Calculate the heat of combustion (kJ) of
propane, \( C_{3} H_{8} \) using the listed standard enthalpy of reaction data:
\[
\begin{array}{c}
C_{3} H_{8}(g)+\mathbf{5} O_{2}(g) \longrightarrow \\
\mathbf{3} C O_{2}(g)+4 H_{2} O(g) \\
\mathbf{3} C(s)+4 H_{2}(g) \longrightarrow \\
C_{3} H_{8}(g) \Delta H / k J=-103.8 \\
C(s)+O_{2}(g) \longrightarrow C O_{2}(g) \Delta H / k J= \\
-393.5 \\
H_{2}(g)+1 / 2 O_{2}(g) \longrightarrow \\
H_{2} O(g) \Delta H / k J=-241.8
\end{array}
\]
A . - 2043.9
B. -1532.9
c. -1021.9
D. -739.


If the mode of a distribution is 18 and
the mean is 24 , then median is
A . 18
B. 24
c. 22
D. 21


A convex mirror has a length of \( 20 \mathrm{cm} \)
find the position or position of an object for which the image size is double the object size.


The total energy of an electron in the first excited state of hydrogen is about \( -3.4 e V . \) Its KE in this state is
A \( .3 .4 e V \)
B. \( 6.8 e V \)
c. \( -3.4 e V \)
D. - \( 6.8 e V \)


Let \( \lim _{x \rightarrow a} f(x) \) exists but it is not equal to
\( f(a) . \) Then \( f(x) \) is discontinuous at \( x=a \)
and a is called a removable
discontinuity. If \( \lim _{x \rightarrow a^{-}} f(x)= \)
land \( \lim _{x \rightarrow a^{+}} f(x)=m \) exist but \( l \neq \)
\( m . \) Then a is called a jump
discontinuity. If one of the limits (left
hand limit or right hand limit ) does not
exist, then a is called an infinite
discontinuity. \( \operatorname{Let} f(x)=\left\{\begin{array}{cl}x^{2}+|x|, & x<-5 \\ 25 & x=-5 \\ \frac{3 x^{2}}{5}+15 & x>-5\end{array} . \) Then \right.
\( \boldsymbol{x}=-\mathbf{5} \) is
A. a point of discontinuity
B. a jump discontinuity
c. a removable discontinuity
D. an infinite discontinuity


Which reaction of ammonia forms the
first step of Ostwald's process?
A. The catalytic oxidation of ammonia by platinumm catalyst
B. The catalytic oxidation of ammonia by cobalt catalyst
catalyst
D. The oxidation of ammonia


Four identical planks each of length a are arranged one above the other over a
table as shown. Each projects a
distance beyond the edge of the one
that is below it. The maximum value for
L so that no block topple is
A \( \cdot \frac{a}{2} \)
B. \( \frac{3 a}{4} \)
c. \( \frac{25 a}{24} \)
D. \( \frac{11 a}{12} \)


The equation of a wave pulse is given as \( y=\frac{0.8}{(4 x+5 t)+4}, \) the amplitude of the
pulse is:
A. 0.2 units
B. 0.4 units
c. 0.6 units
D. 0.8 units


The extraction of metals from it's
compound by electrolysis is known as
A. electroplating
B. electrorefining
c. electrometallurgy
D. extraction of metals


Which of the following is the correct direction of flow of electrical impulses?
\( A \cdot C \)
в. \( C \)
\( c \cdot C \)
D. \( C \)


For the following nuclear disintegration process \( _{92}^{238} \boldsymbol{U} \rightarrow_{82}^{206} \boldsymbol{P b}+\boldsymbol{x}\left[_{2}^{4} \boldsymbol{H} e\right]+\left[_{-2}^{0} \boldsymbol{e}\right] \)
then value of \( x \) is
\( \mathbf{A} \cdot \mathbf{8} \)
B. 6
\( c \cdot 4 \)
D. 10


\( \mathbf{1} \)
\( \left[\begin{array}{ll}1 & 1 \\ 0 & 1\end{array}\right]\left[\begin{array}{ll}1 & 2 \\ 0 & 1\end{array}\right]\left[\begin{array}{ll}1 & 3 \\ 0 & 1\end{array}\right] \cdot\left[\begin{array}{cc}1 & n-1 \\ 0 & 1\end{array}\right]= \)
\( \left[\begin{array}{ll}1 & 78 \\ 0 & 1\end{array}\right], \) then the inverse of \( \left[\begin{array}{ll}1 & n \\ 0 & 1\end{array}\right] \) is?
A. \( \left[\begin{array}{cc}1 & -13 \\ 0 & 1\end{array}\right] \)
в. \( \left[\begin{array}{ll}1 & 0 \\ 12 & 1\end{array}\right] \)
c. \( \left[\begin{array}{cc}1 & -12 \\ 0 & 1\end{array}\right] \)
D. \( \left[\begin{array}{ll}1 & 0 \\ 13 & 1\end{array}\right] \)


In case of \( C_{4} \) plants, the acceptor of
\( C O_{2} \) is
A. Phosphoglyceraldehyde
B. Ribulose monophosphate.
c. Phosphoenolpyruvate.
D. Ribulose diphosphate


Body is projected vertically with velocity \( 10 \mathrm{m} / \mathrm{s} \) on reaching the ground, change in its velocity is(upwards direction is taken as positive)
\( A \cdot 20 \mathrm{m} / \mathrm{s} \)
B. \( -20 \mathrm{m} / \mathrm{s} \)
c. zero
D. none


To distinguish between real gems and artificial gems a merchant may use which of the following radiations?
A. Infrared rays
B. \( \gamma \) -rays
c. x-rays
D. Ultraviolet rays


The linear velocity of a rotating body is given by \( \overrightarrow{\boldsymbol{v}}=\overrightarrow{\boldsymbol{\omega}} \times \overrightarrow{\boldsymbol{r}}, \) where \( \overrightarrow{\boldsymbol{\omega}} \) is the
angular velocity and \( \vec{r} \) is the radius vector. The angular velocity of a body is \( \vec{\omega}=\hat{i}-2 \hat{j}+2 \hat{k} \) and the radius vector
\( \vec{r}=4 \hat{j}-3 \hat{k}, \) then \( |\vec{v}| \) is:
B. \( \sqrt{31} \) units
c. \( \sqrt{37} \) units
D. \( \sqrt{41} \) units


Show that the Lagrange's mean value theorem is not applicable to the function \( \boldsymbol{f}(\boldsymbol{x})=\frac{1}{\boldsymbol{x}} \) on [-1,1]


Which of the following is/are Indian breed of sheep?
A. Beetal
B. Barbari
c. Jamunapari
D. all of them


Assertion
\( \boldsymbol{\operatorname { T r }}(\boldsymbol{A})=\mathbf{0} \)
Reason
\( |A|=0 \)
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. Both Assertion and Reason are incorrect


If \( f(x)=\frac{x-e^{x}+\cos 2 x}{x^{2}}, x \neq 0 \) is
continuous at \( x=0, \) then
A \( \quad f(0)=\frac{-5}{2} \)
B . \( [f(0)]=-2 \)
c. \( f(0)=-0.5 \)
D. \( [f(0)] . f(0)=-1.5 \)


\( 50 H z \) alternative current current of
crest value \( 1 A \) flows through the primary of a transformer. If mutual
inductance between the primary and secondary is \( 0.5 ~ H, \) then crest voltage
induced in the secondary is:
\( \mathbf{A} \cdot 100 V \)
B. \( 150 V \)
\( \mathrm{c} .75 \mathrm{V} \)
D. \( 50 V \)


Two cells of unequal emfs, \( \boldsymbol{E}_{1} \) and \( \boldsymbol{E}_{2} \)
the internal resistance \( r_{1} \) and \( r_{2} \) are
joined as shown. \( V_{A} \) and \( V_{B} \) are the potentials at \( A \) and \( B \) respectively
This question has multiple correct options
A. one cell with continuously supply energy to the other
B. the potential difference across both the cells will be equal
c. the potential difference across one cell will be grater than its emf
D. \( V_{A}-V_{B}=\frac{\left(E_{1} r_{2}-E_{2} r_{1}\right)}{\left(r_{1}+r_{2}\right)} \)


Beta diversity is diversity
A . In a community
B. Between communities
c. In a mountain gradient
D. on a plain


The electronic configuration of cerium is:
\( \mathbf{A} \cdot[X e] 4 f^{0} 5 d^{1} 6 s^{2} \)
B \( \cdot[X e] 4 f^{1} 5 d^{1} 6 s^{2} \)
\( \mathbf{c} \cdot\left[X e \mid 4 f^{2} 5 d^{0} 6 s^{2}\right. \)
D. Both 2 and 3


Which of the following is a polynomial
with only one zero?
\( \mathbf{A} \cdot p(x)=2 x^{2}-3 x+4 \)
B \( \cdot p(x)=x^{2}-2 x+1 \)
C \( . p(x)=2 x+3 \)
D \( . p(x)=5 \)


In the purification of zirconium by van Arkel process which halogen is used?
A. Fluorine
B. Chlorine
c. Bromine
D. lodine


Pre-natal sex determination has been
prohibited by law. State the necessity of inforcement of this law.


Multiply the following and write your answer in lowest terms:
\( \frac{x^{2}-3 x-10}{x^{2}-x-20} \times \frac{x^{2}-2 x+4}{x^{3}+8} \)
A \( \cdot \frac{1}{x+4} \)
B. \( \frac{1}{x-4} \)
c. \( \frac{3}{x+4} \)
D. None of these


\( \left[\begin{array}{lll}\mathbf{1} & \mathbf{1} & \boldsymbol{x}\end{array}\right]\left[\begin{array}{lll}\mathbf{1} & \mathbf{0} & \mathbf{2} \\ \mathbf{0} & \mathbf{2} & \mathbf{1} \\ \mathbf{2} & \mathbf{1} & \mathbf{0}\end{array}\right]\left[\begin{array}{l}\mathbf{1} \\ \mathbf{1} \\ \mathbf{1}\end{array}\right]=\mathbf{0}, \) then
find \( x \)


\( f \angle C=\angle D=50^{\circ}, \) then four points \( A, B \)
\( C, D: \)
A. Are con-cyclic
B. Do not lie on same circle
c. Are collinear
A,B.D and A,B,C lie on different circles


Match the following.
\( \begin{array}{llll}\text { I } & \text { Isothermal process } & \mathbf{1} & \boldsymbol{\Delta} \boldsymbol{Q}=\mathbf{0} \\ \text { II } & \text { Isobaric process } & 2 & \Delta V=0 \\ \text { III } & \text { Isochoric process } & 3 & \Delta P=0 \\ \text { IV } & \text { Adiabatic process } & 4 & \Delta T=0\end{array} \)
\( A \)
\( |-4,||-3,|||-2, \mid V-1 \)
B. \( \mid-3, \) । \( -2, \) II \( -1, \) IV- 4
c. \( |-1,| \mid-2, \) ।I \( -3, \) ।V -4
D. \( |-4,||-2,| 1|-3,| V-1 \)
E . \( |-1,||-4,|||-2, \mid v-3 \)


When two gases are mixed at \( -30^{0} C \)
the blue coloured gas is formed. The gas
is:
A. \( N_{2} O_{3} \)
в. \( N_{2} \)
\( c \cdot N O_{2} \)
D. \( N_{2} O_{5} \)


Solve the systems of equations:
\( \boldsymbol{a} \boldsymbol{x}+\boldsymbol{b} \boldsymbol{y}=\boldsymbol{c} ; \boldsymbol{b} \boldsymbol{x}-\boldsymbol{a} \boldsymbol{y}=\boldsymbol{c} \)
A \( \cdot \frac{c(a-b)}{a^{2}+b^{2}},-\frac{c(a+b)}{a^{2}+b^{2}} \)
в. \( \frac{c(a-b)}{a^{2}+b^{2}}, \frac{c(a+b)}{a^{2}+b^{2}} \)
c. \( \frac{c(a-b)}{a^{2}+b^{2}}, \frac{c(a+b)}{a^{2}-b^{2}} \)
D. \( \frac{c(a+b)}{a^{2}+b^{2}},-\frac{c(a-b)}{a^{2}+b^{2}} \)


Assertion
There is no current in the metals in the
absence of electric field.
Reason
Motion of free electrons are random.
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


An object moving at constant velocity
must:
A. have a net force on it
B. eventually stop due to gravity
c. not have any force of gravity on it
D. have zero net force on it


A beam of helium atoms moves with a
velocity of \( 2 \times 10^{4} . \) Find the wavelength of particles constituting with the beam


If a wire is stretched to make it \( 0.1 \% \)
Ionger, its resistance will:
A. Increase by \( 0.2 \% \)
B. Decrease by \( 0.2 \% \)
c. Decrease by \( 0.05 \% \)
D. Increases by \( 0.05 \% \)


Twenty-seven rain drops of same diameter fall through air with terminal velocity ' \( V \) '. If they coalesce forming a
single drop, then the terminal velocity of the resultant drop is
A. \( V \)
B. 3V
c. \( 9 V \)
D. \( \frac{V}{9} \)


The vapour pressure of solution at 293
\( \mathrm{K} \)
A .0 .0229
B. 0.4
\( c .0 .6 \)
D. 0.9


At what temperature semiconductors behaves as an ideal insulator?
A. \( 273.15^{\circ} \mathrm{C} \)
B . -459.67 ॰ \( F \)
c. \( -273^{\circ} F \)
D. Room temperature


Find the general solution of each of the following differential equations:
\( \left(e^{x}+e^{-x}\right) d y-\left(e^{x}-e^{-x}\right) d x=0 \)


A transverse wave is described by the equation \( \boldsymbol{y}=\boldsymbol{y}_{0} \sin 2 \pi\left(\boldsymbol{f} \boldsymbol{t}-\frac{\boldsymbol{\pi}}{\boldsymbol{\lambda}}\right) . \) The
maximum particle velocity is equal to four times the wave velocity if :
A \( \cdot \lambda=\frac{\pi y_{0}}{4} \)
B. \( \lambda=\frac{\pi y_{0}}{2} \)
c. \( \lambda=\pi y_{0} \)
D. \( \lambda=2 \pi y_{0} \)


If the pressure remains constant, at what temperature, the volume of a gas
will be double of its volume at \( 0^{0} C ? \)
A \( \cdot 100^{0} C \)
В . \( 546^{0} C \)
c. \( 273 K \)
D. \( 546 K \)


Evaluate the following functions w.r.t. \( \int\left(3 x^{2}-5\right)^{2} d x \)


Which of the following is a non-metal?
A . \( K \)
в. \( A \) s
c. \( B e \)
D. \( S e \)
E . \( I r \)


A neutral conducting spherical shell is kept near a charge \( q \) as shown. The
potential at point \( P \) due to the induced
charges is :
\( A \cdot \frac{k q}{r} \)
в. \( \frac{k q}{r^{\prime} q} \)
с. \( \frac{k q}{r}-\frac{k q}{r^{\prime}} \)
D. \( \frac{k q}{C P} \)


Two resistors of \( 2 \Omega \) and \( 4 \Omega \) are
connected in parallel. Two more
resistors \( 3 \Omega \) and \( 6 \Omega \) are also connected
in parallel. These two combinations are in series with a battery of emf \( 5 V \) and internal resistance \( 0.7 \Omega . \) Calculate the
current through \( 6 \Omega \) resistor.


