в. \( =\sqrt{10} \)
\( c \)
\( =\sqrt{1-x} \)
D. \( =\sqrt{13} \)


Assertion
For a singular square matrix \( \mathbf{A}, \boldsymbol{A} \boldsymbol{B}= \)
\( \boldsymbol{A C} \Rightarrow \boldsymbol{B}=\boldsymbol{C} \)
Reason
If \( |A|=0, \) then \( A^{-1} \) does not exist.
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


Prove that the locus of the point of intersection of the lines
\( x \cos \alpha+y \sin \alpha=a \)
and \( x \sin \alpha-y \cos \alpha=b \)
is a circle whatever \( \alpha \) may be.


In aqueous solution, the following mixture acts as buffer:
A. \( H N O_{3}+K N O_{3} \)
в. \( H_{2} S O_{4}+K_{2} S O_{4} \)
c. \( N H_{4} O H+N H_{4} C l \)
D. \( C H_{3} C O O H+N a C l \)


What are endocrine glands? Identify chief endocrine glands, the hormones produced by them, the function of the hormones and diseases produced due to imbalances.


Differentiate the following functions
w.r.t. \( \boldsymbol{x} \)
\( \sqrt{x+\frac{1}{x}} \)


If \( S_{n}=\sum_{r=1}^{n} \frac{2 r+1}{r^{4}+2 r^{3}+r^{2}} \) then \( S_{20}= \)
A \( \cdot \frac{220}{2210} \)
в. \( \frac{420}{44} \)
c. \( \frac{439}{221} \)
D. \( \frac{440}{441} \)


Use Euclid's division lemma to show
that cube of any positive integer is either of the form \( 9 \mathrm{m}, 9 \mathrm{m}+1 \) or \( 9 \mathrm{m}+8 \)
for some integer 'm'


\( \int \sqrt{1+x^{2}} d x \) is equal to
A \( \cdot \frac{x}{2} \sqrt{1+x^{2}}+\frac{1}{2} \log |+\sqrt{1+x^{2}}|+C \)
B. \( \frac{2}{3}\left(1+x^{2}\right)^{\frac{2}{3}}+C \)
c. \( \frac{2}{3} x\left(1+x^{2}\right)^{\frac{3}{2}}+C \)
D \( \cdot \frac{x^{2}}{2} \sqrt{1+x^{2}}+\frac{1}{2} x^{2} \log |x+\sqrt{1+x^{2}}|+C \)


Water blooms are formed by
A . Lemna
B. Hydrilla
c. water Hyacinth
D. Planktonic algae


A mixer of \( 100 \Omega \) resistance is
connected to an A.C. source of \( 200 \mathrm{V} \) and 50 cycles/sec. The value of average potential difference across the mixer will be:
\( A \cdot 308 V \)
B. 264
c. 220
D. zero


\( \pi^{c} \)
\( \frac{\pi}{5} \) in sexagesimal measure is
A \( \cdot 18^{\circ} \)
B. \( 36^{\circ} \)
\( c \cdot 54^{\circ} \)
D. 72


When two dice are rolled, find the
probability of getting a greater number on the first die than the one on the
second, given that the sum should equal 8
A \( \cdot \frac{1}{5} \)
B. \( \frac{2}{5} \)
\( c \cdot \frac{3}{5} \)
D. None of these


A solid sphere is rolling down an
inclined plane without slipping. If the inclined plane has inclination \( \theta \) with the
horizontal, then the coefficient of
friction \( \mu \) between the sphere and the
inclined plane should be
A \( \cdot \mu \geq 2 / 7 \cot \theta \)
B. \( \mu \geq 2 / 7 \tan \theta \)
c. \( \mu \geq 2 / 7 \cos \theta \)
D. \( \mu \geq 4 / 7 \sin \theta \)


The kinetic energy of a body of mass
\( 4 k g \) and momentum \( 6 N s \) will be
\( \mathbf{A} \cdot 2.5 J \)
B. \( 3.5 J \)
c. \( 4.5 J \)
D. \( 5.5 J \)


\( \boldsymbol{C a}(\boldsymbol{O H})_{2} \) is formed when calcium oxide dissolves in water
A. True
B. False


\( \int \cos ^{-1} \sqrt{\frac{1-x}{2}} d x= \)
A. \( \frac{\pi}{2} x-\frac{1}{2} x \cos ^{-1} x+c \)
B. \( \frac{\pi}{2} x-\frac{1}{2} x \cos ^{-1} x+\frac{1}{2} \sqrt{1-x^{2}}+c \)
C \( \cdot \frac{\pi}{2} x-\frac{1}{2} x \cos ^{-1} x-\sqrt{1-x^{2}}+c \)
D. \( \frac{\pi}{2} x+\frac{1}{2} x \cos ^{-1} x+c \)


A convex lens \( (\boldsymbol{f}=\mathbf{2 0} \boldsymbol{c m}) \) is placed at
\( 80 \mathrm{cm} \) from a concave mirror. An object
is placed at \( 30 \mathrm{cm} \) in front the lens such
that position of its final image is same
or without the mirror. The maximum
distance of object and mirror for virtual image to be formed if only mirror is
present is:
A \( .10 \mathrm{cm} \)
B. \( 20 \mathrm{cm} \)
\( c .30 \mathrm{cm} \)
D. \( 50 \mathrm{cm} \)


In a full-wave rectifier, the output is
taken across a load resistor of 800 ohm.
If the resistance of diode in the forward
biased condition is 200 ohm,
the efficiency of rectification of ac power into dc power is(in percentage)


A laeal barometer tube or neglıgıble
mass is suspended from a spring balance as shown. The mass of mercury
in the tube is \( m \) and atmospheric
pressure is \( P_{0} . \) The cross section area of
tube is \( A . \) The reading of spring balance
is :
This question has multiple correct options
\( \mathbf{A} \cdot m g \)
B \( . P_{0} A \)
\( \mathbf{c} \cdot P_{0} A-m g \)
D. \( \frac{P_{0} A+m g}{2} \)


If \( f(x)=x^{2}+\frac{1}{x^{2}}, \) then find the value of
\( \boldsymbol{f}(\mathbf{5}) \)
A \( \cdot \frac{424}{25} \)
в. \( \frac{626}{25} \)
c. \( \frac{536}{25} \)
D. \( \frac{428}{25} \)


Which of the following types of plant grow in water scarcity?
A. Xerophytes
B. Hydrophytes
c. Both A and B
D. None


Evaluate: \( \int \frac{e^{x}}{e^{x}+1} d x \)


If a current of 0.3 ampere is drawn from
a Daniell cell for 1 hour, what would be
the change in mass of electrodes? (At. mass of \( C u=63.5 \) and \( Z n=65.37 \)


From a circle with radius \( 21 \mathrm{cm} \) a
sector is cut off for which the measure
of the angle at the centre is \( 150 . \) Find
the length of the arc of that sector and
also find the area of the sector.


Which of the following elements never show positive oxidation number?
A.
B. Fe
\( c \cdot \) Ga
\( D \)


Fill in the blanks with suitable words:
Light has and
nature.


Which of the following are \( A p s ? \) If they
form an \( A P, \) find the common
difference \( d \) and write three more terms.
\( 2, \frac{5}{2}, 3 \frac{7}{2}, \dots \)


A man can swim in still water with a
velocity 5 m/s. He wants to reach at
directly opposite point on the other bank of a river which is flowing at a rate of \( 4 m / s . \) River is 15 m wide and the man can run with twice the velocity
as compared with velocity of swimmer
with respect to river. If he swims
perpendicular to river flow and then run along the bank. Time, in seconds, taken by him to reach the opposite point is
A. 4.0
B. 4.2
\( c .5 .4 \)
D. 3.6


Which of the following forms the connecting link between glycolysis and Kreb's cycle?
A. Glucose
B. Ethyl alcohol
c. Lactic acid
D. Pyruvic acid


In a disturbed site in a community recovers and moves again toward the climax state.
A . area effect
B. primary succession
c. distance effect
D. secondary succession


If the coefficients of \( (r-5) \) th and
\( (2 r-1) \) th terms in the expansion of
\( (1+x)^{34} \) are equal, then write the value
of \( r \)


Capitulum inflorescence is found in
A. Liliaceae
B. Papilionaceae
c. compositae
D. Rosaceae


Form the differential equation from the following primitive, where constant is arbitrary. \( \boldsymbol{x} \boldsymbol{y}=\boldsymbol{a}^{2} \)


Moss peat is used as a packing material for sending flowers and live plants to distant places because
A. It reduces transpiration.
B. It serves as a disinfectant
C. It is easily available.
D. It is hygroscopic


Suppose your writing desk is titled a little. A book kept on it starts sliding
down. Show the direction of frictional
force acting on it.


Define electric potential due to a point charge and arrive at the expression for the electric potential at a point due to a point charge in its vicinity.


A uniform electric field and a uniform
magnetic field exist in a region in the same direction. An electron is projected with velocity pointed in the same
direction the electron will
A. turn to its right
B. turn to its left
c. keep moving in the same direction but its speed will increase
D. keep moving in the same dirction but its speed will decrease


Give any two difference between
lanthanoids and actinoids.


If \( P \) and \( Q \) are points of trisection of the diagonal BD of a parallelogram ABCD, \( \boldsymbol{C Q} \| \boldsymbol{A P} \)
A. True
B. False


Highly energetic electrons are bombarded on a target of an element containing 30 neutrons. The ratio of radii of nucleus to that of Helium
nucleus is \( (14)^{1 / 3} . \) The atomic number
of nucleus will be
A . 25
B . 26
c. 56
D. 30


Both temporary and permanent hardness in water is removed by:
A. boiling
B. filtration
c. distillation
D. decantation


Prove that \( n^{2}-n \) is divisible by 2 for
every positive integer \( n \)


fi \( a, b \& c \) are non-zero real numbers \( \operatorname{then} D=\left|\begin{array}{lll}b^{2} c^{2} & b c & b+c \\ c^{2} a^{2} & c a & c+a \\ a^{2} b^{2} & a b & a+b\end{array}\right|= \)
A \( \cdot a b c \)
B \( \cdot a^{2} b^{2} c^{2} \)
c. \( b c+c a+a b \)
D. zero


The hydroxide ion concentration of a
solution is \( 10^{-6} \) mol/litre. The \( p H \) of the
solution is:
A . 8
B. 6
c. -8
D. - 6


If \( n(A)=4, n(B)=3, n(A \times B \times C)= \)
\( 24, \) then \( n(C) \) is equal to
A . 288
в.
\( c \cdot 2 \)
D. 12


A railway track is banked for a speed \( \mathbf{v} \)
by making the height of the outer rail h
higher than that of the inner rail. The
distance between the rails is d. The
radius of curvature of the track is \( r \)
Then,
\( \mathbf{A} \cdot \frac{h}{d}=\frac{v^{2}}{r g} \)
B. \( \tan \left(\sin ^{-1} \frac{h}{d}\right)=\frac{v^{2}}{r g} \)
\( ^{\mathbf{C}} \tan ^{-1}\left(\frac{h}{d}\right)=\frac{v^{2}}{r g} \)
\( \mathbf{D} \cdot \frac{h}{r}=\frac{v^{2}}{d g} \)


