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What is radioactivity? Show that radioactive decay is exponential in nature. The half-life of a certain
substance is 5 days. How many days does this substance take for \( 31 / 32^{t h} \) of the initial mass of disintegrate?
| 3 |
Physics
|
A solution prepared by dissolving 2.8 \( \mathrm{gm} \) of lime. \( \mathrm{CaO} \) in enough water to make 100 L of lime water
\( \left(\operatorname{Ca}(O H)_{2}(a q .)\right) . \) If solubility of
\( \boldsymbol{C a}(\boldsymbol{O} \boldsymbol{H})_{2} \) in water is 148 gm. The \( \boldsymbol{p} \boldsymbol{H} \)
of the solution obtained will be:
\( [\log 2=0.3, \text { Atomic masses are } C a= \) \( \mathbf{4 0}, \boldsymbol{O}=\mathbf{1 6}, \boldsymbol{H}=\mathbf{1 1}] \)
A . 12.3
B. 1.3
c. 12.6
D. 13
| 1 |
Chemistry
|
A man wearing a wingsuit glides through the air with a constant velocity
of \( 47 ~ m s^{-1} \) at an angle of \( 24^{\circ} \) to the horizontal. The path of the man is shown
in Fig.
The total mass of the man and the
wingsuit is 85 kg. The man takes a time
of 2.8 minutes to glide from point \( A \) to
point \( \boldsymbol{B} \)
For the movement of the man from \( A \) to
\( B, \) determine:
the magnitude of the force on the man
due to air resistance.
| 3 |
Physics
|
Assertion
All the isotopes of a given element show same chemical behaviour.
Reason
Isotopes have different number of
neutrons present in the nucleus.
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
| 1 |
Chemistry
|
Evaluate \( \int_{-\pi / 4}^{\pi / 4}|\sin x| d x \)
| 2 |
Maths
|
The function \( f(x)=\sin ^{-1}(\tan x) \) is not
differentiable at-
A \( . x=0 \)
В. \( x=-\pi / 6 \)
c. \( x=\pi / 6 \)
D. \( x=\pi / 4 \)
| 2 |
Maths
|
f \( y=\log \sqrt{\frac{1+\tan x}{1-\tan x}}, \) prove that \( \frac{d y}{d x}= \)
\( \sec 2 x \)
| 2 |
Maths
|
Resonance is an example of
A. Tuning fork
B. Forced vibration
C. Free vibration
D. Damped vibration
| 3 |
Physics
|
\( A 25 \mathrm{cm} \) long solenoid has radius \( 2 \mathrm{cm} \) and 500 total number of turns. It carries
a current of 15 A. If it is equivalent to magnet of the same size and magnetization \( \vec{M} \) Magnetic moment vloume), then \( \overrightarrow{|M|} \) is.
B. 30000Am"
c. \( 30000 \pi A m^{-1} \)
D. \( 3 \pi A m^{-1} \)
| 3 |
Physics
|
The colour of dye formed in the reaction between benzene diazonium chloride
and phenol is:
A . yellow
B. orange
c. purple
D. blue
| 1 |
Chemistry
|
If \( \boldsymbol{A}=\{\mathbf{1}, \mathbf{2}, \mathbf{3}\}, \boldsymbol{B}=\{\mathbf{3}, \mathbf{4}\} \)
find \( (A \times B) \cup(B \times A) \)
\( \mathbf{A} \)
\[
\{(1,3),(2,3),(3,3),(1,4),(2,4),(3,4),(3,1),(4,1),(3,2)
\]
B.
\[
\{(2,3),(3,3),(1,4),(2,4),(3,4),(3,1),(4,1),(3,2),(4,2)
\]
\( \mathbf{c} \)
\{(1,3),(2,3),(3,3),(1,4),(2,4),(3,4),(3,1),(4,1),(4,2)
D. None of these
| 2 |
Maths
|
The electric potential at any point
inside the first shell is:
\( \mathbf{A} \cdot 18 \times 10^{4} V \)
B. \( 9 \times 10^{4} V \)
c. \( 4.5 \times 10^{4} V \)
D . \( 1.8 \times 10^{4} V \)
| 3 |
Physics
|
Construct the graphs of the following
function.
