lonization constant \( \left(K_{a}\right) \) for three weak
monobasic acids \( H A, H B \) and \( H D \) are
\( 10^{-3}, 10^{-7} \) and \( 10^{-9}, \) respectively at
\( 25^{\circ} \mathrm{C} . \) Which of the following is correct
prediction?
\( \mathbf{A} \cdot(p H)_{N a A}>(p H)_{N a B} \)
B. \( (p H)_{N a A}<(p H)_{N a B} \)
\( \mathbf{c} \cdot(p H)_{N a A}>(p H)_{N a D} \)
D. \( (p H)_{N a B}=7 \)


\( \lim _{x \rightarrow \frac{\pi}{2}}(1+3 \cos x)^{\sec x}= \)
A \( \cdot e^{2} \)
B \( \cdot e^{3} \)
\( c \cdot e^{-2} \)
D. \( e^{-3} \)


Study the following lists
\begin{tabular}{l|l|l}
List I & List II \\
A) & Early seed production in conifers & I) & Indole substance \\
\hline B) & Seed development and maturation & II) & Terpene substance \\
C) & Lateral shoot growth & III) & Volatile substance \\
D) & Root hair formation & IV) & Adenine derivative \\
\hline
\end{tabular}
\( \mathbf{A} \)
\( A-\| I, B-I, C-V, D-I \)
B. \( A-11, B-V, C-I V, D-1 \)
C. \( A-11, B-1, C-V, D-I V \)
D. \( A-I V, B-11 I, C-11, D- \)


Phosphoric acid is formed when phosphorus pentoxide reacts with:
A. oxygen
B. carbon dioxide
c. alcohol
D. water


\( \int\left(1+x-x^{-1}\right) e^{x+x^{-1}} d x \) is equal to
A \( \cdot(x+1) e^{x+x^{-1}}+C \)
B . \( (x-1) e^{x+x^{-1}}+C \)
c. \( x e^{x+x^{-1}}+C \)
D. \( x e^{x+x^{-1}} x+C \)


Explain Kolbe-Schmitt reaction and Fries-rearrangement reaction.


Find the altitude of a parallelopiped determined by \( \vec{a}, \vec{b}, \vec{c} \) if yhe base \( \vec{a}, \& \vec{b} \) and if \( \vec{a}=\hat{i}+\hat{j}+\hat{k} ; \vec{b}=2 \hat{i}+4 \hat{j}- \)
\( \hat{\boldsymbol{k}} \& \overrightarrow{\boldsymbol{c}}=\hat{\boldsymbol{i}}+\hat{\boldsymbol{j}}+\mathbf{3} \hat{\boldsymbol{k}} \)


The principle involved in potentiometer
is
A. variation of current with variati wire on in the diameter of the potentiometer
B. similar to the principle of Wheatstone bridge
C. variation of resistance with temperature
D. both (a) and (b)


Total number of \( S_{N} 1 \) products formed during given reaction will be:


Explain using circuit diagram the working of \( n \) -p-n transistor as \( \mathrm{CE} \) amplifier. Hence obtain expression for
its voltage gain in common emitter configuration.


Which of the processes is being shown
in the figure?
A. Electrodialysis
B. Dialysis
c. Electroosmosis
D. Electrophoresis


If \( \boldsymbol{f}: \boldsymbol{A} \rightarrow \boldsymbol{A}, \) then range of \( \boldsymbol{f} \) where
\( \boldsymbol{A}=\{1,2,3,4\} \) and \( \boldsymbol{f}(\boldsymbol{x})=\boldsymbol{x}^{2}+\boldsymbol{x}+\boldsymbol{2} \)


\[
\begin{aligned}
\operatorname{Let} A &=\left\{\theta: 2 \cos ^{2} \theta+\sin \theta \leq 2\right\} \text { and } \\
B &=\{\theta: \pi / 2 \leq \theta \leq 3 \pi / 2\} . \text { Then }
\end{aligned}
\]
find the value of \( \boldsymbol{A} \cap \boldsymbol{B} \)


The roots of the equation \( \left|\begin{array}{ccc}\boldsymbol{x}-\mathbf{1} & \mathbf{1} & \mathbf{1} \\ \mathbf{1} & \boldsymbol{x}-\mathbf{1} & \mathbf{1} \\ \mathbf{1} & \mathbf{1} & \boldsymbol{x}-\mathbf{1}\end{array}\right|=\mathbf{0} \operatorname{are} \)
A. 1,2
в. -1,2
c. -1,-2
D. 1,-2


The energy diagram of a reaction \( \boldsymbol{P}+ \)
\( Q \rightarrow R+S \) is given.What are \( A \) and \( B \)
in the graph?
A. \( A \rightarrow \) activation energy, \( B \rightarrow \) heat of reaction
B. \( A \rightarrow \) threshold energy, \( B \rightarrow \) heat of reaction
C. \( A \rightarrow \) heat of energy, \( B \rightarrow \) activation reaction
D. \( A \rightarrow \) potential energy, \( B \rightarrow \) energy of reaction


There are 4 horizontal and 6 vertical
equispaced lines as shown.lf a
rectangle is randomly selected then
probability that is a square is
\( ^{A} \cdot \frac{7}{45} \)
в. \( \frac{13}{45} \)
c. \( \frac{11}{18} \)
\( D \)


Two particles of masses \( 4 k g \) and \( 6 k g \)
are at rest separated by 20 m. If they
move towards each other under mutual
force of attraction, the position of the point where they meet is
\( \mathbf{A} \cdot 12 m \) from \( 4 k g \) body
B. \( 12 \mathrm{m} \) from \( 6 \mathrm{kg} \) body
c. \( 8 m \) from 4 kg body
D. \( 10 m \) from \( 4 k g \) body


A kite is flying with the string inclined
at \( 45^{\circ} \) to the horizontal If the string is
straight and \( 50 \mathrm{m} \) long the height at which the kite is flying is
A \( .25 \sqrt{2} m \)
в. \( 50 \sqrt{2} \mathrm{m} \)
c. \( 25 \mathrm{m} \)
D. 50 \( m \)


Assertion
In froth floatation method, collectors
such as pine oil xanthates are added to
the suspension of powdered ore.
Reason

Collectors stabilizes the froth.
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


Fill in the blank.
The time taken by oscillation to
complete is called time period.
A. one
B. Two
c. Three
D. Four


In the reaction, \( \boldsymbol{C}(\boldsymbol{s})+\boldsymbol{C O}_{2}(\boldsymbol{g}) \rightleftharpoons \)
\( 2 C O(g), \) the equilibrium pressure is 12
atm. If \( 50 \% \) of \( C O_{2} \) reacts, \( K_{p} \)
is


\( \int \frac{x \sin ^{-1} x}{\sqrt{1-x^{2}}} d x \) is equal to
A. \( x-\sqrt{1-x^{2}} \sin ^{-1} x+c \)
B. \( x+\sqrt{1-x^{2}} \sin ^{-1} x+c \)
c. \( x+\sin ^{-1} x+c \)
D. \( x-\sin ^{-1} x+c \)


What happens to the following after
fertilization?
Petals


The horizontal component of the weight of a body of mass \( m \) is
A . \( m g \)
B. \( \frac{\mathrm{mg}}{2} \)
c. 0
D. Infinity


Arrange in the order of nucleophilicity:
\( \boldsymbol{H O}^{-}, \boldsymbol{C H}_{3} \boldsymbol{O}^{-}, \boldsymbol{C H}_{3} \equiv \)
\( \boldsymbol{C}^{-}, \boldsymbol{C} \boldsymbol{H}_{3} \boldsymbol{C O O}^{-} \)
A. \( H O^{-}>C H_{3} O^{-}>C H_{3} \equiv C^{-}>C H_{3} C O O \)
в. \( C H_{3} C O O^{-}>H O^{-}>C H_{3} O^{-}>C H_{3} \equiv C^{-} \)
C. \( H O^{-}<C H_{3} O^{-}<C H_{3} \equiv C^{-}<C H_{3} C O O^{-} \)
D. \( C H_{3} C O O^{-}<H O^{-}<C H_{3} O^{-}<C H_{3} \equiv C^{-} \)


To draw water from a well, we have to
(push, pull) the rope.


A quadratic polynomial has at the most zero(es).
A . zero
B. one
c. three
D. two


Fill in the blanks by putting appropriate choices.During adsorption there is \( _{-}- \) -in enthalpy and in the
entropy of a system but adsorption is a
spontaneous process and thus AG must be \( \quad \) Rate of
physisorption with increase in
pressure.
A. decrease, decrease, negative, increases
B. increase, increase, positive, decreases
c. decrease, increase, negative, decreases
D. increase, decrease, positive, increases


An article is marked at Rs. \( 500 . \) The
wholesaler sells it to a retailer at \( 20 \% \)
discount and charges sales-tax on the remaining price at 12.5\%. The retailer, in turn, sells the article to a customer at
its marked price and charges sales-tax at the same rate. Calculate:
(i) the price paid by the customer
(ii) the amount of VAT paid by the retailer.
A . (i) Rs. 662.50
(ii) Rs. 11.50
B . (i) Rs. 562.50
(ii) Rs. 12.50
c. (i) Rs. 472.50
(ii) Rs. 13.50
D. (i) Rs. 410.50
(ii) Rs. 14.50


A sum of Rs.3.75 was paid in 25 paisa,
10 paisa and 5 paisa coins.The number
of 10 paisa coins was four times the number of 25 paisa coins and twice of
the number of 5 paisa coins.How many were there of each type?


Use remainder theorem to find
remainder when \( p(x) \) is divided by \( q(x) \) in the following questions: \( p(x)=x^{4}+ \)
\( \boldsymbol{x}^{3}+\boldsymbol{x}^{2}-\mathbf{5} \boldsymbol{x}+\mathbf{1}, \boldsymbol{q}(\boldsymbol{x})=\boldsymbol{x}+\mathbf{1} \)


If \( z \) is internuclear axis, then which type of overlapping is/are not possible? This question has multiple correct options
A \( . \) sand \( p_{x} \)
B. \( s \) and \( p_{y} \)
\( \mathbf{c} \cdot p_{x}+p_{z} \)
D. \( p_{y}+p_{z} \)


Energy gap between valence band and conduction band of a semiconductor is
A. Zero
B. Infinite
\( c \cdot 1 e V \)
D. 10 eV


How many photons per second enter one
eye if you look directly at a 100 W light bulb \( 2.00 \mathrm{m} \) away? Assume a pupil diameter of \( 4.00 \mathrm{mm} \) and a wavelength of 600 nm. How many photons per
second enter your eye if a \( 1.00 \mathrm{m} \) W laser beam is directed into your eye? \( \lambda= \)
\( 633 n m) \)


A heater coil is cut into two equal parts
and only one part is now used in the heater. The heat generated will now be:
A. doubled.
B. four times
c. one-fourth
D. halved


The electrical resistance in ohms of a
certain thermometer varies with
temperature according to the approximate law:
\( \boldsymbol{R}=\boldsymbol{R}_{\boldsymbol{o}}\left[\mathbf{1}+\boldsymbol{\alpha}\left(\boldsymbol{T}-\boldsymbol{T}_{\boldsymbol{o}}\right)\right] \)
The resistance is \( 101.6 \Omega \) at the triple-
point of water \( 273.16 \mathrm{K}, \) and \( 165.5 \Omega \) at the normal melting point of lead (600.5
K). What is the temperature when the resistance is \( 123.4 \Omega ? \)


Find the inverse of \( \boldsymbol{A}= \)
\( \left[\begin{array}{ccc}\cos \alpha & -\sin \alpha & 0 \\ \sin \alpha & \cos \alpha & 0 \\ 0 & 0 & 1\end{array}\right] \) using elementary
transformation.


\( \int\left(\tan ^{10} x+\tan ^{12} x\right) d x= \)
A. \( \frac{\tan ^{9} x}{9}+c \)
B. \( \frac{\tan ^{13} x}{13}+c \)
c. \( \frac{\tan ^{11} x}{11}+c \)
D. \( \frac{\tan ^{8} x}{8}+c \)


The velocity-time graph of a particle moving in a straight line is shown in
figure. The acceleration of the particle
at \( t=9 \) s is
A. zero
B \( \cdot 5 m / s^{2} \)
\( \mathrm{c} \cdot-5 m / s^{2} \)
D. \( -2 m / s^{2} \)


n figure, show that \( 2(A C+B D)>A B+B C \)
\( +\mathrm{CD}+\mathrm{DA} \)


Clathrates are
A. Inert gases
B. Inert gases + organic or inorganic compounds
C. Halogen + carbon black
D. Halogen + transition elements


A bar of iron is \( 10 \mathrm{cm} \) at \( 20^{\circ} \mathrm{C} \). At \( 19^{\circ} \mathrm{C} \) it
will be \( \left(\alpha_{F e}=11 \times 10^{-6} /^{o} C\right) \)
A. \( 11 x 10^{-6} \mathrm{cm} \) longer
B. \( 11 x 10^{-6} \) cm shorter
\( \mathrm{c} \cdot 11 x 10^{-5} \mathrm{cm} \) shorter
D. \( 11 x 10^{-5} \mathrm{cm} \) longer


The magnitude of force experienced by
the arc \( M N \) is
A. zero
B. \( \frac{\mu_{0} V I_{0}}{\pi R b} \)
C \( \frac{\mu_{0} V I_{0}}{2 \pi R b} \)
D. none of these


If \( f(x)=(\cos x+i \sin x)(\cos 3 x+ \)
\( i \sin 3 x) \ldots(\cos (2 n-1) x+i \sin (2 n- \)
1) \( x \), then \( f^{\prime \prime}(x)= \)
\( \mathbf{A} \cdot n^{2} f(x) \)
B . \( -n^{4} f(x) \)
\( \mathbf{c} \cdot-n^{2} f(x) \)
D. \( n^{4} f(x) \)


The total mechanical energy E
possessed by a body of mass 'm', moving with a velocity 'v' at a height 'h' is given by \( : E=\frac{1}{2} m v^{2}+m g h . \) Make
\( \mathrm{m}^{\prime} \) the subject of formula.
A \( \cdot m=\frac{2 E}{v^{2}+g h} \)
B. \( m=\frac{2 E}{v^{2}+2 g h} \)
c. \( _{m}=\frac{3 E}{v^{2}+2 g h} \)
D. \( _{m}=\frac{E}{v^{2}+2 g h} \)


If \( \theta \) be the angle between the lines
whose direction cosines's are given by \( \mathbf{3} l+\boldsymbol{m}+\mathbf{5} \boldsymbol{n}=\mathbf{0}, \boldsymbol{6} \boldsymbol{m} \boldsymbol{n}-\boldsymbol{2} \boldsymbol{n} l+\mathbf{5} \boldsymbol{l} \boldsymbol{m}= \)
0. Find value of \( 6 \cos \theta \)


Atoms in a \( P_{4} \) molecule of white phosphorus are arranged regularly in which of the following way?
A. At the corners of a cube
B. At the corners of an octahedron
c. At the corners of a tetrahedron
D. At the centre and corners of a tetrahedron


A car accelerates on a horizontal road
due to the force exerted by
A. The engine of the car
B. The driver of the car
c. The car on earth
D. The road on the car


Prove that the line segment joining the
mid points of the sides of a triangle form four triangles, each of which is similar to the original triangle.


