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\( A B C D \) a parallelogram, \( A_{1} \) and \( B_{1} \) are the midpoints of sides \( B C \) and \( C D \) respectively. If \( \boldsymbol{A} \boldsymbol{A}_{1}+\boldsymbol{A} \boldsymbol{B}_{1}=\boldsymbol{\lambda} \boldsymbol{A} \boldsymbol{C} \)
then \( \lambda \) is equal to
A \( \cdot \frac{1}{2} \)
B. 1
\( c \cdot \frac{3}{2} \)
D. 2
| 2 |
Maths
|
If
(2,4) and (10,10) are the ends of a latus - rectum of an ellipse with eccentricity \( \frac{1}{2}, \) then the length of semi major axis is
A \( \cdot \frac{20}{3} \)
в. \( \frac{15}{3} \)
c. \( \frac{40}{3} \)
D. None of these
| 2 |
Maths
|
Solve the following pairs of linear (simultaneous) equation by the method of elimination by substitution: \( 2 x+ \)
\( \mathbf{3} \boldsymbol{y}=\mathbf{8}, \mathbf{2} \boldsymbol{x}=\mathbf{2}+\mathbf{3} \boldsymbol{y} \)
A \( \cdot x=2, y=\frac{3}{2} \)
в. \( x=3, y=5 \)
c. \( _{x}=\frac{5}{2}, y=1 \)
D. \( x=\frac{3}{2}, y=4 \)
| 2 |
Maths
|
The value of \( \int \frac{d x}{x\left(x^{n}+1\right)} \) is
A \( \cdot \frac{1}{n} \log \left(\frac{x^{n}}{x^{n}+1}\right)+C \)
в. \( \log \left(\frac{x^{n}+1}{x^{n}}\right)+C \)
c. \( \frac{1}{n} \log \left(\frac{x^{n}+1}{x^{n}}\right)+C \)
D. \( \log \left(\frac{x^{n}}{x^{n}+1}\right)+C \)
| 2 |
Maths
|
A cars initially at rest, 330m away from a stationary observer. It begins to move towards the observer with an
acceleration of \( 1.1 m s^{-2}, \) sounding its horn continuously. 20 s later, the driver stops sounding the horn. The velocity of sound in air is \( 330 m s^{-1} \). The observer
will hear the sound of the horn for a
duration of
A . \( 20 s \)
в. \( 21 s \)
\( \mathrm{c} \cdot 20 \frac{2}{3} s \)
D・ \( 19 \frac{1}{3} s \)
| 3 |
Physics
|
Potassium ferrocyanide is an example of
A. Complex salts
B. Normal salts
c. Double salts
D. Basic salts
| 1 |
Chemistry
|
Silver is monovalent and has an atomic
mass of \( 108 . \) Copper is divalent and has an atomic mass of \( 63.6 . \) The same
electric current is passed, for the same length of time through a silver
coulometer and a copper coulometer. If \( 27.0 \mathrm{g} \) of silver is deposited, then the corresponding amount if copper deposited is:
A. \( 31.80 g \)
B. 15.90 g
c. \( 7.95 \mathrm{g} \)
D. none of these
| 1 |
Chemistry
|
\( s=u+\frac{1}{2} a(2 t-1) ; \) make 't' the
subject of formula.
A \( t=\frac{(s-u)+a}{2 a} \)
B. \( t=\frac{2(s-u)+a}{2 a} \)
c. \( t=\frac{2(s-u)-a}{2 a} \)
D. \( t=\frac{2(s+u)+a}{2 a} \)
| 2 |
Maths
|
A triangular transverse wave is
propagating in the positive \( X \) -direction
Velocity of \( \boldsymbol{P} \) at this instant will be
B. Vertically downward
c. At rest
D. Cannot be determined
| 3 |
Physics
|
If the speed of electron in the Bohr's first
orbit of hydrogen is \( x, \) the speed in the third orbit is:
A. \( x / 9 \)
B. \( x / 3 \)
\( c .3 x \)
D. \( 9 x \)
| 1 |
Chemistry
|
Let \( f(x) \) is a quadratic function such that \( \boldsymbol{f}(\mathbf{0})=\mathbf{1}, \boldsymbol{f}(\mathbf{1})=\mathbf{7}, \boldsymbol{f}(-\mathbf{1})=\mathbf{1} \) and
\( \int \frac{f(x) d x}{x^{2}(x+1)^{3}} \) is a rational function
Find the value of \( \boldsymbol{f}^{\prime}(\mathbf{0}) \)
A . 3
B.