\( \boldsymbol{y}=\boldsymbol{x}|\boldsymbol{x}-\mathbf{3}| \)
| 2 |
Maths
|
The smog is essentially caused by the
presence of
| 1 |
Chemistry
|
Let \( \boldsymbol{f}(\boldsymbol{x})=\boldsymbol{x}^{4}+\boldsymbol{3} \boldsymbol{x}+1,[-\boldsymbol{2},-1] \) then
\( A \cdot f \) has exactly two zeros in [-2,-1]
B. f has exactly one zero in [-2,-1
C \( \cdot \) f has at least one zero in [-2,-1]
D. f has no zero in [-2,-1]
| 2 |
Maths
|
The IUPAC name of \( C_{6} H_{5} \) COCl is :
A. benzoyl chloride
B. benzene chloro ketone
c. oxochloro benzene
D. chlorophenyl ketone
| 1 |
Chemistry
|
Which one of the following is correctly
matched ?
A. Aerosol-smoke
B. Foam-mist
c. Emulsion-curd
D. All of these
| 1 |
Chemistry
|
A steel rope has length \( L \), area of cross-
section \( A \), Young's modulus \( Y \). Density \( =d \) ]. If the steel rope is
vertical and moving with the force acting vertically up at the upper end, find the strain at a point \( \frac{L}{3} \) from lower
end.
\( \mathbf{A} \cdot(d g L) / 2 Y \)
в. \( (d g L) / 4 Y \)
\( \mathbf{c} \cdot(d g L) / 6 Y \)
D. \( (d g L) / 8 Y \)
| 3 |
Physics
|
According to Bohr's model, the angular
momentum of an electron in 4th orbit
is:
\( \mathbf{A} \cdot h / 3 \)
B. \( h / 2 \)
c. \( 2 h / \pi \)
D. none of these
| 1 |
Chemistry
|
ff \( x_{1}, y_{1} \) are the roots of \( x^{2}+8 x-20= \)
0 and \( x_{2}, y_{2} \) are the roots of \( 4 x^{2}+ \)
\( 32 x-57=0 \) and \( x_{3}, y_{3} \) are the roots of
\( 9 x^{2}+72 x-112=0 \) such that \( y_{i}<0 \)
then the points \( \left(x_{1}, y_{1}\right),\left(x_{2}, y_{2}\right) \) and
\( \left(x_{3}, y_{3}\right) \)
A. are collinear
B. form an equilateral triangle
c. form a right angled isosceles triangle
D. are concyclic
| 2 |
Maths
|
Zinc can displace copper from copper
sulfate solution because zinc is
A. more reactive than copper
B. less reactive than copper
c. more stable than copper
D. less stable than copper
| 1 |
Chemistry
|
Evaluate \( \int x^{2} e^{x} d x= \)
A \( \cdot e^{x}\left(x^{2}-2 x+2\right)+c \)
B . \( e^{x}\left(x^{2}+2 x+2\right)+c \)
c. \( x^{2}+e x+c \)
D. \( e^{x}\left(x^{2}+x+2\right)+c \)
| 2 |
Maths
|
Average kinetic energy in one time
period of a simple harmonic oscillator whose amplitude is \( A, \) angular velocity \( \omega \) and mass \( m, \) is
A \( \cdot \frac{1}{4} m \omega^{2} A^{2} \)
B \( \cdot \frac{1}{2} m \omega^{2} A^{2} \)
\( \mathrm{c} \cdot m \omega^{2} A^{2} \)
D. Zero
| 3 |
Physics
|
How many order of magnitude are there in one million?
A. 5
B. 4
\( c \cdot 6 \)
D. None of above
| 3 |
Physics
|
Which of the following ion will give colourless aqueous solution?