In the expression \( y=a \sin (\omega t+\theta), y \)
is displacement and \( t \) is the time. Write
the dimensions of \( \omega \)
\( \mathbf{A} \cdot\left[M^{0} L T^{0}\right] \)
В \( \cdot\left[M^{0} L^{0} T^{0}\right] \)
C . \( \left[M^{0} L^{0} T^{-1}\right. \)
\( \mathbf{D} \cdot\left[M^{1} L^{0} T^{0}\right] \)


The displacement \( x \) of a particle in
motion is given in terms of time by \( x(x- \)
4) \( =1-5 \cos \omega t \)
A. The particle executes SHM
B. The particle executes oscillatory motion which is not SHM
C. motion of the particle is neither oscillator; nor simple harmonic
D. The particle is not acted upon by a force when it is at \( x \) \( =4 \)


The tones that are separated by three octaves have a frequency ratio of
A . 3: 1
B. 6: 1
c. 8: 1
D. 16: 1


The IUPAC name of given compound is:
A. 2,2 -dimethylbutanal
B. 2,3 -dimethylbutnal
C. 2,3 -dimethylbutanol
D. 2,3 -dimethylbutanal


What is the order of rotational
symmetry about the marked point?


Photosynthesis is absent in
A. Photic layer
B. Aphotic layer
c. Benthic layer
D. Pelagic layer


Which does not represent correct
method?
\( \mathbf{A} \cdot T i C l_{4}+2 M g \stackrel{\Delta}{\longrightarrow} T i+2 M g C l_{2}: K \) roll process
B. \( N i(C O)_{4} \stackrel{\Delta}{\longrightarrow} N i+4 C O: \) Mond's process
\( \mathbf{c} \cdot P b I_{2} \stackrel{\Delta}{\longrightarrow} P b+I_{2}: \) Van arkel process
D. \( Z r I_{4} \stackrel{\Delta}{\longrightarrow} Z r+2 l_{2}: \) Van arkel process


The pH of 0.05 M aqueous solution of
diethyl amine is 12. calculate its \( K_{b} \)
A. \( 2 \times 10^{-3} \)
В. \( 2.5 \times 10^{-4} \)
c. \( 2.5 \times 10^{-3} \)
D. \( 2 \times 10^{-4} \)


Assertion: A resistance is connected to
an ac source. Now a capacitor is included in the series circuit. The
average power absorbed by the resistance will remain same.
Reason: By including a capacitor or an inductor in the circuit average power
across resistor does not change.
A. A and R both are true and R is correct explanation of
B. A and R both are true but R is not the correct explanation of
c. A is true R is false
D. A is false and R is true


The stage of meiosis at which sperm
cell precursor contain two sister chromatids.
A. Anaphase!
B. Metaphase II
c. Prophase I
D. Anaphase II
E. Telophase II


\( \operatorname{Let} \boldsymbol{S}=\{(\boldsymbol{a}, \boldsymbol{b}, \boldsymbol{c}) \in \boldsymbol{N} \times \boldsymbol{N} \times \boldsymbol{N}: \boldsymbol{a}+ \)
\( \boldsymbol{b}+\boldsymbol{c}=\mathbf{2 1}, \boldsymbol{a} \leq \boldsymbol{b} \leq \boldsymbol{c}\} \) and \( \boldsymbol{T}= \)
\( \{(a, b, c) \in N \times N \times N: \)
\( a, b, c a r e i n A P\}, \) where \( N \) is the set of
all natural numbers. Then, the number
of elements in the set \( S \cap T \) is
\( A \cdot 6 \)
B. 7
c. 13
D. 14


The correct IUPAC name of \( M n_{3}(C O)_{12} \)
is:
A. mangesedodecylcarbonyl(0)
B. dodecacarbonylmanganate(0)
c. dodecacarbonylmanganic(II)
D. dodecacarbonyltrimanganese(0)


A square metal wire loop of side \( 10 \mathrm{cm} \)
and of resistance \( 2 \Omega \) moves with
constant velocity in the presence of a uniform magnetic field of induction \( 4 \mathrm{T} \)
perpendicular and into the plane of the loop. The loop is connected to a network
of resistance as shown in the Figure. If
the loop should have a steady current of \( 2 \mathrm{mA} \), the speed of the loop must be (in \( \left.\mathrm{cm} \mathrm{s}^{-1}\right): \)
4
B.
\( c \)
)


Using Binomial theorem, evaluate \( (\mathbf{9 9})^{5} \)


Solve \( : \sin ^{-1}\left(\frac{2 \pi}{4}\right) \)


Which reaction conditions would be
best for the synthesis of isobutyl sec-
butyl ether \( \boldsymbol{C H}_{3} \boldsymbol{C H}_{2} \boldsymbol{C H}\left(\boldsymbol{C H}_{3}\right)-\boldsymbol{O} \)
\( \boldsymbol{C H}_{2} \boldsymbol{C H}\left(\boldsymbol{C H}_{3}\right)_{2} ? \)
A \( \cdot\left(C H_{3}\right)_{2} C H C H_{2} O H+H_{2} S O_{4}+ \) heat
B . \( C H_{3} C H_{2} C H\left(C H_{3}\right) O H+H_{2} S O_{4}+ \) heat
c. \( C H_{3} C H_{2} C H\left(C H_{3}\right) O N a+\left(C H_{3}\right)_{2} C H C H_{2} B r \)
D. \( \left(C H_{3}\right)_{2} C H C H_{2} O N a+C H_{3} C H_{2} C H\left(C H_{3}\right) B r \)


A radioactive sample of \( U^{238} \) decay to \( P b \)
through a process for which half life is
\( 4.5 \times 10^{9} \) years. The ratio of number of
nuclei of \( P b \) to \( U^{238} \) after a time of \( 1.5 \times \)
\( 10^{9} \) years.
(Given \( 21 / 3=1.26) \)
A . 0.12
B. 0.26
\( c \cdot 1.2 \)
D. 0.37


Metals generally form:
A. basic oxides
B. acidic oxides
c. neutral oxides
D. none


Represent the cell in which the following
reaction takes place \( M g(s)+ \)
\( \mathbf{2} \boldsymbol{A} \boldsymbol{g}^{+}(\mathbf{0 . 0 0 0 1} \boldsymbol{M}) \rightarrow \)
\( M g^{2+}(0.130 M)+2 A g(s) \)
Calculate its \( E_{(c e l l)} \) if \( E_{(c e l l)}^{o}=3.17 V \)


\( \triangle P Q R \) is an isosceles triangle with
\( P Q=P R, Q P \) is produced to \( S \) and \( P T \)
bisects the extension angle \( 2 x^{\circ} . \) Prove
that \( \angle Q=x^{o} \) and hence prove that
\( \boldsymbol{P T} \| \boldsymbol{Q} \boldsymbol{R} \)


Find mean deviation from the mean for
the given data
\( \mathbf{8} \quad \mathbf{1 0} \quad \mathbf{1 2} \quad \mathbf{1 4} \) Item
Frequency \( \quad 10 \quad 5 \quad 11 \)
A .2 .12
в. 3.04
c. 10.45
D. 5.76


State True or False.
Electrolysis of molten \( K C l \) gives \( \mathrm{Cl}_{2} \) at
cathode.
A. True
B. False


What is the work of progesterone which is present in oral contraceptive pills?
A. To inhibit ovulation
B. To check oogenesis
c. To check entry of sperms in to cervix and to make them inactive
D. To check sexual behaviour


60 percent people in a group of 10 people, have brown eyes. Two people are to be selected at random from the
group. What is the probability that neither person selected will have brown
eyes?
A . 0.13
B. 0.18
c. 0.25
D. 0.36


Show that \( f(x)= \) \( \left\{\begin{array}{ll}\frac{\cos a x-\cos b x}{x^{2}}, & \text { if } x \neq 0 \\ \frac{1}{2}\left(b^{2}-a^{2}\right), & \text { if } x=0\end{array}\right. \)
where \( a \) and \( b \) are real constants, is
continuous at \( \boldsymbol{x}=\mathbf{0} \)


If \( \cos (A-B)=\frac{3}{5} \& \tan A \tan B=2 \)
then
This question has multiple correct options
A \( \cdot \cos A \cos B=\frac{1}{5} \)
B. \( \sin A \sin B=-\frac{2}{5} \)
\( c \cdot \cos (A+B)=-\frac{1}{5} \)
D. \( \sin A \sin B=\frac{2}{5} \)


Branchless angiosperm trees are called
as
A. Excurrent
B. caudex
c. shrub
D. Deliquscent


Factorial of negative numbers is always
greater than 1
A. True
B. False
c. Either
D. Neither


Keystone species deserve protection
because these
A. Are capable of surviving in harsh environmental conditions
B. Indicates presence of certain minerals in the soil
C. Have become rare due to the over-exploitation
D. Play an important role in supporting other species


Name five objects which can be made
from wood.


Assertion
Hemichordata are connecting link between Chordata and non-Chordata.
Reason In vertebrates the origin of coelom is schizocoelic formed by splitting of mesoderm, whereas all invertebrates except echinoderms are enterocoelic.
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


\( \underbrace{y} \)


Two bodies of mass \( 10 \mathrm{kg} \) and \( 2 \mathrm{kg} \) are moving with velocities \( 2 \hat{i}-7 \hat{j}+ \) \( 3 \hat{k} m s^{-1} \) and \( -10 \hat{i}+35 \hat{j}-3 \hat{k} m s^{-1} \)
respectively. The velocity of their centre of mass is:
A . 2 ims \( ^{-1} \)
B. \( 2 \hat{k} m s^{-1} \)
\( \mathbf{c} \cdot(2 \hat{j}+2 \hat{k}) m s^{-1} \)
D. \( (2 \hat{j}+2 \hat{k}+\hat{k}) m s^{-1} \)


Which of the following relation is
incorrect?
A \( . \Delta S=\Delta H+T \Delta G \)
B . \( \Delta S=\frac{\Delta H-\Delta G}{T} \)
c. \( -\Delta G=-W_{\text {non exp}} \)
D. \( W_{P V}=-P \Delta V \)


For an A.P., find \( S_{7} \) if \( a=5 \) and \( d=4 \)


The following reaction happens in which
test?
\( \boldsymbol{N} \boldsymbol{a}_{2} \boldsymbol{S}+\boldsymbol{N} \boldsymbol{a}_{2}\left[\boldsymbol{F} e(\boldsymbol{C} \boldsymbol{N})_{5} \boldsymbol{N} \boldsymbol{O}\right] \longrightarrow \)
\( N a_{4}\left[F e(C N)_{5} N O S\right] \)
A. Sodium sulphide test
B. Sodium nitroprusside test
c. Both \( A \) and \( B \)
D. None of the above


Find the angular fringe width in Young's double slits experiments with a bluegreen light of wavelength 6000 A. The separation between the slits is \( 3.0 x \)
\( 10^{-3} m \)


What do you think would be the observation if the \( \alpha \) -particle
scattering experiment is carried out
using a foil of a metal other than gold?
A. \( \alpha \) particles would deflect by the foil by large angles
B. Most of the fast moving \( \alpha \) particles would not pass straight through the metal foil
c. There would be no change in the observation
D. All particles would appear rebound


Two circular coils \( X \) and \( Y \)
having radii \( \mathrm{R} \) and \( \mathrm{R} / 2 \) respectively are placed in horizontal plane with their centres coinciding with each other. Coil X has current I flowing through it in the clockwise sense. What must be the
current in the coil \( Y \) to make the total
magnetic field at the centre of two coils zero?


Write the sum of geometrical isomers \( \operatorname{in}\left[\mathrm{Pt}\left(\mathrm{H}_{2} \mathrm{N}-\mathrm{CH}\left(\mathrm{CH}_{3}\right)-\mathrm{COO}^{-}\right)_{2}\right] \) complex
and stereoisomers of \( \left[\mathrm{Pt}(\mathrm{gly})_{3}\right]^{+} \) complex.


Express \( (1-i)-(1+i 6) \) as \( a+i b \)


Find the species which is not perfectly planar.
A \( \cdot \dot{C} H_{3} \)
B . \( \dot{C} H F_{2} \)
\( \mathbf{c} \cdot: C H_{2} \)
D. \( \dot{N} O_{2} \)


Predict the \( \beta \) -elimination product(s) formed when each chloroalkane is
treated with sodium ethoxide in
ethanol. If two or more products might be formed, predict which is the major
product.


Assertion
In acidic medium, \( Z n^{2+} \) is not
precipitated by \( S^{2-} \) ions.
Reason
Common ion effect reduces the
concentration of \( S^{2-} \) ions to the
minimum level.
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


Monthly expenditures on milk in 100 familes of a housing
\( \begin{array}{llll}\text { Monthly } & 0- & 175- & 350- \\ \begin{array}{l}\text { expenditure } \\ \text { (in Rs) }\end{array} & \begin{array}{l}\mathbf{1 7 5} \\ \mathbf{3 5 0}\end{array} & \mathbf{5 2 5}\end{array} \)
Number of
10
14
familes
Find the mean, mode and median for this distribution


In Amoeba, cell membrane help in engulfing the food during the process called as endocytosis


A minute spherical air bubble is rising slowly through a column of mercury contained in a deep jar. If the radius of the bubble at a depth of \( 100 \mathrm{cm} \) is 0.1
\( \mathrm{mm}, \) calculate its depth where its radius is \( 0.126 \mathrm{mm} \) given that the surface tension of mercury is 567 dyne/cm. Assume that the atmospheric pressure is \( 76 \mathrm{cm} \) of mercury
A \( \cdot h_{2}=9.48 \mathrm{cm} \)
В . \( h_{2}=18.48 \mathrm{cm} \)
\( \mathbf{c} \cdot h_{2}=9.48 \mathrm{m} \)
D. \( h_{2}=19.48 \mathrm{cm} \)


Which of the following quantities is zero, when a uniform object is being supported at its center of gravity?
A . Mass
B. Weight
c. Force
D. Moment


An edge of a variable cube is increasing at the rate of \( 5 \mathrm{cm} / \mathrm{s} \). How fast is the
volume of the cube increasing when the
edge is \( 10 \mathrm{cm} \) long?