c. 2
D. 6
| 2 |
Maths
|
Two plane mirrors are inclined at an
angle by \( 120^{\circ}, \) as the figure shows. If a
ray strikes mirror \( M_{1} \$, \) at a \( 65^{\circ} \) angle
of incidence, at what angle \( \theta \) does it
leave mirror \( \boldsymbol{M}_{2} \)
\( A \cdot 35^{\circ} \)
B. \( 45^{\circ} \)
\( c \cdot 55^{\circ} \)
\( D \cdot 65^{\circ} \)
| 3 |
Physics
|
Which of the following metal occurs in native state?
A . ca
B. Au
\( c \cdot z n \)
\( D \cdot A \)
| 1 |
Chemistry
|
Assertion
Origin of seed habit begins in Pteridophyta.
Reason
It is suggested by heterosporous Selaginella.
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.
| 0 |
Biology
|
If \( \boldsymbol{A}=\left[\begin{array}{c}-2 \\ 4 \\ 5\end{array}\right] \) and \( B=\left[\begin{array}{lll}1 & 3 & -6\end{array}\right], \) then
verify that \( (A B)^{T}=B^{T} A^{T} \)
| 2 |
Maths
|
"KO \( _{2} \) is \( O_{2} \) absorber and \( C O_{2} \)
producer." It is also used in
submarines."
Answer whether the above statement is
true or false.
If true enter 1 , else enter 0 .
| 1 |
Chemistry
|
What is/are true statement?
This question has multiple correct options
A. lons of \( d \) -block elements are colored due to \( d-d \)
transition
B. Ions of \( f \) -block elements are colored due to \( f-f \)
transtition
\( ^{\mathbf{C}} \cdot\left[\operatorname{Sc}\left(H_{2} O\right)_{6}\right]^{3+},\left[T i\left(H_{2} O\right)_{6}\right]^{4+} \) are colored complexes.
D. \( C u^{+} \) is colorless ion.
| 1 |
Chemistry
|
A body starts from rest, what is the ratio of the distance travelled by the body during the 4 th and 3 rd second?
\( A \cdot \frac{7}{5} \)
B. \( \frac{5}{7} \)
\( c \cdot \frac{7}{3} \)
D. \( \frac{3}{7} \)
| 3 |
Physics
|
Nitrogen does not form pentahalides.
Give reason
| 1 |
Chemistry
|
How many molecules are planar among the following molecules?
\( \boldsymbol{I}_{3}^{-}, \boldsymbol{H}_{2} \boldsymbol{O}, \boldsymbol{I} \boldsymbol{C l}_{2}^{-}, \boldsymbol{C}_{2} \boldsymbol{H}_{4}, \boldsymbol{C}_{2} \boldsymbol{H}_{2}, \boldsymbol{H}_{3} \boldsymbol{O}^{+} \)
| 1 |
Chemistry
|
Aromatic amines are generally:
A. pleasant in smell.
B. toxic in nature.
C . low melting solids.
D. none of these
| 1 |
Chemistry
|
The arithmetic mean between two
distinct positive numbers is twice the
geometric mean between them. Find the ratio of greater to smaller.