When dielectric medium of constant
is filled between the plates of a charged parallel-plate condenser, then the energy stored becomes, as compared to its previous value,
\( \mathbf{A} \cdot K^{-3} \)times
B. \( K^{-2} \)times
c. \( K^{-1} \)times
D. Ktimes


The value of \( \sin ^{-1}\left\{\cos \left(\frac{33 \pi}{5}\right)\right\} \) is
\( ^{A} \cdot \frac{3 \pi}{5} \)
в. \( \frac{7 \pi}{5} \)
c. \( \frac{\pi}{10} \)
D. \( \frac{-\pi}{10} \)


Find the square root of:
\( \mathbf{3 1}+\mathbf{4} \sqrt{\mathbf{2 1}} \)
A. \( \sqrt{24}+\sqrt{3} \)
В. \( \sqrt{28}+\sqrt{3} \)
c. \( \sqrt{36}+\sqrt{3} \)
D. \( \sqrt{28}+\sqrt{2} \)


Which of the following statement is true regarding Bohr's Model of hydrogen atom?
I. Orbiting speed of an electron
decreases as it falls to discrete orbits
away from the nucleus
II. Radii of allowed orbits of electrons
are proportional to the principal quantum number III. Frequency with which electrons orbit around the nucleus in discrete
orbits is inversely proportional to the cube of principal quantum number
\( I V . \) Binding force with which the electron is bound to nucleus increases
as it shifts to outer orbits.
Select the correct answer using the
codes given below:
A. \( I \) and \( I I I \)
B. II and \( I V \)
c. \( I, I I \) and \( I I I \)
\( D \)
and \( I V \)


The outer shell electronic configuration
of \( \operatorname{Gd}(Z=64) \) is:
A \( \cdot 4 f 5 d^{1} 6 s^{2} \)
B \( \cdot 4 f^{8} 6 s^{2} \)
c. \( 4 f^{9} 9 s^{\text {। }} \)
D. \( 4 f^{7} 5 d^{1}^{6} s^{2} \)


A man sold his bicycle for Rs. 405 losing one-tenth of its cost price. Find its cost
price
A . Rs. 250
B. Rs. 320
c. Rs. 400
D. Rs. 450


A charge \( Q \) is uniformly distributed over
the surface of two concentric
conducting spheres of radii \( R \) and \( r(R>r) \) Such that surface charge
densities are same for both
spheres.Then potential at common centre of these spheres-
A \( \cdot \frac{K Q(R+r)}{R r} \)
B. \( \frac{K Q(R+r)}{R^{2}+r^{2}} \)
c. \( \frac{K Q}{\sqrt{R^{2}+r^{2}}} \)
\( ^{\mathrm{D}} \cdot \operatorname{KQ}\left(\frac{1}{R}-\frac{1}{r}\right) \)


Pair having elements from same period
is :
A . Na,Ca
B. Na,CI
c. са,С
D. Cl,Br


The angles of a triangle are in \( A . P . . \) The number of degree in the least is to be the number of radians in the greatest
as \( 60: \pi . \) Then the greatest angle is
A \( \cdot 120^{\circ} \)
В. \( 90^{\circ} \)
\( \mathrm{c} \cdot 135^{\circ} \)
D. \( 105^{\circ} \)


Evaluate \( : \int \frac{\cos ^{-1} x}{x^{2}} d x \)


Baking powder is a mixture of:
A. Sodium carbonate and acetic acid
B. Sodium carbonate and tartaric acid
C. Sodium hydrogen carbonate and tartaric acid
D. Sodium hydrogen carbonate and acetic acid


Equilibrium constant for the following reaction is \( 1 \times 10^{-9}: C_{5} H_{5} N(a q)+ \)
\( \boldsymbol{H}_{2} \boldsymbol{O}(\boldsymbol{l}) \rightleftharpoons \boldsymbol{C}_{5} \boldsymbol{H}_{5} \boldsymbol{N} \boldsymbol{H}+(\boldsymbol{a} \boldsymbol{q} \cdot)+ \)
\( O H^{-}(a q .) \) Determine the mole of
pyridirium chloride \( \left(C_{5} H_{5} N . H C l\right) \) that should be added to \( 500 m L \) solution of
\( 0.4 M \) pyridine \( \left(C_{5} H_{5} N\right) \) to obtain a
buffer solution of \( \boldsymbol{p} \boldsymbol{H}=\mathbf{5} \)


Fill in the blanks: Periods are
[5,6,7] horizontal rows of
elements in the periodic table and an element with three electron shells and
two electrons in its valence shell
belongs to period [6,3,1] and
group [3,6,2]


Solve the following differential equation \( \frac{\boldsymbol{d} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}}=\boldsymbol{x}^{2}+\boldsymbol{x}-\frac{\mathbf{1}}{\boldsymbol{x}}, \boldsymbol{x} \neq \mathbf{0} \)


The reactance of a circuit is zero. It is
possible that the circuit contains [more than one option may be correct] This question has multiple correct options
A. an inductor and a capacitor
B. an inductor but no capacitor
c. a capacitor but no inductor
D. neither an inductor nor a capacitor


From a pack of 52 cards, face cards and tens are removed and kept aside, then a card is drawn at random from the
remaining cards. If A: The events that the card is drawn is an ace. H: The
events that the card is drawn is a
heart.S: the events that the card is
drawn is a spade. Then, which of the following holds?
\( \mathbf{A} \cdot 9 P(A)=4 P(H) \)
B. \( P(S)=4 P(A \cap H) \)
c. \( 3 P(H)=P(A \cap S) \)
D. None of these


Compound A undergoes hydrolysis to produce a colourless gas with rotten fish smell. The gas gives a vortex ring. The gas is:
A \( . P H_{3} \)
в. \( P_{2} O_{3} \)
c. \( P_{2} O_{5} \)
D. \( P_{2} S_{5} \)


The line \( y+7=0 \) is parallel to
\( \mathbf{A} \cdot x=2 \)
B. \( x=1 \)
c. \( x=5 \)
D. \( x \) -axis


Which of the following is steam volatile?
A. Nitrobenzene
B. Aniline
c. Both A \& B
D. Neither A nor B


Ampere. A "S" shaped conducting rod AB consisting of two semicircles each of
radius \( r \) is placed in such a way that the
centre \( C \) of the conducting wire is at a
distance \( 2 r \) from the end of the wire.The
rod \( A B \) moves with velocity of \( 5 m s^{-1} \)
along the direction of the current flow as shown in the figure. If the line joining
the ends of the rod makes an angle \( 60^{\circ} \)
with the wire then,
This question has multiple correct options
A. the emf induced between the ends of the rod is \( (\ln 4) \)
\( \mu V \)
B. the end \( A \) is at higher potential than end \( B \).
c. the end \( A \) is at lower potential than end \( B \).
D. the emf induced between the ends of the rod is \( (\ln 3) \)
\( \mu V \)


What changes do you observe in your body during expiration process?


A false balance has equal arms. An
object weights \( \boldsymbol{w}_{1} \) when placed in one
pan and \( w_{2} \) when placed in the other
pan. Then weight \( \boldsymbol{w} \) of the object is :
A \( \cdot \sqrt{w_{1} w_{2}} \)
в. \( \frac{w_{1}+w_{2}}{2} \)
c. \( \left(\frac{w_{1}^{2}+w_{2}^{2}}{2}\right)-1 \)
D. \( \sqrt{w_{1}^{2}+w_{2}^{2}} \)


The sides of right angles triangle are 63,9 find its hypotenuse.


State whether true or false:
In carnot cycle heat removal takes place
at constant pressure?
A. True
B. False


A businessman borrowed the Rs.45 lakh for two years at the rate \( 2.5 \% \) p.a. compounded annually. Calculate the compound interest by simple interest method.
A .2,23000
в. 2,27,812.5
\( \mathbf{c} .5,65,563 \)
D. 2,00,000


Which method is used by astronomers to calculate how far the star is?
A. Parallax
B. Equillax
c. Purplex
D. None


The heat capacity of a diatomic gas is higher than that of a mono-atomic gas.If
true enter 1 else 0


\( \sqrt{2} \int_{0}^{2 \pi} \sqrt{1-\sin x} d x= \)


The ratio of the gravitational force between the Earth and the satellite \( A \) to
the gravitational force to the satellite \( \boldsymbol{B} \)
is equal to :
A \( \cdot \frac{1}{4} \)
B. \( \frac{1}{2} \)
c. 1
D. 2
\( E . \)


The structure of compound (A) is :
\( A \)
в.
\( c \)
D.


The element with highest boiling point in the following is :
A. oxygen
B. Sulphur
c. Tellurium
D. Polonium


The angle between \( \vec{P}+\vec{Q} \) and \( \vec{P}-\vec{Q} \)
will be:
A. \( 90^{\circ} \) only
B. between \( 0^{\circ} \) and \( 180^{\circ} \)
c. \( 180^{\circ} \) only
D. None of these


The geometric mean of 6 and 54 is
A . 12
B. 16
c. 18
D . 20


Solve the following linear programming problem graphically:
Maximize \( Z=7 x+10 y \)
subject to the constraints \( 4 x+6 y \leq 240 \)
\( 6 x+3 y \leq 240 \)
\( x \geq 10 \)
\( \boldsymbol{x} \geq \mathbf{0}, \boldsymbol{y} \geq \mathbf{0} \)


If \( ^{28} C_{2 r}:^{24} C_{2 r-4}=225: 11, \) find \( r \)


Vermiform appendix is made up of
A. Respiratory tissue
B. Excretory tissue
c. Lymphatic tissue
D. Digestive tissue


toppr
Q Type your question
Velocities are shown with the red arrows
ant the corresponding values.
A. blue and yellow tie, green and purple and orange tie
B. purple and orange tie, blue, yellow, green
c. blue, purple and orange tie, green yellow
D. green and purple tie, or orange, blue and yellow tie
E. green and purple and orange tie, blue and yellow tif


Assertion
Let equations \( a x^{2}+b x+c= \)
\( \mathbf{0}(\boldsymbol{a}, \boldsymbol{b}, \boldsymbol{c} \in \boldsymbol{R}) \& \boldsymbol{x}^{2}+\mathbf{2} \boldsymbol{x}+\mathbf{5}=\mathbf{0} \) have
common root, then \( \frac{\boldsymbol{a}+\boldsymbol{c}}{\boldsymbol{b}}=\frac{\mathbf{1}}{\mathbf{3}} \)
Reason
If both roots of \( A x^{2}+B x+K_{1}=0 \& \)
\( \boldsymbol{A}^{\prime} \boldsymbol{x}^{2}+\boldsymbol{B}^{\prime} \boldsymbol{x}+\boldsymbol{K}_{2}=\mathbf{0} \) are identical
\( \operatorname{then} \frac{\boldsymbol{A}}{\boldsymbol{A}_{1}}=\frac{\boldsymbol{B}}{\boldsymbol{B}_{1}}=\frac{\boldsymbol{K}_{1}}{\boldsymbol{K}_{2}}\left(\text { where } \boldsymbol{A}, \boldsymbol{B}, \boldsymbol{K}_{1}\right. \)
and \( \left.A^{\prime}, B,^{\prime} K_{2} \in R\right) \)
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, Reason is correct


