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Subtract the following:
\( \boldsymbol{p}(\boldsymbol{y})=\boldsymbol{3} \boldsymbol{y}^{7}-\boldsymbol{2} \boldsymbol{y}^{2}+\boldsymbol{3} \) and \( \boldsymbol{q}(\boldsymbol{y})=\boldsymbol{y}^{7}+ \)
\( \boldsymbol{y}^{2}+\boldsymbol{y} \) | 2 | Maths |
If \( \bar{a} \) and \( \bar{b} \) are any two non-zero and non-
collinear vectors, then prove that any vector \( \bar{r} \) coplanar with \( \bar{a} \) and \( \bar{b} \) can be
uniquely expressed as \( \overline{\boldsymbol{r}}=\boldsymbol{t}_{1} \boldsymbol{a}+\boldsymbol{t}_{2} \boldsymbol{b} \)
where \( t_{1} \) and \( t_{2} \) are scalars. | 2 | Maths |
\( 2 C+O_{2}=2 C O . \) The rate of
disappearance of \( \boldsymbol{C} \) is \( 2 \times \)
\( 10^{-3} \) mol \( L^{-1} \) sec \( ^{-1} \). What is the
instantaneous rate of the reaction?
A. \( 2 \times 10^{-3} \)
В. \( 1 \times 10^{-3} \)
c. \( 4 \times 10^{-3} \)
D. None of these | 1 | Chemistry |
A perfectly reflecting solid sphere of radius \( r \) is kept in the path of a parallel beam of light of large aperture. If the beam carries an intensity I, find the force exerted by the beam on the sphere. | 3 | Physics |
Find the absolute maximum and
minimum values of a function \( f \) given
by \( f(x)=2 x^{3}-15 x^{2}+36 x+1 \) on the
interval \( [\mathbf{1}, \mathbf{5}] \) | 2 | Maths |
Solve graphically: \( 2 x+y-7=0, x+ \)
\( 3 y-11=0 \) | 2 | Maths |
Write the name of device \( ^{\prime} X^{\prime} \) in the
following given diagram. Explain its working making its circuit diagram. | 3 | Physics |
Two soap bubbles of radius \( r_{1}=r \) and
\( r_{2}=2 r \) coalesce to form a double as
shown, then angle \( p j i, \) is equal to
\( A \cdot 60^{\circ} \)
В \( \cdot 90^{\circ} \)
\( c \cdot 120^{\circ} \)
D. It depends on surface tension of soap solution | 3 | Physics |
Striated muscle fibres possess
A. Longitudinal strips
B. Oblique strips
c. Transverse strips
D. No strips | 0 | Biology |
In the hydrolysis of organic chloride in
the presence of a large excess of water,
\( \boldsymbol{R C l}+\boldsymbol{H}_{2} \boldsymbol{O} \rightarrow \boldsymbol{R O H}+\boldsymbol{H} \boldsymbol{C l} \)
A. Molecularity and order of reaction both are 2
B. Molecularity is 2 but order of reaction is 1
c. Molecularity is 1 but order of reaction is also 1
D. Molecularity is 1 and order of reaction is also 1 | 1 | Chemistry |
1 \( g \) of hydrogen is converted into \( 0.993 g \) of helium in a thermonuclear reaction.
Then energy released is
\( \mathbf{A} \cdot 63 \times 10^{7} J \)
В. \( 63 \times 10^{10} \mathrm{J} \)
\( \mathbf{D} \cdot 63 \times 10^{20} J \) | 3 | Physics |
Assertion
Each of the plates of a parallel-plate capacitor is given equal positive charge
Q. The charges on the facing surfaces will be same.
Reason
A negative charge (-Q) will be induced on each of the facing surfaces.