A \( . N i^{2} \)
B. \( S c^{3} \)
\( c \cdot C u^{2} \)
D. \( M n^{3+} \)
| 1 |
Chemistry
|
Which of the following are fleece and wool-bearing animals?
A. Sheep and goat
B. Camel and Yak
c. Both A and B
D. none of them
| 1 |
Chemistry
|
Condensation of phenol with acetone
gives:
A. bisphenol-A
B. catechol
c. resorcinol
D. hydroquinone
| 1 |
Chemistry
|
An unknown compound has molecular
formula \( C_{7} H_{12} \).It gives two aldehydes shown below upon ozonolysis followed
by workup with \( Z n-H_{2} O . \) What is the
the structure of the original compound?
and
\( A \)
B.
\( c \)
D. None of the above
| 1 |
Chemistry
|
In an isolated parallel plate capacitor of
capacitance \( C, \) the four surfaces have
charges \( Q_{1}, Q_{2}, Q_{3} \) and \( Q_{4} \) as shown.
The potential difference between the
plates is:
\( A \)
в. \( \frac{Q_{2}+Q_{3}}{2 C} \)
c. \( \frac{Q_{2}-Q_{3}}{2 C} \)
D. \( \frac{Q_{1}+Q_{4}}{2 C} \)
| 3 |
Physics
|
Q Type your question.
and \( T_{2}\left(T_{2}>T_{1}\right) . \) Which of the
following plots is correct?
\( A \)
B.
\( c \)
\( D \)
| 3 |
Physics
|
If \( \cos ^{-1} x+\cos ^{-1} y+\cos ^{-1} z=3 \pi \)
then \( x y+y x+z x \) is equal to
A . 1
B.
\( c .-3 \)
D. 3
| 2 |
Maths
|
What are the IUPAC rules for naming
alkyl halides?
| 1 |
Chemistry
|
Which of the following is the strongest base?
A. Aniline
B. N-methylaniline
c. o-methylaniline
D. Benzylamine
| 1 |
Chemistry
|
Out of the following options, which is the base to define the formation place
of cell plate at the end of nuclear
division?
A. Microtubules
B. Vesicles
c. Endoplasmic reticulum
D. Golgi body
| 0 |
Biology
|
Out of \( N O, N O_{2}, N_{2} O, N_{2} O_{4} \) and \( N_{2} O_{2} \)
the paramagnetic species
are
A. \( N_{2} O_{2} \) and \( N_{2} O_{4} \)
B. \( N O_{2} \) and \( N_{2} O_{4} \)
\( \mathrm{c} \cdot \mathrm{N}_{2} \mathrm{O}_{2} \) and \( \mathrm{NO}_{2} \)
D. \( N O \) and \( N O_{2} \)
| 1 |
Chemistry
|
The velocity with which particle strikes the plane \( \boldsymbol{O B} \)
A \( \cdot 15 \mathrm{ms}^{-1} \)
B. \( 30 m s^{-1} \)
\( c \cdot 20 m s^{-1} \)
D. \( 10 \mathrm{ms}^{-1} \)
| 3 |
Physics
|
By which method can ammonium
chloride be separated from sand?
A. By hand picking
B. By filtration
c. By sublimation
D. By diffusion
| 3 |
Physics
|
One mole of acidified \( \boldsymbol{K}_{2} \boldsymbol{C r}_{2} \boldsymbol{O}_{7} \) on
reaction with excess \( \boldsymbol{K} \boldsymbol{I} \) will
liberate \( _{\text {一一一一一一一一一 }} \) mole \( (s) \) of \( I_{2} \)
\( A \cdot 3 \)
B. 1
c. 7
D. 2
| 1 |
Chemistry
|
in a certain region of free space a non-
uniform electric field which depends on
X-coordinates is given by \( \overrightarrow{\boldsymbol{E}}=\boldsymbol{E}_{0} \boldsymbol{x} \hat{\boldsymbol{i}} \)
What is the total amount of electric
potential energy contained within the
cube of sides of length L as shown
below?