| 2 |
Maths
|
The science that deals with the study of
life processes is known as
A. Psychology
B. Physiology
c. Biochemistry
D. Morphology
| 0 |
Biology
|
Consider the following reaction:
\( \boldsymbol{x} \boldsymbol{M} \boldsymbol{n} \boldsymbol{O}_{4}^{-}+\boldsymbol{y} \boldsymbol{C}_{2} \boldsymbol{O}_{4}^{2-}+\boldsymbol{z} \boldsymbol{H}^{+} \rightarrow \)
\( \boldsymbol{x} \boldsymbol{M} \boldsymbol{n}^{2+}+\mathbf{2} \boldsymbol{y} \boldsymbol{C} \boldsymbol{O}_{2}+\frac{\boldsymbol{z}}{2} \boldsymbol{H}_{2} \boldsymbol{O} . \) The values
of \( x, y \) and \( z \) in the reaction are, respectively:
A .2,5 and 16
B. 5,2 and 8
c. 5,2 and 16
D. 2,5 and 8
| 1 |
Chemistry
|
Solve \( \int 2 x^{3} e^{x^{2}} \)
A \( \cdot\left(x^{2} e^{x^{2}}-e^{x^{2}}\right)+C \)
B. \( \frac{1}{2}\left(x^{2} e^{x^{2}}-e^{x^{2}}\right)+C \)
C \( \cdot \frac{1}{2}\left(x^{2} e^{x^{2}}+e^{x^{2}}\right)+C \)
D \( \cdot \frac{1}{4}\left(x^{2} e^{x^{2}}+e^{x^{2}}\right)+C \)
| 2 |
Maths
|
A zener diode is rated as \( 1 W, \) if given
breakdown voltage is \( 6.2 V \) then max
current it can hold is
A \( .224 m A \)
в. \( 161 m A \)
\( \mathrm{c} .239 \mathrm{mA} \)
D. none of the above
| 3 |
Physics
|
In the circuit shown in fig., all wires
have equal resistance \( \mathrm{R}(=5 \Omega) \). The
equivalent resistance between \( A \) and \( B \) :
A \( \cdot 10 / 7 \Omega \)
B. 15/4 \( \Omega \)
\( c .7 \Omega \)
D. 3 \( \Omega \)
| 3 |
Physics
|
Find \( \cos ^{4}(\pi / 8)+\cos ^{4}(3 \pi / 8)+ \)
\( \cos ^{4}(5 \pi / 8)+\cos ^{4}(7 \pi / 8)-3 / 2 \)
| 2 |
Maths
|
State whether given statement is True or False
An alternating current cannot be used for electroplating.
A. True
B. False
| 3 |
Physics
|
Using valance bond theory, explain the type of hybridisation of the following given below:
\( \left[M n(C N)_{6}\right]^{3-},\left[C o\left(N H_{3}\right)_{6}\right]^{3+},\left[C r\left(H_{2} C\right.\right. \)
| 1 |
Chemistry
|
The \( p-V \) diagram of \( 2 g \) of helium gas
for a certain process \( A \rightarrow B \) is shown in
the figure. What is the heat given to the
gas during the process \( \boldsymbol{A} \rightarrow \boldsymbol{B} \) ?
\( A \cdot 4 p_{0} V_{0} \)
B. \( 6 p_{0} V_{0} \)
\( c \cdot 4.5 p_{0} V_{0} \)
\( \mathbf{D} \cdot 2 p_{0} V_{0} \)
| 3 |
Physics
|
The points (-5,12),(-2,-3),(9,-10),(6,5)
taken in order, form
A. Parallelogram
B. rectangle
c. rhombus
D. square
| 2 |
Maths
|
In a child of 15 years age, plasma calcium level is diagnosed below optimum level, which organ is malfunctioning?
A. Thyroid gland
B. Liver
c. Parathyroid
D. Posterior lobe of pituitary
| 0 |
Biology
|
The measurements (in \( \mathrm{mm} \) ) of the
diameters of the heads of the screws are given below. Calculate the mean
diameter of the head of the screws.
\( \begin{array}{ll}36- & 39- \\ 38 & 41\end{array} \) \( \begin{array}{ll}33- & 3 \\ 35 & 3\end{array} \) \( \begin{array}{ll}\text { Diameter } & \text { 3. } \\ \text { (in mm) } & \text { 3) }\end{array} \)
Number of 3
screws \( \left(f_{1}\right) \)
| 2 |
Maths
|
Find the area of four walls of a room
having length, breadth and height as 8 \( \mathrm{m}, 5 \mathrm{m} \) and \( 3 \mathrm{m} \) respectively. Find the cost of white-washing the walls at the rate of Rs. \( 15 / m^{2} \)
| 2 |
Maths
|
Assertion: A combination of two simple
harmonic motions with arbitrary amplitudes and phases is not necessarily periodic. Reason: A periodic motion can always be expressed as a sum of infinite number of harmonic motions with
appropriate amplitudes.