A. If both Assertion and Reason are correct and Reason the correct explanation of Assertion
B. If both Assertion and Reason are correct, but Reason is not the correct explanation of Assertion
c. If Assertion is correct but Reason is incorrect
D. If Assertion is incorrect but Reason is correct | 3 | Physics |
Factorize \( 3 x^{2}+14 x+15 \) | 2 | Maths |
The vector \( \vec{a}=\alpha \hat{i}+2 \widehat{j}+\beta \widehat{k} \) lies in the
plane of the vectors \( \overrightarrow{\boldsymbol{b}}=\widehat{\boldsymbol{i}}+\widehat{\boldsymbol{j}} \) and \( \overrightarrow{\boldsymbol{c}}= \)
\( \widehat{j}+\widehat{k} \) and bisects the angle between \( \overrightarrow{\boldsymbol{b}} \) and \( \vec{c} . \) Then, which one of the following
gives possible values of \( \alpha \) and \( \beta ? \)
A \( \cdot \alpha=2, \beta=2 \)
в. \( \alpha=1, \beta=2 \)
c. \( \alpha=2, \beta=1 \)
D. \( \alpha=1, \beta=1 \) | 2 | Maths |
Which one of the following quantities is negative?
A \( \cdot \cos \left(\tan ^{-1}(\tan 4)\right) \)
B. \( \sin \left(\cot ^{-1}(\cot 4)\right) \)
c. \( \tan \left(\cos ^{-1}(\cos 5)\right) \)
D・cot \( \left(\sin ^{-1}(\sin 4)\right) \) | 2 | Maths |
Which complex compound possesses \( s p^{3} d^{2} \) hybridisation?
A \( \cdot\left[F e\left(N H_{3}\right)_{6}\right]^{3+} \)
B . \( \left[F e(C N)_{6}\right]^{4-} \)
c. \( \left[F e(C N)_{6}\right]^{3} \)
D \cdot \( \left[F e(C l)_{6}\right]^{3-} \) | 1 | Chemistry |
A derived dimension is something
which has some physical sense or is the combination of many fundamental
dimensions.
If true enter 1 , else enter 0 | 3 | Physics |
During interference of waves, the
amplitude of the resulting wave can be found at any position using the principle of:
A. superposition
B. interference
c. diffraction
D. none of these | 3 | Physics |
Find the extreme value of Quadratic
expression \( 2 x-7-5 x^{2} \). Also state
whether it is maximum or minimum
with reason | 2 | Maths |
In one average-life,
A. half the active nuclei decay
B. less than half the active nuclei decay.
C. more than half the active nuclei decay.
D. all the nuclei decay. | 3 | Physics |
With out expanding show that \( \left|\begin{array}{ccc}\mathbf{1} & \boldsymbol{a} & \boldsymbol{a}^{2} \\ \mathbf{1} & \boldsymbol{b} & \boldsymbol{b}^{2} \\ \mathbf{1} & \boldsymbol{c} & \boldsymbol{c}^{2}\end{array}\right|=(\boldsymbol{a}-\boldsymbol{b})(\boldsymbol{b}-\boldsymbol{c})(\boldsymbol{c}-\boldsymbol{a}) \) | 2 | Maths |
The advantage of RBCs being biconcave
is that
A. They increase the surface area
B. They can be packed up like coins.
c. They can fit into capillaries.
D. None of the above | 0 | Biology |
\( N a_{2} O, M g O, A l_{2} O_{3} \) and \( S i O_{2} \) have
heat of formation equal to -416,-602,-1676 and -911
\( k J m o l^{-1} \) respectively. The most stable oxide is:
A. \( N a_{2} O \)
в. \( M g O \)
c. \( A l_{2} O_{3} \)
D. \( \operatorname{si} O_{2} \) | 1 | Chemistry |
If the tangents of the angles \( A \) and \( B \) of \( a \) triangle \( A B C \) satisfy the equation
\( a b x^{2}-c^{2} x+a b=0, \) then
This question has multiple correct options
\( \mathbf{A} \cdot \tan A=\frac{a}{b} \)
B. \( \tan B=\frac{b}{a} \)
\( \mathbf{c} \cdot \cos C=0 \)
D. \( \sin ^{2} A+\sin ^{2} B+\sin ^{2} C=2 \) | 2 | Maths |
If \( n-1 C_{6}+^{n-1} C_{7}>^{n} C_{6}, \) then?