Proportionality constant \( \lambda \) is also known
as -
A. Decay constant
B. Disintegration constant
c. Radioactive constant
D. All of these


In human teeth, which of the
following helps in cutting?
A. Wisdom tooth
B. Incisor
c. Molar
D. Premolar


If \( f^{\prime \prime}(x)<0, \forall x \epsilon(a, b), \) and \( (c, f(c)) \) is
point of maxima, where \( c \epsilon(a, b), \) then
\( f^{\prime}(c) \) is
A \( \cdot \frac{f(b)-f(a)}{b-a} \)
в. \( \left[\frac{f(b)-f(a)}{b-a}\right] \)
c. \( 2\left[\frac{f(b)-f(a)}{b-a}\right] \)
D.


Young's modulus of a metal is \( 15 \times 10^{11} \)
Pa. If its poisson's ratio is \( 0.4 . \) The bulk modulus of the metal in \( P a \) is :
A \( \cdot 25 \times 10^{11} \)
В . \( 2.5 \times 10^{11} \)
c. \( 250 \times 10^{11} \)
D. \( 0.25 \times 10^{11} \)


A cannon ball of mass \( 5 \mathrm{kg} \) is discharged horizontally with a velocity of \( 500 m / s . \) If the cannon be free to move on the horizontal ground, what is the velocity with which it recoils? Mass of
the cannon is \( 100 \mathrm{kg} \)
A . \( 15 \mathrm{m} / \mathrm{s} \)
B. 25m/s
\( c \cdot 35 m / s \)
D. \( 45 \mathrm{m} / \mathrm{s} \)


The freezer in a refrigerator is fitted
near the top:
A. to keep it away from the hot compressor which is near the bottom.
B. because of convenience.
C. so that it can cool the whole interior by setting up convection currents.
D. without any specific purpose.


Two copper wires are of some length,
but one is thicker than the other
Choose the correct option.
A. both have same resistance
B. thin wire has more resistance
c. thin wire has less resistance
D. thicker wire has more resistance


We can drive any themodynamically forbidden reaction in the desired
direction by coupling with:
A. highly exothermic reaction
B. highly endothermic reaction
C. highly exergonic reaction
D. highly endergonic reaction
E. reaction with large positive \( \Delta S \) values


Electric ield on the axis of small electric dipole at a distance \( r \) is \( \vec{E}_{1} \) and \( \vec{E}_{2} \) at \( a \) distance \( 2 \mathrm{r} \) on a line of perpendicular dissector. Then
\( ^{\mathbf{A}} \cdot \vec{E}_{2}=-\frac{\vec{E}_{1}}{8} \)
В \( \quad \vec{E}_{2}=-\frac{\vec{E}_{1}}{16} \)
\( \mathbf{c} \cdot \underset{E_{2}}{\overrightarrow{4}}=-\frac{\vec{E}_{1}}{_{1}} \)
D \( \quad \vec{E}_{2}=\frac{\vec{E}_{1}}{8} \)


An atom does not carry any electric charge because it
A. has an equal number of charged and non charged particles
B. has neutrons in their nuclei
C. has an equal number of electrons and protons, hence positive and negative charge gets neutralized.
D. has an equal number of neutrons and protons


Why do cold drink bottles breaks when
kept in freezer?


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


During meiosis, replication of DNA
occurs in
A. S-phase
B. S-phase and zygotene
c. s-phase and leptotene
D. All the above


Which of the following statements is
correct for oxidation reaction?
A. Loss or removal of electron.
B. Removal of hydrogen atom.
C. Removal or loss of electropositive radical or element
D. All the above statements are correct


Which of the following is not a type of
wire in power supply.
A. Phase Wire
B. Neutral wire
c. zero wire
D. Earth wire


Write the converse and contropositive of
If a parallelogram is a square, then it is a rhombus'.


ff \( f(x)=e^{x} g(x) \)
\( \boldsymbol{g}(\mathbf{0})=\mathbf{1}, \boldsymbol{g}^{\prime}(\mathbf{0})=\mathbf{3}, \) then \( \boldsymbol{f}^{\prime}(\mathbf{0}) \) is
\( \mathbf{A} \cdot \mathbf{0} \)
B. 4
\( c \cdot 3 \)
D.


Match list I with list II. Choose the
correct matching codes from the choices given. List I
(Hydride) hydride)
A. \( B e H_{2} \)
1. Complex
B. \( \boldsymbol{A} \boldsymbol{s} \boldsymbol{H}_{\mathbf{3}} \)
2. Lewis acid
\( \mathbf{C} . \boldsymbol{B}_{2} \boldsymbol{H}_{\mathbf{6}} \)
3. Interstitial
D. \( \boldsymbol{L} \boldsymbol{a} \boldsymbol{H}_{\mathbf{3}} \)
4. Covalent
E. \( \boldsymbol{L} \boldsymbol{i} \boldsymbol{A} \boldsymbol{l} \boldsymbol{H}_{\boldsymbol{4}} \)
5. Intermediate
A. A-6, B-2, C-4, D-5, E-1
B. A-6, B-2, C-4, D-3, E-1
c. \( A-6, B-4, C-2, D-3, E-15 \)
D. A-5, B-4, C-2, D-3, E-1


Find first term 'a' and common
difference 'd' for the following AP.
\( \sqrt{2}, \sqrt{8}, \sqrt{18}, \sqrt{32}, \dots \)
B. \( a=\sqrt{2}, d=\sqrt{2} \)
c. Its not an AP
D. None of these


Rutherford's model of atom could not
hold good because:
A. it did not account for the stability of an atom
B. the atom did not have a nucleus and an electron
C. it did not account for the attraction between a proton and an electron
D. there is actually no space between the nucleus and the electron


The D.E whose solution \( y=A e^{5 x}+ \)
\( B e^{-2 x} \) is
A \( \cdot y_{2}-3 y_{1}-10 y=0 \)
в. \( y_{2}+3 y_{1}-10 y=0 \)
c. \( y_{2}+3 y_{1}+10 y=0 \)
D. \( y_{2}-3 y_{1}+10 y=0 \)


Assertion (A) : Lead is more elastic than
rubber.

Reason (R) : If the same load is attached
to lead and rubber wires of the same
cross-sectional area, the strain of lead
is very much less than that of rubber.
A. Both assertion and reason are true and the reason is correct explanation of the assertion
B. Both assertion and reason are true, but reason is not correct explanation of the assertion
c. Assertion is true, but the reason is false
D. Assertion is false, but the reason is true


What is the first phase of Mitiosis?
Write the changes that take place in that stage.


For \( a, b \in R-\{0\}, \) let \( f(x)=a x^{2}+ \)
\( b x+a \) satisfies \( f\left(x+\frac{7}{4}\right)= \)
\( f\left(\frac{7}{4}-x\right) \forall x \epsilon R \)
Also the equation \( f(x)=7 x+a \) has
only one real distinct solution.
The value of \( (a+b) \) is equal to
A . 4
B. 5
c. 6
\( D \)


The number of \( H C l \) molecules formed
in the oxidation of 1 molecule of
chlorofom to phosgene by air is:
\( \mathbf{A} \cdot \mathbf{0} \)
B.
\( c \cdot 2 \)
D. 3


Two rods \( A \) and \( B \) made up of same metal have same length. The ratio of their resistances is \( 1: 2 . \) If these rods are
immeresed in water then loss in weight will be :-
\( A . \) more in \( A \)
B. more in B
c. same is A and B
D. in the ratio 1: 2


Solve:
\( \frac{\boldsymbol{d}}{\boldsymbol{d} \boldsymbol{x}}\left(\sin ^{-1}\left\{\frac{\sqrt{\mathbf{1}+\boldsymbol{x}}+\sqrt{\mathbf{1}-\boldsymbol{x}}}{\mathbf{2}}\right\}\right) \)
A \( \cdot \frac{-1}{2 \sqrt{1-x^{2}}} \)
в. \( \frac{1}{2 \sqrt{1-x^{2}}} \)
c. \( \frac{1}{\sqrt{1-x^{2}}} \)
D. \( \frac{-1}{\sqrt{1-x^{2}}} \)


Assertion(A): The basicity of
orthophosphours acid is two
Reason (R): In orthophosphorous acids,
two re-placeable hydrogen atoms are
present.
A. Both (A) and (R) are true and (R) is the correct
explanation of \( (A) \)
B. Both (A) and (R) are true and (R) is not the
correct explanation of \( (A) \)
C. (A) is true and (R) is false
D. (A) is false but (R) is true
3


The value of magnetic field induction which is uniform is 2 T. What is the
flux passing through a surface of area \( 1.5 m^{2} \) perpendicular to the field?


A polar covalent bond forms when:
A. two polar atoms combine
B. two ions bond
C. the shared pair of protons are more attracted to one atom than the other
D. the shared pair of electrons are more attracted to one atom than the other
E. the transferred pair of electrons are more attracted to one atom than the other


Current is flowing through a conductor
and creates a magnetic field. Assume
that this is the only source of the
magnetic field. Reversing a current in a straight conductor with no change to
the magnitude(ampere value) will
cause a
A. Reduction in the magnetic field
B. Disappearance of the magnetic field
C. Reversal of the direction of the magnetic field
D. Reversal and reduction of the magnetic field


After the classification of elements
study of elements
become
A. difficult
B. easy
c. both \( A \) and \( B \)
D. None of these


Given \( \boldsymbol{A}=\{\boldsymbol{a}, \boldsymbol{b}, \boldsymbol{c}, \boldsymbol{d}, \boldsymbol{e}, \boldsymbol{f}, \boldsymbol{g}, \boldsymbol{h}\} \) and \( \boldsymbol{B}= \)
\( \{a, e, i, o, u\} \)
then \( B-A \) is equal to
A \( \cdot\{i, o, u\} \)
в. \( \{a, b, c\} \)
c. \( \{c, d, e\} \)
D. \( \{a,, i, z\} \)


Match the column-I and column-I
\( \begin{array}{llll} & \text { Column-I } & & \text { Column-II } \\ \text { (i) } & \text { Chrysophyta } & \text { (a) } & \text { Fungi } \\ \text { (ii) } & \text { Gonyaulax } & \text { (b) } & \text { Diatom } \\ \text { (iii) } & \text { Penicillium } & \text { (c) } & \text { Plasmodium } \\ \text { (iv) } & \text { Slime mould } & \text { (d) } & \text { Dinoflagellate }\end{array} \)
\( A \)
(i) - a, (ii) - b, (iii) - c, (iv) - d
B. (i) \( -b, \) (ii) \( -c, \) (iii) \( -a, \) (iv) \( -d \)
\( c \cdot(i)-b,(\text { ii) }-c,(\text { iii) }-d,(\text { iv })-a \)
D. (i) - b, (ii) - d, (iii) - a, (iv) -


What is the IUPAC name of the given compound? \( \boldsymbol{C H}_{3}-\boldsymbol{C H}=\boldsymbol{C H}-\boldsymbol{C H}_{2} \boldsymbol{B r} \)


The standard electrode potentials
\( \left(\boldsymbol{E}_{\boldsymbol{M}^{+} / M}^{o}\right) \) of four metals \( \mathbf{A}, \mathbf{B}, \mathbf{C} \) and \( \mathbf{D} \)
are \( -1.2 \vee, 0.6 \vee, 0.85 \mathrm{V} \) and \( -0.76 \mathrm{V} \)
respectively. The increasing sequence of deposition of metals on applying potential is :
\( A \cdot A, C, B, D \)
B. B, D, C, A
c. \( c, B, D, A \)
D. D, A, B, C


Which of the following equation shows the above graph?
A \( \cdot f(x)=x^{2}+9 \)
B. \( f(x)=(x-9)^{2} \)
\( \mathbf{c} \cdot f(x)=9-x^{2} \)
D. \( f(x)=-\left|x^{2}+9\right| \)
E \( \cdot f(x)=\mid-x^{2}+9 \)


If \( |z|=5 \) and \( w=\frac{z-5}{z+5}, \) then the
\( \boldsymbol{R} e(\boldsymbol{w}) \) is equal to
\( \mathbf{A} \cdot \mathbf{0} \)
в. \( \frac{1}{25} \)
c. 25
D.


Combustion of \( 3.10 g \) of phosphorous
produces a white, waxy solid with a mass of \( 5.50 g . \) What is the empirical formula for the compound produced in this reaction?
\( \mathbf{A} \cdot P_{4} O_{7} \)
в. \( P_{2} O_{5} \)
c. \( P O \)
D. \( P_{2} O_{3} \)


A body cools at the rate of \( 1.2^{0} C \) per
minute when its temperature is more
that of the surroundings by \( 40^{0} C . \) Find the rate of cooling of the body when its temperature is more than that of
surroundings by \( 25^{0} C \)


Solve \( : \boldsymbol{y}=\sin ^{-1}(\sec \boldsymbol{x}) \)


Carbon monoxide gas is more dangerous than carbon dioxide gas. Why?


Let \( y=x^{3}-8 x+7 \) and \( x=f(t) . \) If
\( \frac{d y}{d t}=2 \) and \( x=3 \) at \( t=0, \) then \( \frac{d x}{d t} \) at
\( t=0 \) is given by
\( \mathbf{A} \cdot \mathbf{1} \)
B. \( \frac{19}{2} \)
\( c \cdot \frac{2}{19} \)
D. None of these


Differentiate \( f(x)=4 x^{2}-5 x \)
\( A \cdot 8 x \)
B. \( 8 x-5 \)
\( c .5 \)
D. None of these


If area of a triangle is \( \left(\frac{4 x^{2}+8 x+4}{2}\right) \) sq.units. Find its base and height


The value of \( (3.1)^{3} \) is
A . 27.971
B. 29.791
c. 29.97
D. 27.197


Complete the following equation:\( 2 H C H O+C o n c . K O H \rightarrow \)


Find the dimensional formula of
coefficient of viscosity \( \boldsymbol{\eta} \)


The high oxidising power of fluorine is due to its :
A. high electron affinity,
B. high heat of dissociation and low heat of hydration.
c. low heat of dissociation and high heat of hydration.
D. high heat of dissociation and high heat of hydration.


The solubility of \( P b S O_{4} \) in water is
\( 0.038 g L^{-1} \) at \( 25^{\circ} C . \) Calculate its
solubility at the same temperature.