Assertion
Graphite is a good conductor of heat and electricity
Reason
Graphite has all the electrons firly held together in \( C-C \sigma \) -bonds
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


If \( \left(i^{413}\right)\left(i^{x}\right)=1, \) then determine the one
possible value of \( x \)
\( \mathbf{A} \cdot \mathbf{0} \)
B.
\( c \cdot 2 \)
D. 3


In the equation \( \boldsymbol{h} \boldsymbol{v}=\boldsymbol{h} \boldsymbol{v}_{0}+\frac{1}{2} \boldsymbol{m}_{e} \boldsymbol{v}^{2}, \boldsymbol{v}_{0} \)
is known as:
A. work function
B. velocity of ejected electron
c. threshold frequency
D. frequency of photon


When chlorine gas is passed throgh an aqueous solution of a potassium halide in the presence of chloroform, a voilet colouration is obtained. On passing more of chlorine water, the voilet colour
is disappered and solution becomes colourless. This test confirms the
presence of ....... in aqueous solution.
A. chlorine
B. fluorine
c. bromine
D. iodine


The interval on which \( f(x)=\sqrt{1-x^{2}} \) is continuous is:
A. \( (0, \infty) \)
(i)
В. \( (1, \infty) \)
c. [-1,1]
D. \( (-\infty,-1) \)


If \( k=\tan 25^{\circ} \) then find \( \frac{k-1}{k+1}+\frac{k+1}{k-1} \)
A. 2 \( \operatorname{cosec} 130^{\circ} \)
B . 2 \( \operatorname{cosec} 45^{\circ} \)
c. \( 2 \sec 130^{\circ} \)
D. \( 2 \sec 400^{\circ} \)


\( \int \frac{x \cos x}{(x \sin x+\cos x)^{2}} d x \)


f \( |z| \leq 1,|w| \leq 1 \) show that
\( |z-w|^{2} \leq(|z|-|w|)^{2}= \)
\( (A r g z-A r g w)^{2} \)


An organic compound contains \( 69 \% \)
carbon and 4.85 hydrogen, the remainder being oxygen. The masses of carbon dioxide and water produced when 0.20 g of this substance is subjected to complete combustion?
A. \( 0.506 g \) and 0.0864 g
в. \( 0.678 \mathrm{g} \) and \( 0.0234 \mathrm{g} \)
c. \( 0.786 g \) and 0.0128 g
D. None


Which of the following hexoses will form the same osazone when treated with
excess phenyl hydrazine?
A. D-glucose, D-fructose and D-galactose
B. D-glucose, D-fructose and D-mannose
c. D-glucose, D-mannose and D-galactose
D. D-fructose, D-mannose and D-galactose


Assertion: In forced oscillations, the
steady state motion of the particle is simple harmonic. Reason : Then the frequency of particle after the free oscillations die out, is the
natural frequency of the particle.
A. If both assertion and reason are true and reason is the correct explanation of assertion.
B. If both assertion and reason are true and reason is not the correct explanation of assertion.
c. If assertion is true but reason is false
D. If both assertion and reason are false


\( (x)^{n}+(a)^{n} \) is completely divisible by
\( x+a, \) then \( n \) can be
A . 7028
в. 861
c. 26
D. 782


A rocket is launched upward from the
earth surface whose velocity time graph is shown in the figure. Then maximum height attained by the rocket is:
A. \( 1 k m \)
B. \( 10 k m \)
c. \( 100 k m \)
\( \mathbf{D} \cdot 60 k m \)


\( R H_{2} \) (ion exchange resin ) can replace
\( C a^{2+} \) in hard water as:
\( \boldsymbol{R} \boldsymbol{H}_{2}+\boldsymbol{C} \boldsymbol{a}^{2+} \rightarrow \boldsymbol{R} \boldsymbol{C} \boldsymbol{a}+\boldsymbol{2} \boldsymbol{H}^{+} \)
One litre of hard water after passing
through \( R H_{2} \) has \( \mathrm{pH}=2 . \) Hence,
hardness in ppm of \( C a^{2+} \) is:
A . 200
B. 100
\( c .50 \)
D. 125


Which parameters shown below are common between uniform circular
motion and uniform linear motion
A. Velocity
B. Speedd
c. Displacement
D. Acceleration


(A) is binary orange coloured paramnetic compound of a univalent cation. 1.422 g of (A) reacts completely with 0.321 g of sulphur ina evacuated and sealed tube to give 1.743 g of a while crystalline solid (B) that forms hydrated
double salt (C) with \( A l_{2}\left(S O_{4}\right)_{3} ; \) Here,
compounds \( (A),(B), \) and \( (C) \) are \( K O_{2} \) \( \boldsymbol{K}_{2} \boldsymbol{S} \boldsymbol{O}_{4} \) and \( \boldsymbol{K}_{2} \boldsymbol{S} \boldsymbol{O}_{4} \cdot \boldsymbol{A} \boldsymbol{l}_{2}\left(\boldsymbol{S} \boldsymbol{O}_{4}\right)_{3} \cdot \boldsymbol{2} \boldsymbol{4} \boldsymbol{H}_{2} \boldsymbol{O} \)
respectively.
If true enter 1 , else enter 0 .


Which is the correct relationship between wavelength and momentum of particles?
A \( \cdot \lambda=\frac{h}{p} \)
B. \( \pi=\frac{h}{p} \)
c. \( p=\frac{\lambda}{h} \)
D. \( h=\frac{P}{\lambda} \)


the perpendiculars from B and \( \mathrm{C} \) to
the opposite sides are equal

If the above statement is true then
mention answer as 1 , else mention 0 if
false


\( \boldsymbol{C}_{6} \boldsymbol{H}_{5} \boldsymbol{C O O H}+\boldsymbol{C H}_{3} \boldsymbol{M} \boldsymbol{g} \boldsymbol{I} \rightarrow ? \)
\( \mathbf{A} \cdot C_{6} H_{5} C O O M g I \)
в. \( C H_{4} \)
c. Both a and \( b \)
D. none


If \( 3 x-\frac{1}{3 x}=5, \) then find \( 81 x^{4}+\frac{1}{81 x^{4}} \)


If the mean of \( 10,12,18,13, x, 17 \) is 15
find ' \( \boldsymbol{x}^{\prime} \)


In comparison with other cells, nerve cells show a higher degree of
A. Metabolism
B. Growth
c. contractility
D. Irritability


Match and find the correct combination
(a)
Trichomes \( \quad \) (i) \( \quad \) Gaseous
exchange
(b)
Tracheids \( \quad \) (ii) \( \quad \) Mechanical
strength
(c) Bast fibres water
(iii) \( \quad \) conduction
\( (d) \)
Guard
cells
(iv) Water
conduction
(v) Synthesis of
food 1
\( \mathbf{A} \)
(a)-(iii), (b)-(v), (c)-(iv), (d)-(ii)
B. (a)-(iii), (b)-(iv), (c)-(ii), (d)-(i)
C. (a)-(i), (b)-(iv), (c)-(ii), (d)-(iii)
D. \( (a)-(v),(b)-(\text { iii) },(c)-(i v),(d)-(i i) \)


Assertion
Anode is the electrode at which
oxidation occurs and cathode is the
electrode at which reduction occurs.
Reason

Anode and cathode in electrochemical
cells and electrolytic cells have opposite
polarity.
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


is the energy released during nuclear reactions


If the radius of a sphere is measured as \( 9 m \) with an error of \( 0.03 m, \) then find
the approximate error in calculating in surface area.


A thermally insulated vessel contains
\( 150 g \) of water at \( 0^{\circ} \mathrm{C} \). Then the air from the vessel is pumped out adiabatically. A fraction of water turns into ice and the
rest evaporates at \( 0^{\circ} \mathrm{C} \) itself. The mass
of evaporated water will be closest to:
(Latent heat of vaporization of water \( = \)
\( 2.10 \times 10^{6} J k g^{-1} \) and Latent heat of
Fusion of water \( \left.=\mathbf{3 . 3 6} \times \mathbf{1 0}^{\mathbf{5}} \mathbf{J} \mathbf{k g}^{-\mathbf{1}}\right) \)
A . \( 130 g \)
B. \( 35 g \)
c. \( 20 g \)
D. \( 150 g \)


What is banking of roads? Why banking is necessary for a curved road?


If \( \vec{a}, \vec{b} \) and \( \vec{c} \) are three non-coplanar vectors, then \( (\vec{a}+\vec{b}-\vec{c}) \cdot[(\vec{a}-\vec{b}) \times \)
\( (\vec{b}-\vec{c}) \) equals
A. 0
В . \( \vec{a} .(\vec{b} \times \vec{c}) \)
C \( . \vec{a} .(\vec{c} \times \vec{b}) \)
D . 3 \( \vec{a} .(\vec{b} \times \vec{c}) \)


Anhydrous calcium chloride is often used as a dessicant. In the presence of
excess of \( C a C l_{2}, \) the amount of the
water taken up is governed by \( \boldsymbol{K}_{\boldsymbol{p}}= \) \( 6.4 \times 10^{8} 5 \) for the following reaction at
room temperature, \( \boldsymbol{C a} \boldsymbol{C l}_{2}(\boldsymbol{s})+ \)
\( 6 H_{2} O(g) \rightleftharpoons C a C l_{2} .6 H_{2} O(s) . \) What is
the equilibrium vapour pressure of
water in a closed vessel that contains
\( \boldsymbol{C a} \boldsymbol{C l}_{2}(\boldsymbol{s}) ? \)
\( \mathbf{A} \cdot P_{H_{2} O}=5 \times 10^{-15} a t m \)
B. \( P_{H_{2} O}=6 \times 10^{-15} a t m \)
C \( \cdot P_{H_{2} O}=7 \times 10^{-15} a t m \)
D. \( P_{H_{2} O}=9 \times 10^{-15} a t m \)


When an unknown resistance and a
resistance of \( 4 \Omega \) are connected in the
left and right gaps of a meter bridge, the balance point is obtained at \( 50 \mathrm{cm} . \) The
shift in the balance point, if a \( 4 \Omega \) resistance is now connected in parallel to the resistance in the right gap, is
A. \( 66.7 \mathrm{cm} \)
в. \( 16.7 \mathrm{cm} \)
\( \mathrm{c} .34 .6 \mathrm{cm} \)
D. 14.6 \( c m \)


Name the chronic respiratory disorder caused mainly by cigarette smoking.
A. Asthma
B. Respiratory acidosis
c. Respiratory alkalosis
D. Emphysema


List List - II
a. Temperature of water e. \( 273 \mathrm{K} \)
at the bottom of a lake
b. \( \gamma_{r} \) of water is - ve f. \( 277 \mathrm{K} \)
between
c. \( \gamma_{r} \) of water is positive
g. above 277
\( k \)
d. Temperature of water
h. \( 273 \mathrm{K} \) and
just below ice layer in \( 277 \mathrm{K} \)
a Lake
\( A \cdot a-g, b-h, c-e, d-f \)
B. a-h, b-e, c-f, d-g
c. a-e, b-f, c-g, d-h
D. a-f, b-h, c-g, d-e


Protonema is
A. Haploid and is found in mosses
B. Diploid and is found in liverworts
C. Diploid and is found In pteridophytes
D. Haploid and is found in pteridophytes


Which one of the following statement is
correct regarding blood pressure?
A. \( 190 / 110 \mathrm{mm} \) Hg may harm vital organs like brain and kidney
B. \( 130 / 90 \mathrm{mm} \) Hg is considered high and requires treatment
C. \( 100 / 55 \mathrm{mm} \) Hg is considered and ideal blood pressure
D. \( 105 / 50 \mathrm{mm} \) Hg makes one very active


\( x, y, z \) are 3 members of
Doheriner Periods. Atomic masses of \( x \)
y are \( 7 \mathrm{u} \) \& \( 23 \mathrm{u} \). What should be the
mass of z? How?