\( \mathbf{A} \cdot n>4 \)
B \( . n>12 \)
\( \mathbf{C} \cdot n \geq 13 \)
D. \( n>13 \) | 2 | Maths |
Which among the following is a nonmetal?
A. Bromine
B. zinç
c. sodium
D. Iron | 1 | Chemistry |
Which compound is unstable at room
temperature?
\( A \)
B.
\( c \)
\( D \) | 1 | Chemistry |
The nucleus of helium atom contains
two protons that are separated by distance \( 3.0 \times 10^{-15} \) m. The magnitude
of the electrostatic force that each
proton exerts on the other is:
A . \( 20.6 N \)
B. 25.6 N
c. \( 15.6 N \)
D. \( 12.6 N \) | 3 | Physics |
\( \sqrt{3}+2 \sqrt{2}+\sqrt{3-2 \sqrt{2}}=\dots ? \)
A \( \cdot 2+2 \sqrt{2} \)
B. \( 2 \sqrt{2} \)
c. 1
D. | 2 | Maths |
During respiration \( C O_{2} \) is transported in the form of
A. Dissolved plasma
B. Sodium carbonate
\( \mathrm{c} \cdot \mathrm{KHCO}_{3} \)
D. Partly dissolved in plasma and partly in the form of sodium and potassium bicarbonate | 0 | Biology |
A wire has a resistance of \( 10 \Omega \). It is
stretched by \( 10 \% \) of its original length, what will be the new resistance?
A . \( 10 \Omega \)
в. \( 11 \Omega \)
\( c .9 \Omega \)
D. 12.12 | 3 | Physics |
"Gulal" a coloured powdery thing, used in Holi festival is obtained from
A. Caesalpinioideae family
B. Mimosoideae family
c. Papilionatae family
D. Liliaceae | 0 | Biology |
The energy stored in one molecule of
NADPH and one molecule of ATP are
and \( \ldots \ldots . \) respectively.
A. 52 kcal, 7 kcal
B. 520 kcal, 70 kcal
c. 150 kcal, 22 kcal
D. 650 kcal, 90 kcal | 0 | Biology |
Find the square root of each of the
following by prime factorization:
\( \mathbf{1 1 6 6 4} \) | 2 | Maths |
Check whether the probabilities \( \boldsymbol{P}(\boldsymbol{A}) \)
and \( P(B) \) are consistently defined \( \boldsymbol{P}(\boldsymbol{A})=\mathbf{0 . 5}, \boldsymbol{P}(\boldsymbol{B})=\mathbf{0 . 7}, \boldsymbol{P}(\boldsymbol{A} \cap \boldsymbol{B})= \)
\( \mathbf{0 . 6} \) | 2 | Maths |
The coefficient of \( x^{160} \) in the expansion
of \( \left(x^{8}+\right. \)
1) \( ^{60}\left(x^{12}+3 x^{4}+\frac{3}{x^{4}}+\frac{1}{x^{12}}\right)^{-10} \)
A. \( ^{30} C_{6} \)
B. \( ^{30} C_{5} \)
c. divisible by 189
D. divisible by 203 | 2 | Maths |
If the distance between two object in increase two times, they by how many times will the mass of one of the object
be change to maintain the same gravitational force? | 3 | Physics |
What amount of work is done in moving a charge of 4 coulombs from a point 220 volts to a point at 230 volts? | 3 | Physics |
\( \operatorname{Det}\left\{\begin{array}{ccc}-2 a & a+b & c+a \\ b+a & -2 b & b+c \\ c+a & c+b & -2 c\end{array}\right\}= \)
\( A \cdot(a+b)(b+c)(c+a) \)
В . \( (a-b)(b-c)(c-a) \)
\( c \cdot 4(a+b)(b+c)(c+a) \)
D. \( 4(a-b)(b-c)(c-a) \) | 2 | Maths |
In the adjoining figure, name the
following pairs of angles.