Find \( \frac{\sqrt[3]{\mathbf{7 2 9}}+\sqrt[3]{\mathbf{3 4 3}}}{\sqrt[3]{\mathbf{5 1 2}}} \)


DNA strands are anti-parallel because
of
A. H-bonds
B. Phosphate diester bonds
c. Disulphide bonds
D. Peptide bonds


Which one among the following has an octet of valence electrons?
A. Cation
B. Inert Gas
c. crystal
D. Anion
E . Element


If \( \mathbf{2} \boldsymbol{A}+\boldsymbol{B}=\left[\begin{array}{cc}\mathbf{1} & \mathbf{-} \mathbf{1} \\ \mathbf{0} & \mathbf{1} \\ \mathbf{1} & \mathbf{-} \mathbf{2}\end{array}\right] \boldsymbol{A}- \)
\( \mathbf{2} \boldsymbol{B}=\left[\begin{array}{cc}\mathbf{0} & \mathbf{1} \\ \mathbf{- 2} & \mathbf{0} \\ \mathbf{1} & \mathbf{- 1}\end{array}\right] \) find \( \boldsymbol{A} \) and \( \boldsymbol{B} \)


A bicycle wheel starts at rest and has a
constant angular acceleration \( \alpha . A \mathrm{t} \) time
\( t, \) it has roated through an angle \( \theta \) and
has an angular velocity \( \omega \).What are \( \omega \) and \( \alpha \) in term of \( \theta \) and \( t \)


Non-Lanthanoid element is:
A . La
B . Lu
\( c \cdot P r \)
D. Pm


A wave of length \( 2 m \) is superposed on
its reflected wave to form a stationary wave. A node is located at \( x=3 m \) The
next node will be located at \( x= \)
A. \( 4 m \)
B. \( 3.75 m \)
\( c .3 .50 m \)
D. \( 3.25 m \)


Asexual reproduction is mostly seen in which type of organism?
A . Unicellular
B. Bicellular
c. Multicellular
D. Both A and B


How many electrons flow through a wire,
when 1 A current passes for a millisecond?


Multiple Correct Answers Type Which of the following pairs have the
same dimensions?
This question has multiple correct options
A. \( h / e \) and magnetic flux
B. \( h / e \) and electric flux
C . Electric flux and \( a / \epsilon_{6} \)
D. Electric flux and \( \mu_{0} I \)


In which of the following mixtures, the London dispersion force is acting as major intermolecular force of attraction?
A. Sodium chloride and water
B. Cyclohexane and carbon tetrachloride
c. water and ethyl alcohol
D. Benzene and acetone


Which of the following is a geminal dihalide?
A. Ethylene dibromide
B. Propylidene chloride
c. Isopropyl bromide
D. None of the above


Percolation tank is constructed to
impound
A. Runoff water
B. Water vapour
c. Purified water
D. None of the above


Their common speed \( \mathbf{v} \) will be
\( \mathbf{A} \cdot \frac{q}{4} \sqrt{\frac{1}{m R \pi \varepsilon_{0}}} \)
\( \mathbf{B} \cdot q \sqrt{\frac{m R \pi \varepsilon_{0}}{4}} \)
\( \mathbf{c} \cdot 4 q \sqrt{m R \pi \varepsilon_{0}} \)
D. \( \frac{4 q}{\sqrt{m R \pi \varepsilon_{0}}} \)


In which of the following pairs, both of them are common greenhouse gases?
A. Oxygen, water vapour
B. Methane, carbondioxide
c. ozone, sulphurdioxide
D. Nitric oxide, chlorofluoro carbons


In Myasthenia gravis, acetylcholine
A. Receptors on motor end plate are reduced
B. Secretion from nerve terminal is reduced
C. Esterase activity is inhibited
D. Secretion from nerve terminals is enhanced


Find the complement of the following angle.
\( 45^{\circ} \)


Which term of the sequence 4,9,14,19
..., is \( 124 ? \)
A . 25
B. 30
c. 15
D. 35


Which of the following are isoelectronic and isostructural?
A \( \cdot N O_{3}^{-}, \mathrm{CO}_{3}^{2} \)
B. \( S O_{3}, N O_{3}^{-} \)
\( \mathrm{c} \cdot \mathrm{CO}_{3}^{-}, \mathrm{CO}_{3}^{2} \)
D. \( \mathrm{CO}_{3}^{2-}, \mathrm{SO}_{3} \)


Two long thin charged rods with charge density \( \lambda \) each are placed parallel to each other at a distance d apart. The
force per unit length exerted on one rod by the other will bewhere \( \left(\boldsymbol{K}=\frac{\mathbf{1}}{\mathbf{4} \boldsymbol{\pi} \varepsilon_{0}}\right) \)
A \( \cdot \frac{K 2 \lambda}{d} \)
в. \( \frac{K 2 \lambda^{2}}{d} \)
c. \( \frac{K 2 \lambda}{d^{2}} \)
D. \( \frac{K 2 \lambda^{2}}{d^{2}} \)


The function \( f(x)=\left\{\begin{array}{cc}\frac{e^{1 / x}-1}{e^{1 / x}+1} & x \neq 0 \\ 0, & x=0\end{array}\right. \)
is
A. continuous at \( x=0 \)
B. discontinuous at \( x=0 \)
c. discontinuous at \( x=0 \) but can be made continuous at
\( x=0 \)
D. None of these


If two events \( A \) and \( B \) are such that
\( \boldsymbol{P}(\overline{\boldsymbol{A}})=\mathbf{0 . 3}, \boldsymbol{P}(\boldsymbol{B})=\mathbf{0 . 5} \) and
\( \boldsymbol{P}(\boldsymbol{A} \cap \boldsymbol{B})=\mathbf{0 . 3}, \) then \( \boldsymbol{P}\left(\frac{\boldsymbol{B}}{\boldsymbol{A} \cup \overline{\boldsymbol{B}}}\right) \) is
equal to
A \( \cdot \frac{5}{8} \)
B. \( \frac{7}{8} \)
\( c \cdot \frac{3}{8} \)
D.


Which rule explains the electronic configuration of chromium is \( [\mathrm{Ar}] \) \( 3 d^{5} 4 s^{1} \) instead of \( [A r] 3 d^{4} 4 s^{2} ? \)
A. Pauli's exclusion principle
B. Aufbau Principle
c. Hund's rule
D. Heisenberg principle


Which of the following is the consequence of man's interference with
nature?
A. Increase in natural resources
B. Biological imbalance
c. Increase in the ozone layer
D. All of the above


Generally solubility of gases in liquids is decreases as increasing temperature. Give reason


Evaluate \( : 125 \sqrt[3]{a^{6}}-\sqrt[3]{125 a^{6}} \)


Which of the following is false regarding an isotope?
A. Same atomic number
B. Different number of neutrons
c. Same mass number
D. Same number of the electrons
E. Same number of protons


Express in centimetres.
\( \mathbf{1 5 . 0 8 m} \)


RQ of sprouting potato is
\( A \)
B. >
\( c \cdot c \)
D. zero


Assertion
If in a \( \triangle A B C, \) a line \( D E \| B C \)
intersects \( A B \) in \( D \) and \( A C \) in \( E, \) then \( \frac{A B}{A D}=\frac{A C}{A E} \)
Reason
If a line is drawn parallel to one side of a triangle intersecting the other two sides, then the other two sides are
divided in the same ratio.
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


In the given figure you find two
triangles. Indicate whether the triangles
are similar. Give reasons in support of
your answer.


The racemic mixture of Alanine
\( \left(\begin{array}{c}\mathbf{C H}_{3} \mathbf{C} \mathbf{H}-\mathbf{C} \mathbf{O} \mathbf{O} \mathbf{H} \\ \mathbf{N} \mathbf{H}_{2}\end{array}\right) \) can be resolved
by using:
(a) \( (+)-2-B u t a n o \)
(b) (I) - 2-Chlorobutanoic acid
\( (c)(\pm)-2-B u t a n o \)
(d) (dl mix)-2-Chlorobutanoic acid
\( A \cdot a \) and \( b \) only
B. a and conly
C. \( b \) and \( d \) only
D. a and donly


Find the probability of successes in
toss of a die, where a success is defined
as
(i) Number greater than 4
(ii) Six appears on die


The incentre of the triangle formed by the points \( \hat{\boldsymbol{i}}+\hat{\boldsymbol{j}}+\hat{\boldsymbol{k}}, \boldsymbol{4} \hat{\boldsymbol{i}}+\hat{\boldsymbol{j}}+\hat{\boldsymbol{k}}, \) and
\( 4 \hat{i}+5 \hat{j}+\hat{k} \) is
A \( \cdot \frac{\hat{i}+\hat{j}+\hat{k}}{3} \)
B. \( \hat{i}+2 \hat{j}+3 \hat{k} \)
c. \( 3 \hat{i}+2 \hat{j}+\hat{k} \)
D. \( \hat{i}+\hat{j}+\hat{k} \)


Assertion: AgCl will not dissolve in a concentrated solution.

Reason: The chloride ions from NaCl
suppress the solubility of AgCl.
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 a chemical reaction, \( \boldsymbol{A} \longrightarrow \boldsymbol{E} \), it is
found that rate of reaction is doubled
when the concentration of \( A \) is
increased four times. The order of the
reaction is:
A . 1
B. 2
c. \( 1 / 2 \)
D. 0


If \( \lim _{x \rightarrow-a} \frac{x^{7}+a^{7}}{x+a}=7 \)
then the value of a is
This question has multiple correct options
\( A \cdot 1 \)
B. -
c. 7
D. none of these


Which of the following has highest boiling point?
A. 1-chloropentane
B. 2-chloropentane
c. 3 -chloropentane
D. All have equal boiling point


The scientists who study ecosystems
are called
A. Ecologists
B. Economists
c. Engineers
D. Environmentalists


Two strings \( A \) and \( B \) with \( \mu=2 k g / m \)
and \( \mu=8 k g / m \) respectively are joined
in series and kept on a horizontal table with both the ends fixed. The tension in
the string is \( 200 \mathrm{N} \). If a pulse of amplitude \( 1 \mathrm{cm} \) travels in \( \mathrm{A} \) towards the junction, then find the amplitude of reflected and transmitted pulse.
A \( . A_{r}=2 A_{T}=7 \)
в. \( _{A_{r}}=\frac{-1}{3} A_{T}=\frac{2}{3} \)
c. \( A_{r}=8 A_{T}=9 \)
D. \( A_{r}=3 A_{t}=4 \)


If the system is not in free fall, which of
the following statements are true about
hydrostatic pressure?
This question has multiple correct options
A. In a liquid, point at different depths can never be at the
same pressure.
B. In a liquid, points at different depths may be at the
same pressure.
C. In different liquids, points at different depths can be at the same pressure.
D. In different liquids, points at the same depth can never be at same pressure.


The number of nine digit numbers that can be formed with different digits is
A. 9.8
B. \( 8.9 ! \)
c. \( 9.9 ! \)
D. 10


An an arithmetic progression of 50
terms, the sum of first ten terms is 210
and the sum of last fifteen terms is
2565. Find the arithmetic progression.


An equilateral prism is lying on the prism table of a spectrometer in a minimum deviation position. If the
angle of incidence is \( 60^{\circ}, \) then the angle
of deviation will be:
A \( .90^{\circ} \)
B. 60
c. 45
D. \( 30^{\circ} \)


Which of the following pairs of ions are
isoelectronic and isostructural?
A \( \cdot C l O_{3}^{-}, S O_{3}^{2} \)
в. \( \mathrm{ClO}_{3}-, \mathrm{CO}_{3}^{2} \)
c. \( C O_{3}^{2-}, N O_{3} \)
D. \( S O_{3}^{2-}, N O_{3} \)


Soil contain rock particles
A. Water and plants
B. Minerals, organic matter, air and water
C. Air and plants
D. Air, water and plants


Assertion
Frictional force is independ of the
velocity of the body
Reason
Friction is due to surface irreqularities.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


Which of the following is not a green-
house gas?
A. water vapour
B. Carbon dioxide
c. Methane
D. oxygen


For diamagnetic materials, magnetic susceptibility is
A. Small and negative
B. Small and positive
c. Large and negative
D. Large and positive


Convert the following improper fraction into mixed fraction.
\( \frac{27}{4} \)


A current of \( 1 A \) flowing along positive \( x \) axis through a straight wire of length \( 0.5 m \) placed in a region of a magnetic field given by \( \vec{B}=(2 \hat{i}+4 \hat{j}) \) T. The
magnitude and direction of the force experienced by the wire respectively
are:
A. \( \sqrt{18} N, \) along positive \( z \) axis
B. \( \sqrt{20} N \), along positive \( x \) axis
c. \( 2 N \) along positive z axis
D. \( 4 N \) along positive Y axis


Consider the given statements about polysaccharides.
I. These are amorphous solids
II. These are insoluble in water
III. These are sugars
The incorrect statements is/are:
A . only III
B. II and III
c. I and III
D. All


If direction numbers of two lines are
\( a, b, c \) and \( b-c, c-a, a-b \) prove that
they are perpendicular to each other.


Draw \( \angle A B C \) of measure \( 125^{\circ} \) and bisect
¡t


The volume of a hemisphere is \( 2425 \frac{1}{2} c m^{3} . \) Find its curved surface
area. \( \left[\boldsymbol{U s e} \boldsymbol{\pi}=\frac{\mathbf{2 2}}{\mathbf{7}}\right] \)


A line which passes through (5,6) and (-3. -4) has an equation of
A. \( 5 x+4 y+1=0 \)
в. \( 5 x-4 y-1=0 \)
c. \( 5 x-4 y+1=0 \)
D. \( 5 x+y-1=0 \)
E. none of these


toppr
Q Type your question
4
\( B \)
\( c \)
\( D \)


If \( \boldsymbol{y}=\cos ^{-1}(\cos \boldsymbol{x}), \) then \( \frac{\boldsymbol{d} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}}, \boldsymbol{a} \boldsymbol{t} \boldsymbol{x}= \)
\( \frac{5 \pi}{4} \) is equal to
\( \mathbf{A} \cdot \mathbf{1} \)
B . -
c. \( \frac{1}{\sqrt{2}} \)
D. \( -\frac{1}{\sqrt{2}} \)


Adsorption method uses to
separate pollutants from air.
A . funne
B. porous solid
c. sand
D. scrubber


Find the total number of pennies in a tenth of a mole of pennies.
A \( \cdot 6.02 \times 10^{23} \) pennies
B. 10 pennies
c. \( 6.02 \times 10^{22} \) pennies
D. 0.1 pennies
E. 1 penny


If \( x^{3}+a x^{2}+b x+6 \) divided by \( x-2 \) as
factor then remainder becomes \( 0, \) and
leaves remainder 3 when divided by
\( x-3 \) find the values of a and \( b \)


Equilibrium constant for the following
reaction is \( 1 \times 10^{-9} \)
\[
\begin{array}{c}
C_{5} H_{5} N(a q .)+H_{2} O(l) \rightleftharpoons \\
C_{5} H_{5} N H^{+}(a q .)+O H^{-}(a q .)
\end{array}
\]
Determine the mole of pyridirium
cholride \( \left(C_{5} H_{5} N . H C l\right) \) that should be
added to \( 500 m L \) solution of \( 0.4 M \)
pyridine \( \left(C_{5} H_{5} N\right) \) to obtain a buffer
solution of \( \boldsymbol{p} \boldsymbol{H}=\mathbf{5} \)
A. 0.1 mole
B. 0.2 mole
c. 0.3 mole
D. 0.4 mole


State whether given statement is True or False.