Arrange the following in ascending order based on their solute
concentration
\( \begin{array}{ll}\text { Water } & \text { Pressure Potential } \\ \text { Cell } & \begin{array}{l}\text { Potential } \\ (\mathrm{KPa})\end{array} & (\mathrm{KPa}) \\ & \end{array} \) \( \begin{array}{lll}\text { (a) } & -590 & 320 \\ \text { (b) } & -368 & 623 \\ \text { (c) } & -292 & 412 \\ \text { (d) } & -481 & 146\end{array} \)
\( A \)
\( a, a, d, b \)
B. \( \mathrm{d}, \mathrm{c}, \mathrm{a}, \mathrm{b} \)
\( c \cdot a, c, b, d \)
\( D \cdot b, a, c, d \)


The 'blue baby' syndrome is related to
A. Excess of TDS (total dissolved solid)
B. Excess of chloride
c. Methemoglobin
D. Excess of dissolved oxygen


Thomson's atomic model is also called:
A. water melon model
B. christmas pudding model
\( c . \) both a and \( b \)
D. none of above


All except one mentioned below is an incorrectly mentioned rule framed under Environment (Protection) act,
1986. Identify it
A. Ozone Depleting Substanes Rules, 2000
B. Harzardous Wastes Rules, 1989
c. Air Prevention and Control of Pollution Act, 198
D. Biomedical Wastes Rules, 1998


Which of the following is not the
consequence of \( \boldsymbol{H} \) -bonding?
A. Glycerol is more soluble in water than ethanol
B. Boiling point of \( C_{2} H_{5} O H \) is higher than \( C H_{3}-O- \)
\( C H_{3} \)
C. p-nitrophenol has higher boiling point than onitrophenol
D. \( H C l \) is water soluble due to \( H \) -bonding.


A piston of cross-sectional area \( 100 \mathrm{cm}^{2} \) is used in a hydraulic press to exert a force of \( 10^{7} \) dyne on the water. The cross-sectional area of the other piston
which supports an object having a mass of \( 2000 \mathrm{kg} \) is :
A \( \cdot 100 \mathrm{cm}^{2} \)
B. \( 10^{9} \mathrm{cm}^{2} \)
c. \( 2 \times 10^{4} c m^{2} \)
D. \( 2 \times 10^{10} \mathrm{cm}^{2} \)


Q Type your question
One of the chief uses of sodium
carbonate has been in the conversion of
\( \operatorname{Ca}(O H)_{2}(s) \) to concentrated aqueous solution of NaOH which in turn was
used in the manufacture of soap.
\( \boldsymbol{C a}(\boldsymbol{O H})_{2}(\boldsymbol{s})+\boldsymbol{2} \boldsymbol{N} \boldsymbol{a}^{+}(\boldsymbol{a q})+ \)
\( \boldsymbol{C O}_{3}^{2-}(\boldsymbol{a q}) \rightleftharpoons \boldsymbol{C a C O}_{3}(\boldsymbol{s})+ \)
\( \mathbf{2} N \boldsymbol{a}^{+}(\boldsymbol{a} \boldsymbol{q})+\mathbf{2} \boldsymbol{O} \boldsymbol{H}^{-}(\boldsymbol{a} \boldsymbol{q}) \)
In \( 1775, \) in order to gain independence from the importation of natural
\( N a_{2} C O_{3}, \) the French government
offered a prize to anyone who could
devise a process to prepare \( N a_{2} C O_{3} \)
from NaCl

A more economical process but based
on the same principle was given by :
A. Solvay
B. Leblanc
c. williamson
D. Haber


A chord of length \( 20 \mathrm{cm} \) is drawn at a
distance of \( 24 \mathrm{cm} \) from the centre of a
circle. Find the radius of the circle.


In \( \triangle A B C, A B=5 c m, B C= \)
\( \mathbf{6} c \boldsymbol{m}, \boldsymbol{A C}=\mathbf{4} \boldsymbol{c m} . \) Identify the type of
triangle.
A. Right angled triangle
B. Isosceles triangle
c. Equilateral triangle
D. Scalene triangle


An element \( d l=d x i=(w h e r e d x= \)
1 \( c m \) ) is placed at origin and carries a
current \( 10 A . \) What is the magnetic field
on \( y \) - axis at a dist. of \( 0.5 m ? \)
A \( \cdot 2 \times 10^{-8} k T \)
В. \( 4 \times 10^{-8} k T \)
c. \( -2 \times 10^{-8} k T \)
D. \( -4 \times 10^{-8} k T \)


Explain the process of digestion in
Amoeba.


Chlorophyll present in green leaves of plants absorbs light at \( 4.620 \times 10^{14} H z \)
Which part of the electromagnetic spectrum does it belong to?
A. UV
B. IR
c. Far IR
D. Visible


In case of torque of a couple, if the axis is changed by displacing it parallel to itself, torque will
A. Increase
B. Decrease
c. Remain constant
D. None of these


If the density of a certain gas at \( 30^{\circ} \mathrm{C} \)
and 768 torr is \( 1.35 k g / m^{3}, \) the density at STP would be:
A. \( 1.48 \mathrm{kg} / \mathrm{m}^{3} \)
в. 1.58 kg \( / m^{3} \)
c. \( 1.25 \mathrm{kg} / \mathrm{m}^{3} \)
D. \( 1.4 \mathrm{kg} / \mathrm{m}^{3} \)


The compound (A) reacts with sulphur to form a compound in which hybridization state of sulphur atom
is
\( A \cdot s p^{3} d \)
B. \( s p^{3} d^{2} \)
\( c \cdot s p^{3} \)
D. \( s p^{3} d^{3} \)


Assertion
Electron revolves around a positively charged nucleus like a planet revolves around the sun.
Reason
The force acting in both the cases is of
same kind.
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


Charges of \( +\frac{10}{3} \times 10^{-9} C \) are placed at each of the four corners of a square of
side \( 8 \mathrm{cm} . \) The potential at the intersection of the diagonals is
A. \( 150 \sqrt{2} \) volt
в. \( 1500 \sqrt{2} \) volt
c. \( 900 \sqrt{2} \) volt
D. 900 volt


Two identical resistors each of
resistance \( 10 \Omega \) are connected in turn
\( (i) \)
in series and (ii)in parallel to a battery of \( 6 V . \) Calculate the ratio of power
consumed in series and parallel combination:


Two bodies, \( A \) and \( B \) initially, at rest, move towards each other under mutual force of attraction. At the instant when
the speed of \( A \) is \( v \) and that of \( B \) is \( 2 v \)
the speed of the center of mass of the
bodies is
A . \( 3 v \)
B . \( 2 v \)
c. \( 1.5 v \)
D. zero


Match the following books in column \( \mathbf{A} \)
with their authors in column B.
Column A

Column B
(A) Genera Plantarum
(1) Aristotle (3 volumes)
(B) Species Plantarum
(2) Linnaeus
(C) Historia Generalis
(3) Bentham and Plantarum Hooker
(D) Scala Naturae
(4) Plato
(5) John Ray
\( A \cdot A-4, B-2, C-5, D-3 \)
B. A- 4, B- 2, C-1, D-3
c. \( A-4, B-2, C-3, D-1 \)
D. \( A-3, B-2, C-5, D-1 \)


Which of the following is a metallic element?
A. Nitrogen
B. Sodium
c. oxygen
D. Helium


Write the \( I U P A C \) names of the
following ketones and aldehydes. Wherever possible, give also common
names.
A \( \cdot C H_{3} C O\left(C H_{2}\right)_{4} C H_{3} \)
в. \( C H_{3} C H_{2} C H B r C H_{2} C H\left(C H_{3}\right) C H O \)
c. \( C H_{3}\left(C H_{2}\right)_{5} C H O \)
D. \( P h-C H=C H-C H O \)


The element X reacting with chlorine forms a water soluble compound having high melting point. Element \( X \) is:
A. Magnesium
B. Argon
c. carbon
D. Neon


The coils made of the same material in
two moving coil galvanometers have
their areas in the ratio of 2: 3 and the
number of turns in the ratio of 4: 5
These two coils carry the same current and are situated in the same field. The
deflections produced by these two coils will be in the ratio of:
\( \mathbf{A} \cdot 8: 15 \)
B. 15: 8
c. 8: 1
D. 1: 4


Consider the following statements A and B given below and identity the
correct answer.
A) With the help of the relative velocity of rain with respect to man, the direction of the umbrella held by him to save from the rain is determined.
B) A parallelogram has sides represented by vectors \( \vec{a} \) and \( \overrightarrow{\mathrm{b}} \). If \( \overrightarrow{\mathrm{d}}_{1} \) and
\( \overrightarrow{\mathrm{d}}_{2} \) are the
diagonal vectors of the parallelogram then \( 2\left(\mathrm{a}^{2}+\mathrm{b}^{2}\right)=\mathrm{d}_{1}^{2}+\mathrm{d}_{2}^{2} \)
A. Both A and B are true
B. A is true but B is false
c. \( B \) is true but \( A \) is false
D. Both A and B are false


Identify the mirrors
a)
\( \mathbf{b}) \)
A. \( a= \) Convex mirror \( b= \) Concave mirror
B. \( a= \) Concave mirror \( b= \) Convex mirror
C \( . a= \) Concave mirror \( b= \) Concave mirror
D. \( a= \) Convex mirror \( b= \) Convex mirror


The attached circuit diagram shows
connection of 3 resistors. All are
connected in parallel. Thus what is the equivalent resistance.
A. 1 ohm
B. 4 ohm
c. 3ohm
D. 2 ohm


Two cells when connected in series are
balanced on \( 8 m \) on a potentiometer. If
the cells are connected with polarities of one of the cell is reversed, then they
balance on 2 m. The ratio of emf's of two
cells is
A .3: 4
B. 4: 3
\( c .3: 5 \)
D. 5: 3


Find out the correct combinations
concerning components of photosynthetic electron transport, location in relation to thylakoid and action.
I. OEC - lumen side - water reduction.
II. Plastocyanin - lumen side - electron transfer from cyt f to PSI
III. Ferrodoxin - stroma side - reduction
of \( N A D^{+} \) to \( N A D H \)
IV. Cytochrome complex - integral
protein - transfer electrons from \( \boldsymbol{P} \boldsymbol{Q} \boldsymbol{H}_{2} \)
to PC.
Choose the correct answer.
A. Il and IV
B. I and III
c. Il and III
D. I and IV


Which of the following is universal magnetic property.?
A. Ferromagnetism
B. Diamagnetism
c. Paramagnetism
D. Anti-ferromagnetism.