Obstuse vertically opposite angles | 2 | Maths |
Combination of
\( \boldsymbol{P t}(\boldsymbol{I} \boldsymbol{V}), \boldsymbol{N} \boldsymbol{H}_{3}, \boldsymbol{C l}^{-}, \boldsymbol{K}^{+} \) result in the
formation of \( x \) complexes and one such
complex is \( \left[\boldsymbol{P t}\left(\boldsymbol{N} \boldsymbol{H}_{3}\right)_{6}\right] \boldsymbol{C l}_{4} . \boldsymbol{x} \) is : | 1 | Chemistry |
A particle moves along the curve \( y= \)
\( x^{3 / 2} \) in the first quadrant in such a way
that its distance from the origin increases at the rate of 11 units per
second. The value of when \( x=3 \) is
A . 4
B. \( \frac{9}{2} \)
c. \( \frac{3 \sqrt{3}}{2} \)
D. none of these | 2 | Maths |
Which among the following does not
react with a dilute solution of sulfuric
acid?
A \( \cdot \) NaNO \( _{3} \)
В. \( N a_{2} S \)
c. \( N a_{3} P O_{4} \)
D. \( N a_{2} C O_{3} \)
E . NaOH | 1 | Chemistry |
The coefficient of the middle term in the
expansion of \( (1+x)^{2 n} \) is
This question has multiple correct options
A \( \cdot 2^{n} C_{n} \)
в. \( \frac{1.3 .5 \ldots \ldots(2 n-1)}{n !} 2^{\text {। }} \)
c. \( 2.6 \ldots(4 n-2) \)
D \( \cdot 2.4 \ldots \ldots . .2 n \) | 2 | Maths |
Using differentials, find the sum of digits approximate value of the following up to 3 places of decimal. \( (401)^{\frac{1}{2}} \) | 2 | Maths |
Find the matrix \( X \), given that \( X+ \) \( \mathbf{2} \boldsymbol{I}=\left[\begin{array}{cc}\mathbf{3} & \mathbf{- 1} \\ \mathbf{1} & \mathbf{2}\end{array}\right] \) | 2 | Maths |
If the work done in stretching a wire by
1 \( m m \) is \( 2 J, \) the work necessary for
stretching another wire of same
material but with double radius of
cross-section and half the length by
1 mm is:
\( \mathbf{A} \cdot 16 J \)
B. \( 8 J \)
c. \( 4 J \)
D \( \frac{1}{4} J \) | 3 | Physics |
A bidentate ligand has 3 coordination sites.
A . True
B. False | 1 | Chemistry |
In the reaction; \( \boldsymbol{A}+\mathbf{2} \boldsymbol{B} \rightarrow \mathbf{3} \boldsymbol{C}+\boldsymbol{D} \)
which of the following expression does not describe changes in the concentration of various species as a function of time?
A \( \cdot\{d[C] / d t\}=-\{3 d[A] / d t\} \)
B . \( \{3 d[D] / d t\}=\{d[C] / d t\} \)
c. \( \{3 d[B] / d t\}=-\{2 d[C] / d t\} \)
D . \( \{2 d[B] / d t\}=-\{d[A] / d t\} \) | 1 | Chemistry |
From a piece of cardbord, in the shape
of a trapezium \( A B C D, \) and \( A B \| C D \)
and \( \angle B C D=90^{\circ}, \) quarter circle is
removed. Given \( A B=B C=3.5 \mathrm{cm} \) and
\( D E=2 c m . \) Calculate the area of the
remaining piece of the cardboard (Take
to be \( \left.\frac{22}{7}\right) \) | 2 | Maths |
Glycinato ligand is:
\( \mathbf{A} \)
B. bidentate ligand
C \( . \) two donar sites \( N \) and \( O^{-} \)
D. all of the above | 1 | Chemistry |
A prime number is squared and then added to a different prime number. The number thus obtained is:
I. An even number
II. An odd number
III. A positive number
A. I only
B. II only
c. ॥ only
D. I and III only
E . ।, ॥।, and III | 2 | Maths |
The most active nonmetal has:
A. a high electronegativity
B. a low electronegativity
C. a medium electronegativity
D. large atomic radii
E . a deliquescent property | 1 | Chemistry |
Find DF, if \( \mathrm{CG}=11 \mathrm{cm} \)
A. \( 5.6 \mathrm{cm} \)
B. \( 5.5 \mathrm{cm} \)
\( c \cdot 0.55 \mathrm{cm} \)
D. \( 55 \mathrm{cm} \) | 2 | Maths |
A rod of length \( l \) carrying current \( i \) is
kept in uniform magnetic field of
magnitude \( B \) is shown in figure. Then
the force on rod due to magnetic field is:
A. zero
B. ilBsin\theta
\( \mathbf{c} \cdot i l B \cos \theta \)
D. \( i l B \) | 3 | Physics |
The given distribution shows the
number of runs scored by some top
batsmen of the world in one-day
international cricket matches.