Does lightning always strike the tallest object?
A. True
B. False


All of the following statements are true
about Bohr's model of the atom except
which one of the following?
A. An electron may assume an infinite number of velocities
B. An atom is most stable when its electronic configuration is that of the ground state
C. The electron shell numbers represents the principal energy levels
D. Electrons in orbitals closest to the nucleus have the
lowest energy
E. They are all consistent


Figure here shows the frictional force
versus displacement for a particle in
motion. The loss of kinetic energy in
travelling over \( \boldsymbol{x}=\mathbf{0} \) to \( \mathbf{2 0} \boldsymbol{m} \) will be :
A .250 .
В. 200 .
c. 150 )
D. 10 J


The total number of electrons in the
carbon atom of methyl free radical is:
A. six
B. seven
c. eight
D. nine


A committee of three persons is to be randomly selected from a group of three
men and two women and the chair
person will be randomly selected from the committee.The probability that the
committee will have exactly two women and one man, and that the chair person
will be a women, is / are
A \( \cdot \frac{1}{5} \)
B. \( \frac{8}{15} \)
\( c \cdot \frac{2}{3} \)
D. \( \frac{3}{10} \)


Four particles each of mass 'm' are placed at the four vertices of a square of side 'a'. Find the net force on any one of
the particle.


Find the general solution of the trigonometric equation \( \sqrt{16 \cos ^{4} x-8 \cos ^{2} x+1}+ \)
\( \sqrt{16 \cos ^{4} x-24 \cos ^{2} x+9}=2 \)


Three charged particles are in equilibrium under their electrostatic forces only:
This question has multiple correct options
A. The particles must be collinear
B. All the charges cannot have the same magnitude
c. All the charges cannot have the same sign
D. The equilibrium is unstable


The density of nucleus is of the order of:
A \( \cdot 10^{5} k g m^{-3} \)
В. \( 10^{16} \) kgm \( ^{-3} \)
\( \mathbf{c} \cdot 10^{17} k g m^{-3} \)
D. \( 10^{25} \mathrm{kgm}^{-3} \)


Assertion
\( \boldsymbol{H}_{2} \boldsymbol{O} \) is the only hydride of group- 16 which is liquid at ordinary temperature.
Reason

In ice, each oxygen atom is surrounded by two covalent bonds and two hydrogen bonding.
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 isolation of fluorine a number of
difficulties were encountered.Which
statements are incorrect:
This question has multiple correct options
A. Fluorine reacts with moist glass vessels
B. Fluorine has great affinity for hydrogen
C. Electrolysis of aqueous HF gives ozonized oxygen
D. The potential required for the discharge of the fluoride ions lowest


Which is the first stage of life cycle of silkworm?
A. Eggg
B. Pupa
c. cocoon
D. Larva


In a circuit, \( L, C \) and \( R \) are connected in series with an alternating voltage source of frequency \( f \). The current leads
the voltage by \( 45^{\circ} . \) The value of \( C \) is :
A \( \frac{1}{\pi f(2 \pi f L+R)} \)
в. \( \frac{1}{\pi f(2 \pi f L-R)} \)
c. \( \frac{1}{2 \pi f(2 \pi f L+R)} \)
D. \( \frac{1}{2 \pi f(2 \pi f L-R)} \)


Which one of the following options
correctly designate the percent contribution of gases \( (A, B, C \text { and } D) \)
responsible of global warming?
\( N_{2} O(6 \%) \)
(2)\( \quad C F C s(20 \%) \quad C O_{2}(14 \%) \quad N_{2} O(6 \%) \) (3) \( N_{2} O(20 \%) \quad C H_{4}(14 \%) \quad C F C s(6 \% \)
(4)
\( C H_{4}(20 \%) \quad N_{2} O(14 \%) \) \( C F C s\left(6^{\circ}\right. \)
\( A \cdot A \)
B. B
\( c \cdot c \)
\( D . D \)


If the lead-acid battery is discharged too far or left in a discharged condition, it cannot be recharged any more because:
A. terminal voltage becomes too low
B. hard lead sulphate forms on its electrodes
c. internal resistance of the cell becomes very high
D. internal resistance of the cell becomes too low


A wheel of radius 0.5 m rolls without sliding on a horizontal surface, starting from rest, the wheel moves with
constant acceleration \( 6 ~ r a d / s^{2} \). The distance travelled by the centre of the wheel from \( t=0 \) to \( t=3 s \) is:
A . 27 m
в. \( 13.5 \mathrm{m} \)
\( c .18 m \)
D. zero


If \( r \) is radius of first orbit, the radius of
nth orbit of the \( \mathrm{H} \) atom will be :
\( A \cdot m^{2} \)
B. rn
\( c \cdot r / n \)
\( D \cdot r^{2} n^{3} \)


If \( \sin ^{-1} x+\sin ^{-1} y+\sin ^{-1} z=\frac{3 \pi}{2} \) and
\( \boldsymbol{f}(1)=2, f(x+y)=f(x) f(y) \) for all
\( \boldsymbol{x}, \boldsymbol{y} \in \boldsymbol{R} . \) Then \( \boldsymbol{x}^{f(1)}+\boldsymbol{y}^{f(2)}+\boldsymbol{z}^{f(3)}- \)
\( \frac{\boldsymbol{x}+\boldsymbol{y}+\boldsymbol{z}}{\boldsymbol{x}^{f(1)}+\boldsymbol{y}^{f(2)}+\boldsymbol{z}^{f(3)}} \) is equal to
\( A \cdot 0 \)
B. 1
\( c \cdot 2 \)
D. 3


In the following sequences of reactions, the compound \( Q \) formed will be?
\[
\mathbb{P} \stackrel{\text { Oleum }}{\longrightarrow} P \frac{(\mathrm{i}) \mathrm{NaOH}}{(\mathrm{ii}) \mathrm{H}^{+}} \rightarrow Q
\]
A . aniline
B. phenol
c. benzaldehyde
D. benzene sulphonic acid


Using sedimentation analysis, check the correctness of the following
equation \( \boldsymbol{v}^{2}=\boldsymbol{u}^{2}+\mathbf{2} \boldsymbol{a} \boldsymbol{s} \)


The entropy change in a system increases as:
A. solid <liquid < gas
B. liquid < gas < solid
c. solid <gas <liquid
D. gas < solid <liquid


Which of the following are used as free
radical chain initiators ?
This question has multiple correct options
A. Benzoyl peroxide
B. di-tert-butyl peroxide
c. Carbon tetrachloride
D. Benzoquinone


Add:
(i) \( 3 m n,-5 m n, 8 m n,-4 m n \)
(ii) \( \boldsymbol{t}-\mathbf{8} \boldsymbol{t} \boldsymbol{z}, \boldsymbol{3} \boldsymbol{t} \boldsymbol{z}, \boldsymbol{-} \boldsymbol{z}, \boldsymbol{z}-\boldsymbol{t} \)
\( (\text { iii) }-7 m n,+5,12 m n+2,9 m n- \)
\( \mathbf{8}, \mathbf{2 m n},-\mathbf{3} \)
\( (i v) a+b-3, b-a+3, a-b+3 \)
(v) \( 14 x+10 y-12 x y-13,18-7 x \)
\( \mathbf{1 0} \boldsymbol{y}+\mathbf{8} \boldsymbol{x} \boldsymbol{y}, \boldsymbol{4} \boldsymbol{x} \boldsymbol{y} \)
\( (v i) 5 m-7 n, 3 n-4 m+2,2 m- \)
\( 3 m n-5 \)
\( (v i i) 4 x^{2} y,-3 x y^{2},-5 x y^{2}, 5 x^{2} y \)


No image formation occurs on blind-
spot of retina because
A. It is not present of the optical axis of the eye.
B. Here, cones and rods are absent.
C. On this part, only cones are present
D. The nerve fibres of this region do not contribute in the formation of optic chiasma.


The process that you see is used for
purification of copper. A thin plate of
pure copper and a thick rod of impure
copper are used as electrodes. Copper
from impure rod is sought to be
transferred to the thin copper plate.
Which electrode should be attached to
the positive terminal of battery and
why?


What type of wave is represented by displacement-distance graph?
A . Longitudinal wave
B. Transverse wave
c. sound waves
D. water waves


Coke floats on water when dissolved,
this is due to the presence of air in it.


Why can one ignore quantisation of electric charge when dealing with macroscopic i.e., large scale charges?


Select the correct statements.
This question has multiple correct options
A ror the reaction, \( H_{2}(g)+I_{2}(g) \rightleftharpoons 2 H I . \frac{d\left[H_{2}\right]}{d t}= \)
\( K_{b}[H I]^{2} \) for backward reaction and \( -\frac{d\left[H_{2}\right]}{d t}= \) \( K_{f}\left[H_{2}\right]\left[I_{2}\right] \)
B. At equilibrium net rate of change in conc. of \( H_{2} \) is zero for, \( H_{2}+I_{2} \rightleftharpoons 2 H I \)
C. A thermodynamically favourable process actually takes place
D. A thermodynamically favourable process will not actually take place unless it chemical kinetics is favourable


A rod of moment of inertia I and length
is suspended from a fixed end and
given small oscillations about the point of suspension, the restoring torque is
found to be \( -(\boldsymbol{m} \boldsymbol{g} \boldsymbol{L} / \mathbf{2}) \boldsymbol{s} \boldsymbol{i} \boldsymbol{n} \boldsymbol{\theta} . \) What will
be the angular equation of motion of the
SHM
A \( \cdot \frac{d^{2} \theta}{d t^{2}}+(m g L / I) \theta=0 \)
B \( \cdot \frac{d^{2} \theta}{d t^{2}}+(m g L / 2 I) \theta=0 \)
\( ^{\mathbf{c}} \cdot \frac{d^{2} \theta}{d t^{2}}+(2 m g L / I) \theta=0 \)
D. \( \frac{d^{2} \theta}{d t^{2}}+(m g L / 4 I) \theta=0 \)


xand \( \frac{8}{9} \) are the additive inverse of each other.Then the value of \( x \) is
A \( \cdot \frac{-8}{9} \)
в. \( \frac{-4}{9} \)
c. \( \frac{-5}{9} \)
D. \( \frac{-7}{9} \)


The correct set the quantum unpaired electron of chlorine atom is:
A \( \cdot n=2,1=1, m_{1}=0 \)
B . \( n=2,1=1, m_{1}=1 \)
c. \( n=3,1=1, m_{1}=1 \)
D. \( n=3,1=0, m_{1}=0 \)


The logic gate equivalent to the above combination of logic gates is
A. OR
B. NAND
\( c \cdot \) AND
D. NOR


Find the area of a regular polygon of 7 sides whose each side measures \( 4 \mathrm{cm} \)
and the circumradius is \( 3 \mathrm{cm}(\sqrt{5}= \) \( \mathbf{2 . 2 3 6}) \)
A \( \cdot 31.304 \mathrm{cm}^{2} \)
B. \( 31.804 \mathrm{cm}^{2} \)
c. \( 31.304 m^{2} \)
D. None of these


How many outcomes are possible when a coin is tossed
A. 2 times
B. 3 times
c. 4 times
D. 5 times


Blue colour of sky is due to


Evaluate \( \frac{\cos 45^{0}}{\sec 30^{0}+\operatorname{cosec} 30^{0}} \)
A. \( \frac{\sqrt{2}}{\sqrt{3}+1} \)
B. \( \frac{\sqrt{3}}{2 \sqrt{2}+2 \sqrt{6}} \)
c. \( \frac{\sqrt{2}}{\sqrt{2}+1} \)
D. \( \frac{\sqrt{2}}{\sqrt{3}+2} \)


The domain of the function \( f(x)= \) \( \left\{\begin{array}{l}\left(x^{2}-9\right) /(x-3), \text { if } x \neq 3 \\ 6, \quad \text { if } x=3\end{array}\right. \)
A \( .(0,3) \)
в. \( (-\infty, 3) \)
\( \mathbf{C} \cdot(-\infty, \infty) \)
D \cdot \( (3, \infty) \)
E \( .(-3,3) \)


What is the electric potential at the centre of a hemisphere of radius \( \mathrm{R} \) and
having surface charge density \( \sigma ? \)
A \( \cdot \frac{\sigma}{2 \varepsilon_{0}} \)
в. \( \frac{\sigma}{\varepsilon_{0}} \)
c. \( \frac{\sigma}{\varepsilon_{0}} R \)
D. \( \frac{\sigma}{2 \varepsilon_{0}} R \)


An ebonite rod rubbed with fur and a
glass rod rubbed with silk cloth are brought nearer to each other. Then
A. they will attract each other
B. they will repel each other
C. nothing will happen to them
D. they will get heated up


A man weighing 100 kg carries a load of
\( 10 \mathrm{kg} \) on his head. He jumps from a tower with the load on his head. What
will be the weight of the load as experienced by the man?
A. zero
в. \( 10 \mathrm{kg} \)
c. slightly more than \( 10 \mathrm{kg} \)
D. \( 110 \mathrm{kg} \)


T-shape molecules are:
A \( . C l F_{3} \)
в. \( I C l_{3} \)
\( \mathbf{c} \cdot B r F_{3} \)
D. all of these


A student has to secure \( 35 \% \) marks to
pass. He got 80 marks and failed by 60 marks. The maximum marks are
A . 100
в. 200
c. 300
D. 400


A shopkeeper has 124 cycle parts, out of
which 8 are defective. What percentage
is defective


Which of the following statements is
accurate in explaining why Gram
negative bacteria are generally more
resistant to penicillins than Gram
positive bacteria?
A. Gram negative bacteria have a thicker cell wall
B. Gram negative bacteria have an outer hydrophilic membrane that acts as an extra barrier
C. Gram negative bacteria can concentrate \( \beta \) -lactamase enzymes in the periplasmic space
D. Gram negative bacteria produce smaller quantities of transpeptidase enzyme


(A) Used extensively in agriculture and horticulture practice
(B) rapid cell division
(C) Initiate rooting in stem cutting
(D) Speed up malting process
(E) Promotes female flower in cucumbers
(F) Dormancy in seeds/buds. How many function from above perform by the Auxin in plants.
A. Three
в. Two
\( c . \) Five
D. Four


A body is freely rolling down on an
inclined plane whose angle of inclination is \( \theta . \) If \( a \) is acceleration of
it's centre of mass then which of the
relation holds true? ( Given acceleration
due to gravity \( =g) \)
A \( . a=g \sin \theta \)
B. \( a<g \sin \theta \)
c. \( a>g \sin \theta \)
\( \mathbf{D} \cdot a=0 \)


Prove for an a.c. circuit:
\( \boldsymbol{P}_{\boldsymbol{a v}}=\boldsymbol{V}_{\boldsymbol{r m s}} \times \boldsymbol{I}_{\boldsymbol{r m s}} \times \cos \boldsymbol{\phi} \)


The shielding constant ' \( \sigma^{\prime} \) for \( _{7} N \) atom
is :
A . 3.10
B. 3.40
c. 3.80
D. 4.20


If \( \vec{a} \) and \( \vec{b} \) are unit vectors, then angle between \( \vec{a} \) and \( \vec{b} \) for \( \sqrt{3} \vec{a}-\vec{b} \) to be unit
vector is
A \( .60^{\circ} \)
B. \( 90^{\circ} \)
\( c \cdot 45 \)
D. 30


If we change the value of \( R \), then
A. Voltage does not change on \( L \)
B. Voltage does not change on LC combination
C. Voltage does not change on \( \mathrm{C} \)
D. Voltage change on LC combination


Which of the following is the property of carbon monoxide?
A. Oxidising agent
B. Catalytic agent
c. Neutral oxide
D. Reducing agent
E. None of the above


The species having tetrahedral shape is
\( - \)
A \( \cdot\left[P d C l_{4}\right]^{2-} \)
B . \( \left[N i(C N)_{4}\right]^{2} \)
c. \( \left[P d(C N)_{4}\right]^{2} \)
\( \mathbf{D} \cdot\left[N i C l_{4}\right]^{2-} \)


Of the following which one is classified
as polyester polymer?
A. Terylene
B. Backelite
c. Melamine
D. Nylon-66


If \( \sin \theta \) is \( \mathrm{G} . \mathrm{M} \) of \( \sin \phi \) and \( \cos \phi, \) then
prove that \( \cos 2 \theta=2 \cos ^{2}\left(\frac{\pi}{4}+\phi\right) \)


A strong base an abstract an \( \alpha- \)
hydrogen from:
A. alkane
B. alkene
c. amine
D. ketone


If the eccentricities of the hyperbola \( \frac{x^{2}}{a^{2}}-\frac{y^{2}}{b^{2}}=1 \) and \( \frac{y^{2}}{b^{2}}-\frac{x^{2}}{a^{2}}=1 \) be \( e \) and
\( e_{1}, \) then \( \frac{1}{e^{2}}+\frac{1}{e_{1}^{2}}= \)
\( \mathbf{A} \cdot \mathbf{1} \)
B. 2
\( c \cdot 3 \)
D. None of these


The probability of getting a boy in a class is 0.6 and there are 45 students In a class, then find the number of girls in the class.