How many numbers consisting of 5 digits can be formed in which the digits 3,4 and 7 are used only once and the digit 5 is used twice
A . 30
B. 60
c. 45
D. 90


A windmill is pushed by four external
forces as shown. Calculate force
required to make the windmill stand
still.
\( A \cdot 2 N \)
В. -4 N
\( c .6 N \)
D. \( -16 N \)


\( 0^{2} \)
\( 0^{\text {then }} \) \( \sigma \)
\( \sigma \)


How will you compare the e.m.f of two cells using a potentiometer?


Consider a reaction \( a G+b H \longrightarrow \)
Products. When the concentration of
both the reactants \( G \) and \( H \) are
doubled, the rate increases by eight times. However, when the concentration
of \( G \) is doubled keeping the
concentration of \( \boldsymbol{H} \) fixed, the rate is
doubled. The overall order of reaction is:
A . 0
B. 1
c. 2
D. 3


The correct order of the flow of blood
through the heart, entering from vena
cava is
A. Left atrium \( \rightarrow \) left ventricle \( \rightarrow \) right ventricle \( \rightarrow \) right atrium
B. Left ventricle \( \rightarrow \) left atrium \( \rightarrow \) right atrium \( \rightarrow \) right ventricle
C. Right atrium \( \rightarrow \) right ventricle \( \rightarrow \) left atrium \( \rightarrow \) left ventricle
D. Right ventricle \( \rightarrow \) right atrium \( \rightarrow \) left atrium \( \rightarrow \) left ventricle
E. Right ventricle \( \rightarrow \) right atrium \( \rightarrow \) left ventricle \( \rightarrow \) left atrium


The bar graph shows the amount of
money donated by 4 classes to a charity
How much more money must Class \( 4 P \)
donate so that their amount is the
same as that of class \( 4 S ? \)
A. Rs. 20
B. Rs.60
c. Rs. 40
D. Rs.100


lonic solutions are good conductors of
A. heat
B. electricity
c. energy
D. air


Atomic number 112 placed in:
A. s- block
B. d- block
c. f- block
D. p- block


A leaf is identified from
A. Flat green lamina
B. Presence of leaf blade and petiole
C . Presence of axillary bud
D. Occurrence of chlorophyll


Assertion
A particle is moving along x-axis. The resultant force \( \boldsymbol{F} \) acting on it at
position \( x \) is given by \( F=-a x-b \)
Where \( a \) and \( b \) are both positive constants. The motion of this particle is
not SHM
Reason
In SHM, restoring force must be proportional to the displacement from mean position.
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


Two blocks of masses \( 10 \mathrm{kg} \) and \( 4 \mathrm{kg} \) are connected by a spring of negligible mass and placed on a frictionless horizontal surface.An impulse gives a velocity of \( 14 \mathrm{m} / \mathrm{s} \) to the heavier block in
the direction of the lighter block.the velocity of the center of mass is :
\( A \cdot 5 m / s \)
B. 20 \( \mathrm{m} / \mathrm{s} \)
\( c \cdot 30 m / s \)
D. \( 10 \mathrm{m} / \mathrm{s} \)


Nuclear fission and fusion can be
explained on the basis of Einstein's:
A. Theory of relativity
B. Specific heat equation
c. Mass-energy relation
D. Photoelectric equation


The work done in placing a charge of \( 8 \times 10^{-18} \) coulomb on a condenser of
capacity 100 micro-farad is:
A \( \cdot 16 \times 10^{-32} \) joule
B. \( 3.2 \times 10^{-26} \) joule
C \( \cdot 4 \times 10^{-10} \) joule
D. \( 32 \times 10^{-32} \) joule


For a process, entropy change of a system is expressed as:
A. \( H-T S \)
B. \( \frac{q_{r e v}}{T} \)
c. \( \frac{T}{q_{r e v}} \)
D. \( q_{r e v} \times T \)


If the number \( \frac{z-2}{z+2} \) is purely imaginary number, then modulus value of z
satisfies
A. less than 2
B. greater than 2
c. lies between 2 and 2
D \cdot \( |z|=2 \)


Let \( \boldsymbol{A}=\{1,2,3,4,5,6,7,8,9,10\} . \) Then
the number of subsets of \( A \) containing exactly two elements is
A . 20
B. 40
c. 45
D. 90


Which of the following statement(s) is/are correct?
This question has multiple correct options
A. In metal carbonyl complexes \( d_{C-} o \) increases compared to that in \( C O \) molecule
\( B \)
The pair of compounds \( \left[\mathrm{Cr}\left(\mathrm{H}_{2} \mathrm{O}\right)_{6}\right] \mathrm{Cl}_{3} \) and
\( \left[\mathrm{CrCl}\left(\mathrm{H}_{2} \mathrm{O}\right)_{4}\right] 2 \mathrm{H}_{2} \mathrm{O} \) show hydrate isomerism
C \( \quad A l_{2}\left(C H_{3}\right)_{6} \) is a dimeric compound and has a similar
structure to diborane
D. Facial and Meridional isomers associated with
\( \left[M a_{3} b_{3}\right]^{n \pm} \) type complex compound, both are optically
inactive


If \( \boldsymbol{y}=\boldsymbol{x}^{4} \boldsymbol{e}^{2 x} \) then \( \boldsymbol{y}_{10}(\boldsymbol{0}) \) is equal to
\( A \cdot 2^{10} \)
B . \( 315 \times 2^{10} \)
c. \( 195 \times 2^{10} \)
D. \( 315 \times 2^{8} \)


Which of the following is true about a monocot leaf?
A. Reticulate venation
B. Absence of bulliform cells from epidermis
c. Mesophyll not differentiated into palisade and spongy tissues
D. well differentiated mesophyl


A microwave and an ultrasonic sound
wave have the same wavelength.
Their frequencies are in the ratio (approximately)
A \( \cdot 10^{2} \)
B. \( 10^{\text {4 }} \)
\( c \cdot 10^{6} \)
D. \( 10^{8} \)


A particle of mass \( \mathrm{m} \) is attached to one
end of a massless spring of force
constant \( \mathrm{k}, \) lying on a frictionless horizontal plane. The other end of the spring is fixed. The particle starts moving horizontally from its equilibrium position at time \( t=0 \) with
an initial velocity \( u_{0} . \) When the speed of
the particle is \( 0.5 u_{0} . \) It collides elastically with a rigid wall. After this collision.
This question has multiple correct options
A. The speed of the particle when it returns to its equilibrium position is \( u_{0} \)
B. The time at which the particle passes through the equilibrium position for the first time is \( t=\pi \sqrt{\frac{m}{k}} \)
c. The time at which the maximum compression of the spring occurs is \( t=\frac{4 \pi}{3} \sqrt{\frac{m}{k}} \)
D. The time at which the particle passes through the equilibrium position for the second time is \( t= \) \( \frac{5 \pi}{3} \sqrt{\frac{m}{k}} \)


If \( \mathbf{Y}=(x+\sqrt{x^{2}-1})^{m} \) show that
\( \left(x^{2}-1\right) \frac{d^{2} y}{d x^{2}}+x \frac{d y}{d x}=m^{2} y \)


differentiate :
\( \boldsymbol{y} \log \boldsymbol{x} \)


If (-6,-4),(3,5),(-2,1) are the vertices of a parallelogram, then remaining vertex can be This question has multiple correct options
в. (7,10)
c. (-1,0)
D. (-11,-8)


Which of the following ions is mostly unlikely to exist?
A . \( L i \)
B. \( B e^{2} \)
c. \( B \)
D. \( F \)


A hydraulic machine exerts a force of \( 900 \mathrm{N} \) on a piston of diameter \( 1.80 \mathrm{cm} \) The output force is exerted on a piston of diameter \( 36 \mathrm{cm} . \) What will be the output force?
\( \mathbf{A} \cdot 12 \times 10^{4} N \)
В . \( 16 \times 10^{4} N \)
\( \mathbf{c} \cdot 36 \times 10^{4} N \)
D. \( 38 \times 10^{4} N \)


An emf is induced in an aeroplane
during its ascent and descent in east-
west direction due to
A. The horizontal component of the earth's magnetic field
B. The vertical component of the earth's magnetic field
c. Both 1 and 2
D. None of the above


White washed buildings will be in hot weather than the
darker buildings.
A. hotter
B. colder
c. wetter
D. drier


\( f(x)=\left\{\begin{array}{cl}\frac{\left(1-\sin ^{3} x\right)}{3 \cos ^{2} x}, & x<\frac{\pi}{2} \\ a, & x=\frac{\pi}{2} \\ \frac{b(1-\sin x)}{(\pi-2 x)^{2}}, & x>\frac{\pi}{2}\end{array}\right. \)
continuous at \( x=\frac{\pi}{2}, \) then the value of
\( \left(\frac{b}{a}\right)^{5 / 3} \) is
\( \mathbf{A} \)
B.
\( c \cdot 32 \)
D. 54


What is the \( p H \) of 0.2 M aqueous
solution of sodium butyrate \( \left(\boldsymbol{K}_{\boldsymbol{a}}=\right. \) \( \left.2.0 \times 10^{-5}\right) ? \)


In a liquid, heat is transferred mainly by
A. conduction
B. convection
c. radiation
D. conduction and convection both


Which of the following is polar
dielectrics?
\( \mathbf{A} \cdot H C L \)
в. \( N H_{3} \)
\( \mathrm{c} \cdot \mathrm{H}_{2} \mathrm{O} \)
D. All of the above


Why do alcohols possess higher boiling
points as compared to those of corresponding alkanes?


Henderson-Hasselbalch equation among the following is :
A \( \cdot p H=\frac{1}{2} p K_{a}-\log C \)
B \cdot \( p O H=\frac{1}{2} p K_{b}-\log C \)
c. \( _{p H}=p K_{a}+\frac{[\text {salt}]}{[\text {acid}]} \)
D. \( _{K_{h}}=\frac{K_{w}}{K_{a} \times K_{b}} \)


A typical weighing machine measures of an object.
A. only the weight
B. only the mass
c. both mass and weight
D. none of these


In the figure given below, \( A B C D \) is a
trapezium in which \( A B \| D C . E \) and \( F \)
are the midpoint of \( A D \) and \( B C \)
respectively. \( D F \) and \( A B \) are produced
to meet at \( G . \) Also \( A C \) and \( E F \) intersect
at point \( O . \) Show that :
\( (i) E O \| A B \)
\( (i) A O=C O \)


Heat flows between two bodies due to
difference in their temperature.
A. True
B. False


Let \( R \) is the equivalence relation in the \( \operatorname{set} A=\{0,1,2,3,4,5\} \) given by \( R= \)
\( \{(a, b): 2 \) divides
\( (a-b)\} . \) Write the equivalence class


Assertion
The \( N-N \) bond distance in \( N \) is
shorter than the \( N-N \) bond distance
in \( \boldsymbol{N}_{2} \boldsymbol{H}_{4} \)
Reason
The atomic radius of \( \boldsymbol{H} \) is smaller than
the atomic radius of \( N \)
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


The most important function of
diaphragm of the mammals is
A. To divide the body cavity into compartment
B. To protect lungs
C. To aid in ventilation
D. None of the above


Differentiate the following with respect
to \( x \)
\( \cos ^{-1} 2 x \sqrt{1-x^{2}}, \frac{1}{\sqrt{2}}<x<1 \)


What will be the difference between
simple and compound interest on Rs. 8.000 at the rate of 5 percent per
annum at the end of 3 years?
\( A \cdot \) Rs. 61.00
B. Rs. 122.00
c. Rs. 91.50
D. Rs. 152.50


The most electropositive element is :
A . \( C s \)
в. \( C \)
c. \( C l \)
D. \( K \)


Which of the following is not a synthetic rubber?
A. Cis - 1,4 - polyisoprene
B. Neoprene
c. Buna -s
D. Buna - N


A beam of a parallel rays is brought to a focus by a convex lens. If a thin concave lens of equal focal length is joined to the convex lens, the focus will be
A. Shifted to infinity
B. Shifted to a small distance
c. Remained undisturbed
D. Shifted to the back side


A chemical reaction is at equilibrium
when:
A. reactants are completely transformed into products
B. the rates of forward and backward reactions are equal
C. formation of products is minimised
D. equal amounts of reactants and products are present


A monkey of mass \( m k g \) slides down a light rope attached to a fixed spring balance, with an acceleration \( a \). The
reading of the spring balance is \( \mathrm{W} \) kg. \( [\mathrm{g} \) \( = \) acceleration due to gravity]. Then:
This question has multiple correct options
A. the force of friction exerted by the rope on the monkey is \( m(g-a) N \)
в. \( m=\frac{W g}{g-a} \)
c. \( m=W\left(1+\frac{a}{g}\right) \)
D. the tension in the rope is \( W g N \)


A line joining places of equal horizontal field is called
A . aclinic
B. isoclinic
c. isodynamic
D. isogonal


The directing power of the groups
\( -N H_{2},-O C H_{3},-C_{6} H_{5} \quad \) and
\( N O_{2} \) follows the order
A. \( -N H_{2}>-O C H_{3}>-C_{6} H_{5}>-N O_{2} \)
B. \( -N O_{2}>-C_{6} H_{5}>-O C H_{3}>-N H_{2} \)
c. \( -O C H_{3}>-N H_{2}>-C_{6} H_{5}>-N O_{2} \)
D. \( -O C H_{3}>-N O_{2}>-N H_{2}>-C_{6} H_{5} \)


\( \int \sin x \log (\sec x+\tan x) d x=f(x)+ \)
\( \boldsymbol{x}+\boldsymbol{c} \) then \( \boldsymbol{f}(\boldsymbol{x})= \)
A \( \cdot \cos x \log (\sec x+\tan x)+c \)
B. \( \sin x \log (\sec x+\tan x)+c \)
c. \( -\cos x \log \sec x+\tan x)+c \)
D. - \( \cos x \log \sec x+c \)


f \( a(a+2)=24 \) and \( b(b+2)=24 \)
where \( a \neq b, \) then \( a+b= \)
A . - 48
B . - -
\( c \cdot 2 \)
D. 46
E. 48


The orbital angular momentum of an electron corresponding to \( n=4 \) and
\( \boldsymbol{m}=-\mathbf{3} \) is:
A . 0
в. \( \frac{h}{\sqrt{2} \pi} \)
c. \( \frac{\sqrt{6} h}{2 \pi} \)
D. \( \frac{\sqrt{3} h}{\pi} \)


If \( f(x)=x^{x}, \) then \( f(x) \) is increasing in
interval:
A . \( [0, e] \)
B. \( \left(\frac{1}{e}, \infty\right) \)
c. [0,1]
D. None of these


The total surface area of the cube is 216
sq. cm. The length of the longest pole that can be kept inside the cube is
A \( .6 \sqrt{3} \)
B. 6
\( c \cdot 8 \)
D. \( 7 \sqrt{3} \)