A \( \cdot \frac{1}{5} \varepsilon_{0} E_{0}^{2} L^{5} \)
B \( \cdot \frac{1}{5} \varepsilon_{0} E_{0}^{2} L^{6} \)
C \( \cdot \frac{1}{6} \varepsilon_{0} E_{0}^{2} L^{6} \)
D \( \cdot \frac{1}{2} \varepsilon_{0} E_{0}^{2} L^{5} \)
| 3 |
Physics
|
If true enter 1 , else enter 0 .
Following reaction is disproportionation
reaction:
\( N H_{4}^{+}+N O_{3}^{-} \longrightarrow N_{2} O+2 H_{2} O \)
\( A \)
| 1 |
Chemistry
|
The diagram given below represents the location and structure of an endocrine
gland. Study the same and answer the questions that follow:
Name the endocrine gland shown in the diagram.
| 0 |
Biology
|
Value of \( \int \frac{d x}{x^{2}\left(x^{4}+1\right)^{3 / 4}} \) is :
A \( -\left(1+\frac{1}{x^{4}}\right)^{\frac{1}{4}}+c \)
B. \( \quad\left(1+\frac{1}{x^{4}}\right)^{\frac{1}{4}}+c \)
c. \( \quad-\left(1-\frac{1}{x^{4}}\right)^{\frac{1}{4}}+c \)
D. None of these
| 2 |
Maths
|
Which of the following is an assumption of Kinetic theory of matter?
A. Molecules are in a state of continuous motion and possess kinetic energy
B. The kinetic energy of molecules increases with increase in temperature.
c. The molecules of matter always attract each other due to forces of cohesion and adhesion
D. All of the above
| 3 |
Physics
|
Ethyl alcohol on distillation with \( \boldsymbol{X} \)
gives chloroform, \( \boldsymbol{X} \) is:
A. a paste of bleaching powder
B. chlorine
c. methyl chloride
D. \( C a(O H)_{2} \)
| 1 |
Chemistry
|
The side of a cube is 2.5 metre, the volume of the cube to the correct
significant figures is :
A . 15
B. 16
\( c \cdot 1.5 \)
D. 1.6
| 3 |
Physics
|
The range of the function \( f(x)= \)
\( \left(8^{x}+4^{x}+8^{-x}+4^{-x}+5\right) \) is
\( A \cdot\left(\frac{7}{4}, \infty\right) \)
B. \( \left[\frac{7}{4}, \infty\right) \)
c. \( (9, \infty) \)
D \( \cdot[9, \infty) \)
| 2 |
Maths
|
The rate of the reaction starting with
initial concentrations \( 2 \times 10^{3} M \) and
\( 1 \times 10^{3} M \) are equal to \( 2.40 \times \)
\( 10^{4} M s^{1} \) and \( 0.60 \times 10^{4} M s^{1} \)
respectively. Calculate the order of reaction with respect to reactant:
| 1 |
Chemistry
|
A half cell reaction is one which:
A. involves only half a mole of electrolyte
B. goes only half way to completion
C. takes place at one electrode
D. consumes half a unit of electricity
| 1 |
Chemistry
|
Given that \( \vec{A} \) and \( \vec{B} \) are greater than one, then the magnitude of \( (\vec{A} \times \vec{B}) \) can not be
A . equal to \( \overrightarrow{A B} \)
B. less than \( \vec{B} \)
c. more than \( |\vec{A}||\vec{B}| \)
D. equal to \( \vec{A} / \vec{B} \)
| 3 |
Physics
|
Peptization denotes:
A. digestion of food
B. hydrolysis of proteins
C. breaking of dispersion into colloidal state
D. precipitation of a solid from colloidal state
| 1 |
Chemistry
|
The average human eye sees colors with
wavelength between \( 430 n m \) to \( 680 n m \)
For what visible wavelength(s) will a \( 350 n m \) thick \( (n=1.35) \) soap film
produce maximum destructive
interference?