Gastric glands, crypts of Liberkuhn, goblet cells are formed by
A. Mucosa
B. Epithelial lining of Mucosa
c. Sub-mucosa
D. Serosa


The plot of \( \sqrt{\boldsymbol{v}} \) vs \( \mathbf{Z}, \) where \( \boldsymbol{v} \) is frequency and \( z \) is atomic number, is :
A. a straight line
B. an exponential curve
c. a hyperbolic
D. a curve with - ve slope


Why are the ionization energies of \( 5 d \) elements greater than 3 d elements?


A force \( \overrightarrow{\boldsymbol{F}}=2 \hat{\boldsymbol{i}}-\boldsymbol{3} \hat{\boldsymbol{k}} \) acts on a particle
at \( \vec{r}=0.5 \hat{j}-2 \hat{k} . \) The torque \( \vec{\Gamma} \) acting
on the particle relative to a point with co-ordinates \( (2.0 \mathrm{m}, 0 ;-3.0 \mathrm{m}) \) is?


A coin flicked across a table will stop,
because:
A. It is heavy
B. No force is acting on it
c. Earth attracts the coin
D. Table exerts a frictional force


The relation between \( B_{v}, B_{h} \) and B is
\( \mathbf{A} \cdot B=\sqrt{B_{h}^{2}+B_{v}^{2}} \)
B . \( B=B_{h} \cdot B_{v} \)
c. \( _{B}=\frac{B_{v}}{B_{h}} \)
D. \( B=\frac{B_{h}}{B_{v}} \)


How fast is the farther end of the
shadow moving on the pavement?
A. \( 2 k m / h r \)
в. \( 4 k m / h r \)
\( \mathrm{c} .6 \mathrm{km} / \mathrm{hr} \)
D. \( 8 k m / h r \)


If you are travelling by car during thunderstorm which place is safe?
A. Under a tree
B. Near street light
C. Elevated places
D. None of the above


Re write each of the following
statements in the form "p if and only if
\( q^{\prime \prime} \)
(i) \( p: \) If you watch television then your mind is free and if your mind is free then you watch television
(ii) \( q: \) For you to get an A grade it is necessary and sufficient that you do all the homework regularly
(iii) \( r: \) If a quadrilateral is equiangular then it is a rectangle and if a quadrilateral is a rectangle then it is equiangular


find the value of \( x \) in each of the
following figures.
(a)


Which of the following is incorrect?
A. Among \( C l, A r \) and \( K, K \) has the smallest ionization potential.
B. Among \( C H_{4}, N H_{3} \), and \( H F, H F \) has the highest boiling point
C. Among \( C l_{2}, B r_{2}, \) and \( l_{2}, B r_{2} \) has the lowest boiling point.
D. None of the above.


Separation of chromosome with associated chromatid at centromere
occurs in?
A. Anaphase
B. Anaphase
c. Anaphase II
D. Anaphase and Anaphase


If \( \boldsymbol{y}=(\boldsymbol{A}+\boldsymbol{B} \boldsymbol{x}) e^{m \boldsymbol{x}}+(\boldsymbol{m}-\mathbf{1})^{-2} \boldsymbol{e}^{\boldsymbol{x}} \)
\( \operatorname{then} \frac{\boldsymbol{d}^{2} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}^{2}}-2 \boldsymbol{m} \frac{\boldsymbol{d} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}}+\boldsymbol{m}^{2} \boldsymbol{y} \) is equal to:
A \( \cdot e^{x} \)
B. \( e^{m} \)
\( \mathbf{c} \cdot e^{-m x} \)
D. \( e^{(1-m) x} \)


Which of the following hydrocarbon acids will be a constituent of the
highest melting point?
\( A \)
B.
\( c \)
\( D \)


What is the greatest integer value of \( x \) for which \( 2 x-20<0 ? \)
\( A \cdot 8 \)
B.
c. 10
D. 1


Polycyclic stele is seen in
A. Riccia
B. Matonia
c. Funaria
D. Pinus


A body, projected vertically upwards, crosses a point twice its journey at a
height \( h \) just after \( t_{1} \) and \( t_{2} \) seconds. Maximum height reached by the body is
\( \mathbf{A} \cdot \frac{g}{4}\left(t_{1}+t_{2}\right)^{2} \)
\( ^{\mathrm{B}} \cdot\left[\frac{t_{1}+t_{2}}{4}\right]^{2} \)
\( ^{\mathrm{c}} \cdot_{2 g}\left[\frac{t_{1}+t_{2}}{4}\right]^{2} \)
D. \( \frac{g}{4}\left(t_{1} t_{2}\right) \)


A metal wire of diameter \( 4 \mathrm{mm} \) and
length \( 100 \mathrm{m} \) has a resistance of
\( \mathbf{0 . 4 0 8} \mathbf{\Omega} \) at \( \mathbf{1 0}^{\circ} \mathbf{C} \) and \( \mathbf{0 . 5 0 8} \mathbf{\Omega} \) at \( \mathbf{1 2 0}^{\circ} \boldsymbol{C} \)
Find the value of
a. temperature coefficient of resistance
b. its resistance at \( 0^{\circ} \mathrm{C} \)
c. its resistivities at \( 0^{\circ} \mathrm{C} \) and \( 120^{\circ} \mathrm{C} \)


A ceiling fan is rotating about its own
axis with uniform angular velocity \( \omega \) The electric current is switched off then
due to constant opposing torque its angular velocity is reduced to \( \frac{2 \omega}{3} \) as
it completes 30 rotations. The number of rotations further it makes before
coming to rest is :
A . 18
B. 12
\( c .9 \)
D. 24


Prove that \( \cos 40^{\circ}+\cos 50^{\circ}+ \)
\( \cos 70^{\circ}+\cos 80^{\circ}=\cos 20^{\circ}+\cos 10^{\circ} \)


Which term is used for pollutants which degrade naturally?


An examination consists of 8 questions in each of which the candidate must
say which one of the 5 alternatives is
correct one. Assuming that the student has not prepared earlier choose for each
of the question any one of 5 answer with equal probability.
(i) Prove that the probability that he gets more than one correct answer is
\( \left(5^{8}-3 \times 4^{8}\right) / 5^{8} \)
(ii) Find the probability that he gets
correct answer to \( x \) or more questions.
(iii) Find the standard deviation of this
distribution.


Latent heat depends on the mass of the substances.
A . True
B. False


Equivalent weight of \( S O_{2} \) is found to be 32 in a reaction taking place in acidic medium. This reaction is represented
as \( \boldsymbol{S O}_{2}+\mathbf{2 H}_{2} \boldsymbol{O} \rightarrow \boldsymbol{S} \boldsymbol{O}_{4}^{2-}+\boldsymbol{4} \boldsymbol{H}^{+}+ \)
\( \mathbf{2} e^{-} \)
State whether the given reaction take place in backward direction or forward
direction?


A hospital uses an ultrasonic scanner
to locate tumours in a tissue. What is
the wavelength of sound in the tissue in
which the speed of sound is \( 1.7 \mathrm{km} \mathrm{s}^{-1} \) ?
The operating frequency of the scanner
is 4.2 MHz.


Compound A contains 20\% C, 46.66\% N and
\( 6.66 \% \) H. It gave \( N H_{3} \) on heating with
NaOH.
A can be :
A. \( C H_{3} C O N H_{2} \)
в. \( N H_{2} C O N H_{2} \)
c. \( C_{6} H_{5} \) СОМН\( _{2} \)
D. \( C H_{3} N H C O N H_{2} \)


When a ceiling fan is switched off, its angular velocity reduces by \( 50 \% \) while it makes 36 rotations. How many more
rotations will it make before coming to rest? (Assume uniforms angular retardation)
A . 48
B . 36
c. 12
D. 18


As a result of pyrolysis, which one of the following is produced
A. Alcohol
B. Charcoal
c. charcoal and gas
D. Charcoal, gas and oil


A steady current of magnitude \( I \) and an
\( A C \) current of peak value \( I \) are allowed to pass through identical resistor for
the same time. The ratio of heat
produced in the two resistors will be :
A .2: 1
B. 1: 2
c. 1: 1
D. None of these


Solve the following simultaneous equations using graphical method \( \boldsymbol{x}+\boldsymbol{y}=\boldsymbol{6} \)
\( \boldsymbol{x}-\boldsymbol{y}=\mathbf{2} \)


The rate of a certain reaction at different times are as follows:
\( \begin{array}{ll}\text { Time } & \text { rate }\left(\text { mole } l i t^{-1} \sec ^{-1}\right) \\ \text {1) } 0 & \text { a) } 2.8 \times 10^{-2}\end{array} \) ") 10 \( \quad \) b) \( 2.78 \times 10^{-2} \) -2 A
\( \begin{array}{ll}\text { III) } 20 & \text { с) } 2.81 \times 10^{-2}\end{array} \) -2
\( \begin{array}{ll}\text { ।V) } 30 & \text { d) } 2.79 \times 10^{-2}\end{array} \) \( j \) \( ^{2} \)
The correct matching is:
A. zero order
B. first order
c. second order
D. third order


Under same depth, atmospheric
pressure is water
pressure.
A. less than
B. greater than
C. equal to
D. none of these


Assertion
Speed of a particle moving in a circle varies with time as, \( \boldsymbol{v}=(\mathbf{4} \boldsymbol{t}-\mathbf{1 2}) . \) Such
type of circular motion is not possible.
Reason

Speed cannot change linearly with time.
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 is incorrect and Reason is correct


Evaluate the following definite integral:
\( \int_{0}^{1} \frac{2 x+3}{5 x^{2}+1} d x \)


Sea water contains \( -\ldots-\ldots- \) oxygen
which is utilized by animals and plants for respiration.