When a vibrating tuning fork is placed on a sound box of a sonometer, 8 beats
per second are heard when the length of
the sonometer wire is kept at \( 101 \mathrm{cm} \) or
\( 100 \mathrm{cm} . \) Then the frequency of the tuning fork is (consider that the tension in the wire is kept constant):
A \( .1616 \mathrm{Hz} \)
В. \( 1608 \mathrm{Hz} \)
\( \mathbf{c} \cdot 1632 H z \)
D. \( 1600 \mathrm{Hz} \)


Fill in the blanks.
In Flemings rule the middle finger
indicates the direction
of


Divide 20 into four parts which are in arithmetic progression such that the product of the first and fourth is to the
product of the second and third is in the ratio 2: 3 then least value of them is
A .2
B. 4
\( c \cdot 6 \)
D. 8


A hydraullic press contains \( 250 l i t \) of oil Find the decrease in volume of the oil
when its pressure increases to \( 10^{7} \) Pa.
The bulk modulus of the oil is \( \boldsymbol{K}=\mathbf{5} \times \)
\( \mathbf{1 0}^{\mathbf{5}} \boldsymbol{P a} \)
A. \( -0.8 l i t \)
B. - \( 0.5 l i t \)
c. \( -0.6 l i \)
D. - \( 0.9 l i t \)


Water can drain easily though
A. clayey soil
B. loamy soil
c. sandy soil
D. bricks


Which of the following statements regarding molecularity of the reaction
is correct?
A. Molecularity relates to mechanism of reaction
B. It cannot be negative or fractional
c. Molecularity of a complex reaction has two(or) more steps and each individual step has its own molecularity
D. All are correct


Pole Star is a member of the solar
system
A. True
B. False


Ring of radius \( R \) rotating about axis of ring such that angular velocity is given as omega \( =5 t . \) Find acceleration of a
point \( \boldsymbol{P} \) on rim after \( \mathbf{5} \) sec?
\( \mathbf{A} \cdot 5 R \)
в. 25 В
c. \( \sqrt{650} R \)
D. None of these


Motor vehicles equipped with catalytic converter are advised to use unleaded
petrol because
A. Lead is a heavy metal
B. Lead causes inactivation of catalyst present in catalytic converter
c. Lead decreases the efficiency of vehicle
D. Lead increases burning of petrol


A Nicol prism is based on the principle
of.
A. Refraction
B. Scattering
c. Dichroism
D. Double refraction


lonic compounds are soluble in:
A. water
B. benzene
c. ether
D. alcohol


What is a pressure on the smaller
piston if both the pistons are at same
horizontal level? (Take \( \left.g=10 m s^{-2}\right) \)
\( \mathbf{A} \cdot 3 P a \)
В. \( 4 \times 10^{3} P a \)
c. \( 6 \times 10^{5} P a \)
D. \( 1000 P a \)


Name the type of Pollination mechanism found in members of
Fabaceae.


An example of destructive metabolism (catabolism) is
A. Photosynthesis
B. Respiration
c. Glycogenesis
D. Both B and C


Which one of the following has 7 valence electrons?
A . Nat
B. Al
\( c \cdot F \)
D. Ti
\( E \cdot B r \)


Of dia, para and ferromagnetism, the universal property of all substance is
A. diamagnetism
B. paramagnetism
c. ferromagnetism
D. all of the above


Carbinol is a trivial name of :-
\( \mathbf{A} \cdot C_{2} H_{5} O H \)
в. \( C H_{3} O H \)
c \( . H C O O H \)
D. \( C H_{3} \) СООН


Select the correct option with respect to the fungi forms the fruiting body in which reduction division occurs.
A. Agaricus, Aspergillus and Alternaria
B. Peziza, Saprolegnia and Trichoderma
c. Penicillium, Agaricus and Claviceps
D. Claviceps, Mucor and Rhizopus


State true or false:
In quadrilateral \( A B C D, A D=B C \) and
the diagonals \( A C \) and \( B D \) intersect at
point \( \boldsymbol{O}, \) such that \( \frac{\boldsymbol{O} \boldsymbol{C}}{\boldsymbol{O} \boldsymbol{A}}=\frac{\boldsymbol{O} \boldsymbol{D}}{\boldsymbol{O B}}=\frac{1}{\mathbf{3}}, \) then the quadrilateral
\( A B C D \) is a trapezium.
A. True
B. False


Which of the following represents the oxide of cerium?
This question has multiple correct options
A. \( C e_{3} O_{4} \)
в. \( C e O_{4} \)
\( \mathrm{c} \cdot \mathrm{Ce}_{2} \mathrm{O}_{3} \)
D. \( \operatorname{Ce} \mathrm{e}_{2} \)


From below which are the
disadvantages of nuclear energy?
A. High set up cost
B. low set up cost
c. waste products are useful
D. None


The number of geometrical isomers of
\( A \) can be :
\( (\mathbf{A}) \)
\( A \)
B. 3
\( c \)
\( D \)


In the nuclear reaction
\( \frac{14}{7} \boldsymbol{N}+_{2}^{4} \boldsymbol{H} e \rightarrow_{8}^{17} \boldsymbol{O}+\ldots \ldots \ldots \ldots \)
What is the missing particle?
A \( \cdot \frac{4}{2} \mathrm{He} \)
B . \( _{1}^{1} H \)
c. \( _{0}^{1} n \)
\( D \)


Addition of 0.643 g of a compound to 50 mL of benzene (density 0.879 glmL)
lowers the freezing point from \( 5.51^{\circ} \mathrm{C} \) to
\( 5.03^{\circ} \mathrm{C} . \) If \( K_{f} \) for benzene is 5.12
calculate the molecular mass of the
compound.
A . 126
B. 166
\( c \cdot \) १५
D. 146


The total flux associated with given
cube will be-
where \( ^{\prime} \boldsymbol{a}^{\prime} \) is side of cube \( :\left(\frac{\mathbf{1}}{\boldsymbol{\epsilon}_{\mathbf{0}}}=\mathbf{4} \boldsymbol{\pi} \times\right. \)
\( 9 \times 10^{9} \) SI unit)
A \( \cdot 162 \pi \times 10^{-3} N m^{2} / C \)
B . \( 162 \pi \times 10^{3} \mathrm{Nm}^{2} / \mathrm{C} \)
C \( \cdot 162 \pi \times 10^{-6} N m^{2} / C \)
D. \( 162 \pi \times 10^{6} \mathrm{Nm}^{2} / \mathrm{C} \)


Cyanohydrin of which compound on hydrolysis will give lactic acid?
A. \( C_{6} H_{5} C H O \)
в. \( H C H O \)
c. \( C H_{3} C H O \)
D. \( C H_{3} C H_{2} C H O \)


Hydroponics is
A. Nutrient less culture
B. Water less culture
C. Soilless culture
D. None of the above


A glass slab has concave surface of
radius of curvature \( 2.0 \mathrm{cm} . \) The glass
has refractive index of \( 1.5 . \) If a point object is placed on axis in air at a
distance of \( 18 \mathrm{cm} \) from concave face,
find the position and nature of the image.


The value of \( \sin ^{-1}\left(\sin 5 \frac{\pi}{3}\right)= \)
A \( \cdot-\frac{\pi}{3} \)
B .
\( \mathbf{c} \cdot \frac{4 \pi}{3} \)
D. \( \frac{3 \pi}{3 \pi} \)


A rigid spherical body is spinning
around an axis without any external
torque. Due to change in temperature, the
volume increases by \( 1 \% . \) Its angular speed
A. Will increase approximately by \( 1 \% \)
B. Will decrease approximately by 1 \%
C. Will decrease approximately by 0.67 \%
D. Will increase approximately by 0.33 \%


A merry go round has a radius of \( 4 m \)
and completes a revolution in 2 s. Then
acceleration of a point on its rim will be:
\( \mathbf{A} \cdot 4 \pi^{2} \)
В . \( 2 \pi^{2} \)
\( \mathbf{c} \cdot \pi^{2} \)
D. zero


Differential equation having
\( \mathbf{y}=\left(\sin ^{-1} \mathbf{x}\right)^{2}+\mathbf{A}\left(\cos ^{-1} \mathbf{x}\right)+\mathbf{B} \) where
A, B are arbitrary constants as general solution is
A \( \cdot\left(1-x^{2}\right) y_{2}-x y_{1}=2 \)
B \( \cdot\left(1-x^{2}\right) y_{2}-x y_{1}=1 \)
c. \( (1-x) y_{2}-x y_{1}=2 \)
D. \( \left(1-\mathrm{x}^{2}\right) \mathrm{y}_{2}-\mathrm{xy}_{1}=4 \)


if a line makes angles \( \alpha, \beta, \gamma, \delta \) with
four diagonals a cube then value of
\( \sin ^{2} \alpha+\sin ^{2} \beta+\sin ^{2} \gamma+\sin ^{2} \delta \) equals
\( A \cdot 2 \)
B. \( \frac{4}{3} \)
\( c \cdot \frac{8}{3} \)
D.


A disc and a ring of same mass are rolling and if their kinetic energies are equal, then the ratio of their velocities
will be:
A. \( \sqrt{4}: \sqrt{3} \)
B. \( \sqrt{3}: \sqrt{4} \)
c. \( \sqrt{3}: \sqrt{2} \)
D. \( \sqrt{2}: \sqrt{3} \)


The force of attraction that holds the
hydrogen atom of one molecule to the strongly electronegative atom of adjacent molecule is called:
A. electrostatic force of attracton
B. vanderwaal's forces
c. hydrogen bonding
D. None of these


An iron cylinder of radius \( 1.4 \mathrm{cm} \) and
length \( 8 \mathrm{cm} \) is found to weigh \( 369.6 \mathrm{g} \)
Calculate the density of iron.
A \( \cdot 7500 \mathrm{kg} / \mathrm{m}^{3} \)
B. \( 7500 g / c m^{3} \)
c. \( 7500 k g / c m^{3} \)
D. None of the above


Which one is a short day plant?
A. Brassica campestris
B. Raphanus sativus
c. Glycine maxx
D. Papaver somniferumm


Let \( \vec{a}, \vec{b} \) and \( \vec{c} \) br non-coplanar unit vectors equally inclined to one another at an acute angle \( \theta . \) Then \( [\vec{a} \vec{b} \vec{c}] \) in terms
of \( \theta \) is equal to
A \( \cdot(1+\cos \theta) \sqrt{\cos 2 \theta} \)
B. \( (1+\cos \theta) \sqrt{1-2 \cos 2 \theta} \)
c. \( (1-\cos \theta) \sqrt{1+2 \cos 2 \theta} \)
D. none of these


Using the standard electrode potentials given in Table \( 3.1, \) predict if the reaction between the following is feasible:
(i) \( F e^{3+}(a q) \) and \( I^{-}(a q) \)
(ii) \( A g^{+}(a q) \) and \( C u(s) \)
(iii) \( F e^{3+}(a q) \) and \( B r^{-}(a q) \)
(iv) \( A g(s) \) and \( F e^{3+}(a q) \)
\( (v) B r_{2}(a q) \) and \( F e^{2+}(a q) \)


The pteridophyte, popularly known as 'horsetail' or a 'scouring rush' is
A. Equisetum
B. Fern
c. Lycopodium
D. Psilotum


A DNA molecules measuring \( 680 A^{\circ} \)
contains


Total number of meiosis that occur in
the sporangium of Nephrolepis is
\( \mathbf{A} \cdot \mathbf{1} \)
B. 4
\( c \cdot 16 \)
D. None of the above


\( \frac{\sin 70^{\circ}+\cos 40^{\circ}}{\cos 70^{\circ}+\sin 40^{\circ}}= \)
A \( \cdot \frac{1}{\sqrt{3}} \)
B. \( \sqrt{3} \)
\( c \cdot \frac{1}{2} \)
D.


\( p H \) scale:
A. ranges from \( 0-5 \)
B. ranges from \( 0-7 \)
C . ranges from \( 0-14 \)
D. none of these


Which of the following species is/are
isostructural with \( \boldsymbol{X} \boldsymbol{e} \boldsymbol{F}_{\mathbf{4}} \) ?
This question has multiple correct options
\( \mathbf{A} \cdot I C l_{6}^{-} \)
в. \( I_{5}^{-} \)
c. \( B r F_{4}^{-} \)
D. \( X e O_{4} \)


Find the value of \( \lim _{x \rightarrow 0} \frac{\sqrt{2+x}-\sqrt{2-x}}{x} \)
\( ^{\mathrm{A}} \cdot \frac{1}{2 \sqrt{2}} \)
B. \( \sqrt{2} \)
c. \( \frac{1}{\sqrt{2}} \)
D.


The value of absolute zero temperature in Fahrenheit scale is
\( \mathbf{A} \cdot-273^{\circ} F \)
B. \( -32^{\circ} F \)
c. \( -460^{\circ} F \)
D. \( -132^{\circ} F \)


At CMC, the surfactant molecules:
A. decompose
B. become completely soluble
c. associate
D. dissociate


In which of the following molecules octet rule is not followed?
A \( . N H_{3} \)
в. \( C H_{4} \)
\( c \cdot C O_{2} \)
D. \( N O \)


The number of molecules in 1.5 litres of
water are:
(Density of water is \( 1 g / c m^{3} \) )
в. \( 83.33 \times 6.023 \times 10^{23} \)
D. \( 73.33 \times 6.023 \times 10^{2} \)


At a certain temperature, the reaction
\( \boldsymbol{P C l}_{5}(\boldsymbol{g}) \rightleftharpoons \boldsymbol{P C l}_{3}(\boldsymbol{g})+\boldsymbol{C l}_{2}(\boldsymbol{g}) \) has an
equilibrium constant \( \boldsymbol{K}_{c}=\mathbf{5} \cdot \mathbf{8} \times \mathbf{1 0}^{-\mathbf{2}} \)
Calculate the equilibrium
concentrations of \( \boldsymbol{P C l}_{5}, \boldsymbol{P C l}_{3} \) and \( \boldsymbol{C l}_{2} \) if
only \( P C l_{5} \) is present initially at a
concentration of \( \mathbf{0 . 1 6 0 M} \)
A \( \cdot\left[P C l_{3}\right]=\left[C l_{2}\right]=0.071 M,\left[P C l_{5}\right]=0.089 M \)
B . \( \left[P C l_{3}\right]=0.034 M,\left[C l_{2}\right]=0.071 M,\left[P C l_{5}\right]=0.056 M \)
c. \( \left[P C l_{3}\right]=0.075 M\left[C l_{2}\right]=0.088 M,\left[P C l_{5}\right]=0.099 M \)
D \( \cdot\left[P C l_{3}\right]=\left[C l_{2}\right]=0.043 M,\left[P C l_{5}\right]=0.089 M \)


The total spin resulting from a d \( ^{7} \) configuration is :
\( \mathbf{A} \cdot \mathbf{1} \)
B. 2
\( c \cdot 5 / 2 \)
D. 3/2


A very thin film in reflected white light
appears
A . coloured
B. white
c. black
D. red


Assertion: Pure \( C H C l_{3} \) does not
give precipitate with \( A g N O_{3} \) solution.
Reason: \( C H C l_{3} \) is covalent compound.
A. Both Assertion and Reason are true and Reason is the correct explanation to Assertion
B. Both Assertion and Reason are true and Reason is not the correct explanation to Assertion
c. Assertion is true but Reason is false
D. Assertion is false but Reason is true


Assertion
Radio waves can be polarised
Reason
Sound waves in air are longitudinal in
nature
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


In the case of p-njunction diode at a high value of reverse bias, the current rises sharply. The value of reverse bias is known as
A. cut off voltage
B. zener voltage
c. inverse voltage
D. critical voltage


The value of universal gas constant is
\( 8.3 J / \)mole\( / K, \) the mean kinetic
energy of \( 32 g m \) of oxygen at \( -73^{\circ} C \) will
be
\( \mathbf{A} \cdot 480 J \)
в. \( 4980 J \)
c. \( 2490 J \)
D. \( 100 J \)


A planet revolves around the sun in an elliptical orbit of eccentricity e. If T is the time period of the planet, then the time spent by the planet between the ends of the minor axis and major axis close to the sun is
A \( \cdot \frac{T \pi}{2 e} \)
B \( \cdot T\left(\frac{2 e}{\pi}-1\right) \)
c. \( \frac{T e}{2 \pi} \)
D \( \cdot T\left(\frac{1}{4}-\frac{e}{2 \pi}\right) \)


The drain cleaner, drainex contains
small bits of aluminium which react
with caustic soda to produce dihydrogen.What volume of dihydrogen
at \( 20^{\circ} C \) and one bar will be released
when \( 0.15 g \) of aluminium reacts?