A. \( 945 n m \)
В. \( 473 n m \)
\( c .315 n m \)
D. None of these
| 3 |
Physics
|
In Colon, constrictions of the wall form a series of small pockets called
A. Haustra
B. Crypts of lieberkuhn
c. zymogen cells
D. Taenial
| 0 |
Biology
|
sets of students who have opted for
Mathematics (M) physics (P) Chemistry
(C) and Electronics (E)
What does the shaded region represent
A. Students who oped for Physic, Chemistry and Electronics
B. Students who oped for Mathematics, Physics
Chemistry
c. Students who opted for Mathematics, Physics and Electronics
D. Students who opted for Mathematics, Chemistry and ectron
| 2 |
Maths
|
If \( f \) be a continuous function on \( [\mathbf{0}, \mathbf{1}] \)
differentiable in (0,1) such that
\( f(1)=0, \) then there exists some \( c \in \)
(0,1) such that
A \( \cdot c f^{\prime}(c)-f(c)=0 \)
B. \( f^{\prime}(c)+c f(c)=0 \)
c. \( f^{\prime}(c)-c f(c)=0 \)
D. \( c f^{\prime}(c)+f(c)=0 \)
| 2 |
Maths
|
Sewage purification is performed by
A. Microbes
B. Fertilisers
C. Antibiotics
D. Antiseptics
| 0 |
Biology
|
Cell division can not be stopped in phase of the cell cycle.
A. Gi phase
B. Ga phase
c. s phase
D. Prophase
| 0 |
Biology
|
Boiling does not occur in a closed vessel. Give reason.
| 1 |
Chemistry
|
Find the \( x \) in terms of \( a, b, c \)
| 2 |
Maths
|
Factorise \( (x-2 y)^{2}+7(x-2 y)+12 \)
| 2 |
Maths
|
A litre of dry air at STP expands adiabatically to a volume of 3 litres. If
\( \gamma=1.40, \) the work done by air is:
\( \left(3^{1.4}=4.6555\right) \) [Take air to be an ideal gas \( ] \)
A . \( 48 \mathrm{J} \)
в. \( 100.8 \mathrm{J} \)
c. \( 60.7 J \)
D. \( 90.5 J \)
| 3 |
Physics
|
If \( \frac{\sin ^{-1} x}{\sqrt{1-x^{2}}}=y, \) show that \( (1- \)
\( \left.x^{2}\right) \frac{d^{2} y}{d x^{2}}-3 x \frac{d y}{d x}-y=0 \)
| 2 |
Maths
|
Carbon belongs to second period and 14
group. Silicon belongs to third period and group 14. If atomic number of carbon is \( 6, \) the atomic number of
silicon is :
A. 7
B. 14
\( c \cdot 24 \)
D. 16
| 1 |
Chemistry
|
The dimension of the ratio of angular
momentum to linear momentum is
\( \mathbf{A} \cdot L^{0} \)
B . \( L^{1} \)
c. \( L^{2} \)
D. \( M L T \)
| 3 |
Physics
|
In \( N_{2} \) molecule, the atoms are bonded
by:
A . one \( \sigma, \) two \( \pi \) bonds
в. one \( \sigma \), one \( \pi \) bonds
c. \( t w o \sigma, \) one \( \pi \) bonds
D. three \( \sigma \), one \( \pi \) bonds
| 1 |
Chemistry
|
\( 2^{n} d \) separation energy of an electron in
H atom?