Coefficient of linear expansion of a crystal in 3 mutually perpendicular directions are \( 8.5 \times 10^{-6} /^{o} C, 10.5 \times \)
\( 10^{-6} /^{o} C, 11 \times 10^{-6} /^{o} C . \) If mass of
crystal is \( 25 g m, \) its volume at \( 60^{\circ} C \) is (given density at \( 0^{\circ} C \) is 5 gm \( / c c \) ):
A. 5.009 cc
B. 4.991 cc
c. \( 5.9 \mathrm{cc} \)
D. 5.999 cc


A block of mass \( 5 ~ K g \) is at rest on a smooth horizontal surface. Water
coming out of a pipe horizontally at the
rate of \( 2 K g s^{-1}, \) hits the block with a
velocity of \( 6 m s^{-1} \). The initial
acceleration of the block is:
A. zero
В. \( 1.2 \mathrm{ms}^{-2} \)
c. \( 2.4 \mathrm{ms}^{-2} \)
D. \( 0.6 m s^{-2} \)


Under what condition an elliptical orbit corresponds to circular orbit?
\( A \cdot n>k \)
B . \( n=k \)
\( c \cdot n<k \)
D \( . n \geq k \)


\( \frac{\sin 2 x}{2 \cos x}=\tan x ? \)
A. True
B. False


A temporary magnet is made of
A. cast iron
B. steel
C. soft iron
D. stainless steel


A social forest tree is
A. Teak
B. Sandal wood
c. Subabul
D. Rosewood


The number of \( \pi \) -bonds in the structure
of aspirin are:
\( A \)
\( B \)
\( c \)
D


Which one of the following hormones is not involved in sugar metabolism?
A. Glucagon
B. Cortisone
c. Aldosterone
D. Insulin


A baseball player can throw a ball to a
maximum distance of 60 \( m . \) He can
throw it vertically to a maximum height
of
A . \( 10 m \)
в. \( 30 m \)
\( c .60 m \)
D. \( 100 m \)


A charged particle is released from rest in a region of steady and uniform electric and magnetic field which are parallel to each other. The nature of light
A . circle
B. Parabola
c. Straight line
D. Helix


Pyruvic acid \( \frac{\text { Pyruvate }}{\text {dehydrogenase}} \) Acetyl CoA\( + \)
\( \boldsymbol{C O}_{2}+\boldsymbol{N a D H}_{2} \)
In this given reaction which of the following coenzyme is not used?
A. \( M g^{+}+ \)
B. \( N A D \)
c. \( C o-A \)
D. \( T P P \)


Draw a Histogram for the following data
\( \begin{array}{ll}\text { Class Interval } & \text { Frequency } \\ 0-10 & 35 \\ 10-20 & 70 \\ 20-30 & 20 \\ 30-40 & 40 \\ 40-50 & 50\end{array} \)


The conversion of ozone into oxygen is
exothermic. Under what conditions is
ozone the most stable?
\( \mathbf{2} \boldsymbol{O}_{3}(\boldsymbol{g}) \rightleftharpoons \mathbf{3} \boldsymbol{O}_{2}(\boldsymbol{g}) \)
A. At low pressure and low temperature
B. At high pressure and high temperature
C. At high pressure and low temperature
D. At low pressure and high temperature


Brinjal, tobacco, potato and tomato are
same as
A. All these plants belong to Solanaceae.
B. All these plants belong to Malvaceae
c. All are vegetables.
D. Fruit of all has economic importance


By eliminating the arbitrary constants A and \( \mathrm{B} \) from \( \boldsymbol{y}=\boldsymbol{A} \boldsymbol{x}^{2}+\boldsymbol{B} \boldsymbol{x}, \) we get the
differential equation:
A \( \cdot \frac{d^{3} y}{d x^{3}}=0 \)
B. \( x^{2} \frac{d^{2} y}{d x^{2}}-2 x \frac{d y}{d x}+2 y=0 \)
c. \( \frac{d^{2} y}{d x^{2}}=0 \)
D. \( x^{2} \frac{d^{2} y}{d x^{2}}+y=0 \)


PQRS is the diameter of a circle of
radius 3 cm. The lengths PQ, QR and RS
are equal. Find the area of the shaded
portion
\( \mathbf{A} \cdot 2 \pi c m^{2} \)
в. \( \frac{5 \pi}{2} \mathrm{cm}^{2} \)
c. \( \frac{9 \pi}{2} c m^{2} \)
D. \( \frac{11 \pi}{2} c m^{2} \)


After a sperm has penetrated an ovum in the process of fertilisation, entry of further sperms is prevented by
A. Development ofthe pigment coat
B. Development of the vitelline membrane
c. condensation of yolk
D. Formation of fertilisation membrane


Find the multiplicative inverse of 3 and
-7


A ray of light falls on a prism
\( A B C(A B=B C) \) and travels as shown
in the figure. The refractive index of the
material of prism should be at least:
4
\( 3 \cdot \sqrt{2} \)
\( c \)
\( D \cdot \sqrt{3} \)


Chloroform gives salicylaldehyde on treatment with phenol in the presence of a base. This reaction is called as:
A. Wurtz reaction
B. Reimer - Tiemann reaction
C. Friedel - Craft's reaction
D. Cannizaro's reaction


The heat of carbon combustion with the
\( C O_{2} \) formation, is \( -393.5 K J / m o l \)
and the heat of \( C O \) combustion with
the formation of \( C O_{2}, \) is \( -283 K J / \) mol calculate the heat of combustion of
carbon there in \( C O \)


Teflon, a polymer of tetrafluoroethylene, is an excellent plastic material for films and coatings. Which of the following is
not the property of Teflon?
A. It is unaltered by radiation
B. It can withstand high temperatures
c. It is one of the most chemically-resistant plastic in the world
D. It is an ideal insulator for high-frequency fittings


Identify the salts which on heating produce mixture of gases. This question has multiple correct options
A. \( N a N O_{3} \)
В \( \cdot \operatorname{Pb}\left(\mathrm{NO}_{3}\right)_{2} \)
c. \( c u\left(N O_{3}\right)_{2} \)
D. \( K N O_{3} \)


The dimensions of a rectangular box are in the ratio 1: 2: 4 and the difference
between the costs of covering it with the cloth and sheet at the rate of \( R s .20 \) and
Rs.20.50 per square metre, respectively
is \( R s .126 . \) Find the dimensions of the
box
A. \( 4 c m, 7 c m \) and \( 10 c m \)
B. \( 2 c m, 4 c m \) and \( 11 c m \)
c. \( 3 c m, 6 c m \) and \( 12 c m \)
D. \( 7 c m, 8 c m \) and \( 13 c m \)


Evaluate \( \lim _{x \rightarrow 0} \frac{\sin x}{x} \)


When water is boiled to \( 100^{\circ} \mathrm{C} \), it converts
into steam which on condensation gives back water. Here, the heat given out is
called latent heat of condensation which
is equal to the latent heat of vapourisation.
A. True
B. False


Explain the trends in the following propertie, with reference to group - 16?
(a) Ionisation enthalpy.


Air is pumped into an automobile Tyre's tube up to a pressure of 200 kPa in the morning when the air temperature is
\( 20^{\circ} . \) During the day the temperature
rises to \( 40^{\circ} \) and the tube expands by \( 2 \% \)
Calculate the pressure of the air in the tube at this temperature


The sum of all the quantum numbers of helium atom is :


Differentiate the following w.r.t. \( x \)
\( \left(3 x^{2}+2\right)\left(4 x-3 x^{3}\right) \)
\( \mathbf{A} \cdot 45 x^{4}+18 x^{2}+8 \)
B. \( -45 x^{4}+18 x^{2}+8 \)
c. \( -45 x^{4}+15 x^{2}+8 \)
D. \( -45 x^{4}+18 x^{2}+18 \)


The given compound is used as:
A. antihistamine
B. analgesic
C . insecticide
D. antacid


Using elementary operations, find the inverse of the following matrix:
\( \left(\begin{array}{ccc}-1 & 1 & 2 \\ 1 & 2 & 3 \\ 3 & 1 & 1\end{array}\right) \)


A steel tape is calibrated at \( 20^{\circ} \mathrm{C} \). It is used to measure a length of an object on a hot summer day when the
temperature is \( 40^{\circ} \mathrm{C} \). If measured length is \( 5 \mathrm{m} \), the actual
length is \( \left(a=1 \times 10^{-5} /^{\circ} \mathrm{C}\right) \)
A. \( 5.001 \mathrm{m} \)
B. 5.01 \( m \)
\( c .5 .1 \mathrm{m} \)
D. 4.99 \( m \)


the pulse in the figure shown has a speed of \( 0.1 m s^{-1} . \) the linear mass
density of the right string is 0.25 that of the left string. At what speed does the transmitted wave travel?
A \( .25 \mathrm{cms}^{-1} \)
B. 20cms-
\( \mathrm{c} \cdot 15 \mathrm{cms}^{-1} \)
D. \( 17.5 \mathrm{cms}^{-1} \)


Waldsterben is an effect of
A. Ozone
B. Nitrogen oxide and sulphur oxide
c. Acid rain
D. All of the above


\( \boldsymbol{C}_{6} \boldsymbol{H}_{5} \boldsymbol{C} \boldsymbol{H}_{3}-\frac{C r \boldsymbol{O}_{2} C l_{2}}{\longrightarrow} \boldsymbol{Z} \)
In the given sequence, \( Z \) is:
A. Benzaldehyde
B. Toluic acid
c. Phenul acetic acid
D. Benzoic acid


Select the answer with correct
matching of the structure, its location
and function.
A. Structure - Eustachian tube, Location - Anterior part of internal ear, Function - Equalises air pressure on either sides of tympanic membrane
B. Structure - Cerebellum, Location - Midbrain, Function Controls respiration and gastric secretions
C. Structure - Hypothalamus, Location - Forebrain, Function - Controls body temperature, urge for eating and drinking
D. Structure - Blind spot, Location - Near the place where optic nerve leaves the eye, Function - Rods and cones are present but inactive here.