Let \( \vec{A}, \vec{B} \) and \( \vec{C} \) be unit vectors. Suppose that \( \vec{A} \cdot \vec{B}=\vec{A} \cdot \vec{C}=0 \) and that the
angle between \( \vec{B} \) and \( \vec{C} \) is \( \frac{\pi}{6} \) then \( \overrightarrow{\boldsymbol{A}}= \)
A \( \cdot \pm 2(\vec{B} \times \vec{C}) \)
B \( \cdot \pm(\vec{B} \times \vec{C}) \)
c. \( \pm 2(\vec{B}+\vec{C}) \)
D. \( \pm(\vec{B}+\vec{C}) \)


For transistor action, which of the
following statements are correct:
This question has multiple correct options
A. Base, emitter and collector regions should have similar size and doping concentrations
B. The base region must be very thin and lightly doped
C. The emitter junction is forward biased and collector junction is reverse biased
D. Both the emitter junction as well as the collector junction are forward biased


Two uniform solid spheres of equal radii
\( R, \) but mass \( M \) and \( 4 M \) have a centre
to centre separation \( 6 R \), as shown in Figure. The two spheres are held fixed. A projectile of mass \( m \) is projected from
the surface of the sphere of mass \( M \)
directly towards the centre of the second sphere. Obtain an expression for the minimum speed \( v \) of the projectile
so that it reaches the surface of the
second sphere.


The best method to determine the age
of a tree is to
A. Measure its diameter
B. Count the number of leaves
C. Count the number of annual rings at the base of main stem
D. Find out the number of branches


Find the multiplicative inverse of:
(0.11)\( (\sqrt{0.11}) \)


Mother is responsible for the sex of a baby.
A . True
B. False


Kepler's second law is based on:
A. Newton's first law
B. Newton's second law
C . special theory of relativity
D. conservation of angular momentum


The profile of advancing liquid is the same at a given point at all times, then the flow is:
A. turbulent
B. rapid
c. viscous
D. streamlined


What per cent is \( 3 \% \) of \( 5 \% ? \)
A . \( 15 \% \)
B . 30\%
c. \( 50 \% \)
D. 60\%


Toothpaste is in nature.
A. acidic
B. basic
c. neutral
D. Both (A) and (B)


Density of a solid is \( 18300 k g / m^{3} . \) What
is its relative density?
A. 1830
B. 183
\( c \cdot 18.3 \)
D. 1.83


Discuss with your teacher and find out how to distinguish between.
(a) Plasmid DNA and Chromosomal DNA
(b) RNA and DNA
(c) Exonuclease and Endonuclease


What can be the causes of helical
motion of a charged particle?


What is the action of Biuret reagent on
proteins?


A force \( f_{1} \) pushes on an object of mass
\( 10 \mathrm{kg} \) with a force of \( 5 \mathrm{N} \) to the right. \( \mathrm{A} \) force pushes on the same object with a
force \( f_{2} \) of \( 15 \mathrm{N} \) to the left. What is the
acceleration of the object?
A \( \cdot 0.3 \mathrm{m} / \mathrm{s}^{2} \) to the left
B. \( 0.5 \mathrm{m} / \mathrm{s}^{2} \) to the left
C. \( 1 \mathrm{m} / \mathrm{s}^{2} \) to the left
D. \( 1.5 \mathrm{m} / \mathrm{s}^{2} \) to the left
E \( \cdot 10 m / s^{2} \) to the left


The length of the tube of a compound microscope \( 15 \mathrm{cm} . \) The focal length of objective and eye lenses are \( 1 \mathrm{cm} \) and \( 5 \mathrm{cm} \) respectively. The magnifying power of microscope for relaxed vision is:
\( \mathbf{A} \cdot 50 \mathrm{cm} \)
B. \( 75 \mathrm{cm} \)
\( \mathbf{c} \cdot 25 c m \)
D. \( 100 \mathrm{cm} \)


Fill in the blanks to complete the
following sentences:
i) A ray travelling towards the mirror is
the
ii) Angle between reflected ray and normal is the
iii) The angle between reflecting
surface and the reflected ray is the
A. i-incident ray, ii-angle of reflection, iii-glancing angle of reflection
B. i-normal ray, ii-glancing angle of reflection, liii-angle of incidence
C. i-reflected ray, ,ii glancing angle of incidence , iiiglancing angle of reflection
D. i-reflected ray, ,ii-angle of incidence, iii- angle of reflection


During reproduction in certain fungi when the two hyphae fuse together, there is fusion of cytoplasm, but the nuclei remain separate. What is this phenomenon known as?
A. Syncytum
B. Karyogamy
c. Plasmogamy
D. Fibroblast


The rms velocity of hydrogen is \( \sqrt{7} \) times the rms velocity nitrogen. If \( \boldsymbol{T} \) is
the temperature of the gas.
\( \mathbf{A} \cdot T\left(H_{2}\right)=T\left(N_{2}\right) \)
B . \( T\left(H_{2}\right)>T\left(N_{2}\right) \)
c. \( T\left(H_{2}\right)<T\left(N_{2}\right) \)
D. \( T\left(H_{2}\right)=\sqrt{7} T\left(N_{2}\right) \)


If an electron and a proton having same momenta enter perpendicular to a magnetic field, then :
A. curved path of electron and proton will be same (ignoring the sense of revolution)
B. They will move undeflected
c. curved path of electron is more curved than that of the proton
D. Path of proton is more curved


Find the first term of the sequence
whose \( n^{t h} \) is given as:
\( \boldsymbol{t}_{\boldsymbol{n}}=\mathbf{4} \boldsymbol{n}-\boldsymbol{3} \)
A .2
B. 1
\( c .3 \)
D. 4


State whether the statement is True or
False.
Evaluate: \( (a+b c)(a-b c)\left(a^{2}+b^{2} c^{2}\right) \) is
equal to \( a^{4}-b^{4} c^{4} \)
A. True
B. False


Which of the following is used as a food preservative?
A. Aldehydes
B. Ketones
c. carboxylic acid
D. Alcohol


The radius of a sphere is \( 1.41 \mathrm{cm} \). Its volume to an appropriate number of significant figures is then
\( \mathbf{A} \cdot 11.73 \mathrm{cm}^{3} \)
B . 11.736 \( c m^{3} \)
\( \mathrm{c} \cdot 11.7 \mathrm{cm}^{3} \)
D. \( 117 \mathrm{cm}^{3} \)


\( \mathrm{n} O_{3}, \) central oxygen atom is
hypervalent. It shares electron
pairs.


A bag contains n white and n red balls.
Pairs of balls are drawn without
replacement until the bag is empty. Show that the probability that each pair consists of one white and one red ball is
\( \frac{\mathbf{2}^{n}}{2 n} \mathbf{C}_{n} \)


What are emulsions? What are their
different types? Give one example of
each type.


Simplify:
i) \( \left(a^{2}-b^{2}\right)^{2} \)
ii) \( (2 x+5)^{2}-(2 x-5)^{2} \)


\( \mathbf{3}(\boldsymbol{x}-\mathbf{1})=\mathbf{3}(\boldsymbol{x})-\mathbf{3} \)
Classify this equation as a conditional equation
A. An identity
B. A contradiction
c. Association
D. None of the above


When two magnetic poles one of which
is four times greater than the other in pole strength, are placed \( 5 \mathrm{cm} \) apart in air. They exert a mutual force of 144
mg.wt. on each other. The pole strengths of the poles are (in ampere metre)
\( \left(g=10 \mathrm{m} / \mathrm{s}^{2}\right) \)
A .6,3
B. 9,3
c. 12,3
D. 18,6


In figure, the wires \( P_{1} Q_{1} \) and \( P_{2} Q_{2} \) are
made to slide on the rails with same
speed of \( 5 c m s^{-1} . \) In this region, a
magnetic field of \( 1 T \) exists. The electric
current in the \( 9 \Omega \) resistance is
This question has multiple correct options
A. zero if both wires slide toward left
B. zero if both wires slide in opposite directions
C. \( 0.2 m A \) if both wires move toward left
D. \( 0.2 m A \) if both wires move in opposite directions


Match the column I with column II
What is and \( \begin{array}{lllll} & \text { Column I } & & \text { Column II } \\ \text { A. } & \text { Ethylene } & \text { 1. } & \text { Pigment } \\ \text { B. } & \text { Cytokinin } & \text { 2. } & \begin{array}{l}\text { Growth } \\ \text { inhibitor }\end{array} \\ \text { C. } & \text { Phytochrome } & \text { 3. } & \begin{array}{l}\text { Flowering } \\ \text { hormone }\end{array} \\ \text { D. } & \text { Florigen } & \text { 4. } & \text { Zeatin }\end{array} \)
\( \mathbf{A} \)
\( A-4, B-3, C-2, D-1 \)
B. \( A-3, B-4, C-2, D-1 \)
C. \( A-2, B-4, C-1, D-3 \)
D. \( A-2, B-1, C-3, D-4 \)


Potential energy is defined as:
A. The energy of motion
B. Electrical energy
C. The energy of heat
D. Mechanical energy
E. The energy of position and composition


For the following arithmetic progressions write the first term \( a \) and
the common difference \( d \) :
\( -1.1,-3.1,-5.1,-7.1, \dots . \)


The ratio of slopes of adiabatic and
isothermal curves is :
A \( \cdot x \)
B. \( \frac{1}{\gamma} \)
\( c \cdot \gamma^{2} \)
D. \( \gamma^{3} \)


Which one of the following is noncombustible?
A. Stone piece
B. Paper
c. Straw
D. Matchsticks


NItrogen is less reactive at room
temperature Comment on the above statement.


1 kilowatt hr = - - joules.
A \( .10 .6 \times 10^{6} \)
B . \( 3.6 \times 10^{6} \)
c. \( 30.6 \times 10^{6} \)
D. \( 3.6 \times 10^{5} \)


A coil of inductance \( L \) is carrying a
steady current I what is the nature of its stored energy?
A. Magnetic
B. Electrical
c. Both magnetic and electrical
D. Heat


Derive the expression for the capacitance of a parallel plate
capacitore having plate area \( A \) and plate separation d.


The ............ when multiplied always give a new unique natural number.
A. decimal numbers
B. fractions
c. irrational numbers
D. prime numbers


Rewrite the following choosing the correct word from each pair given in
brackets:

The hydrocarbons containing at least
one carbon to carbon
(double/triple) bond are called
(alkenes/alkynes). They have the
general formula \( C_{n} H_{2 n} . \) These were
previously called (olefins/paraffins). When this compound is treated with (bromine/lime) water, decolourisation occurs because
it is
(saturated/unsaturated).


An electric dipole kept in a uniform electric field experiences:
A. Force and a torque
B. A force, but no torque
c. A torque but no force
D. Neither a force nor a torque


Tanning of leather is the:
A. colouring of leather by chemicals
B. drying process to make the leather hard
C. polishing of leather to make it look attractive
D. coagulative hardening of the leather by chemicals


The relation between volume \( V \), pressure
\( \mathrm{P} \) and absolute temperature \( \mathrm{T} \) of an ideal
gas is \( \mathrm{PV}=\mathrm{xT} \), where \( \mathrm{xis} \) a constant. The
value of \( x \) depend upon
A. the mass of the gas molecule
B. the average kinetic energy of the gas molecules
C. P, V and T
D. the number of gas molecules in volume \( V \)


Two charges of \( -2 Q \) and \( Q \) are located at points \( (a, 0) \) and \( (4 a, 0) \) respectively. What is the electric flux through a sphere of radius \( 3 a \) centred at the
origin?
A \( \cdot \frac{Q}{\epsilon_{0}} \)
в. \( \frac{-Q}{\epsilon_{0}} \)
c. \( \frac{-2 Q}{\epsilon_{0}} \)
D. \( \frac{3 Q}{\epsilon_{0}} \)


A seed is protected by and


In a p-type semiconductor, the electron current is \( _{-}-_{-}-_{-}- \) the hole current.
A. equal to
B. less than
c. greater than
D. none of the above


Electromagnetic radiation of wavelength \( 242 \mathrm{nm} \) is just sufficient to ionise the sodium atom. Calculate the
ionisation energy of sodium atom? \( (c= \)
\( 3 \times 10^{8} \mathrm{ms}^{-1}, \mathrm{h}=6.626 \times 10^{-34} \mathrm{Js} \)
A \( \cdot 5.6 \times 10^{-19} k J \)
В . \( 6.9 \times 10^{-18} k J \)
c. \( 8.2 \times 10^{-19} \mathrm{J} \)
D. 495 kJ


\( \cos ^{2} A+\cos ^{2}\left(120^{\circ}+A\right)+ \)
\( \cos ^{2}\left(120^{\circ}-A\right)= \)
A \( \cdot \frac{3}{2} \)
в. \( \frac{1}{2} \)
\( c \cdot \frac{3}{18} \)
D.