A. If both assertion and reason are true and reason is the correct explanation of assertion
B. If both assertion and reason are true and reason is not the correct explanation of assertion
c. If assertion is true but reason is false.
D. If both assertion and reason are false
| 3 |
Physics
|
Transition metals are often para
magnetic owing to
A. high melting point and boiling point
B. the presence of vacant orbitals
C. the presence of unpaired electrons
D. malleability and ductility
| 1 |
Chemistry
|
\( \frac{x}{5} \)
| 2 |
Maths
|
In which one of the following processes
\( C O_{2} \) is not released?
A. Aerobic respiration in plants
B. Aerobic respiration in animals
C. Alcoholic fermentation
D. Lactate fermentation
| 0 |
Biology
|
The total molar concentration of ions in
\( 0.47 \mathrm{M} \) solution of \( \mathrm{Na}_{2} \mathrm{SO}_{4} \) assuming
its complete ionisation is:
A . 1.88 M
В. 0.94 М
c. 1.43 М
D. 0.47 М
| 1 |
Chemistry
|
If two coins are tossed, then find the
probability of the event that at the most one tail turns up.
| 2 |
Maths
|
One of the commonly used plant growth hormone in tea plantation is
A. Ethylene
B. Abscisic acid
c. zeatin
D. Indole-3-acetic acid and indole butyric acid
| 0 |
Biology
|
Let there be four articles having colours blue, red, black and white. When they are heated together and allowed to cool,
the article that cool earlier is :
A. Blue
B. Red
c. Black
D. white
| 3 |
Physics
|
The pH indicators are:
A. salts of strong acids and strong bases
B. salts of weak acids and weak bases
C. either weak acids or weak bases
D. either strong acids or strong bases
| 1 |
Chemistry
|
To keep a body moving with constant velocity on a frictionless surface, an external force:
A. should act continuously
B. should be a variable force
c. is not required
D. should act opposite to the direction of motion
| 3 |
Physics
|
The inner transition elements are the
elements in which last electrons enters
into:
\( A \cdot(n-1) \) d-orbitals
B. (n-2) f-orbitals
C. \( (n-1) \) d-orbitals and \( (n-1) \) f-orbitals
D. \( (n-1) \) d-orbitals and ns orbitals
| 1 |
Chemistry
|
Q Type your question
shown in figure are connected at one
end to a charged capacitor through a
switch \( S, \) which initially open. At the
other end, they are connected by a loose
wire. The capacitor has charge \( Q \) and
mass per unit length of the rod is \( \lambda \). The
effective resistance of the circuit after
closing the switch is \( R \). If the velocity of
each rod when the capacitor is discharged after closing the switch is \( \boldsymbol{v}=\frac{\boldsymbol{\mu}_{0} \boldsymbol{Q}^{2}}{\boldsymbol{x} \pi \boldsymbol{d} \boldsymbol{R} \boldsymbol{\lambda} \boldsymbol{l}} . \) Find \( \boldsymbol{x} \)
(Assume that the displacement of rods during the discharging time is
negligible)
| 3 |
Physics
|
Beads on string of A are seen in B which
condense to form chromosomes in \( C \)
stage of cell division.
A. A- Chromonema B- Chromatin C- Metaphase
B. A-Chromatin B- Metaphase C- Metaphase
c. A- chromonema
B-Chromosome C- Anaphase
D. A- chromonema B- Chromatid C- Anaphase
| 0 |
Biology
|
Assertion
\( (A): P(n)=n^{2}+n+41 \) is a prime
\( \forall \boldsymbol{n} \in \boldsymbol{N} \)
Reason
(R): If a number is prime then it
contains only two factors; 1 and number itself.
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)
c. (A)is true but (R) is false.