A. 27.2 ev
B. 1.51 ev
c. 3.4 ev
D. 13.6 ev
| 1 |
Chemistry
|
Derive the formula \( \omega=\frac{D \lambda}{2} \) for fringe width in Young's double slit experiment
The symbols used have their usual meanings.
| 3 |
Physics
|
A swimming pool is \( 100 \mathrm{m} \) long and \( 15 \mathrm{m} \) wide its deep and \( 24 \mathrm{m} \) height
respectively. Find the capacity of the
pool
A. \( 36,000 \mathrm{m} \)
в. \( 36,000 m^{3} \)
c. \( 36,000 m^{2} \)
D. 36,000 \( c m \)
| 2 |
Maths
|
Factorise the following expression by finding common factor. \( \boldsymbol{p}^{3}-\mathbf{1 6} \boldsymbol{p}^{2}=\mathbf{0} \)
| 2 |
Maths
|
\( A \& B \) are two separate reservoirs of water. The capacity of reservoir A is double the capacity of reservoir B. Both the reservoirs are filled completely with water, their inlets are closed and then
the water is released simultaneously
from both the reservoirs. The rate of flow
of water out of each reservoir at any
instant of time is proportional to the quantity of water in the reservoir at that time. One hour after the water is
released, the quantity of water in reservoir A is 1.5 times the quantity of water in reservoir B. After how many hours do both the reservoirs have the
same quantity of water? (Enter \( n \) if the answer is \( T=\log _{4 / 3} n \) )
| 2 |
Maths
|
What is the IUPAC name of
\( \left[\boldsymbol{C o}\left(\boldsymbol{N} \boldsymbol{H}_{3}\right)_{5}(\boldsymbol{O} \boldsymbol{N} \boldsymbol{O})\right] \boldsymbol{S} \boldsymbol{O}_{4} ? \)
A. pentaammine nitrito-0-cobalt
(III) sulphate
B. pentaammine nitro-N-cobalt (III) sulphate
c. pentaamine nitro-0-cobalt (III) sulphate
D. pentaammonia nitro-0-cobalt
(III) sulphate
| 1 |
Chemistry
|
Name a moneran which shows
pendulum like movements
| 0 |
Biology
|
A reaction is spontaneous at all
temperature when
A. \( \Delta H \) is -ve and \( \Delta S \) is +ve
B. \( \Delta H \) is +ve and \( \Delta S \) is -ve
C. Both \( \Delta H \& \Delta S \) are -ve
D. Both \( \Delta H \) \& \( \Delta S \) are +ve
| 1 |
Chemistry
|
\( \mu=\{a, b, c, d, e, f, g, h, i, j\} \)
\( P=\{a, b, c, e\} \)
\( Q=\{b, c, d, f\} \) and
\( R=\{c, f, h, i, j\} \)
Number of elements of the set
\( \boldsymbol{P} \cup \boldsymbol{Q} \cup \boldsymbol{R} \) is:
A \( \cdot 12 \)
B. 11
c. 10
\( D \)
| 2 |
Maths
|
Elemental analysis results obtained for cortisone, an anti-inflammatory agent,
are \( 69.98 \% \) C, \( 7.83 \mathrm{H} \) and \( 22.19 \% \) 0. What
is the empirical formula of cortisone?
A \( \cdot C_{4} H_{6} O \)
в. \( C_{18} \mathrm{H}_{22} \mathrm{O}_{3} \)
\( \mathbf{c} \cdot C_{20} H_{25} O_{4} \)
D. \( C_{12} H_{28} O_{5} \)
| 1 |
Chemistry
|
Calculate the normal temperature of
human body in celsius scale if it is
\( \mathbf{9 8 . 4}^{\circ} \boldsymbol{F} \) in Fahrenheit scale
| 3 |
Physics
|
Let \( \boldsymbol{f}:(-\mathbf{1}, \mathbf{1}) \rightarrow \boldsymbol{R} \) be a differentiable
function satisfying
\[
\begin{array}{c}
\left(f^{\prime}(x)\right)^{4}=16(f(x))^{2} \text { for all } x \in \\
(-1,1) \\
f(0)=0
\end{array}
\]
The number of such functions is
\( A \cdot 2 \)
B. 3
\( c \cdot 4 \)
D. more than 4
| 2 |
Maths
|
Moist iodine reacts with ozone to form :
A. \( H I \)
в. \( H I O_{3} \)
\( c \cdot I_{2} O_{3} \)
D. \( I_{2} O_{7} \)
| 1 |
Chemistry
|
Assertion
\( L i^{+} \) forms series of trihydrates \( L i X \)
\( \mathbf{3} \boldsymbol{H}_{\mathbf{2}} \boldsymbol{O}[\boldsymbol{X}= \)
\( \boldsymbol{C l}, \boldsymbol{B r}, \boldsymbol{I}, \boldsymbol{C l O}_{2}, \boldsymbol{C l o}_{4}, \boldsymbol{M n O}_{4}, \boldsymbol{N O}_{3}, \boldsymbol{b} \)
Reason
This is due to its smaller size \( \left(L i^{+}\right) \) and highest ion dipole interaction.