Chemical leaching is useful in the concentration of:
A. bauxite
B. copper pyrities
c. cassiterite
D. None of the above


The atomic number of an element which
shows a valency of +3 is :
A . 13
B. 32
\( c .33 \)
D. 17


Electronic configuration \( [\boldsymbol{K} \boldsymbol{r}] \boldsymbol{4} \boldsymbol{d}^{10} \)
belongs to:
A. Period(4) Group(10) Block(d)
B. Period(5) Group(12) Block (d)
c. Period(5) Group(10) Block \( (d) \)
D. Period(4) Group(12) Block(d)


Infective stage of Entamoeba histolytica
is
A. Trophozoite
B. Pre-cyst
c. Uninucleate cyst
D. Tetranucleate cyst


Explain the sex determination in baby?


Is every continuous function
differentiable?


The function \( \boldsymbol{f}(\boldsymbol{x})=\frac{\boldsymbol{x}}{\mathbf{1}+|\boldsymbol{x}|} \) is
differentiable at which of the following?
A. Everywhere
B. Everywhere except at \( x=1 \)
c. Everywhere except at \( x=0 \)
D. Everywhere except at \( x=0 \) or 1


The position vectors of points \( \overrightarrow{\boldsymbol{A}}, \overrightarrow{\boldsymbol{B}}, \overrightarrow{\boldsymbol{C}} \)
are respectively \( \vec{a}, \vec{b}, \vec{c} \). If \( P \) divides \( \overrightarrow{A B} \) in the ratio 3: 4 and \( Q \) divides \( \overrightarrow{B C} \) in
the ratio 2: 1 both externally then \( \overrightarrow{P Q} \)
is
A. \( \vec{b}+\vec{c}-\overrightarrow{2 a} \)
and
В . \( 2(\vec{b}+\vec{c}-\overrightarrow{2 a}) \)
c. \( 4 \vec{a}-\vec{b}-\vec{c} \)
D. \( \frac{-2 \vec{a}-\vec{b}-\vec{c}}{2} \)


The value of \( \tan (90-\theta) \) in the graph
gives :
A. Young's modulus of elasticity
B. compressibility
c. Shear strair
D. Tensile strength


If \( x-y=7 \) and \( x^{3}-y^{3}=133 ; \) find:
the value of \( x y \)
A . 12
B. - -
\( c .-10 \)
D. 5


A bas contains 4 white, 7 black and 5
red balls. Three balls are drawn one after
the other without replacement. Find the probability that the balls drawn are white, black and red respectively.


A body rests on a rough horizontal plane. A force is applied to the body directed towards the plane at an angle
\( \alpha \) with the vertical. The body can be
moved along the plane
A. only if \( \alpha \) is greater than the angle of friction
B. only if \( \alpha \) is lesser than the angle of friction
c. only if \( \alpha \) is equal to the angle of friction
D. for all values of \( \alpha \)


Evaluate: \( \int \frac{x^{3}-x^{2}+x-1}{x-1} d x \)


Which one of the following function is continuous everywhere in its domain but has at least one point where it is not
differentiable?
A \( . f(x)=x^{1 / 3} \)
в. \( f(x)=\frac{|x|}{x} \)
\( \mathbf{c} \cdot f(x)=e^{-x} \)
D. \( f(x)=\tan x \)


A bullet when fired into a target loses half of its velocity after penetrating 20 cm. Further distance of penetration
before it comes to rest is :
A. \( 6.66 \mathrm{cm} \)
B. 3.33 сm
\( c \cdot 12.5 \mathrm{cm} \)
D. \( 10 \mathrm{cm} \)
E. \( 5 \mathrm{cm} \)


A metal cylinder 0.628 m long and \( 0.04 m \) in diameter has one end in
boiling water at \( 100^{\circ} \mathrm{C} \) and other end is melting ice. The co-efficient of Thermal conductivity of the metal is
\( 378 W m^{-1} k^{-1} . \) Latest heat of lce is
\( 3.36 \times 10^{5} J k g^{-1} . \) Find the mass of ice
melts in one hour.


The substance which does not produce
\( \mathrm{O}_{2} \) after
reacting with ozone is:
A. \( H_{2} O_{2} \)
в. \( H g \)
c. \( K O H \)
\( \mathrm{D} \cdot \mathrm{SO}_{2} \)


Refer to the given figure and identify
structure \( X \) in cockroach.
A. Testis
B. Ovary
c. sperms


Angular width of principal maximum in Fraunhoffer single slit diffraction is 0.1
radian. Angular width of secondary maxima is then
A . 0.05 radian
B. 0.1 radian
c. 0.5 radian
D. 0.25 radian


Find the value of
\( \sin 135^{\circ} \)


When magnesium is burnt in air, the weight of magnesium:
A. increases
B. decreases
c. remains same
D. Depends on the atmosphere


Five equal forces of \( 10 \mathrm{N} \) each are
applied at one point and all are lying in one plane. If the angles between any two adjacent forces are equal, the resultant of these forces will be :
A . zero
B. 10N
c. 20N
D. \( 10 \sqrt{2} N \)


The cobalt hexammine cation has an
atom of cobalt in the centre, surrounded by six molecules of ammonia that are
attached to it. The shape of this ion is?
A . Tetrahedral
B. Square
c. Linear
D. Octahedral


Four resistance \( 5 \Omega, 10 \Omega, 15 \Omega \) and an
unknown \( X \Omega \) are connected in series
so as to from Wheatstones network.
Determine the unknown resistance \( \boldsymbol{X} \)
if the network is balanced with these
numerical value of resistance.


If \( \boldsymbol{A}=\left[\begin{array}{ccc}1 & 2 & 2 \\ 2 & 1 & -2 \\ a & 2 & b\end{array}\right] \) is a matrix
satisfying the equation \( \boldsymbol{A} \boldsymbol{A}^{\boldsymbol{T}}=\mathbf{9} \boldsymbol{I} \)
where \( I \) is \( 3 \times 3 \) identity matrix, then
the ordered pair \( (a, b) \) is equal:
A \( .(2,-11) \)
в. (-2,1)
c. (2,1)
()
D. (2,-1)


Determine the electric potential at point P due to two point charges each of charge \( +Q, \) with one point charge being at a distance \( \mathrm{R} \) and the other being at a distance \( 2 R \)
\( A \)
\[
\frac{3 Q}{8 \pi_{6} R}
\]
в.
\[
\frac{2 Q}{12 \pi \epsilon_{0} R}
\]
\( c \)
\[
\frac{3 Q}{12 \pi \epsilon_{0} R}
\]
D.
\[
\frac{2 Q}{8 \pi \epsilon_{0} R}
\]


A particle is going in a spiral path as
shown in Fig. with constant speed. Then
A. its velocity is constant
B. its acceleration is constant
C. magnitude of its acceleration is constant
D. The magnitude of acceleration decreases continuously


What is the probability that the sum of two number on two rolled dices will
yield a 10 or lower?
A \( \cdot \frac{1}{4} \)
в. \( \frac{7}{12} \)
c. \( \frac{5}{12} \)
D. \( \frac{11}{12} \)


\( \int_{0}^{\pi / 2} x \sin x \cos x d x \)


The equivalent resistance between
points \( A \) and \( B \) of the circuit given
below is


A point dipole \( \overrightarrow{\boldsymbol{p}}=\boldsymbol{p}_{0} \hat{\boldsymbol{x}} \) is kept at the
origin. The potential and electrical field due to this dipole on the y-axis at a distance \( d \) are, respectively:
(Take \( V=0 \text { at infinity }) \)
A \( \cdot \frac{|\vec{p}|}{4 \pi \varepsilon_{d} d^{2}}, \frac{-\vec{p}}{4 \pi \varepsilon_{0} d^{3}} \)
В. \( 0, \frac{\vec{p}}{4 \pi \varepsilon_{0} d^{3}} \)
c. \( \frac{|\vec{p}|}{4 \pi \varepsilon_{0} d^{2}}, \frac{\vec{p}}{4 \pi \varepsilon_{0} d^{3}} \)
D. \( _{0,} \frac{-\vec{p}}{4 \pi \varepsilon_{0} d^{3}} \)


In silicon dioxide:
A. Each silicon atom is surrounded by four oxygen atoms and each oxygen atom is bonded to two silicon atoms
B. Each silicon atom is surrounded by two oxygen atoms and each oxygen atom is bonded to two silicon atoms.
C. Silicon atom is bonded to two oxygen atoms.
D. There are double bonds between silicon and oxygen
atoms.


In a room where the temperature is
\( 30^{\circ} \mathrm{C}, \) a body cools from \( 61^{\circ} \mathrm{C} \) to \( 59^{\circ} \mathrm{C} \)
in 4 min. The time (in min) taken by the
body to cool from \( 51^{\circ} \mathrm{C} \) to \( 49^{\circ} \mathrm{C} \) will be:
A . 4
B. 6
c. 5
D.


If \( \alpha \) is a repeated root of \( a x^{2}+b x+ \)
\( \mathbf{c}=\mathbf{0} \operatorname{then} \lim _{x \rightarrow \boldsymbol{\alpha}} \frac{\tan \left(\boldsymbol{a} \boldsymbol{x}^{2}+\boldsymbol{b} \boldsymbol{x}+\boldsymbol{c}\right)}{(\boldsymbol{x}-\boldsymbol{\alpha})^{2}}= \)
\( A \)
B.
\( c \)
D.


Assertion
\( \operatorname{Let} \boldsymbol{A}(\overline{\boldsymbol{a}}) \)
\( \& B(\bar{b}) \) be two points in
space. Let \( \boldsymbol{P}(\bar{r}) \) be a variable point
which moves in space such that \( \overline{\boldsymbol{P} \boldsymbol{A}} \) \( P B \leq 0 \) such a variable points traces a
three-dimensional figure whose volume is given by \( \frac{\pi}{6}\left\{\bar{a}^{2}+\bar{b}^{2}-2 \bar{a} \cdot \bar{b}\right\} \)
\( |\bar{a}-\bar{b}| \)
Reason
Diameter of sphere subtends acute angle at any point inside the sphere \( \& \) its volume is given by \( \frac{4}{3} \pi r^{3} \)
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
C. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


A small ball of mass \( m \) starts at a point
\( A \) with speed \( v_{0} \) and moves along a
frictionless track \( A B \) as shown. The
track \( B C \) has the coefficient of friction
\( \mu . \) The ball comes to stop at \( C \) after
travelling a distance \( L \) which is
\( ^{\mathrm{A}} \cdot \frac{h}{2 \mu}+\frac{v_{0}^{2}}{2 \mu g} \)
в. \( \frac{h}{\mu}+\frac{v_{0}^{2}}{2 \mu g} \)
c. \( \frac{2 h}{\prime \prime}+\frac{v_{0}^{2}}{2 \mu g} \)


Find the mean and standard deviation
respectively for the following data.
Year 10
20 30 40
Number of persons
(cumulative)
32 51
1
A . 34.95 , 4.01
B. 32.95, 2.97
c. 34.95,1.99
D. 32.95 , 3.49


A flywheel is in the form of a uniform circular disc of radius \( 1 \mathrm{m} \) and mass 2
kg. The work which must be done on it to increase its frequency of rotation from 5 rev / \( s \) to 10 rev / s is
approximately
A \( \cdot 1.5 \times 10^{2} J \)
B. \( 3.0 \times 10^{2} J \)
c. \( 1.5 \times 10^{3} J \)
D. \( 3.0 \times 10^{3} J \)


On a humid day, water vapor condenses on a cold surface. During condensation, the entropy of the water:
A . increases
B. decreases
c. remains constant
D. decrease or remains constant


Assertion
\( P C l_{5} \) is a covalent in gaseous and
liquid states but ionic in solid state.
Reason
\( P C l_{5} \) in solid state consists of
tetrahedral \( P C l_{4}^{+} \) cation and octahedral
\( P C l_{6}^{-} \) anion
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 an experiment, the values of two
resistances were measured as \( \boldsymbol{R}_{1}= \)
\( (5.00 \pm .2) \Omega \) and \( R_{2}=(10.00 \pm .1) \Omega \)
The percentage error in the combined resistance in parallel is :
A \( .(4.46 \%) \)
B. \( (7.00 \%) \)
\( c .(5.55 \%) \)
D. \( (3.35 \%) \)


If \( \triangle \boldsymbol{H}_{\text {vaporisation}} \) of substance \( \boldsymbol{X}(\boldsymbol{l}) \)
(molar mass: \( 30 g / m o l \) ) is \( 300 J / g \) at
it's boiling point \( 300 K \), then molar entropy change for reversible condensation process
is
A. \( 30 J / \) mol. \( K \)
в. \( -300 \mathrm{J} / \mathrm{mol.K} \)
c. \( -30 \mathrm{J} / \mathrm{mol} . \mathrm{K} \)
D. None of these


Rate constant of a reaction is 175
litre \( ^{-2} \) mol \( ^{-2} \) sec \( ^{-1} \). What is the order
of reaction?
A. First
B. Second
c. Third
D. zero


Solve:
\( \frac{2 x+7}{5}-\frac{3 x+11}{2}=\frac{2 x+8}{3}-5 \)


\( \ln H_{3} P O_{4} \) which of the following is true?
This question has multiple correct options
A \( \cdot K_{a}=K_{a_{1}} \times K_{a_{2}} \times K_{a_{3}} \)
B . \( K_{a_{1}}<K_{a_{2}}<K_{a_{3}} \)
C \( \cdot K_{a_{1}}>K_{a_{2}}>K_{a_{3}} \)
D. \( K_{a_{1}}=K_{a_{2}}=K_{a_{3}} \)


Maintenance-free batteries, now in use, in
place of common batteries, have :
A. Electrodes made of lead-lead oxide
B. Electrodes made of calcium-containing lead alloy
C. Non-aqueous solvents as medium
D. Platinum electrodes


Neutron ratio(r) (availability for fusion) of an atomic reactor and atom bomb are
A. \( r>1 \) in atomic reactor and \( r<1 \) in bomb
B. \( r=1 \) in atomic reactor and \( r>1 \) in bomb
c. \( r>1 \) in both atomic reactor and bomb
D. r \( <1 \) in both atomic reactor and bomb


Pyrroles are five-membered nitrogencontaining heterocyclic compounds present in heme which is a constituent
of hemoglobin. Draw all the significantly contributing resonance structures of pyrrole (K).

How many resonance structures can be
found?