Deduce the condition for the vectors \( 2 \hat{i}+3 \hat{j}-4 \hat{k} \) and \( 3 \hat{i}-a \hat{j}+b \hat{k} \) to be
parallel Find the value of \( a \) and \( b ? \)


Find the coefficient of \( \frac{1}{y^{2}} \) in \( \left(y+\frac{c}{y^{2}}\right)^{10} \)
A \( \cdot 210 c^{4} \)
B . \( 210 c^{5} \)
\( \mathbf{c} \cdot 120 c^{3} \)
D. \( 120 c^{4} \)


When \( 25 \mathrm{mL} \) of \( 0.1 M A g N O_{3} \) is mixed
with \( 50.0 \mathrm{mL} \) of \( 0.08 M N a_{2} C O_{3} \)
solution, then the molar concentration
of \( N a_{2} C O_{3} \) in the solution is \( x \times \)
\( \mathbf{1 0}^{-\mathbf{2}} \boldsymbol{M} . \) Here \( \boldsymbol{x} \) is:


A car is travelling along a circular curve that has a radius of \( 50 \mathrm{m} \). If its speed is
\( 16 \mathrm{m} / \mathrm{s} \) and is incrcasing uniformly at \( 8 m / s^{2} . \) Determine the magnitude of its acceleration at this instant.
A \( \cdot 7.5 m s^{-2} \)
B. \( 8.5 m s^{-2} \)
c. \( 9.5 m s^{-2} \)
D. \( 9.8 m s^{-2} \)


A cricket 11 is to be chosen from 16
players of whom 7 are bowlers, 4 can do the wicketkeeping. Number of ways this can be done to contain exactly 5 bowlers, 2 wicket keepers is
A . 945
в. 885
c. 630
D. 715


"Dolipore septum" is the characteristic
of
A. Myxomycetes
B. Phycomycetes
c. Deuteromycetes
D. Basidiomycetes


The minimum velocity (in \( \mathrm{m} / \mathrm{s} \) ) with which a car driver must traverse a flat
curve of radius \( 150 \mathrm{m} \) and coefficient of
friction 0.6 to avoid skidding is:
A. \( 60 \mathrm{m} / \mathrm{s} \)
B. 30 \( \mathrm{m} / \mathrm{s} \)
\( c \cdot 15 m / s \)
D. 25 \( \mathrm{m} / \mathrm{s} \)


n the figure if \( B D \| E F \), then \( \angle C E F \) is
A \( \cdot 100^{\circ} \)
В. 120
\( c \cdot 140^{\circ} \)
\( 0.160^{\circ} \)


cost of 10 mangoes is Rs. 100 The cost of
18 mangoes is
A . Rs. 18
B. Rs. 108
c. Rs. 200
D. Rs. 180


If \( f(x)=x^{3}-\frac{1}{x^{3}}, \) prove that \( f(x)+ \)
\( \boldsymbol{f}\left(\frac{1}{x}\right)=\mathbf{0} \)


A wire is lying parallel to a square coil. Same current is flowing in same direction in both of them. The magnetic induction at any point P inside the coil
will be :
A . zero
B. more than that produced by only coil
c. less than that produced by only coil
D. equal to that produced by only coil


\( \int \frac{x}{x^{4}+x^{2}+1} d x, \) Integration gives
\( \frac{1}{\sqrt{(k)}} \tan ^{-1} \frac{2 x^{2}+1}{\sqrt{(k)}} \) find \( k^{2} \)


Assertion
In photoelectron emission the velocity of electron ejected from near the surface is larger than that coming from interior of metal.
Reason
The velocity of ejected electron will be
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. If Assertion is incorrect but Reason is correct


If the variable takes values
\( \mathbf{0}, \mathbf{1}, \mathbf{2}, \mathbf{3}, \cdots, \boldsymbol{n} \) with frequencies
proportional to \( ^{n} c_{0},^{n} c_{1},^{n} c_{2}, \cdots,^{n} c_{n} \)
respectively, the variance is
A \( \cdot \frac{n}{4} \)
в. \( \frac{n}{3} \)
\( c \cdot \frac{2 n}{5} \)
D. none of these


The concept of temperature is related to
A. zeroeth law of thermodynamics
B. first law of thermodynamics
C. second law of thermodynamics
D. third law of thermodynamics


A coil carrying electric current is placed in uniform magnetic field, then :
A. Torque is formed
B. emf is induced
c. Both (a) and (b) are correct
D. None of the above


At high concentration of soap in water, soap behaves as:
A. molecular colloid
B. associated colloid
c. macromolecular colloid
D. Iyophilic colloid


When a beam of white light is passed through sodium vapours and then through a spectrometer, spectrum so obtained has two dark lines present in
the yellow region. This spectrum is called
A. band spectrum
B. continuous spectrum
c. absorption spectrum of sodium
D. emission spectrum of sodium


Solve: \( 2(\sin x-\cos 2 x)-\sin 2 x(1+ \)
\( 2 \sin x)+2 \cos x=0 \)


Show that if \( \boldsymbol{f}: \boldsymbol{A} \rightarrow \boldsymbol{B} \) and \( \boldsymbol{g}: \boldsymbol{B} \rightarrow \boldsymbol{C} \)
are onto, then \( g o f: A \rightarrow C \) is also onto.


A rocky barren land after some time
changes into fertile rich, crop yielding land. Which sequence might have
occured?
A. Lichens, mosses, shrubs, herbs
B. Lichens, mosses, herbs, shrubs
C. Mosses, herbs, shrubs, lichens
D. Herbs, shrubs, lichens, mosses


Which element exhibits highest density
in 3d series?
A . Sc
B. cr
\( c \cdot z n \)
D. cu


A light pointer fixed to one prong of a tuning fork touched a vertical plate. The fork is set vibrating and plate is allowed
to fall freely. 8 complete oscillations are counted when the plate falls through 10cm. What is the frequency of the
tuning fork?
A. \( 40 \sqrt{2} \)
в. \( 40 \sqrt{3} \)
c. \( 20 \sqrt{2} \)
D. \( 70 \sqrt{2} \)


A boy has a collection of blue and green marbles. The number of blue marbles
belong to the sets \( 2,3,4,13 . \) If two marbles are chosen simultaneously and at random from his collection, then the
probability that they have different colour is \( 1 / 2 . \) Possible number of blue marbles is:
A . 2
B. 3
\( c \cdot 6 \)
D. 10


Which word equation represents \( \boldsymbol{\beta}^{+} \)
decay?
A. Proton \( \rightarrow \) neutron \( + \) electron \( + \) electron antineutrino
B. Proton \( \rightarrow \) neutron \( + \) electron \( + \) electron neutrino
c. Proton \( \rightarrow \) neutron \( + \) positron \( + \) electron antineutrino
D. Proton \( \rightarrow \) neutron \( + \) positron \( + \) electron neutrino


The energy released by the Hiroshima bomb was originally thought to be equivalent to the destructive power of approximately
A. 2000 tons of TNT
B. 20000 tons of TNT
c. 200000 tons of TNT
D. 2000000 tons of TNT


A circular coil of 16 turns and radius
10cm carrying a current of \( 0.75 A \) rests
with its plane normal to an external
field of magnitude \( 5.0 \times 10^{2} \) T. The coil
is free to turn about an axis in its plane perpendicular to the field direction.
When the coil is turned slightly and released, it oscillates about its stable
equilibrium with a frequency of \( 2 s^{-1} \)
What is the moment of inertia of the
coil about its axis of rotation.?


A lens of power \( 6 D \) is put in contact
with a lens of power -4 D. The
combination will behave like a:
A. Divergent lens of focal length \( 25 \mathrm{cm} \)
B. Convergent lens of focal length 50 \( c m \)
c. Divergent lens of focal length \( 20 \mathrm{cm} \)
D. Convergent lens of focal length \( 100 \mathrm{cm} \)


Convert the following fraction into simple decimal recurring form. \( \frac{5}{6}=? \)
A . \( 0.4 \overline{3} \)
B. \( 0.1 \overline{3} \)
c. \( 0 . \overline{4} \)
D. 0.83


Write the domain of the real function
\( \boldsymbol{f}(\boldsymbol{x})=\sqrt{\boldsymbol{x}-[\boldsymbol{x}]} \)


The angle of a prism is \( 6^{0} \) and its refractive index for green light is \( 1.5 . \) If a green ray passes through it, the deviation will be :-
A . \( 30^{\circ} \)
В. \( 15^{\circ} \)
\( c \cdot 9^{0} \)
D. \( 3^{\circ} \)


In scattering experiment, find the distance of closest approach, if a \( 6 M e V \alpha- \) particle is used
A \( .3 .2 \times 10^{-16} m \)
В. \( 2 \times 10^{-14} \mathrm{m} \)
c. \( 4.6 \times 10^{-15} \mathrm{m} \)
D. 3.2 \( \times 10^{-15} \mathrm{m} \)


If \( 0.765 g \) of an organic compound on combustion gives \( 0.535 \mathrm{g} C O_{2} \) and \( 0.138 g \) of \( H_{2} O, \) then the ratio of the
percentage of carbon and hydrogen is:
A \( \cdot 19: 2 \)
B. 18: 11
c. 20: 17
D. 1:7


If \( \sin ^{x} \alpha+\cos ^{x} \alpha \geq 1,0<\alpha<\frac{\pi}{2}, \) then
A. \( x \in[2,+\infty) \)
в. \( x \in(-\infty, 2] \)
c. \( x \in[-1,1] \)
D. none of these


From a supply of identical capacitors rated \( 8 m F, 250 V \), the minimum
number of capacitors required to form a composite \( 16 m F, 1000 V \) is :
A . 2
B. 4
c. 16
D. 32


In cyclotron the charged particle may be accelerated upto energies
A. several ev
B. Mev
c. Bev
D. Kev


A person wishes to use a plane mirror on a wall to view both his head and his
feet as he stands in front of the mirror,
the required length of the mirror
A. Is equal to the height of the man
B. Is equal to one half of the height of the man
c. Depends on the distance from the man to the mirror
D. Depends on both the height of the man and the distance from the man to the mirror


Why the lower members of aldehyde and ketone are soluble in water while higher
members are sparingly soluble or insoluble in water?


Assertion
Vectors \( \vec{a}, \vec{b}, \vec{c} \) are coplanar.
Reason
\( (x \vec{a}+y \vec{b})=\overrightarrow{0} \Rightarrow x=0 \) and \( y=0 \)
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


The standard \( E_{r e d}^{o} \) values of \( A, B \) and \( C \) \( \operatorname{are}+\mathbf{0 . 6 8} \boldsymbol{V},-\mathbf{2 . 5 4} \boldsymbol{V},-\mathbf{0 . 5 0} \boldsymbol{V} \)
respectively. The order of their reducing power is:
A. \( A>B>C \)
в. \( A>C>B \)
c. \( C>B>A \)
D. \( B>C>A \)


Which logic gate is represented by the following combination of logic gates?
A. OR
в. NOR
\( c \cdot \) AND
D. NAND


This star is made up of equilateral
triangles: What is the order of rotational
symmetry of the star?
\( A \)
\( B \)
\( c \)
D. 12


Identify the compounds which give
yellow precipitate with \( \boldsymbol{I}_{2}+ \) NaOH
(a) Ethyl alcohol
(b) Acetone
(c) Propyl alcohol
(d) 2-propanol
(e) 3 - butanone
(f) Butanal
\( A \cdot c, e \) and \( f \)
B. a, dand f
c. e, f and a
D. a, b and d


Then the distance from the thrower to
the point where the ball returns to the same level is
\( A \cdot 58 \mathrm{m} \)
B. \( 68 \mathrm{m} \)
\( c \cdot 78 m \)
D. 88 m


Find the angles \( x \) and \( y \) in the adjoining
figure.