Which of the following is preferentially formed on reaction of oxygen and potassium?
A \( \cdot K_{2} O_{2} \)
в. \( K O_{2} \)
\( \mathrm{c} \cdot \mathrm{K}_{2} \mathrm{O} \)
D. \( K_{2} O_{3} \)


A bag contains 5 white and 7 black
balls; if two balls are drawn what is the
chance that one is white and the other
black?


\( P C l_{5} \) dissociates into \( P C l_{3} \) and \( C l_{2} . \) If
the total pressure of the system in equilibrium is \( P \) at a density \( \rho \) and
temperature \( T, \) show that the degree of dissociation \( \boldsymbol{\alpha}=\frac{\boldsymbol{P} \boldsymbol{M}}{\boldsymbol{\rho} \boldsymbol{R} \boldsymbol{T}}-1, \) where \( \boldsymbol{M} \) is
the relative molar mass of \( \boldsymbol{P} \boldsymbol{C l}_{5} \). If the
vapour density of the gas mixture at
equilibrium has the value of 62 when
the temperature is \( 230^{\circ} \mathrm{C} \), what is the
value of \( \boldsymbol{P} / \rho ? \)


At \( 21.5^{\circ} \mathrm{C} \) and a total pressure of
\( 0.0787 a t m, N_{2} O_{4} \) is \( 48.3 \% \) dissociated
into \( N O_{2} . \) At what total pressure will the percent dissociation be \( 10.0 \% ? \)


Write the chemical formula of
Chloroform.


The value of k for which the quadratic
equation, \( k x^{2}+1=k x+3 x-11 x^{2} \)
has real and equal roots are
A. \( -11 .-3 \)
3 \( 3.31-31-3 \)
B. 5,7
c. 5,-7
D. None of these


In manufacture of sodium carbonate
from Solvay (or ammonia soda) process
the raw material used is :
A . NaOH
в. \( N a_{2} S O_{4} \)
c. Naci
D. \( \operatorname{NaH} \mathrm{CO}_{3} \)


A stationary ball weighing \( 0.25 \mathrm{kg} \) acquires a speed of \( 10 \mathrm{m} / \mathrm{s} \) when hit by a hockey stick. The impulse imparted to the ball is :
A . 2.5 Ns
B. 2.0Ns
c. \( 1.5 \mathrm{Ns} \)
D. 0.5Ns


On the basis of 'sugar' differentiate
D.N.A. and R.N.A:


Growth rings are formed by the activity
of.
A. Extrastelar cambium
B. Intrastelar cambium
c. Interstelar cambium
D. Both B and C


The plane through the intersection of the planes \( x+y+z=1 \) and \( 2 x+ \)
\( 3 y-z+4=0 \) and parallel to \( y \) -axis
also passes through the point.
A. (-3,0,1)
В. (3,3,-1)
c. (3,2,1)
D. (-3,1,1)


If \( A \) has 2 elements and \( B \) has 2
elements, then the number of elements
\( \operatorname{in} B \times A \) is :


What are genes and where these are
located?


If fluid has constant density then it is
said to be
\( A \). thick
B. in-viscous
c. compressible
D. incompressible


Let \( \boldsymbol{f}(\boldsymbol{x})=\boldsymbol{x}^{3}-\boldsymbol{x}^{2}+\boldsymbol{x}+1 \) and
\( \boldsymbol{g}(\boldsymbol{x})= \)
\( \left\{\begin{array}{lll}\max (\boldsymbol{f}(\boldsymbol{t})) & \text { for } & \mathbf{0} \leq \boldsymbol{t} \leq \boldsymbol{x} \\ \boldsymbol{3}-\boldsymbol{x}+\boldsymbol{x}^{2} & \text { for } & \mathbf{1}<\boldsymbol{x} \leq \mathbf{2}\end{array}\right. \)
then
A. \( g(x) \) is continuous and derivable at \( x=1 \)
B. \( g(x) \) is continuous but not derivable at \( x=1 \)
c. \( g(x) \) is neither continuous nor derivable at \( x=1 \)
D. \( g(x) \) is derivable but not continuous at \( x=1 \)


The length of an edge of a cube is \( l \). Find
the formula for the sum of lengths of all the edges of the cube


The shifting of a number from one side of an equation to the other is called as
A. Transposition
B. Distributing
c. commutiving
D. Associativity


In figure, an air lens of radius of curvature of each surface equal to
10cm is cut into a cylinder of glass of
refractive index \( 1.5 . \) The focal length
and the nature of lens are
A. \( 15 \mathrm{cm} \) diverging
B. \( 15 \mathrm{cm} \) converging
c. \( 10 \mathrm{cm} \) diverging
D. \( 10 \mathrm{cm} \) converging


Centre of mass of two body system
divides the distance between two
bodies, is proportional to
A. Inverse of square of the mass
B. Inverse of mass
c. The ratio of the square of mass
D. The ratio of mass


Nitrogen molecule has bond.
A. single
B. double
c. triple
D. multiple (>3)


At \( 1000^{\circ} \mathrm{C}, \Delta G^{\circ} \) of the reaction is:
\( Z n O+C \longrightarrow Z n+C O \)
A. \( -v e \)
B. \( +v e \)
c. zero
D. None of these


This question has multiple correct options
A. If \( 11=12 \), then \( B \) cannot be equal to zero at the origin \( (0, \) 0,0)
B. If \( 11>0 \) and \( 12<0, \) then \( B \) can be equal to zero at the origin (0,0,0)
C. If \( 11<0 \) and \( 12>0, \) then \( B \) can be equal to zero at the origin (0,0,0)
D. all of above


Consider a magnet surround by a wire with a on/of switch \( \mathrm{S} \) (figure) if the
switch is thrown from the off position (open circuit) to the on position (closed circuit.)
A. The current will flow in clock wise direction as seen from left side
B. The current will flow in anti clock wise direction as seen from left hand side
c. The current will not flow
\( D \)
be decided


The foci of the hyperbola \( 16 x^{2}-9 y^{2}- \)
\( 64 x+18 y-90=0 \) are
\( ^{\mathrm{A}} \cdot\left(\frac{24 \pm 5 \sqrt{145}}{12}, 1\right) \)
B. \( \left(\frac{21 \pm 5 \sqrt{145}}{12}, 1\right) \)
c. \( \left(1, \frac{24 \pm 5 \sqrt{145}}{2}\right) \)
D \( \cdot\left(1, \frac{21 \pm 5 \sqrt{145}}{2}\right) \)
E \( \cdot\left(\frac{21 \pm 5 \sqrt{145}}{2},-1\right) \)


If the velocity of a body does not change with time, its acceleration is


For a constant hydraulic stress on an object, the fractional change in the object's volume \( (\Delta V / V) \) and its bulk modulus (B) are related as:
A \( \cdot \frac{\Delta V}{V} \propto B \)
B. \( \frac{\Delta V}{V} \propto \frac{1}{B} \)
c. \( \frac{\Delta V}{V} \propto B^{2} \)
D. \( \frac{\Delta V}{V} \propto B^{-2} \)


A wire \( 1 m \) long has cross-section
\( 1 m m^{2} \) and \( Y=1.2 \times 10^{11} P a . \) Find the
work done in stretching it by \( 2 m m \)
A . 2.4
B. 0.24J
c. 0.024J
D. 1.2.


If \( \left.\left.\right|_{2} ^{4} 1\right|^{2}=\left|\begin{array}{cc}3 & 2 \\ 1 & x\end{array}\right|-\left|\begin{array}{cc}x & 3 \\ -2 & 1\end{array}\right|, \) then \( x= \)
\( A \cdot 6 \)
B. 7
\( c \cdot 8 \)
D. 16


\( \lim _{x \rightarrow 0}(\sin x)^{2 \tan x}=? \)
\( A \cdot 2 \)
B.
\( c \cdot 0 \)
D. Does not exist


A lift is moving up with acceleration a. \( A \) person inside the lift throws the ball
upwards with a velocity u relative to hand. What is the time of flight of the ball?
A \( \cdot \frac{2 u}{(g+a)} \)
в. \( \frac{u}{(g+a)} \)
c. \( \frac{u}{2(g+a)} \)
D. \( \frac{2 u}{(g-a)} \)


Which chambers of human heart carry
deoxygenated blood?
A . Left ventricle and left auricle
B. Right ventricle and right auricle
c. All four chambers of heart
D. No chamber carries deoxygenated blood


The gravitational force between two objects is proportional to \( \frac{1}{R} \) (and not as \( \left.\frac{1}{R^{2}}\right) \) where \( R \) is separation between them then a particle in a circular orbit under such a force would have its orbital speed
\( \nu \) proportional to
A \( \cdot \frac{1}{R^{2}} \)
B . \( R^{0} \)
c. \( R^{\text {। }} \)
D. \( \frac{1}{R} \)


A sonar device on a submarine send out
a signal and receives an echo 5 sec later.
Calculate the speed of sound in water, if the distance of object from the submarine is \( 3625 m \)
A. \( 1440 \mathrm{ms}^{-1} \)
B. \( 1460 \mathrm{ms}^{-1} \)
c. \( 1450 m s^{-1} \)
D. \( 1470 \mathrm{ms}^{-1} \)


Explain the process of sewage water treatment before it can be discharged into natural water bodies.Why is this
treatment essential?


Find the number of all real solution to
the quadratic equation \( x^{2}+2 x=-1 \)


Low temperature favours physical adsorption and high temperature favours chemical adsorption.
A. True
B. False


A student performs an experiment to determine the Young's modulus of a
wire, exactly \( 2 m \) long, by Searle's method. In a particular reading, the student measures the extension in the
length of the wire to be \( 0.8 m m \) with an
uncertainty of \( 0.05 m m \) at a load of
exactly \( 1.0 \mathrm{kg} \). The student also
measures the diameter of the wire to be
\( 0.4 m m \) with an uncertainty of \( 0.01 m m . \) Take \( g=9.8 m s^{-2}(\text {exact }) \)
The Young's modulus obtained from the reading is
A \( \cdot(2.0 \pm 0.3) \times 10^{11} N m^{-2} \)
в. \( (2.0 \pm 0.2) \times 10^{11} \mathrm{Nm}^{-2} \)
c. \( (2.0 \pm 0.1) \times 10^{11} \mathrm{Nm}^{-2} \)
D. \( (2.0 \pm 0.05) \times 10^{11} \mathrm{Nm}^{-2} \)


The time after which they are closest to
each other
A \( .1 / 3 s \)
в. \( 8 / 3 s \)
\( c \cdot 1 / 5 s \)
D. \( 8 / 5 s \)


A person sitting in the rear end of the compartment throws a ball towards the
front end.The ball follows a parabolic path.The train is moving with velocity of \( 20 m / s . A \) person standing outside on the ground also observes the ball.How
will the maximum heights \( y_{m} \) attained
and the ranges \( R \) seen by the thrower
and the outside observer compare with
each other?
A. same \( y_{m} \) different \( R \)
B. same \( y_{m} \) and \( R \)
C. differently \( y_{m} \) same \( R \)
D. differently \( y_{m} \) and \( R \)


Which compound amongst the following has the highest oxidation
number of \( M n ? \)
A. \( K M n O_{4} \)
в. \( K_{2} M n O_{4} \)
\( \mathrm{c} \cdot M n O_{2} \)
D. \( M n_{2} O_{3} \)


The salary of 43 employees are given in the following table. Find the median.
Salary (in \( \quad 4000 \quad 5500 \quad 6000 \)
Rs
Number of employees


Aluminium does not react with water at
room temperature but reacts with both dil. \( H C l \) and \( N a O H \) solutions. Verify
these statements experimentally. Write your observations with chemical equations. From these observations,
can we conclude that \( A l \) is a metalloid?


Total number of inert gases among the following is :
\( \mathrm{H}, \mathrm{He}, \mathrm{Ne}, \mathrm{F}, \mathrm{Ar}, \mathrm{Kr}, \mathrm{K} \)
A . 1
B. 2
\( c \cdot 3 \)
D. 4


Figure shows two coherent sources \( S_{1} \)
and \( S_{2} \) emitting wavelength \( \lambda \). The
separation \( S_{1} S_{2}=1.5 \lambda \) and \( S_{1} \) is
ahead in phase by \( \pi / 2 \) relative \( S_{2} \). Then the maxima occur in direction \( \theta \) given
by \( \sin ^{-1} \) of
\( (i) 0 ;(i i) 1 / 2 ;(i i i)-1 / 6 ;(i v)-5 / 6 \)
Correct options are:
A. \( (i i),(i i i),(i v) \)
B. (i),( \( (i i),(i i i) \)
c. \( (i),(i i i),(i v) \)
D. all of the above


In a infinite G.P., the sum of first three
terms is \( 70 . \) If the extreme terms are multiplied by 4 and the middle term is multiplied by \( 5, \) the resulting terms form an A.p. then the sum to infinite
terms of G.p.
A . 120
B. -40
\( c \cdot 160 \)
D. 80


Explain why? Rate of reaction is change in concentration in a given time interval The change in concentration is (final concentration - initial concentration).
As the reaction progresses the change in concentration of reactants decreases
and that of products increases. D C gets a negative sign in case of reactants and positive sign in case of products.