At what velocity does water emerge from an orifice in a tank in which gauge
pressure is \( 3 \times 10^{5} N m^{-2} \) before the flow starts?
(Take the density of water \( =1000 \mathrm{kg} \mathrm{m}^{-3} \)
.)
\( \mathbf{A} \cdot 24.5 m s^{-1} \)
B . \( 14.5 \mathrm{ms}^{-1} \)
c. \( 34.5 m s^{-1} \)
D. \( 44.5 \mathrm{ms}^{-1} \)


Derive Poynting vector expression for a straight wire of resistance R carrying a current I having length


For 'invert sugar', the correct statement(s) is(are).
(Given: specific rotations of \( (+) \)
sucrose, \( (+) \) -maltose, \( L-(-) \) -glucose
and \( L-(+) \) -fructose in aqueous solution
\( \operatorname{are}+66^{\circ},+140^{\circ},-52^{\circ} \) and \( +92^{\circ} \)
respectively)
This question has multiple correct options
A. 'Invert sugar' is prepared by acid catalyzed hydrolysis of maltose
B. 'Invert sugar' is an equimolar mixture of D-(+)-glucose and \( D-(-) \) -fructose
C. specific rotation of 'invert sugar' is \( -20^{\circ} \)
D. On reaction with \( B r_{2} \) water, 'invert sugar'forms
saccharic acid as one of the products


The type of elements present in group \( 1[\mid A] \) is:
A . alkal
B. alkaline
c. transition
D. halogen


Which compound is soluble in water:
This question has multiple correct options
\( \mathbf{A} \)
\( \left[\left(C H_{3}\right)_{2} N H_{2}\right]^{+} C l^{-} \)
B \( \cdot\left[C H_{3} N H_{3}\right]^{+} C l^{-} \)
\( \mathbf{c} \)
\( \left[\left(C H_{3}\right)_{3} N H\right]^{+} C l^{-} \)
\( \mathbf{D} \cdot P h N O_{2} \)


You are provided with floral buds of Chrysanthemum in your class and are asked to count the chromosomes, then which of the following stages would you prefer to look into?
A. Prophase
B. Metaphase
c. Anaphase
D. Interphase


A car driven round curved path of radius
\( 18 m \) without the danger of skidding. The coefficient of friction between the
tyres of the car and the surface of the
curved path is \( 0.5 . \) What is the maximum speed in kmph of the car for
safe driving nearly? \( \left(\boldsymbol{g}=\mathbf{1 0 m} \boldsymbol{s}^{-\mathbf{2}}\right) \)
A . 9.3
B. 34.48
c. 18.42
D. 20.15


The stress-strain curves for three wires
of different materials are shown in
figure, where \( P, Q \) and \( R \) are the elastic
limits of the wires. The figure shows
that
A. Elasticity of wire \( P \) is maximum
B. Elasticity of wire \( Q \) is maximum
C. Elasticity of wire \( R \) is maximum
D. None of the above is true


Assertion
\( (\mathrm{A}): \) If \( \boldsymbol{a}_{\boldsymbol{n}}=\sqrt{\mathbf{7}+\sqrt{\mathbf{7}+\sqrt{\mathbf{7}+\ldots}}} \)
having \( n \) radical signs, then \( a_{n}< \)
\( 4, \forall n \geq 1 \)
Reason
\( (\mathrm{R}): \) If \( a_{n}<4, \) then \( a_{n+1}<4 \)
A. Both (A) \& (R) are individually true \&
(R) is correct explanation of (A)
B. Both (A) \& (R) are individually true but (R) is not the correct (proper) explanation of (A)
\( \mathrm{c} . \) (A) is true but (R) is false
D. (A) is false but (R) is true


The mean deviation about median for
the following data is \( 4.4 . \) calculate value
of \( x \)
\( 2,3, x, 10,17 \)
A . 3
B. 5
\( c \cdot 7 \)
D. 17


toppr \( E \)
Q Type your question
\( A \)
and
B.
and
\( c \)
and
\( D \)
and


Draw a diagram to represent the nature, position and relative size of the image formed by a i) convex lens for the object
placed at \( 2 F \) ii) concave lens for the
object placed between \( \boldsymbol{F} \) and \( 2 \boldsymbol{F} \)


\( A 60 \mathrm{W} / 120 \mathrm{V} \) bulb is connected to a
\( 240 / 60 \mathrm{Hz} \) supply with an inductance in series. Find the value of inductance so
that bulb gets correct voltage.
A \( \cdot \frac{2.3}{\pi} \) н
в. \( 2 \sqrt{3} \) н
с. \( \pi \) н
D. \( \frac{2 \sqrt{3}}{\pi} \) н


Female reproductive part of Bryophyte
is
A. Antheridium
B. Oogonium
c. Archegonium
D. Sporangium


What is the bond angle in \( C l O_{2} ? \)
A \( \cdot 90^{\circ} \)
B. \( 118^{\circ} \)
\( c \cdot 105^{\circ} \)
D. \( 111^{\circ} \)


The volume of oxygen at NTP evolved when \( 1.70 \mathrm{g} \) of sodium nitrate is heated to a constant mass is:
A. 0.112 litre
B. 0224 litre
c. 22.4 litre
D. 11.2 litre


The role of a catalyst is to change
A. the Gibbs energy of reaction
B. enthalpy of reaction
C . activation energy of reaction
D. equilibrium constant


Q Type your question
nú, kangaroo rat, showing the relative size
of cortex and medulla. Coypu is found in
freshwater and is never of short of water
to drink. Brown rats are able to go some
days without drinking. Kangaroo rats are able to live in deserts without
drinking at all. Which kidney belongs to
which animal?
A. Brown rat
coypu Kangaroo rat
B. Brown rat Kangaroo rat coypu
c. Kangaroo rat Brown rat coypu
D. Kangaroo rat coypu Brown


ABCD is a quadrilateral in which \( A D= \)
BC. If \( P, Q, R, S \) be the mid-points of \( A B \)
\( A C, C D \) and \( B D \) respectively, show that PQRS is a rhombus.


Let \( C \) be the set of all complex numbers
and \( C_{0} \) be the set of all non-zero
complex numbers. Let a relation \( \boldsymbol{R} \) on
\( C_{0} \) be defined as
\( z_{1} R z_{2} \Leftrightarrow \frac{z_{1}-z_{2}}{z_{1}-z_{2}} \) is real for all \( z_{1}, z_{2} \in \)
\( C_{0} \)
Show that \( R \) is an equivalence relation.


Which of the following is the correct one
\( ? \)
A. The resistivity of an alloy is equal that of pure metals.
B. The resistivity of an alloy is lower than that of pure metals
c. The resistivity of an alloy is higher than that of pure metals
D. None of above


A piece of ice at 0 is put into a vessel containing water at \( 0 . \) The ice will
A. melt
B. not melt
c. slightly melt
D. vanish in no time


If \( \boldsymbol{A}=\left[\begin{array}{ll}\mathbf{0} & \mathbf{1} \\ \mathbf{1} & \mathbf{0}\end{array}\right], \) then \( \boldsymbol{A}^{4}= \)
A. \( \left[\begin{array}{ll}1 & 0 \\ 0 & 1\end{array}\right] \)
в. \( \left[\begin{array}{ll}1 & 1 \\ 0 & 0\end{array}\right] \)
c. \( \left[\begin{array}{ll}0 & 0 \\ 1 & 1\end{array}\right] \)
D. \( \left[\begin{array}{ll}0 & 1 \\ 1 & 0\end{array}\right] \)


Which of the following organs absorbs food nutrients through villi?
A. Small intestine
B. Oesophagus
c. Rectum
D. Stomach


How many spherical nodes are present in \( 4 s \) orbital in a hydrogen atom?
A. 0
B. 2
\( c \cdot 3 \)
\( D \)


Give the IUPAC names of the given amine:
ii) \( \mathrm{CH}_{3}-\mathrm{NH}-\mathrm{CH}-\mathrm{CH}_{2}-\mathrm{CH}-\mathrm{CH} \)


The Carnot cycle of a reversible heat
engine consists of:
A. one isothermal and two adiabatic processes
B. two isothermal and one adiabatic processes
\( \mathrm{C} \). two isothermal and two adiabatic processes
D. two isobaric and two isothermal processes
E. two isochoric and two adiabatic processes


\( C O \) and \( C N^{-} \) are harmful.
If true enter 1 , else enter 0 .


Show that \( \tan ^{-1} 1 / 2+\tan ^{-1} 2 / 11+ \)
\( \tan ^{-1} 4 / 3=\pi / 2 \)


The pressure on a square plate is measured by measuring the force on the plate and the length of the sides of the plate by using the formula \( \boldsymbol{P}= \)
\( \boldsymbol{F} / \boldsymbol{l}^{2} . \) If the maximum errors in the
measurement of force and length are \( 4 \% \) and \( 2 \%, \) respectively, then what is the maximum error in the
measurement of pressure?


Which of the following statement is not
true?
A. phenol is soluble in Naol
B. phenol is a weak acid
C. phenol gives violet colouration with neutral \( F e C l_{3} \)
D. phenol liberates \( C O_{2} \) from \( N a_{2} C O_{3} \) solution


Find the maximum and the minimum
values, if any, without using derivatives
of the following function:
\( f(x)=4 x^{2}-4 x+4 \) on \( R \)


Which of the following statements is the most accurate with regard to the significance of Avogadro's number, \( 6.02 \times 10^{23} ? \)
A. It is the conversion factor between grams and atomic mass units
B. It is a universal physical constant just as the speed of light
C. It is the number of particles that is required to fill a 1 liter container
D. It is the inverse diameter of an H atom.
E. It is the number of electrons in the universe


If the \( m^{t h} \) term of an A.P be \( \frac{1}{n}, n^{t h} \) term be \( \frac{1}{m}, \) show that it's \( m n^{t h} \) term is 1


Find the value of \( c \) if (2,3) lies on the circle \( x^{2}+y^{2}+2 x+3 y+c=0 \)


A commercial sample of hydrogen peroxide is labelled as 10 volume. Its percentage strength is nearly?
A . \( 3 \% \)
B. 1\%
c. \( 90 \% \)
D. \( 10 \% \)


A stone of mass \( 5 k g \) falls from the top of
a cliff \( 50 m \) high and buries \( 1 m \) in sand
Find the average resistance offered by
the sand and the time it takes to
penetrate


A block of wood of mass \( 24 \mathrm{kg} \) floats on
water. The volume of wood is \( 0.032 m^{3} \)
Find the density of wood.(Density of
water \( \left.=1000 \mathrm{kg} m^{-3}\right) \)


Place value of 9 in 7,92,83,456
\( \mathbf{A} \). Ten lakhs
B. 9 lakhs
c. 90,00,000
D. 90,000


If the lattice constant of this
semiconductor is decreased, then
which of the following is correct? (where
\( \boldsymbol{E}_{c} \) is conduction bandwidth, \( \boldsymbol{E}_{\boldsymbol{g}} \) is Band
gap and \( E_{v} \) is valence bandwidth)
A \( \cdot \) All \( \mathrm{E}_{\mathrm{c}}, \mathrm{E}_{\mathrm{g}}, \mathrm{E}_{\mathrm{V}} \) decrease
B. All E \( _{c}, E_{g}, \) Ev increase
c. \( \mathrm{E}_{c} \), and \( \mathrm{E}_{\mathrm{v}} \) increase but \( \mathrm{E}_{\mathrm{g}} \) decreases
D. E \( _{c} \), and Ev, decrease Eg increases


PP (Polypropylene) is used for making
A. disposable cups
B. liquid detergents
c. grocery bags
D. electric switches


f \( \triangle A B C \cong \triangle P R Q \) then \( A B=P Q \).If
true enter 1 else 0


Sound waves in air cannot be polarized because :
A. their speed is small
B. they require medium
c. these are longitudinal
D. their speed is temperature dependent


If \( x \) and \( y \) coordinate of a point is (3,10)
then the \( x \) co-ordinate is
A . 0
B. 3
c. 10
D. None of the above


Solve :
\( \int_{0}^{\pi} \frac{1}{a^{2}-2 a \cos x+1} d x \)


Assertion \( \operatorname{Let} \boldsymbol{A}=\left[\begin{array}{ll}\boldsymbol{a}_{11} & \boldsymbol{a}_{12} \\ \boldsymbol{a}_{21} & \boldsymbol{a}_{22}\end{array}\right], \boldsymbol{X}=\left[\begin{array}{l}\boldsymbol{x}_{1} \\ \boldsymbol{x}_{2}\end{array}\right], \boldsymbol{Y}= \)
\( \left[\begin{array}{l}\boldsymbol{y}_{1} \\ \boldsymbol{y}_{2}\end{array}\right] \)
If \( \boldsymbol{X}^{\prime} \boldsymbol{A} \boldsymbol{X}=\boldsymbol{0} \) for each \( \boldsymbol{X}, \) then \( \boldsymbol{A} \) must
be a symmetric matrix.
Reason
If \( \boldsymbol{A} \) is symmetric and \( \boldsymbol{X}^{\prime} \boldsymbol{A} \boldsymbol{X}=\mathbf{0} \) for
\( \operatorname{each} X, \) then \( A=0 \)
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. Assertion is incorrect but Reason is correct


A unit charge moves on an equipotential surface from a point \( A \) to
point \( \mathrm{B} \), then :
A. \( V_{A}-V_{B}=+v e \)
в. \( V_{A}-V_{B}=0 \)
\( \mathbf{c} \cdot V_{A}-V_{B}=-v e \)
D. it is stationary


An electric bulb is designed to draw
power \( P_{0} \) at voltage \( V_{0} . \) If the voltage is
\( v, \) it draws a power \( P, \) then
\( ^{A} \cdot P=\left(\frac{V}{V_{0}}\right) P_{0} \)
в. \( P=\left(\frac{V_{0}}{V}\right) P_{0} \)
\( ^{\mathrm{c}} P=\left(\frac{V_{0}}{V}\right)^{2} P_{0} \)
\( P=\left(\frac{V}{V_{0}}\right)^{2} P_{0} \)


of green plants are called factories of food production.
A. Mitochondria
B. Chloroplasts
c. Endoplasmic- recticulum
D. Nucleus


f \( \boldsymbol{x} \times \mathbf{1 6}=\mathbf{2 5 6}, \) what is \( \boldsymbol{x}=\mathbf{?} \)


Solve: \( \int \frac{\boldsymbol{d x}}{\boldsymbol{x}\left(\boldsymbol{a}+\boldsymbol{b} \boldsymbol{x}^{n}\right)^{2}} \)


Which one of the following pair of quantities has same dimension?
A. Force and work done
B. Momentum and impulse
c. Pressure and force
D. Surface tension and stress


\( \left|\begin{array}{lll}1 & 2 & 3 \\ 0 & 2 & 4 \\ 0 & 0 & 5\end{array}\right| \)


For matrix \( \boldsymbol{A} \)
\( |\mathbf{0} \boldsymbol{A}|= \)
This question has multiple correct options
A . 0
в. \( |A| \)
\( c \cdot|O| \)
D. None


If \( A B C \) and \( B D E \) are two equilateral
triangles such that \( D \) is the mid-point then find \( a r(\triangle A B C): a r(\triangle B D E) \)


Propan - 2 - ol on reacting with \( C l_{2} \)
produces?
A. Trichloroethanol
B. Trichloroacetone
c. Acetone
D. None


The variance of first ' \( n \) ' natural number
is
A \( \frac{n^{2}+1}{12} \)
B. \( \frac{n^{2}-1}{12} \)
c. \( \frac{(n+1)(2 n+1)}{6} \)
D. None of these


The formula for the velocity of electromagnetic waves in vacuum is given by
A. \( c=\sqrt{\mu_{0} \varepsilon} \)
B. \( c=\frac{1}{\sqrt{\mu_{0} \varepsilon_{0}}} \)
c. \( _{c}=\sqrt{\frac{\mu_{0}}{\varepsilon_{0}}} \)
D. \( c=\sqrt{\frac{\varepsilon_{0}}{\mu_{0}}} \)


When \( 0.273 g \) of \( M g \) is heated strongly
in a nitrogen \( \left(N_{2}\right) \) atmosphere, \( 0.378 g \)
of the compound is formed. Hence, the compound formed is :
в. \( M g_{3} N \)
c. \( M g_{2} N_{3} \)
D. \( M g N \)


Answer the following questions.
(i) An electrostatic field line is a
continuous curve. That is, a field line
cannot have sudden breaks. Why is it
so?
(ii) Explain why two field lines never
cross each other at any point.