\( \operatorname{Let} A=\{1,2,3\} \) and \( R= \)
\{(1,2),(1,1),(2,3)\} be a relation on \( A \)
What minimum number of ordered
pairs may be added to \( R \), so that it may
become a transitive relation on \( A \) ?


Select the incorrect statement(s) about
\( N_{2} F_{4} \) and \( N_{2} H_{4} \)
(i) \( \ln N_{2} F_{4}, \) d-orbitals are contracted by
electronegative fluorine atoms, but dorbital contraction is not possible by H-
\( \operatorname{atoms} \operatorname{in} N_{2} H_{4} \)
(ii) The \( N-N \) bond energy in \( N_{2} F_{4} \) is
more than \( N-N \) bond energy in \( N_{2} H_{4} \)
(iii) The \( N-N \) bond length in \( N_{2} F_{4} \) is
more than that in \( N_{2} H_{4} \)
(iv) The \( N-N \) bond length in \( N_{2} F_{4} \) is
less than that in \( N_{2} H_{4} \)
Choose the correct code.
A. I, II and III
B. I and III
c. Il and IV
D. II and III


Any sample of pure water, irrespective of its source, contains \( 88.89 \% \) oxygen
and \( 11.11 \% \) hydrogen by mass. The data
supports the:
A. Law of conservation of mass
B. Law of constant composition
c. Law of multiple proportion
D. Law of reciprocal proportion


In a Young's double slit experiment, a
slab of thickness \( 1.2 \mu m \) and refractive
index 1.5 is placed in front of one slit
and another slab of thickness t and
refractive index 2.5 is placed in front of
the second slit. If the position of the central fringe remains unaltered, then
the thickness is
A. \( 0.4 \mu m \)
B. \( 0.8 \mu m \)
c. \( 1.2 \mu m \)
D. \( 0.72 \mu m \)


If \( e^{x y}=y+\sin ^{2} x, \) then at \( x=0, d y / d x \)
is equal to


Obtain an expression for the frequency of radiation emitted when a hydrogen
atom de-excites from level n to level \( \left(n_{1}\right. \)
For large \( n \), show that this frequency equals the classical frequency of revolution of the electron in the orbit.


Lignified elongated dead cells
are
A. Parenchyma
B. collenchyma
c. sclerenchyma
D. None of these


Calculate the order of reaction from the
following data:
\[
\begin{array}{l}
\qquad \mathbf{2} N \boldsymbol{H}_{3} \rightarrow \boldsymbol{N}_{2}+\mathbf{3} \boldsymbol{H}_{2} \text { (reaction) } \\
\text { Pressure }(\mathbf{m m} \mathrm{Hg}) \quad \mathbf{5 0} \quad 100 \quad 200 \\
\text { Half lives }(\min ) \quad \text { 3.52 } \quad 1.82 \quad 0.93
\end{array}
\]


Explain the functions of polysaccharides.


If a line makes angles \( \alpha, \beta, \gamma \) with the
coordinate axes, then the value of
\( \cos 2 \alpha+\cos 2 \beta+\cos 2 \gamma \) is
\( A \cdot 3 \)
B. - -
\( c \cdot 2 \)
D. -


Froth floatation process is used for the concentration of sulphide ores. This process is an illustration of the
practical application of:
A. adsorption
B. absorption
c. sedimentation
D. coagulation


In which of the following reaction, one of
the product is a carboxylic acid:
This question has multiple correct options
A \( \cdot C H_{3} C H_{2} C H O+A g\left(N H_{3}\right)_{2}^{+} \rightarrow \)
B.
\( c \)
\( D \)


A hollow dielectric sphere has \( R_{1} \) and
\( R_{2} \) as its inner and outer radii. The total
charge carried by the sphere is \( +\mathrm{Q} \) which is uniformly distributed throughout the dielectric sphere
between \( R_{1} \) and \( R_{2} \). The electric field
for \( R_{1}<r<R_{2} \) is given by :
\( ^{A} \cdot \frac{Q}{4 \pi r \in R_{1}} \)
в. \( \frac{Q}{4 \pi \epsilon r_{2}} \)
c. \( \frac{Q}{4 \pi \in R_{1}^{2}} \)
D. \( \frac{Q\left(r^{3}-R_{1}^{2}\right)}{4 \pi \in r^{2}\left(R_{2}^{3}-R_{1}^{3}\right)} \)


A turn of radius \( 20 \mathrm{m} \) is banked for the vehicle of mass \( 200 \mathrm{kg} \) going at a speed of \( 10 \mathrm{m} / \mathrm{s} \). Find the direction and
magnitude of frictional force acting on a vehicle if it moves with a speed 15 \( \mathrm{m} / \mathrm{s} . \) Assume that friction is sufficient
to prevent slipping. \( \left(\boldsymbol{g}=\mathbf{1 0 m} / \boldsymbol{s}^{2}\right) \)


Describe the construction and working of a potentiometer. Explain, drawing circuit diagram, how emfs of two cells can be compared with its help?


Beryl, cryolite are minerals of:
A. boron
B. aluminium
c. thallium
D. indium


In a cyclic process shown in the figure
an ideal gas is adiabatically taken from
\( A \) to \( B, \) the work done on the gas during
the process \( A \rightarrow B \) is \( 80 J, \) when the
gas is taken from \( B \) to \( A \) the heat
absorbed by the gas is 40 J. What will
be work done by the gas in process
\( \boldsymbol{B} \rightarrow \boldsymbol{A} ? \)


\( \boldsymbol{C l}-\boldsymbol{C H}_{2}-\dot{\boldsymbol{C}}-\boldsymbol{C H}_{2}-\boldsymbol{C H}_{2}- \)
\( \boldsymbol{C H}_{3} \)
\( C l+I^{-} \frac{ }{D M F} \) product
в. \( \quad C l-C H_{2}-\stackrel{C H_{3}}{C}-C H_{2}-C H_{2}-I \)
c. \( \quad \) снз
\[
H_{2} C=C \text { - } C H_{2}-C H_{2}=C l
\]
D. \( \quad C l C H_{2}-C_{I}^{C H_{3}}-C H_{2}=C H_{2} \)


What is the symbol of atomic number
\( 117 ? \)
A. Uus
B. Uns
c. uno
D. uut


Find the order and degree of the differential equations.
a) \( y^{\prime \prime}+3 y^{\prime}^{2}+y^{3}=0 \)
b) \( \left(\frac{d y}{d x}\right)^{2}+\frac{1}{d y d x}=2 \)
c) \( \frac{\boldsymbol{d}^{2} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}^{2}}+\boldsymbol{4} \boldsymbol{y}=\mathbf{0} \)


Which of the following reactant will not
favour nucleophilic substitution
reaction?
\( \mathbf{A} \)
\( \mathbf{B} \cdot P h-B r \)
\( \mathbf{c} \)
D. All of the above


When a die is thrown, list the outcomes
of an event of getting prime number.
A \( \cdot\{2,3,5\} \)
в. \{2,4,6\}
D. \{1,3,5\}


Which alkene on heating with alkaline
\( K M n O_{4} \) solution gives acetone and a
gas, which turns lime water milky:
A. 2-Methyl-2-butene
B. Isobutylene
c. 1-Butene
D. 2-Butene


A solid cylinder of mass \( \mathrm{m} \) is attached
to a horizontal spring with force constant k. The cylinder can roll without slipping along the horizontal plane. (See the accompanying figure.) Show that the center of mass of the cylinder executes simple harmonic motion with a period \( \boldsymbol{T}=\boldsymbol{2} \boldsymbol{\pi} \sqrt{\frac{\boldsymbol{3} \boldsymbol{m}}{\boldsymbol{2} \boldsymbol{k}}}, \) if displaced
from mean position.


0
0
0


The given diagram represents
A. An onto function
B. A constant function
c. An one-one function
D. Not a function


Write the chemical formula of 2 -chloro-
2-methylpropane.


The \( x \) -coordinate of a point on the line joining the points \( P(2,2,1) \) and \( Q(5,1,-2) \) is \( 4 . \) Find its z-coordinate.
A . -1
B. -2
\( c .1 \)
D.


Prove that the matrix \( B^{\prime} A B \) is
symmetric or skew symmetric
according as \( A \) is symmetric or skew symmetric.


Which of these forms wrist joint along with styloid process of radioulna?
A. Trapezium, trapezoid, capitate and hamate
B. Scaphoid, lunate, triquetral and pisiform
c. Talus, cuboid, cuneiform and calcaneous
D. Both A and B


In the degenerate orbitals, unpaired electrons have same spin.
A. True
B. False


Magnesium powder burns in air to give:
A. \( M g O \) only
в. \( M g O \) and \( M g\left(N O_{3}\right)_{2} \)
c. \( M g O \) and \( M g_{3} N_{2} \)
D. \( M g\left(N O_{3}\right)_{2} \) and \( M g_{3} N_{2} \)


The oxidation number of \( C r \) in \( C r O_{5} \)
which has the following structure is:
\( A \cdot+4 \)
B. +5
\( c \cdot+6 \)
\( D \)


What is the correct term for the phase
change from solid directly to gas?
A. Deposition
B. Sublimation
c. Liquefaction
D. Fusion


If the concentration of the reactants in
the reaction \( 2 A+B \rightarrow C+D \) is
increased by three folds, the rate of the reaction will be increased by:
A. 27 times
B. 9 times
c. 64 times
D. 01 times


Which of the following is not properly matched?
A. Formaldehyde - Carcinogenic
B. Sulphur dioxide - Respiratory problems
c. Nitrogen oxide - Brown air
D. Photochemical smog - Green air


How much \( N H_{3} \) should be added to
a \( 0.004 \mathrm{M} A g^{+} \) solution to prevent
the precipitation of AgCl when \( C l^{-} \) ion
reaches \( 0.001 ? K_{s p} A g C l=1.8 \times \)
\( \mathbf{1 0}^{-\mathbf{1 0}}, \boldsymbol{K}_{\boldsymbol{d}} \boldsymbol{A} \boldsymbol{g}\left(\boldsymbol{N} \boldsymbol{H}_{3}\right)_{2}^{+}=\mathbf{6} \times \mathbf{1 0}^{-\boldsymbol{8}} \)
A. 0.0011 molar
B. 0.36 molar
c. 0.0036 molar
D. 1.6 molar


Two particles move parallel to \( x- \) axis
about the origin with same amplitude
\( a^{\prime} \) and frequency \( \omega . \) At a certain instant they are found at a distance \( a / 3 \) from
the origin on opposite sides but their velocities are in the same direction.
What is the phase difference between the two?
A \( \cdot \cos ^{-1} \frac{7}{9} \)
B. \( \cos ^{-1} \frac{5}{9} \)
\( ^{\mathbf{C}} \cdot \cos ^{-1} \frac{4}{9} \)
D. \( \cos ^{-1} \frac{1}{9} \)