What is the ratio of the number of
people who prefer playing Cricket in
2001 to the number of people who prefer
playing Tennis in the year \( 2003 ? \)
A . 14: 17
B . 16: 13
c. 15: 11
D. 13: 15


Which of the following is a compound?
A . \( N a C l \)
в. КСl
c. \( N a O H \)
D. All of the above


Assertion
The vascular cambium is absent in
monocots.
Reason
The monocots never show secondary growth.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


Find the slope of the line \( 4 x+3 y=2 \)


The value of \( \sqrt[3]{-512} \times \sqrt[3]{8} \) is \( \ldots \)
A . -16
B. 4
\( c \cdot-5 \)
\( D \cdot-4 \)


A recent investigation of the
complexation of \( \boldsymbol{S C N}^{-} \) with \( \boldsymbol{F} \boldsymbol{e}^{\boldsymbol{3}+} \)
represented by constant \( \boldsymbol{K}_{1}, \boldsymbol{K}_{2} \) and \( \boldsymbol{K}_{3} \)
as 130,16 and 1.0 respectively. What is the overall formation constant of
\( \boldsymbol{F} \boldsymbol{e}(\boldsymbol{S} \boldsymbol{C} \boldsymbol{N})_{3} \) from its component ions
and what is the dissociation constant of
\( F e(S C N)_{3} \) into its simplest ions on the basis of these data?


This is the branch of chemistry deals with chemistry of elements other than carbon and of their compounds:
A. Physical chemistry
B. Inorganic chemistry
c. organic chemistry
D. Analytical chemistry


A convex lens of power +6 dioptre is placed in contact with a concave lens of
power -4 dioptres. What will be the nature and focal length of this combination?
A. Concave, \( 25 \mathrm{cm} \)
B. Convex, \( 50 \mathrm{cm} \)
c. concave, \( 20 \mathrm{cm} \)
D. Convex, \( 100 \mathrm{cm} \)


The following pie chat gives the marks second in an examination by a student
in Hindi, English, Mathematics, Social
Science and Science. If the total marks
obtained by the student were 540 answer the following questions. All values are shown in degrees.
Examine whether the sum of the marks
obtained in Social Science and
Mathematics is more than that in
Science and Hindi.


When conc. \( H_{2} S O_{4} \) was treated with
\( \boldsymbol{K}_{4}\left[\boldsymbol{F} e(\boldsymbol{C} \boldsymbol{N})_{6}\right], \boldsymbol{C} \boldsymbol{O} \) gas was evolved. By
mistake, somebody used dilute \( \boldsymbol{H}_{2} \boldsymbol{S} \boldsymbol{O}_{4} \)
instead of conc. \( \boldsymbol{H}_{2} \boldsymbol{S} \boldsymbol{O}_{4} \) then the gas
evolved was:
A. \( C O \)
в. \( H C N \)
c. \( N_{2} \)
D. \( C O_{2} \)


The primary winding of a transformer has 500 turns whereas its secondary has 5000 turns. The primary is connected to an ac supply of \( 20 \vee, 50 \)
Hz. What will be the output of the secondary?


The \( _{\text {十一一一一一一一一 }} \) present in the compound is oxidised to water which condenses on the cooler parts of the
test-tube or in the bulb of delivery tube:
A. Hydrogen
B. copper
c. carbon soot
D. None of the above


Assertion(A): However long a fuse wire may be, the safe current that can be
allowed is the same.
Reason (R) : The safe current that can be allowed to pass through a fuse wire depends on the radius of the wire.
A. Both (A) and (R) are true and (R) is the correct explanation of A
B. Both (A) and (R) are true but (R) is not the correct explanation of
c. (A) is true but (R) is false
D. (A) is false but (R) is true


Consider a tank made of
glass(refractive index 1.5 ) with a thick bottom. It is filled with a liquid of
refractive index \( \mu . \) A student finds that,
irrespective of what the incident angle (see figure) is for a beam of light entering the liquid, the light reflected from the liquid glass interface is never completely polarized. For this to happen the minimum value of \( \mu \) is :
A \( \cdot \frac{3}{\sqrt{5}} \)
в. \( \frac{5}{\sqrt{3}} \)
c. \( \sqrt{\frac{5}{3}} \)
\( D \)


Find the differential equation of the
family of concentric circles \( x^{2}+y^{2}= \)
\( \boldsymbol{a}^{2} \)


Which of the following are correct?
(i) Sponges: Cellular level of organisation
(ii) Cnidaria : Tissue level of
organisation
(iii) Platyhelminthes: Organ level of organisation
(iv) Annelids, Arthropods, Molluscs, Echinoderms and Chordates: Organ
system level of organisation.
A. (i) and (ii) only
B. (ii) and (iv) only
C. (ii) and (iii) only
D. (i), (ii), (iii) and (iv)


Which of the following is true regarding dimagnetic substances (symbols have their usual meaning)?
\( \mathbf{A} \cdot \mu_{r}>1, \chi_{m}>1 \)
B \( \cdot \mu_{r}>1, \chi_{m}<1 \)
\( \mathbf{c} \cdot \mu_{r}<1, \chi_{m}<0 \)
D. \( \mu_{r}<1, \chi_{m}>0 \)


If \( D_{x}=25, D=5 \) are the values of the
determinants for certain simultaneous
equations in \( x \) and \( y, \) find \( x \)


The degree of dissociation of \( \boldsymbol{P C l}_{5}(\boldsymbol{\alpha}) \)
obeying the equilibrium,
\[
\boldsymbol{P C l}_{5}(\boldsymbol{g}) \rightleftharpoons \boldsymbol{P C l}_{3}(\boldsymbol{g})+\boldsymbol{C l}_{2}(\boldsymbol{g})
\]
is approximately related to the pressure at equilibrium by :
\( A \cdot \alpha \propto P \)
в.
\[
\alpha \propto \frac{1}{\sqrt{P}}
\]
\( c \)
\[
\alpha \propto \frac{1}{P^{2}}
\]
\( D \)
\[
\alpha \propto \frac{1}{P^{4}}
\]


Arrange the following in increasing lattice energy: \( L i F, L i B r, L i I \)


The rocket works on the principle of conservation of:
A. Energy
B. Angular momentum
c. Momentum
D. Mass


The area enclosed by the velocity-time sketch below the time axis represents
A . positive displacement
B. negative displacement
c. zero displacement
D. total displacement


Solve:
\( \boldsymbol{x}+\mathbf{3} \boldsymbol{y}=\mathbf{4} \)
\( 2 x-y=1 \)


Coulomb's law is used to calculate the
energy of an ion pair.
A. Gas law is used to calculate the energy of an ion pair.
B. Coulomb's law is used to calculate the velocity of an ion pair
C. Coulomb's law states that the potential energy (E) of interaction of two ions is directly proportional to the product of their charges and inversely proportional to the distance between them, so the statement is True
D. Ideal gas law is used to calculate the velocity of an ion pair.


If the number of shot in a triangular pile is to the number of shot in a square pile
of double the number of courses as 13
to \( 175 ; \) find the number of shot in each
pile.


Which of the following options is
correct?
A. Transfer of pollen grains from the anther to the stigma of the same flower-Autogamy
B. Transfer of pollen grains from the anther of one flower to the stigma of another flower of same plantGeitonogamy
C. Transfer of pollen grains from the anther to the stigma of a genetically different plant of same speciesXenogamy
D. All of these


Solve the following systems of
inequalities graphically: \( \boldsymbol{x}+\boldsymbol{y} \leq \)
\( \mathbf{9}, \boldsymbol{y}>\boldsymbol{x}, \boldsymbol{x} \geq \mathbf{1} \)


\( \operatorname{Let} \boldsymbol{f}(\boldsymbol{x})=\left\{\begin{array}{ll}\mathbf{3} \boldsymbol{x}-\mathbf{4}, & \mathbf{0} \leq \boldsymbol{x} \leq \mathbf{2} \\ \mathbf{2} \boldsymbol{x}+\boldsymbol{\lambda}, & \mathbf{2}<\boldsymbol{x} \leq \mathbf{3}\end{array} . \text { If } \boldsymbol{f} \) is \right.
continuous at \( x=2, \) then \( \lambda \) is
\( A \)
B.
c. -2
\( D \)


State whether the statement is True or
False.
Expanding \( (a-b+c)^{2} \) we get \( a^{2}+ \)
\( b^{2}+c^{2}-2 a b-2 b c+2 c a \)
A. True
B. False


The ratio of fifth term from the
beginning to the fifth term from the end in the expansion of \( \left(\sqrt[4]{2}+\frac{1}{\sqrt[4]{3}}\right)^{n} \) is
\( \sqrt{6}: 1 . \) If \( n=\frac{20}{\lambda}, \) find the value of \( \lambda \)


The energy change accompanying the
equilibrium reaction \( \boldsymbol{A} \rightleftharpoons \boldsymbol{B} \) is
\( -33.0 k J m o l^{-1} \)
Assuming that pre-exponential factor is
same for forward and backward
reaction. The equilibrium constant K for
the reaction at \( 300 \mathrm{K} \)
\( \mathbf{A} \cdot 5.55 \times 10^{5} \)
B . \( 5.67 \times 10^{3} \)
\( \mathbf{c} \cdot 5.55 \times 10^{6} \)
\( \mathbf{D} \cdot 5.67 \times 10^{2} \)


Mixture of \( \boldsymbol{N a I}(\boldsymbol{s})+\boldsymbol{K}_{2} \boldsymbol{C r}_{2} \boldsymbol{O}_{7}(\boldsymbol{s})+ \)
conc. \( H_{2} S O_{4} \) when heated in a test
tube dark vapours evolve
A. \( I_{2} \)
в. \( N a_{2} \)
\( \mathrm{c} \cdot H_{2} \)
D. All the above


The pair with minimum difference in electronegativity is
A . F, C
в. с, н
c. \( P, H \)
D. Na, cs


Consider the above sequence and
answer the following
\[
\text { Conversion } \boldsymbol{R}-\boldsymbol{C H} \boldsymbol{O} \rightarrow \boldsymbol{R}-\boldsymbol{C O}_{2} \boldsymbol{H}
\]
can be done by :
\( \mathbf{A} \cdot K M N O_{4} \)
\( \mathbf{B} \cdot H_{2} C r O_{4} \)
\( \mathbf{c} \cdot K_{2} C r_{2} O_{7} \)
D. All of these


What is the degree of the following polynomial expression:
\( \frac{4}{3} x^{7}-3 x^{5}+2 x^{3}+1 \)
A. 7
B. 4
\( c \cdot 5 \)
D.


The correct arrangement for decreasing order of reactivity towards electrophilic
substitution reaction is:
\( A \cdot\|I>\mid>\|>I V \)
B. IV > |> || > || ||
c. \( \||>| V>||>\mid \)
D. \( \|>|V>|||>\mid \)


In an experiment on the photo-electric effect, singly ionized helium is excited
electronically to different energy levels. The light emitted by ionized helium is incident on a photo-electric plate in a photocell. When helium is excited to
fourth energy level, then the observed stopping potential of the photocell is found to be five times the stopping
potential measured when the photoelectrons are produced by using light emitted by hydrogen atom, excited to the third energy level. Determine the
work function of the material of the
photo-electric plate.


If \( x^{y}=e^{x-y}, \) then \( \frac{d y}{d x} \) is equal to
A \( \cdot \frac{\log x}{1+\log x} \)
B. \( \frac{\log x}{1-\log x} \)
c. \( \frac{\log x}{(1+\log x)^{2}} \)
D. \( \frac{y \log x}{x(1+\log x)^{2}} \)


In the figure shown, A ray of light is
falling at the angle of incidence \( \boldsymbol{\theta} \)
Identify which of the following best
describe the angle of reflection?
\( A \)
B. 2
\( c \cdot 3 \)
D. 4
\( E \cdot 5 \)


Water mixed with milk is taken in
beaker \( A \) and sugar solution is taken in breaker \( B \). Light is passed through both the beakers. In which beaker the path of light is visible? Why?


The probability of finding an electron in the \( p_{x} \) orbital:
A. zero at nucleus
B. the same on all the sides around nucleus
c. zero on the z-axis
D. maximum on the two opposite sides of the nucleus along the x-axis


Type your question
List-I
\[
\begin{array}{l}\text { List-II } \\ \text { I) } \cos x=-\frac{1}{2} & \text { a) } \mathrm{x}=\frac{7 \pi}{3}\end{array}
\]
\( \begin{array}{ll}\text { II) } \sin x=\frac{\sqrt{3}}{2} & \text { b) } x=\frac{7 \pi}{6} \\ \text { ( } \| \text { ) } \tan x=\sqrt{3} & \text { c) } x=\frac{8 \pi}{3}\end{array} \)
\( A \cdot b, d, c, a \)
\( B \cdot c, a, b, e \)
\( \mathbf{C} \cdot b, c, e, a \)
\( \mathbf{D} \cdot b, e, e, a \)


Which of the following metals is required as a cofactor by all enzymes utilizing ATP in phosphate transfer?
\( A \cdot K \)
в. са
c. Na
D. Mg


The equations of motion of a projectile
are given by \( \boldsymbol{x}=\mathbf{3 6} \boldsymbol{t m} \) and \( \mathbf{2} \boldsymbol{y}=\mathbf{9 6} \boldsymbol{t}- \)
\( 9.8 t^{2} \mathrm{m} . \) The angle of projection is
\( A \cdot \sin ^{-1}(4 / 5) \)
B. \( \sin ^{-1}(3 / 5) \)
\( c \cdot \sin ^{-1}(4 / 3) \)
\( D \cdot \sin ^{-1}(3 / 4) \)


The band structure determines the
conductive behaviour of a solid.
A. True
B. False


A shopkeeper purchases 11 pens for Rs. 10 and sells them at the rate of 10 for
Rs. \( 11, \) then the profit is
A . \( 18 \% \)
в. \( 19 \% \)
c. \( 20 \% \)
D. \( 21 \% \)


Benzoic acid (molecular weight \( =122 \) g
mol \( ^{-1} \) ) associates to form dimer when
dissolved in benzene and the osmotic
pressure of a solution of 5 g of benzoic acid in \( 100 \mathrm{ml} \) benzene is 5.73 atm at
\( 10^{\circ} \mathrm{C} . \) What is the percentage
association of benzoic acid?
A . \( 8 \% \)
B. \( 80 \% \)
c. \( 40 \% \)
D. \( 20 \% \)


Benzene can:
\( \mathbf{A} \cdot \) Discharge colour of \( K M n O_{4} \)
B. Discharge colour of bromine water
C . Polymerise
D. Undergo substitution reactions


Which valve constitutes its presence
between left atrium and left ventricle of
human heart?
A. Bicuspid Valve
B. Tricuspid Valve
c. semi-circular Valve
D. None of the given three


The line drawn from center of circle to
bisect a chord is perpendicular to the chord. Is this true? If true enter 1 else 0 .