find the mode of the data. | 2 | Maths |
Find the angle marked \( a \)
4.77
8. 36
\( c \cdot 41^{\circ} \)
\( \mathbf{D} \cdot 13^{\circ} \) | 2 | Maths |
For a reaction, \( \boldsymbol{A}(s)+\mathbf{2} \boldsymbol{B}^{+} \leftrightharpoons \boldsymbol{A}^{2+}+ \)
\( 2 B, K_{c} \) has been found to be \( 10^{12} \). The
\( \boldsymbol{E}_{c e l l}^{o} \) is:
A . \( 0.354 V \)
в. \( 0.708 V \)
c. \( 0.0098 V \)
D. \( 1.36 V \) | 1 | Chemistry |
If \( 2 x=t+\sqrt{t^{2}+4} \) and \( 3 y=t- \)
\( \sqrt{t^{2}+4} \) then the value of \( y \) when \( x=\frac{2}{3} \)
is
A . -2
B. 1
\( c \cdot-1 \)
D. | 2 | Maths |
The equilibrium constant for the
reaction: \( N_{2(g)}+3 H_{2(g)} \rightleftharpoons 2 N H_{3(g)} \) at
\( \mathbf{7} 15 K, \) is \( 6.0 \times 10^{-2} . \) If, in a particular
reaction, there are 0.25 mol \( L^{-1} \) of \( H_{2} \)
and \( 0.06 m o l L^{-1} \) of \( N H_{3} \) present
calculate the concentration of \( N_{2} \) at
equilibrium. | 1 | Chemistry |
Assertion
If \( \boldsymbol{x}^{2}-\boldsymbol{p} \boldsymbol{x}+\boldsymbol{q}=\mathbf{0} \) where \( \boldsymbol{p} \) is twice the
tangent of the arithmetic mean of
\( \sin ^{-1} x \) and \( \cos ^{-1} x ; \) q is the geometric
mean of \( \tan ^{-1} x \) and \( \cot ^{-1} x \) then \( x=1 \)
Reason
\( \tan \left(\sin ^{-1} x+\cos ^{-1} x\right)=1 \)
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 | 2 | Maths |
What is the substrate for lipase enzyme?
A. Protein
B. Lipid
c. carbohydrate
D. Nucleic acid | 0 | Biology |
The number of ciritical points of \( \mathbf{f}(\mathbf{x})= \) \( \frac{|\boldsymbol{x}-\mathbf{1}|}{\boldsymbol{x}^{2}} \) is
A . 1
B . 2
\( c \cdot 3 \)
D. | 2 | Maths |
Find the product(s) when methane,
\( C H_{4}, \) burns in excess of oxygen?