D. (A)is false but (R) is true
| 2 |
Maths
|
If \( \boldsymbol{A}=\int_{0}^{\pi} \frac{\cos \boldsymbol{x}}{(\boldsymbol{x}+\mathbf{2})^{2}} \boldsymbol{d} \boldsymbol{x}, \) then
\( \int_{0}^{\frac{\pi}{2}} \frac{\sin 2 x}{(x+1)} d x \) is equal to
A \( \cdot \frac{1}{2}+\frac{1}{\pi+2}-A \)
B. \( \frac{1}{\pi+2}-A \)
\( c \cdot 1+\frac{1}{\pi+2}-A \)
D. \( _{A-} \frac{1}{2}-\frac{1}{\pi+2} \)
| 2 |
Maths
|
A bag contains 10 red balls and 8 green balls. 2 balls are drawn at random one
by one with replacement. Find the probability that both the balls are green that a second year student is chosen.
| 2 |
Maths
|
Draw the graph of equation \( 3 x+2 y=6 \) Find the sum of the co-ordinates of the
point where the graph intersects the \( Y \) axis.
| 2 |
Maths
|
In which classes, the polymers are
classified on the basis of molecular
forces?
| 1 |
Chemistry
|
Stomatal index I is equal to
A \( \cdot \frac{s}{E-S} \)
B. \( \frac{s}{E+s} \)
\( \mathbf{c} \cdot \frac{E}{E+S} \)
D. \( \frac{E+S}{E} \)
| 0 |
Biology
|
Which is true statement about \( \boldsymbol{H}_{2} \boldsymbol{O} \) ?
A. Hardness can be removed by passing through ion exchange resin
B . Its pressure can be detected by anhydrous \( C u S O_{4} \)
c. It is amphoprotic
D. All of the above
| 1 |
Chemistry
|
At \( 25^{\circ} C, \) the standard oxidation
potential of \( Z n \) and \( A g \) in water are:
\( Z n(s) \rightarrow Z n^{+2}(a q)+2 e^{-}, E^{0}= \)
\( 0.76 V \)
and \( A g(s) \rightarrow A g^{+}(a q)+e^{-}, E^{0}= \)
\( -0.80 V \)
Which of the following reaction actually takes place?
A \( \cdot Z n^{2+}(a q)+2 A g(s) \rightarrow 2 A g^{+}(a q)+Z n(s) \)
B. \( Z n(s)+2 A g^{+}(a q) \rightarrow Z n^{2+}(a q)+2 A g(s) \)
C. \( Z n^{2+}(a q)+2 A g^{+}(a q) \rightarrow Z n(s)+2 A g(s) \)
D. \( Z n(s)+A g(s) \rightarrow Z n^{2+}(a q)+A g^{+}(a q) \)
| 1 |
Chemistry
|
The displacement-time graph for an object is given below. What results can you find out for its velocity?
| 3 |
Physics
|
In \( S \) and \( P \) -block elements the oxidation
state changes by 2 units. But in transition elements, it changes by 1 unit
of
1. Explain.
| 1 |
Chemistry
|
\( \ln s p^{3} d^{3} \) hybridisation, which orbitals are involved?
A \( \cdot d_{x^{2}-y^{2}}, d_{z^{2}}, d_{x y} \)
B . \( d_{x y}, d_{y z}, d_{z x} \)
c. \( d_{x^{2}-y^{2}}, d_{x y}, d_{x z} \)
D. \( d_{z^{2}}, d_{y z}, d_{z x} \)
| 1 |
Chemistry
|
The elements \( A, B, C, D \) and \( E \) have atomic number 9,11,17,12 and 13 respectively. Which pair of elements belongs to the same group?