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
| 1 |
Chemistry
|
The frequency of a sound wave is \( 256 \mathrm{Hz} \) and its wavelength is \( 1.2 \mathrm{m} \). Calculate its wave velocity.
| 3 |
Physics
|
Radium disappears at a rate
proportional to the amount present. If \( 5 \% \) of the original amount disappears
in 50 years, how much will remain at
the end of 100 years. \( \left[\text { Take } A_{0} \) as the \right. initial amount].
| 2 |
Maths
|
Which one of the following differential equations represents the family of straight lines which are at unit distance from the origin?
\( ^{A} \cdot\left(y-x \frac{d y}{d x}\right)^{2}=1-\left(\frac{d y}{d x}\right)^{2} \)
\( ^{\mathrm{B}}\left(y+x \frac{d y}{d x}\right)^{2}=1+\left(\frac{d y}{d x}\right)^{2} \)
\( ^{\mathrm{c}}\left(y-x \frac{d y}{d x}\right)^{2}=1+\left(\frac{d y}{d x}\right)^{2} \)
\( ^{\mathrm{D} \cdot}\left(y+x \frac{d y}{d x}\right)^{2}=1-\left(\frac{d y}{d x}\right)^{2} \)
| 2 |
Maths
|
Area of circle in which a chord of length
\( 2 \sqrt{3} \) units, subtends angle \( 120^{\circ} \) at its
centre is :
A . \( \pi \) sq units
B. 2 \( \pi \) sq units
c. \( 4 \pi \) sq units
D. \( 5 \pi \) sq units
| 2 |
Maths
|
Given that \( A+B+C=0 . \) Out of three
vectors, two are equal in magnitude and the magnitude of third vector is \( \sqrt{2} \) times that of either of the two having equal magnitude. Then, the angles between the vectors are given by.
A . \( 30^{\circ}, 60^{\circ}, 90^{\circ} \)
в. \( 45^{\circ}, 45^{\circ} \), \( 90^{\circ} \)
c. \( 45^{\circ}, 60^{\circ}, 90^{\circ} \)
D. \( 90^{\circ}, 135^{\circ}, 135^{\circ} \)
| 2 |
Maths
|
What are the expected products of
hydrolysis of lactose?
| 1 |
Chemistry
|
Hardness of water is estimated by the simplest complex formation titration Complex formed by cation in hard water during estimation of hardness is:
\( \mathbf{A} \cdot N a_{2}\left[C a\left(P O_{3}\right)_{6}\right] \)
B . \( N a_{2}[M g(E D T A)] \)
c. \( N a_{2}[P b(E D T A)] \)
D. \( \left[C a\left(S O_{4}\right)_{2}\right]^{2} \)
| 1 |
Chemistry
|
Order of decreasing basic strength of halides is:
A \( \cdot F^{-}>C l^{-}>I^{-}>B r^{-} \)
B . \( F^{-}>C l^{-}>B r^{-}>I^{-} \)
c. \( I^{-}>B r^{-}>C I^{-}>F^{-} \)
D. \( I^{-}>C l^{-}>B r^{-}>F^{-} \)
| 1 |
Chemistry
|
Which of the following is minimum at the equator?