Let \( f(x)=x^{\frac{2}{3}}, x \geq 0 . \) Then the area of
the region enclosed by the curve \( y= \) \( f(x) \) and the three lines \( y=x, x=1 \)
and \( x=8 \)
A \( \cdot \frac{63}{2} \)
в. \( \frac{93}{5} \)
c. \( \frac{105}{7} \)
D. \( \frac{129}{10} \)


Solve:
\( \lim _{x \rightarrow 27} \frac{x^{2 / 3}-9}{x-27} \)


topp
"


There is a small black dot at the centre
C of a solid glass sphere of refractive index \( \mu . \) When seen from outside, the
dot will appear to be located:
A. Away from C for all values of \( \mu \)
B. At C for all values of \( \mu \)
c. At \( \mathrm{C} \) for \( \mu=1.5 \), but away from \( \mathrm{C} \) for \( \mu \neq 1.5 \)
D. At C only for \( \sqrt{2} \leq \mu \leq 1.5 \)


Which of the following explains bidirectional transport of solutes in phloem tissue
A. Mass flow hypothesis
B. Transcellular strands hypothesis
c. Electro-osmotic hypothesis
D. All of these


Reaction of calgon with hard water
containing \( C a^{2+} \) ions produces;
\( \mathbf{A} \cdot\left[N a_{2} C a P_{6} O_{18}\right]^{2-} \)
в. \( C a_{2}\left(P O_{4}\right)_{3} \)
\( \mathrm{c} \cdot \mathrm{CaCO}_{3} \)
D. \( \operatorname{CaSO}_{4} \)


If the numbers \( a, b, c, d, e \) form an A.P.
then the value of \( a-4 b+6 c-4 d+e \)
is?
\( A \cdot 1 \)
B . 2
\( c \cdot 0 \)
D. None of these


ff \( x_{1}, x_{2}, \dots, x_{n} \) are \( ^{\prime} n^{\prime} \) positive real
numbers; then \( A . M \geq G . M \geq H . M \)
\( \frac{x_{1}+x_{2}+x_{3}+\ldots+x_{n}}{n} \geq\left(x_{1} x_{2} x_{3} \ldots x_{n}\right)^{n} \geq \)
\( \frac{n}{\frac{1}{x_{1}}+\frac{1}{x_{2}}+\frac{1}{x_{3}}+\ldots+\frac{1}{x_{n}}} \) equality occurs when
numbers are same using this concept.Here equality occurs numbers are of same.Using this concept answer the following f \( a>0, b>0, c>0 \) and the minimum
value of \( a\left(b^{2}+c^{2}\right)+b\left(c^{2}+a^{2}\right)+ \)
\( c\left(a^{2}+b^{2}\right) \) is \( \lambda a b c, \) then \( \lambda \) is
\( \mathbf{A} \cdot \mathbf{1} \)
B. 2
\( c .3 \)
D.


A gold leaf electroscope can be used to:
A. detect the presence of charge only
B. test the kind of charge only
C. measure the charge only
D. detect the presence of charge and test the kind of charge


A charge \( q \) is located at the centre of a
cube.The electric flux through any face is -
\( \mathbf{A} \cdot \frac{2 \pi q}{6(4 \pi \varepsilon)} \)
В. \( \frac{4 \pi q}{6(4 \pi \varepsilon)} \)
\( \mathbf{c} \cdot \frac{\pi q}{6(4 \pi \varepsilon)} \)
D. \( \frac{q}{6(4 \pi \varepsilon 0)} \)


Which of the following is/are true statement(s)?

This question has multiple correct options
A. Water vapour is absorbed by anhydrous calcium chloride while it is adsorbed by silica gel.
B. \( N H_{3} \) is absorbed by water but adsorbed by charcoal
c. Sugar is decolourized by animal charcoal based on adsorption
D. water is absorbed by conc. \( H_{2} S O_{4} \)


Who amongst the following used corpuscular theory to explain reflection and refraction of light?
A. Newton
B. Maxwell
c. Young
D. Hertz


Which of the following is a set of green
house gases?
A. \( O_{3}, N O_{2}, S O_{2}, C l_{2} \)
в. \( C O_{2}, C H_{4}, N_{2} O, O_{3} \)
\( \mathrm{c} \cdot O_{3}, N_{2}, C O_{2}, \mathrm{NO}_{2} \)
D. \( C H_{4}, O_{3}, N_{2}, S O_{2} \)


Large quantity of \( K M n O_{4}, \) on
treatment with cold conc. \( \boldsymbol{H}_{2} \boldsymbol{S} \boldsymbol{O}_{4} \) forms
a compound \( (X) \) which decomposed
explosively, on heating forming \( (Y) \). The
\( (X) \) and \( (Y) \) are
respectively.
\( \mathbf{A} \cdot M n_{2} O_{7}, M n O_{2} \)
в. \( M n_{2} O_{7}, M n_{2} O_{3} \)
c. \( M n S O_{4}, M n_{2} O_{3} \)
D. \( M n_{2} O_{3}, M n O_{2} \)


Find the middle term in the expansion of \( \left(\frac{2 x}{3}+\frac{3}{2 x}\right)^{10} \)
A . 210
в. 630
\( c .252 \)
D. 756


A wave travels on a light string. The equation of the wave is \( \boldsymbol{Y}= \)
\( \boldsymbol{A} \sin \left(\boldsymbol{k} \boldsymbol{x}-\boldsymbol{\omega} \boldsymbol{t}+\boldsymbol{3} \boldsymbol{0}^{\circ}\right) . \) It is reflected
from a heavy string tied to an end of the
light string at \( x=0 . \) If \( 64 \% \) of the
incident energy is reflected the equation of the reflected wave is
A. \( Y=0.8 A \sin \left(k x-\omega t+30^{\circ}+180^{\circ}\right) \)
B. \( Y=0.8 A \sin \left(k x+\omega t+30^{\circ}+180^{\circ}\right) \)
C. \( Y=0.8 A \sin \left(k x+\omega t-30^{\circ}\right) \)
D. \( Y=0.8 A \sin \left(k x+\omega t+30^{\circ}\right) \)


The resistance of \( 0.01 \mathrm{N} \) solution of an
electrolyte \( A B \) at \( 328 \mathrm{K} \) is 100 ohm. The specific conductance of solution is :
\( \left[\text { cell constant }=1 \mathrm{cm}^{-1}\right] \)
A. 100 ohm
B. \( 10^{-2} \) ohm \( ^{-1} \)
\( \mathbf{c} \cdot 10^{-2} \operatorname{ohm}^{-1} c m^{-1} \)
D. \( 10^{2} \) ohm \( -c m \)


Which type of motion of an object that moves at a fixed distance from a fixed
point?
A. Periodic motion
B. Rectilinear motion
c. circular motion
D. None of the above


What are \( P, Q, R, S \) in the given figure?
A. P- -Right ventricle, Q - Left ventricle, R - Right atrium
- Left atrium
B. P- Right atrium, Q - Left atrium, R - Right ventricle, S Left ventricle
c. P-Right ventricle, Q - Left atrium, R - Right atrium, S Left ventricle
D. P- -Right atrium, Q- Right ventricle, R - Left atrium, S Left ventricl


Percentage ratio of fibroin to sericin in silk is
A .50: 40
B. 80: 20
c. 30: 70
D. 40: 60


The initial enzyme of Calvin cycle is
A. Ribulose 1,5-diphosphate carboxylase
B. Triose phosphate dehydrogenase
c. Phosphopentokinase
D. cytochrome oxidase


Cerium \( (Z=58) \) is an important
member of lanthanides. Which of the
following statements about cerium is
correct?
A. The common oxidation states of cerium are +3 and +4
B. The +3 oxidation states of cerium is more stable than the +4 state
c. The +4 oxidation states of cerium is not known in solutions
D. Cerium (IV) acts as an oxidising agent.


An engine working on Carnot cycle rejects \( 40 \% \) of absorbed heat from the source, while the sink temperature is
maintained at \( 27^{0} C \), then what is
the source temperature \( \left(\text { in }^{0} C\right) ? \)
A . 477
B. 346
\( c \cdot 564 \)
D. none of the above


Assertion
Benzene is highly volatile, and most exposure is through inhalation.
Reason
Benzene is soluble in water.
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


At what phase the entire illuminated portion of the moon is seen?
A. New Moon
B. Full Moon
c. waxing gibbous
D. First Quater


Let \( * \) be the binary operation on \( \boldsymbol{N} \)
defined by \( a * b=H . C . F . \) of \( a \) and \( b . \) Is
\( * \) commutative? Is \( * \) associative? Does
there exist identity for this binary
operation on \( N ? \)


A small body is thrown at an angle to
the horizontal with the initial velocity \( \vec{v}_{0} \) Neglecting the air drag, find the mean
velocity vector \( \langle\vec{v}\rangle \) averaged over the
first \( t \) sec and over the total time of
motion.
A \( \cdot(\vec{v})_{t}=\vec{v}_{0}-\frac{g t}{2},\langle\vec{v}\rangle=\vec{v}_{0}-g \frac{\left(\vec{v}_{0} g\right)}{g^{2}} \)
B \( \cdot(\vec{v})_{t}=\vec{v}_{0}-\frac{g t}{2},\langle\vec{v}\rangle=\vec{v}_{0}+g \frac{\left(\vec{v}_{0} g\right)}{g^{2}} \)
c. \( (\vec{v})_{t}=\vec{v}_{0},\langle\vec{v}\rangle=\vec{v}_{0}-g \frac{\left(\vec{v}_{0} g\right)}{g^{2}} \)
D. None of these


Which of the following numbers are not perfect cubes?
1. २१६
2. 125
3.1000
4.46656


\( N a C l \) and \( C a C l_{2} \) are also added to
fused \( M g C l_{2} \) in the electrolysis of
\( M g C l_{2} . \) Select the correct statement.
This question has multiple correct options
A. melting point is decreased and conductivity is increased
B. melting point is increased and conductivity is decreased
c. melting point and conductivity both are decreased
D. melting point and conductivity both are increased


There are 6 letters and 3 post-boxes. The number of ways in which these letters can be posted is
A \( \cdot 6^{3} \)
B . \( 3^{6} \)
\( \mathrm{c} \cdot^{6} C_{3} \)
D. \( ^{6} P_{3} \)


\( \int \sin ^{2 / 3} x \cos ^{3} x d x \)


Prove that the Greatest Integer Function \( \boldsymbol{f}: \boldsymbol{R} \rightarrow \boldsymbol{R} \operatorname{given} \) by \( \boldsymbol{f}(\boldsymbol{x})=[\boldsymbol{x}], \) is
neither one-one nor onto, where \( [\boldsymbol{x}] \)
denotes the greatest integer less that or
equal to \( x \)


Pick out the correct statement(s):
This question has multiple correct options
\( \mathbf{A} \cdot M n O_{2} \) dissolves in conc. \( H C l \) but does not form \( M n^{4+} \)
ions.
B. Decomposition of acidic \( K M n O_{4} \) is not catalysed by sunlight
C \( . M n O_{4}^{2-} \) is strongly oxidising and stable only in a very strong alkali. In dilute alkali, water or acidic solutions it dispropotionates.
D. \( K M n O_{4} \) does not act as oxidising agent in alkaline medium.


Temperature coefficient of resistance of
platinum is \( 4 \times 10^{-3} / K \) at \( 20^{\circ} C \)
Temperature at which increase in resistance of platinum is \( 10 \% \) is value
at \( 20^{\circ} C \) is
A \( \cdot 25^{\circ} \mathrm{C} \)
B . \( 70^{\circ} \mathrm{C} \)
\( \mathbf{c} \cdot 45^{\circ} C \)
D. \( 100^{\circ} \mathrm{C} \)


\( A \) starts from rest and moves with an
acceleration \( a_{1} . \) Two seconds later, \( B \)
starts from rest and moves with an
acceleration \( a_{2} \). If the displacement of
\( A \) in the \( 5^{t h} \) second is the same as that
of \( B \) in the same interval, the
accelerations \( a_{1} \) and \( a_{2} \) are
A \( \cdot 2 m / s^{2}, 35 m / s^{2} \)
B . \( 5 \mathrm{m} / \mathrm{s}^{2}, 9 \mathrm{m} / \mathrm{s}^{2} \)
C. \( 11 \mathrm{m} / \mathrm{s}^{2}, 2 \mathrm{m} / \mathrm{s}^{2} \)
D. \( 1 \mathrm{m} / \mathrm{s}^{2}, 10 \mathrm{m} / \mathrm{s}^{2} \)


For the following system of equation
determine the value of \( k \) for which the
given system of the equation has a unique solution. \( \boldsymbol{x}-\boldsymbol{k} \boldsymbol{y}=\mathbf{2} \)
\( \mathbf{3} \boldsymbol{x}+\mathbf{2} \boldsymbol{y}=-\mathbf{5} \)


Which of the following action describes pushing by a body?
A. kicking
B. liffing
c. picking
D. opening


The B-H curve (i) and (ii) shown in fig.,
associated with
A. (i) diamagnetic and (ii) paramagnetic substance
B. (i) paramagnetic and (ii) ferromagnetic substance
C. (i) soft iron and (ii) steel respectively
D. (i) steel and
(ii) soft iron respectively


Calculate the wavelength of photon
associated with an energy of 1 electron volt.
A . \( 19.875 \times 10^{-17} \mathrm{cm} \)
в. \( 1.24 \times 10^{-5} \mathrm{cm} \)
c. \( 12.41 \times 10^{-5} \mathrm{cm} \)
D. \( 20.11 \times 10^{-5} \mathrm{cm} \)


Choose the correct statement.
\( \mathbf{A} \cdot A \) is more volatile than \( B \)
B. \( B \) is more volatile than \( A \)
\( \mathrm{C} . A \) is formed more rapidly at a higher temperature
D. \( A \) is formed in higher yield at a low temperature


The change in focal length of an eye lens is caused by the action of the :
A. pupil
B. iriss
c. ciliary muscles
D. retina


How much will the potential of
\( Z n / Z n^{2+} \) change if the solution of
\( Z n^{2+} \) is diluted 10 times?
A. increase by \( 0.03 \mathrm{V} \)
B. decreases by \( 0.03 \mathrm{V} \)
c. increases by \( 0.059 \mathrm{V} \)
D. decreases by \( 0.059 \mathrm{V} \)


Which of the following statements is
not true for acetaldehyde?
A. It will undergo an aldol condensation reaction.
B. It will undergo a Cannizzaro reaction.
C. It wit undergo a haloform reaction
D. Enolisation is catalysed by acid or base.