A. A and B
B. B and D
c. A and \( c \)
D. D and E
| 1 |
Chemistry
|
If force \( F, \) acceleration \( a, \) and time \( T \)
are taken as the fundamental physical quantities, the dimensions of length on
this system of units are
\( \mathbf{A} \cdot F A T^{2} \)
в. \( F A T \)
c. \( F T \)
D. \( A T^{2} \)
| 3 |
Physics
|
Find matrix \( \boldsymbol{A} \) such that
\( \left[\begin{array}{cc}2 & -1 \\ 1 & 0 \\ -3 & 4\end{array}\right] A=\left[\begin{array}{cc}-1 & -8 \\ 1 & -2 \\ 9 & 22\end{array}\right] \)
| 2 |
Maths
|
\( \ln \) a \( \Delta A B C, \) if \( \angle B=60^{\circ}, \) prove that
\( (a+b+c)(a-b+c)=3 c a \)
| 2 |
Maths
|
\( (i)^{457} \)
\( A \cdot-1 \)
B . \( -i \)
\( \mathbf{c} \cdot i \)
D. 1
| 2 |
Maths
|
Assertion (A): All the radioactive
elements are ultimately converted into lead
Reason (R): All the elements above lead
are unstable
A. Both A and R are true and R is correct explanation of A
B. Both A and R are true and R is not correct explanation of
c. A is true but R is false
D. A is false but R is true
| 3 |
Physics
|
If the temperature is increased above
\( 35^{\circ} \mathrm{C} \)
A. Rate of decline of respiration will be earlier than of photosynthesis.
B. Rate of decline of photosynthesis will be earlier than decline of respiration.
C. Both decline simultaneously.
D. Both do not show any fixed pattern.
| 0 |
Biology
|
If \( (3, \lambda, \mu) \) is a point on the line then
\( 2 x+y+z=0=x-2 y+z-1 \) then
A \( \cdot \lambda=\frac{-8}{3}, \mu=-\frac{1}{3} \)
B. \( \lambda=\frac{-1}{3}, \mu=-\frac{8}{3} \)
c. \( \lambda=\frac{-4}{3} \mu=\frac{-14}{3} \)
D. \( \lambda=-5, \mu=-1 \)
| 2 |
Maths
|
Which among the following are
intramolecular redox reactions?
This question has multiple correct options
A. \( P C l_{5} \rightarrow P C l_{3}+C l_{2} \)
в. \( C H O-C H O+O H^{-} \rightarrow C O O^{-}-C H_{2} O H \)
c. \( 2 K C l O_{3} \rightarrow 2 K C l+3 O_{2} \)
D. \( N H_{4} N O_{2} \longrightarrow N_{2}+2 H_{2} O \)
| 1 |
Chemistry
|
In a single throw of a die, the probability of getting a multiple of 3 is
A \( \cdot \frac{1}{2} \)
B. \( \frac{1}{3} \)
\( c \cdot \frac{1}{6} \)
D. \( \frac{3}{4} \)
| 2 |
Maths
|
A large sheet of uniform charge passes
through a hypothetical spherical
surface. The figure shows principle
section of situation. The electric flux
through the spherical surface is given
by
\( ^{\mathbf{A}} \cdot \frac{\pi R^{2} \sigma}{\epsilon_{0}} \)
B. \( \frac{2 \pi\left(R^{2}-x^{2}\right) \sigma}{\epsilon_{0}} \)
\( c \)
\( D \)
| 3 |
Physics
|
Calculate the pH of an aqueous solution of \( 1.0 M \) ammonium formate assuming
complete dissociation. \( \boldsymbol{p} \boldsymbol{K}_{\boldsymbol{a}} \) for formic
acid \( =3.8 \) and \( p K_{b} \) of ammonia \( =4.8 \)
| 1 |
Chemistry
|
In electro-chemical corrosion of metals,
the metal undergoing corrosion:
A. Becomes anode
B. Becomes cathode
c. Becomes inert
D. None is correct
| 1 |
Chemistry
|
Using suitable identity, evaluate \( (-32)^{3}+(18)^{3}+(14)^{3} \)
| 2 |
Maths
|
What is the common difference, if \( a_{1}= \)
100 and \( a_{2}=250 \)
A. 100
в. 150
c. 200
D. 210
| 2 |
Maths
|
If \( x_{1}, x_{2}, x_{3}, x_{4} \) are in G.P then its
common ratio is,
\( ^{\mathbf{A}} \cdot\left(\frac{a r}{c p}\right)^{\frac{1}{4}} \)
\( ^{\mathrm{B}}\left(\frac{c r}{a p}\right)^{\frac{1}{3}} \)
\( ^{c} \cdot\left(\frac{c r}{a p}\right)^{\frac{1}{2}} \)