In the leaves of which of the following are bulliform cells found?
A. Sunflower
B. Wheat
c. Tinospora
D. Potato


A tunnel is dug along the diameter of the earth. A mass \( m \) is dropped into it. How much time does it take to cross the
earth?
A. 169.2 minutes
B. 84.6 minutes
c. 21.2 minutes
D. 42.3 minutes


Which of the following is/are correct about magnetic lines of force?
A. Are mere directions
B. Have no physical reality
c. can be used to indicate the direction of the magnetic field at a point
D. All of these


Find adjoint of matrix \( \boldsymbol{A}=\left[\begin{array}{ll}\mathbf{1} & \mathbf{2} \\ \mathbf{3} & \mathbf{4}\end{array}\right] \)


The teeth used to grind are marked as
\( A \cdot C \) and \( D \)
3. A and B
\( c . \) D and
D. D and E


In the adjoining figure, \( A B \) and \( A C \) are
two equal chords of a circle of radius 5
\( \mathrm{cm} . \) If \( \mathrm{AB}=\mathrm{AC}=6 \mathrm{cm}, \) find the length of
chord BC


One of the following is a Bronsted acid
but not a Bronsted base
A \( . H_{2} \)
в. \( H_{2} \) о
\( \mathrm{c} \cdot \mathrm{H} \mathrm{CO}_{3}^{\circ} \)
D. \( N H_{3} \)


An oil drop, carrying six electronic
charges and having a mass of \( 1.6 \times \)
\( 10^{-12} g, \) falls with some terminal
velocity in a medium. What magnitude of vertical electric field is required to make the drop move upward with the same speed as it was formerly moving downward with? Ignore buoyancy
A \( \cdot 10^{5} N C^{-1} \)
B . \( 10^{4} N C^{-1} \)
c. \( 3.3 \times 10^{4} N C^{-1} \)
D. \( 3.3 \times 10^{5} N C^{-1} \)


Prove that the associative property hold true for the addition \( \left(\frac{7}{8}+\frac{2}{5}\right)+\frac{8}{3} \)


Statement -1: Kinetic energy can be divided by volume and
Statement -2: Dimensions of kinetic
energy and volumeare different
A. Statement- -1 is True Statement-2 is True
Statement-2 is a correct explanation for Statement-
B. Statement- - - is True Statement-2 is True:
Statement-2 is NOT a correct explanation for Statement-1
c. statement - - is True Statement - - 2 is False.
D. Statement-1 is False Statement- -2 is True


The main reason for the extremely low solubility of carbon dioxide in benzene
\( \left(C_{6} H_{6}\right) \) at room temperature is due to which of the following?
A. The increased disorder due to mixing of the solute and solvent
B. The relatively low strength of the intermolecular forces between carbon dioxide and benzene
c. The strong hydrogen bonding in benzene
D. The weak solvation of carbon and oxygen ions by benzene


In an LCR series a.c. circuit, the voltage
across each of the components. \( L, C \) and \( \mathrm{R} \) is \( 50 \mathrm{V} \). The voltage across the \( \mathrm{LC} \) combination will be;
A . \( 50 \mathrm{V} \)
B. \( 50 \sqrt{2} \mathrm{v} \)
c. \( 100 \mathrm{V} \)
D. \( 0 \mathrm{V} \) (zero)


Simplify: \( (14+2 i)(7+12 i) \) where \( i= \)
\( \sqrt{-1} \)


What is fixed in coke?
A. Amount of carbon
B. Fuel portion in coke
c. \( C O_{2} \) portion
D. All of above


Find \( r \) if \( ^{15} C_{3 r}=^{15} C_{r+3} \)


A slab \( X \) is placed between the two parallel isolated charged plates as
shown in the figure. If \( E_{p} \) and \( E_{q} \) denotes the intensity of electric field at
\( P \) and \( Q, \) then :
A. \( E_{p} \) is reduced by the presence of \( x \), if \( x \) is metallic
B. \( E_{q} \) is increased by presence of \( X \), if \( X \) is dielectric
\( \mathrm{c} . E_{q} \) is in the opposite sense to \( E_{p}, \) if \( \mathrm{X} \) is dielectric
D. \( E_{q} \) is zero, if \( x \) is metallic


What is the two principal thrust in Physics?
A. Unification and Reduction
B. Unification and Oxidation
c. Magnification and Reduction
D. simplification and Reduction


Migration of colloidal particles under
the influence of electric field is known
as electrolysis. If true enter 1 , else enter 0 .
A .


Assertion
A vessel carrying water at room
temperature is kept on a flame. As a result, its heat increases.
Reason
Heat flows from higher temperature to
lower temperature
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


When a body has the same temperature as that of its surroundings:
A. It does not radiate heat
B. It radiates same quantity of heat as it receives from the surroundings
c. It radiates less quantity of heat as it receives from the surroundings
D. It radiates more quantity of heat as it receives from the surroundings


The volume of a gas at constant pressure increases by \( 2 \% \) when the temperature is increased by \( 5^{0} \) K, It's initial temperature
is
\( \mathbf{A} \cdot 100^{0} \mathbf{K} \)
B . 250^ K
\( c \cdot 500^{0} \mathrm{K} \)
D. \( 1000^{\circ} \) к


Choose incorrect statements about
isotopes.
A. Isotopes have same number of electrons
B. Isotopes have same number of neutrons
c. Isotopes have same no of protons
D. Isotopes have same chemical properties


In acidic medium \( N_{2} H_{4}: \)
This question has multiple correct options
A. is oxidised to \( N_{2} \)
B. loses four electrons
C. has equivalent mass 8
D. reduces \( A u C I_{3} \) to \( A u C I \)


The number of times a standard
quantity is present in a given physical quantity, is called its units.
A. True
B. False


Two particles \( X \) and \( Y \), of equal mass
and with unequal positive charges, are free to move and are initially far away
from each other. With \( Y \) at rest, \( X \)
begins to move towards it with initial
velocity \( u \). After a long time, finally
A. \( X \) will stop, \( Y \) will move with velocity \( u \)
B. \( X \) and \( Y \) will both move with velocities \( u / 2 \) each
c. \( X \) will stop, \( Y \) will move with velocity \( <u \)
D. both will move with velocities \( <u / 2 \)


External forces are always balanced State whether true or false.
A. True
B. False


place two substances, 1 and 2 in
contact with each other so that they exchange heat with each other only, until they come to the same temperature. The mass of substance 1
is twice as much as the mass of
substance 2. The temperature change for substance 2 is three times as much
as the temperature change for substance 1. How does the specific heat of substance 2 compare to the specific
heat of substance 1?
A. The specific heat of substance 2 is \( 3 / 2 \) as much as the specific heat of substance 1
B. The specific heat of substance 2 is \( 2 / 3 \) as much as the specific heat of substance 1
c. The specific heat of substance 2 is bigger than the specific heat of substance 1, but we cannot determine how much bigger
D. The specific heat of substance 2 is smaller than the specific heat of substance 1, but we cannot determine how much smaller
E. We cannot determine how the specific heat of substance 2 is related to the specific heat of substance


Carotid artery supplies
A. Oxygenated blood to lungs
B. Oxygenated blood to intestine
C. Oxygenated blood to brain
D. None of these


One second is defined to be equal to:
A. 1650763.73 periods of krypton clock
B. 652189.63 period of krypton clock
C. 1650755.73 periods of cesium clock
D. 9,19,26,31,770 periods of cesium clock


If \( x \) and \( y \) are two intensive variables
then:
This question has multiple correct options
A. \( x y \) is an intensive variable
B. \( \frac{x}{y} \) is an intensive variable
c. \( (x+y) \) is an intensive variable
D \( \cdot \frac{d x}{d y} \) is an extensive property


In a YDSE with two identical slits, when
the upper slit is covered with a thin, perfectly transparent sheet of mica, the intensity at the centre of screen reduces to \( 75 \% \) of the initial value.
Second minima is observed to be above
this point and third maxima below it. Which of the following can be a possible value of phase difference caused by the mica sheet
A \( \cdot \frac{\pi}{3} \)
в. \( \frac{13 \pi}{3} \)
c. \( \frac{17 \pi}{3} \)
D. \( \frac{11 \pi}{3} \)


\( \int \frac{1}{9 x^{2}-25} d x= \)
A \( \cdot \frac{1}{30} \log \mid \frac{3 x+5}{3 x-5} \)
B \cdot \( \log |x+\sqrt{3 x-5}| \)
c. \( \frac{1}{30} \log \left|\frac{3 x-5}{3 x+5}\right| \)
D \cdot \( \log \mid x-\sqrt{3 x-5} \)


Identify the product


Calculate the number of neutrons produced along with \( _{54}^{139} X e \) and \( _{38}^{94} S r \) from the absorption of a slow neutron by \( 235 \boldsymbol{U} \)
\( . \)


Consider the following two compounds.
Would you expect compound \( C \) to have
a resonance stabilization that is more
similar to compound \( A \) or to compound
\( \boldsymbol{B} ? \)
Compound A Compound B
Compound


The number of solutions of the equation \( 1+\sin ^{4} x=\cos ^{2} 3 x, x \in\left[-\frac{5 \pi}{2}, \frac{5 \pi}{2}\right] \)
is?
\( \mathbf{A} \cdot \mathbf{5} \)
B. 4
\( c \cdot 7 \)
\( D \)


Find the product. \( \left(a^{2}\right)\left(2 a^{22}\right)\left(4 a^{26}\right) \)
\( \mathbf{A} \cdot 8 a^{40} \)
B. \( 8 a^{50} \)
\( c \cdot 8 a^{30} \)
D. \( 8^{20} \)


The boiling points of methanol, water
and dimethyl ether are \( 338 \mathrm{K}, 373 \mathrm{K} \) and
\( 307.5 \mathrm{K} \) respectively.Which one of the following statements gives the best explanation for these wide variations in
b.p.?
A. The molecular mass increases from water (18) to methanol
(32) to diethyl ether (74)
B. The extent of intermolecular H-bonding decreases from water to methanol and it is absent in ether
c. The extent of intramolecular H-bonding decreases from ether to methanol to water.
D. The density of water is greater than that of methanol which is in turn less than dimethyl ether


Casting of shadows and eclipses are
based on which property of light?
A. Light does not change the property of medium through which it travels
B. Light can also travel through vaccum
C. Rectilinear property of light
D. Light can be monochromatic or polychromatic


In a meniscus of radius \( r, \) with excess
pressure \( p \) in atmospheric pressure \( p_{0} \) the force experienced
A \( \cdot\left(p-p_{0}\right) \pi r^{2} \)
в. \( \left(p-p_{0}\right) 2 \pi r \)
c. \( p \pi r^{2} \)
D. \( p_{0} 2 \pi r \)


Which of the following is a commercial blood cholesterol lowering agent?
A. cyclosporin A
B. Statin
c. streptokinase
D. Lipases


Those gases or particles that are pumped into the air to make it unclean
are called
A. primary air pollutant
B. secondary air pollutant
c. teritiary air pollutant
D. none of above


Calculate the mole fraction of HCl in the
solution of HCl containing \( 24.8 \% \) of \( \mathrm{HCl} \) by mass. \( [\boldsymbol{H}=\mathbf{1}, \boldsymbol{C l}=\mathbf{3 5 . 5}] \)


Three solid spheres of diameter
\( 2 c m, 12 c m \) and \( 16 c m \) are melted and
made into a single sphere. Find the radius of the new sphere?


A ruptured follicle in mammalian ovary
after the release of ovum, which later gets fertilized, forms
A . Corpus albicans
B. Corpus callosum
c. corpus luteum
D. Graafian follicle


\( \int \frac{\sin x+4 \sin 3 x+6 \sin 5 x+3 \sin 7 x}{\sin 2 x+3 \sin 4 x+3 \sin 6 x} \)
equals.
\( \mathbf{A} \cdot-2 \sin x+c \)
B. \( 2 \sin x+c \)
c. \( 2 \cos x+c \)
D. \( -2 \cos x+c \)


Tails of comets are visible due to:
A. Tyndall effect
B. Reflection
c. Brownian movement
D. None of these


A trolley is under the action of a
constant force \( F \). The sand contained by
it is poured out through a hole in the
floor at the rate of \( m \) per second.lf initial
mass of sand and trolley was \( M \) and
initial speed was \( u, \) the acceleration of
trolley at time \( t \) is given by
\( A \)
в.
c. \( \frac{F}{M-m} \)
D. \( \frac{F}{M+m} \)


The atomic radius decreases in a period
due to :
A. increase in nuclear attraction
B. decrease in nuclear attraction
c. increase in number of electrons
D. decrease in number of electrons


Hydrogen exists in atomic state in
which of the following compounds?
A. Metallic hydrides
B. Ionic Hydride
c. Molecular hydrides
D. \( H_{2} O \)


Sundew is the common name of an
insectivorous plant. Its botanical name
is
A. Drosera
B. Nepenthes
c. Dioenea
D. Utricularia


A ball is initially moving with a velocity
\( 0.5 m s^{-1} . \) Its velocity decreases at a rate
of \( 0.05 m s^{-2} \). How much time will it take
to stop?
\( \mathbf{A} \cdot 5 s \)
в. \( 10 s \)
\( c .15 s \)
D. 20


Find range of \( \boldsymbol{y}=\frac{\boldsymbol{x}}{\mathbf{1}+|\boldsymbol{x}|} \)


Derive expression for the intensity of magnetic field at a point in end on position due to a short bar magnet


What is the \( p H \) of \( 0.1 M N a H C O_{3} ? \)
(Given \( \boldsymbol{K}_{\mathbf{1}}=\mathbf{4 . 5} \times \mathbf{1 0}^{-\mathbf{7}}, \boldsymbol{K}_{\mathbf{2}}=\mathbf{4 . 5} \times \)
\( 10^{-11} \) for carbonic acids.