A. Angle of dip
B. Horizontal component of earth's magnetic field
c. Angle of declination
D. Intensity of the earth's field
| 3 |
Physics
|
Each step in a food chain is called a
A. trophical level.
B. consumer level.
\( c . \) food web.
D. producer.
| 0 |
Biology
|
Pick the group which does not contain a neutral oxide.
A. \( N O_{2}, P_{4} O_{10}, A l_{2} O_{3}, N O \)
в. \( M g O, N_{2} O_{5}, S O_{3}, N_{2} O \)
\( \mathrm{c} \cdot \mathrm{CO}_{2}, \mathrm{SO}_{3}, \mathrm{CaO}, \mathrm{XeO}_{3} \)
D. \( C O, S i O_{2}, S n O_{2}, N a_{2} O_{3} \)
| 1 |
Chemistry
|
open end of a cylindrical vessel of
radius \( R \) and height \( 2 R \) as shown in figure. the flux of the electric field
through the surface (curved surface \( + \)
base ) of the vessel is
\( \mathbf{A} \cdot \frac{Q}{\varepsilon_{0}} \)
B. \( \frac{Q}{2 \varepsilon_{\text {d }}} \)
\( c \cdot \frac{Q}{4 \varepsilon_{0}} \)
D. \( \frac{Q}{\sqrt{5} \varepsilon_{0}} \)
| 3 |
Physics
|
When an ebonite rod is rubbed with
wool, they get oppositely charged due to conduction. Explain
| 3 |
Physics
|
The same ratio of corresponding sides is referred to as the factor for
polygons.
\( A \). scale
B. vernier
c. similar
D. congruence
| 2 |
Maths
|
Production of zoospores is characteristic of members of :
A. Ascomycetes
B. Phycomycetes
c. Basidiomycetes
D. Deuteromycetes
| 0 |
Biology
|
A particle is projected from horizontal
making an angle \( 60^{\circ} \) with initial
velocity \( 40 m s^{-1} . \) Find the time taken by
the particle to make angle \( 45^{\circ} \) from
horizontal.
A . \( 1.5 s \)
в. 2.5 \( s \)
\( c .3 .5 s \)
D. 4.5
| 3 |
Physics
|
Plasma has water to the extent of
A. \( 80 \% \)
в. \( 60 \% \)
c. \( 70 \% \)
D. \( 90 \% \) or more
| 0 |
Biology
|
The measure of angle \( y \) in the given
figure is
A. \( \angle y=65^{\circ} \)
B . \( \angle y=85^{\circ} \)
c. \( \angle y=75^{\circ} \)
D. \( \angle y=80^{\circ} \)
| 2 |
Maths
|
If \( N \) is the number of positive integral
solutions of \( \boldsymbol{x}_{1} \times \boldsymbol{x}_{2} \times \boldsymbol{x}_{3} \times \boldsymbol{x}_{4}=\mathbf{7 7 0} \)
then:
This question has multiple correct options
A. \( N \) is divisible by 4 district primes
B. \( N \) is a perfect square
C. \( N \) is a perfect fourth power
D. \( N \) is a perfect \( 8^{t h} \) power
| 2 |
Maths
|
Match the Column-I with Column-II:
| 1 |
Chemistry
|
Can lighting occur thunder? Justify
your answer.
| 3 |
Physics
|
The figure shows cross section of a
hollow glass tube of internal radius \( r \)
external radius \( \boldsymbol{R} \) and index of
refraction \( n . \) For two rays DE and \( A B C \) (in
which DE lies on ODE and DE is parallel
to BC), the separation \( r_{1} \) will be :
A \( \cdot r_{1}=(n-1) R \)
\( \mathbf{B} \cdot r_{1}=n^{2} R \)
\( \mathbf{c} \cdot r_{1}=n r \)
\( \mathbf{D} \cdot r_{1}=n^{2} r \)
| 3 |
Physics
|
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