\( ^{\mathrm{D}}\left(\frac{a p}{b q}\right)^{\frac{1}{2}} \)
| 2 |
Maths
|
If \( \int \frac{d x}{\sqrt{x}(x+9)}=f(x)+ \) constant, then
\( \boldsymbol{f}(\boldsymbol{x})= \)
A \( \cdot \frac{2}{3} \tan ^{-1} \sqrt{x} \)
B \( \cdot \frac{2}{3} \tan ^{-1}\left(\frac{\sqrt{x}}{3}\right) \)
C. \( \tan ^{-1} \sqrt{x} \)
D. \( \tan ^{-1}\left(\frac{\sqrt{x}}{3}\right) \)
| 2 |
Maths
|
Magnetic flux passing through a coil is initially \( 4 \times 10^{-4} \) Wh. It reduces to \( 10 \% \)
of its original value in 't' second. If the
e.m.f. induced is \( 0.72 \mathrm{mV} \) then 't' in
second is:
A . 0.3
B. 0.4
c. 0.5
D. 0.6
| 3 |
Physics
|
What is the reduction electrode potential (in volts) of copper electrode when \( \left[C u^{2+}\right. \)
\( =0.01 \mathrm{M} \) in a solution at \( 25^{0} \mathrm{C} \) ?
(EO of \( \left.C u^{2+} / C u \text { electrode is }+0.34\right) \)
A . 0.399
B. 0.2809
c. 0.3105
D. 0.3695
| 1 |
Chemistry
|
Assertion
A light ray is incident on a glass slab.
Some portion of its is reflected and portion of it is reflected and some is refracted. Refracted and reflected rays
are always perpendicular to each other.
Reason
Angle of incidence is equal to angle of
reflection.
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
| 3 |
Physics
|
Assertion
Hussain died turning blue in the body
colour.
Reason
This is due to deficiency of oxygen.
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
|
The two adjacent sides of a rectangle
\( \operatorname{are} 5 p^{2}-2 p+3 \) and \( 7 p^{2}-14 p+2 \)
find the perimeter.
| 2 |
Maths
|
Which of the following units denotes the dimensions \( M L^{2} / Q^{2}, \) where \( Q \) denotes the electric charge?
A. Weber (Wb)
в. \( W b / \mathrm{m}^{2} \)
c. Henry \( (H) \)
D. H / m \( ^{2} \)
| 3 |
Physics
|
Formation of \( N i(C O)_{4} \) and its subsequent decomposition into Ni and CO (recycled) makes basis of Mond's
process. \( N i+4 C O \stackrel{T_{1}}{\longrightarrow} N i(C O)_{4} \stackrel{T_{2}}{\longrightarrow} N i+ \)
\( 4 C O \)
\( T_{1} \) and \( T_{2} \) are:
A \( \cdot 100^{\circ} \mathrm{C}, 50^{\circ} \mathrm{C} \)
в. \( 50^{\circ} \mathrm{C}, 100^{\circ} \mathrm{C} \)
c. \( 50^{\circ} \mathrm{C}, 230^{\circ} \mathrm{C} \)
D. \( 230^{\circ} \mathrm{C}, 50^{\circ} \mathrm{C} \)
| 1 |
Chemistry
|
Using elementary tranormtion, find the
\[
\text { inverse of }\left[\begin{array}{ccc}
\mathbf{1} & \mathbf{3} & -\mathbf{2} \\
-\mathbf{3} & \mathbf{0} & -\mathbf{5} \\
\mathbf{2} & \mathbf{5} & \mathbf{0}
\end{array}\right]
\]
| 2 |
Maths
|
A ray of light is incident on a plane
mirror at an angle of \( 30^{0} \). what is the
angle of reflection?
| 3 |
Physics
|
A single unit membrane surrounds the
organelle
A. Nucleus
B. Mitochondrion
c. Lysosome
D. chloroplast
| 0 |
Biology
|
A rocket is moving in a gravity free space with a constant acceleration of
\( 2 m s^{-2}, \) along \( +x \) direction (see figure) The length of a chamber inside the
rocket is \( 4 \mathrm{m} \). A ball is thrown from the
left end of the chamber in \( +x \) direction with a speed of \( 0.3 m s^{-1} \) relative to the rocket. At the same time, another ball
is thrown in - \( x \) direction with a speed of
\( 0.2 m s^{-1} \) from its right end relative to the rocket. The time in seconds when
the two balls hit each other is
\( A \)
\( B .3 \)
\( c \)
\( D \)
| 3 |
Physics
|
If \( \tan ^{-1}(1+x)+\tan ^{-1}(1-x)=\frac{\pi}{2} \)
then \( x=? \)
A .