Calculate \( \theta_{1} \) and \( \theta_{2} \) in shown situation
\begin{tabular}{|cccc|}
\hline \( 200^{\circ} \mathrm{C} \) & \( \theta_{1} \) & \( ^{\theta_{2}} \) & \( 19^{\circ} \mathrm{C} \) \\
\hline \( \mathrm{K} \) & \( 2 \mathrm{K} \) & \( 1.5 \mathrm{K} \) \\
\hline
\end{tabular}


In an LCR circuit having \( \boldsymbol{L}=\mathbf{8 . 0 H}, \boldsymbol{C}- \)
\( 0.5 \mu F \) and \( R=100 \Omega \) in series, the
resonance frequency is:
A . 600 rad/sec
в. \( 600 H z \)
c. 500 rad/sec
D. \( 500 H z \)


Differentiate: \( \boldsymbol{y}=8 \sin \boldsymbol{x} \cos \boldsymbol{x} \) w.r.t \( \boldsymbol{x} \)


Heart of cockroach is
A. Myogenic
B. Neuromyogenic
c. Neurogenic
D. None of the above


\( \boldsymbol{f}(\boldsymbol{x})=\sin \boldsymbol{x} \) and \( \boldsymbol{f}^{\prime}(\boldsymbol{\pi}) \)
A . -1
B.
c. 1
D. None of these


An electric dipole of dipole moment \( \vec{p} \) is placed in a uniform electric field \( \vec{E} \). The
maximum torque experienced by the dipole is
A \( . p E \)
в. \( p / E \)
c. \( E / p \)
D . \( \vec{p} . \vec{E} \)


Development of animal embryo from egg without fertilization is called as
A. Parthenogenesis
B. Parthenocarpy
c. Apospory
D. Apomixis


Plasmogamy is fusion of
A. Two haploid cells including their nuclei
B. Two haploid cells without nuclei fusion
C . Sperm and egg
D. Sperm and two polar nuclei


Say True or False. All the sides of a parallelogram are of equal length.
A. True
B. False


Simplify:
\( 10 a^{2}-15 b^{2}+20 c^{2} \)
A \( \cdot 5\left(2 a^{2}-3 b^{2}+4 c^{2}\right) \)
B. \( 5\left(2 a-3 b^{2}+4 c^{2}\right) \)
C. \( 5\left(10 a^{2}-3 b^{2}+4 c^{2}\right) \)
D. \( 5\left(2 a^{2}+3 b^{2}+4 c^{2}\right) \)


If the plane \( 3 x+2 y+6 z=6 \)
intersects the coordinate axes at
\( A, B, C \) then the area of the \( \Delta A B C \) is
\( \mathbf{A} \cdot 49 \)
B. 7
\( c \cdot \frac{7}{2} \)
D. \( \frac{11}{2} \)


The process by which the percentage of \( U-235^{\prime} \) in \( U-238 \) is increased, is called
A . fission
B. fusion
c. chain reaction
D. enrichment


Let \( A \) and \( B \) be two sets such that \( A \times \)
\( \boldsymbol{B}= \)
\( \{(a, 1),(b, 3),(a, 3),(b, 1),(a, 2),(b, 2) \)
then
A \( \cdot A=\{1,2,3\} \) and \( B=\{a, b\} \)
B . \( A=\{a, b\} \) and \( B=\{1,2,3\} \)
\( \mathbf{c} \cdot A=\{1,2,3\} \) and \( B \subset\{a, b\} \)
D. \( A \subset\{a, b\} \) and \( B \subset\{1,2,3\} \)


During the process of electrolytic refining of copper, some metals present as impurity settle as 'anode mud'. These
are:
A. \( S n \) and \( A g \)
B. \( P b \) and \( Z n \)
c. \( A g \) and \( A u \)
D. Fe and \( N i \)


Q Type your question-
the earth is best represented by \( :(R \rightarrow \)
Radius of the earth)
\( A \)
B.
\( c \)
\( D \)


Smog is formed when fog is mixed with
A. Sulphur
B. Mercury
c. smoke
D. Snow flakes


Heterotrophs may be
A. Holozoic.
B. Saprophytic.
c. Parasitic
D. All of the above.


Verify LMVT for the function \( f(x)=x+ \)
\( \frac{1}{x}, x \in[1,3] \)


\( \frac{k}{k} \)


Which type of polynomial is \( (2+x) ? \)
A. Linear Polynomial
B. Quadratic Polynomial
c. Cubic Polynomial
D. None of above


Given is a diagram showing a defect of
human eye
Study it and answer the following questions:
Name the type of lens used to correct
the defect.
A. Convex
B. Concave
c. Bifocal
D. All of the above can be used


There are three different Urns, Urn-I,
Urn-II and Urn-III containing 1 Blue, 2
Green, 2 Blue, 1 Green, 3 Blue, 3 Green
balls respectively. If two Urns are
randomly selected and a ball is drawn
from each Urn and if the drawn balls are
of different colours then the probability
that chosen Urn was Urn-I and Urn-II is
A \( \cdot \frac{1}{7} \)
B. \( \frac{5}{13} \)
c. \( \frac{5}{14} \)
D. \( \frac{5}{7} \)


A 27 mw laser beam has a cross-
sectional area of \( 10 \mathrm{mm}^{2} \). The
magnitude of the maximum electric field in this electromagnetic wave is given by?[Given permittivity of space \( €_{0} \)
\( =9 \times 10^{-12} \mathrm{Sl} \) units, Speed of light \( c= \)
\( \left.3 \times 10^{8} m / s\right] \)
A. \( 1 \mathrm{kV} / \mathrm{m} \)
B. 2 kv/m
c. \( 1.4 \mathrm{kV} / \mathrm{m} \)
D. \( 0.7 \mathrm{kV} / \mathrm{m} \)


What is the pH range in which phenolphthalein is colourless?
\( A \cdot O \) to 8
B. 8 to 10
\( c \cdot 10 \) to 12
D. 12 to 14


\( C_{2} H_{5} O H \rightarrow C_{2} H_{5} B r . \) In this
conversion, the reagent is:
A. \( H B r \)
B. \( B r_{2}+C C l_{4} \)
c. \( B r_{2} \) water
D. \( K B r \)


Suppose universal gravitational constant starts of decrease, then This question has multiple correct options
A. Length of the day on the earth will increase
B. Length of the year will increase
c. The earth will follow a spiral path of decreasing radius
D. Kinetic energy of the earth will decrease


AND gate
A. it has no equivalence to switching circuit.
B. it is equivalent to series switching circuit.
C. it is equivalent to parallel switching circuit
D. it is a mixture of series and parallel switching circuit.


Which of the following feature is
common for \( \mathrm{NAD}, \mathrm{NAD}^{+}, \mathrm{NADP} \) ?
A. They undergo oxidation reactions
B. They undergo enzyme catalysis
c. They undergo hydrolysis
D. None of the above


Which statements are correct?
This question has multiple correct options
A. Lactose is a disaccharide and is a reducing sugar
B. \( \alpha-D- \) glucopyranoside has an acetal structure and is
non-reducing sugar
c. Methyl\( -\alpha-D- \)glucopyranose has an acetal
structure and is a non-reducing sugar
D. \( \alpha-D- \) Glucopyranose has a hemiacetal structure and
is a reducing sugar


Equation of the plane whose
intercepts are 1,2,3 is
A. \( 6 x+2 y+3 z=1 \)
в. \( x+y+z=6 \)
c. \( 6 x+3 y+2 z=6 \)
D. \( 6 x-3 y-2 z=1 \)


\( C H_{3} C O O H \) is titrated with NaOH
solution. Which of the following
statement is true?
A. conductance increases upto equivalence point, after which it decreases.
B. Conductance decreases upto equivalence point, after which it increases.
c. conductance first increases (but not rapidly) upto equivalence point and then increases rapidly after equivalence point.
D. none


The EN of caesium \( (C s) \) is 0.7 and that
of chlorine ( \( C l \) ) is \( 3.5 . \) Predict the bond
formed between them.


A charge \( Q \) is placed at the corner of a cube. The electric flux through all the faces of the cube is
\( \mathbf{A} \cdot Q / \varepsilon_{0} \)
в. \( Q / 6 \varepsilon_{0} \)
c. \( Q / 8 \varepsilon_{0} \)
D. \( Q / 3 \varepsilon_{0} \)


Both pteridophytes and gymnosperms
have
A. Seeds
B. Independent gametophytes
c. Archegonia
D. ovules


Assertion
In \( C_{4} \) cycle, first stable product has 4
carbon compound
Reason
In \( C_{4} \) plants, \( C_{3} \) cycle is absent
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


Who gave the principle of Electromagnetic Induction?
A. Volta
B. Ampere
c. Faraday
D. orested


\( Z^{X^{A}} \underline{B}^{+\text {ve}} \)decay\( ? \)


\( \boldsymbol{p} \boldsymbol{K}_{a} \) of Quinoline base is \( 4.88 . \) What will
be the \( p K_{a} \) of \( 0.01 \mathrm{M} \) solution of it?
A . 4.88
B. 0.01
c. 9.12
D. 14


The velocity of a particle increases from u to v in a time t during which it covers a distances S. If the particle has a uniform acceleration, which one of the following equations does not apply to the motion?
A \( .2 \mathrm{S}=(\mathrm{v}+\mathrm{u}) \)
B. \( a=\frac{v-u}{t} \)
c. \( v^{2}=u^{2}-2 a S \)
D. \( s=\left[u+\frac{1}{2} a t\right] \)


Find the values of \( k \) for which the given equation has real and equal roots \( \mathbf{2} \boldsymbol{x}^{2}-\mathbf{1} \mathbf{0} \boldsymbol{x}+\boldsymbol{k}=\mathbf{0} \)


\( y=(\sin x)^{\cos x}+(\cos x)^{\sin x}, \) find \( \frac{d y}{d x} \)


Which of the following does not lie in the plane of reflection?
A. Reflecting surface
B. Incident ray
c. Normal at the point of incidence
D. Reflected ray


The quantity of heat flowing for \( 10 s \) through a rod of length \( 40 \mathrm{cm}, \) area
\( 50 \mathrm{cm}^{2} \) is \( 200 \mathrm{J} \). If the temperature
difference at the ends of the rod is \( 80^{\circ} \mathrm{C} \)
the coefficient of thermal conductivity of the rod in \( \mathrm{Wm}^{-1} \mathrm{K}^{-1} \) is:
A . 20
B. 60
c. 80
D. 120


The cardiac impules that results into the heart beat is delayed at
A. Internodal tract
B. AV node
c. Bundle of Hiss
D. Purkinje fibre


Find the potential at the centre of arrangement having 6 charged particles of \( Q=5 \mu C \) each arranged in
the form of a hexagon of side length 0.1
\( \mathrm{m} \)


Assertion
Magnetic lines forms closed loops in
nature.
Reason
Mono-magnetic pole does not exist in
nature.
A. Both Assertion and Reason are correct and Reason is
the correct explanation for Assertion.
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion.
C. Assertion is correct but Reason is incorrect.
D. Both Assertion and Reason are incorrect.


The sum of two numbers is 2000 . If
\( 25 \% \) of the smaller number is one-sixth
of the larger. find the numbers.


If \( f(x)=x^{2}+\frac{x^{2}}{\left(1+x^{2}\right)}+\frac{x^{2}}{\left(1+x^{2}\right)^{2}}+ \)
\( \ldots+\frac{\mathbf{x}^{2}}{\left(1+\mathbf{x}^{2}\right)^{\mathbf{n}}}+\dots \)
then at \( x=0 \) which of the following is
correct?
A \( \cdot \mathrm{f}(\mathrm{x}) \) has no limit
B. \( f(x) \) is discontinuous
c. \( f(x) \) is continuous but not differentiable
D. \( f(x) \) is differentiable


What is the decreasing order of relative basic strengths of following species?
\( A \cdot \|>|V>|>|| \mid \)
c. \( \||>| V>|>| \mid \)


With the help of neat labelled diagram
describe the internal structure of
human heart.


\( A \) and \( B \) are two sets having 3 elements in common.ff \( n(\mathbf{A})=\mathbf{5}, n(\mathbf{B})=\mathbf{4} \) then
Find
\( \boldsymbol{n}(\boldsymbol{A} \times \boldsymbol{B}) \boldsymbol{a} \boldsymbol{n} \boldsymbol{d} \boldsymbol{n}[(\boldsymbol{A} \times \boldsymbol{B}) \cap(\boldsymbol{B} \times \boldsymbol{A})] \)


Assertion: The density of \( \boldsymbol{H}_{2} \boldsymbol{S} \boldsymbol{O}_{4} \)
decreases in lead storage cell during discharging. Reason: Calomel electrode is
a reference electrode and it is better
than hydrogen electrode.
A. Both Assertion and Reason are true and Reason is the correct explanation of Assertion
B. Both Assertion and Reason are true but Reason is not the correct explanation of Assertion
c. Assertion is true but Reason is false
D. Assertion is false but Reason is true
E. Both Assertion and Reason are false


For the expansion occurring from initia to final stage in finite time, which is
correct?
A. Equilibrium exist in initial and final stage
B. Work obtained is maximum
c. Driving force is much greater than the opposing force
D. Both \( (A) \) and \( (B) \)


Select the correct statements:
This question has multiple correct options
A. ferric bromide is obtained when chlorine gas is bubbled through a solution of ferrous bromide.
B. sodium sulphate is obtained when \( S O_{2}(g), H_{2} O(g) \) and air are passed over heated sodium chloride.
\( \mathrm{C} \cdot \mathrm{H}_{2} \mathrm{S} \) gas is liberated when aluminium sulphide becomes damp.
D. nitrogen dioxide gas is liberated by the reaction of ammonia with neutral \( K M n O_{4} \)


If \( m \) and \( n \) are positive real numbers and logm, \( \log \left(\frac{m^{2}}{n}\right), \log \left(\frac{m^{2}}{n^{2}}\right) \) are in A.P then its
general term is-
\( ^{\mathbf{A}} \cdot \log \left(\frac{m^{r}}{n^{r-1}}\right) \)
\( ^{\mathbf{B}} \cdot \log \left(\frac{m^{r+1}}{n^{r}}\right) \)
\( ^{\mathbf{c}} \cdot \log \left(\frac{m}{n}\right)^{n} \)
D. \( \log \left(\frac{m^{r-1}}{n^{r+1}}\right) \)


Let \( 2,6,18, \dots \dots . . \) represents a geometric
progression, then find \( \boldsymbol{S}_{7} \)
A . 2186
в. 2196
\( c .2545 \)
D. 2457


When a charged particle is projected
perpendicular to a magnetic field:
A. Its path is circular in a plane perpendicular to the plane of magnetic field
B. The speed and kinetic energy of the particle remains constant
C. The velocity and momentum of the particle changes only in direction
D. The time period of revolution, angular and frequency of revolution is independent of velocity of the particle and radius of circular path


A particle is projected vertically upwards from a point \( A \) on the ground.
It takes \( t_{1} \) time to reach a point \( B \) but it
still continues to move up. If it takes
further \( t_{2} \) time to reach the ground from
point \( B \) then height of point \( B \) from the ground is
A \( \cdot \frac{1}{2}\left(t_{1}+t_{2}\right)^{2} \)
B. \( g t_{1} t_{2} \)
c. \( \frac{1}{8}\left(t_{1}+t_{2}\right)^{2} \)
D. \( \frac{1}{2} g t_{1} t_{2} \)


Two circles of radii \( 20 \mathrm{cm} \) and \( 37 \mathrm{cm} \)
intersect in \( A \) and \( B . \) If \( O_{1} \) and \( O_{2} \) are
their centres and \( A B=24 \mathrm{cm}, \) then the
distance \( O_{1} O_{2} \) is equal to
A . \( 44 \mathrm{cm} \)
B. \( 51 \mathrm{cm} \)
\( c .40 .5 \mathrm{cm} \)
D. \( 45 \mathrm{cm} \)