B. -
c.
D.
| 2 |
Maths
|
A charge \( q \) is to be distributed on two conducting spheres. What should be the value of the charges on the spheres so that the repulsive force between them is maximum when they are placed at a fixed distance from each other in air?
A \( \cdot \frac{q}{2} \) and \( \frac{q}{2} \)
в. \( \frac{q}{4} \) and \( \frac{3 q}{4} \)
c. \( \frac{q}{3} \) and \( \frac{2 q}{3} \)
D. \( \frac{q}{5} \) and \( \frac{4 q}{5} \)
| 3 |
Physics
|
Urea is transported through
\( A \cdot \) RBCs
B. WBCs
c. Plasma
D. Lymph
| 0 |
Biology
|
Based on equations reducible to linear
equations Solve for \( x \) and \( y: \frac{2}{x-1}+\frac{y-2}{4}= \) \( 2 ; \frac{3}{2(x-1)}+\frac{2(y-2)}{5}=\frac{47}{20} \)
A \( . x=3, y=6 \)
в. \( x=1, y=5 \)
c. \( x=2, y=-7 \)
D. \( x=5, y=-9 \)
| 2 |
Maths
|
The common name of 2-chloro-2-
methylpropane is:
A. tert-butyl chloride
B. sec-butyl bromide
c. both A and B
D. none of these
| 1 |
Chemistry
|
\( \underset{(w h i t e)}{P_{4}}+S O C I_{2}-P C I_{3}+S O_{2}+^{\prime} x^{\prime} \)
identify the 'x'
| 1 |
Chemistry
|
If a full wave rectifier circuit is
operating from \( 50 H z \) mains, the
fundamental frequency in the ripple will
be
\( \mathbf{A} \cdot 25 H z \)
B. \( 50 \mathrm{Hz} \)
c. \( 70.7 \mathrm{Hz} \)
D. \( 100 H z \)
| 3 |
Physics
|
The number of vertices in a cube is
\( A \cdot 6 \)
B. 10
\( c \cdot 8 \)
D. 12
| 2 |
Maths
|
The antioxidant which is used to
prevent rancidity in foods is:
A. butylated hydroxyl anisole
B. sodium hydroxide
c. sodium carbonate
D. methylated hydroxyl anisole
| 1 |
Chemistry
|
Assertion
A rise in \( \mathrm{PCO}_{2}, \mathrm{H}+ \) ions and temperature
shifts the \( \mathrm{Hb} \mathrm{O}_{2} \) dissociation curve to
right.
Reason
A rise in \( \mathrm{PCO}_{2} \) or fall in pH decreases oxygen affinity for haemoglobin.
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
| 0 |
Biology
|
The formation of an optically active compound from a chiral molecule is called:
A. asymmetric synthesis
B. resolution
c. walden inversion
D. epimerisation
| 1 |
Chemistry
|
A hollow cylinder of mass \( M \) and radius
\( \boldsymbol{R} \) is pulled by a horizontal force \( \boldsymbol{F} \) acting at its centre of mass on a horizontal surface where the coefficient
of friction is \( \mu \)
If hollow cylinder is performing pure rolling then frictional force \( f \) will be :
A. \( F \)
в. \( \frac{F}{2} \)
c. \( \frac{F}{3} \)
D. \( 2 F \)
| 3 |
Physics
|
\( \ln \) a triad of \( A, B, C \) elements if the
atomic masses of \( A \) and \( C \) respectively
are 100 and \( 200, \) then the atomic mass
of \( B \) is:
A . 300
в. 175
c. 125
D. 150
| 1 |
Chemistry
|
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