A \( \cdot C H_{4} O_{2} \)
в. \( C O+H_{2} O \)
c. \( C O+C H_{2} O H \)
D. \( C O_{2}+H_{2} O \)
E \( \cdot C O_{2}+2 H_{2} \) | 1 | Chemistry |
0.01 mol of \( A g N O_{3} \) is added to 1 L of a
solution which is \( 0.1 M N a_{2} C r O_{4} \) and
\( 0.005 M \) in \( N a I O_{3} . \) Calculate
\( \left[\boldsymbol{A} \boldsymbol{g}^{\oplus}\right],\left[\boldsymbol{I} \boldsymbol{O}_{3}^{\ominus}\right] \) and \( \left[\boldsymbol{C r} \boldsymbol{O}_{4}^{2-}\right] \)
\( K_{s p} A g_{2} C r O_{4} \) and \( A g I O_{3} \) are \( 10^{-8} \) and \( 10^{-13} \) respectively
\( \mathbf{A} \cdot\left[A g^{\oplus}\right]=0.316 \times 10^{-4} M,\left[I O_{3}^{\ominus}\right]=0.31 \times \)
\( 10^{-10} M,\left[C r O_{2}^{2-}\right]=0.0975 M \)
B \( \cdot\left[A g^{\oplus}\right]=3.16 \times 10^{-4} M,\left[I O_{3}^{\ominus}\right]=3.1 \times \)
\( 10^{-10} M,\left[C r O_{2}^{2-}\right]=0.975 M \)
C \( \cdot\left[A g^{\oplus}\right]=31.6 \times 10^{-4} M,\left[I O_{3}^{\odot}\right]=31 \times \)
\( 10^{-10} M,\left[C r O_{2}^{2-}\right]=9.75 M \)
D. None of these | 1 | Chemistry |
Which part of the atmosphere is called
homosphere?
A. Atmosphere up to \( 70 \mathrm{km} \) from the surface of the earth
B. Atmosphere up to \( 80 \mathrm{km} \) from the surface of the earth
C. Atmosphere up to \( 90 \mathrm{km} \) from the surface of the earth
D. Atmosphere up to \( 110 \mathrm{km} \) from the surface of the earth | 0 | Biology |
The condition that the roots of the
equation \( l x^{2}+m x+n=0 \) may be in
the ratio 3: 4 is
A \( \cdot 14 n^{2}=49 m l \)
B . \( m^{2}=9 n l \)
\( \mathbf{c} \cdot 12 m^{2}=49 n l \)
\( \mathbf{D} \cdot 4 l^{2}=49 m l \) | 2 | Maths |
Write the equation of reaction of chlrobenzene :
Halogenation | 1 | Chemistry |
Which of the following reactions is not
correctly matched?
A \( \cdot 2 C_{2} H_{5} B r+2 N a \stackrel{\text {dry ether}}{\longrightarrow} C_{4} H_{1} 0+2 N a B r \)
Wurtz reaction
B . \( C H_{3} B r+A g F \stackrel{C}{\longrightarrow} H_{3} F+A g B r \)
Etards reaction
\( \mathbf{c} \cdot C_{5} H_{6} B r+2 N a+B r C_{2} H_{5} \stackrel{\text {dry ether}}{\longrightarrow} C_{6} H_{5} C_{2} H_{5}+ \)
\( N a B r \)
Wurtz fitting reaction
D \( \cdot 2 C_{6} H_{5} B r+2 N a \stackrel{\text {dryether}}{\longrightarrow} C_{6} H_{5} C_{6} H_{5}+2 N a B r \)
Fitting reaction | 1 | Chemistry |
When the light rays converge at a point in front of the retina and then divert to
form a blurred image on it, the defect is
known as
A. Myopia
B. Hypermetropia
c. Astigmatism
D. Presbiopia | 3 | Physics |
The ratio of the diameters of wires of
circular and straight parts is
\( ^{A} \cdot \frac{1}{\sqrt{2}} \)
B. \( \frac{2 \sqrt{3}}{\pi} \)
\( c \cdot \frac{3 \sqrt{3}}{2 \pi} \)
\( D \cdot \sqrt{2} \) | 3 | Physics |
A tunnel is dug along a chord of the
\( \boldsymbol{R} \)
earth at a perpendicular distance
from the earth's centre. Assume wall of
the tunnel is frictionless. Find the force
exerted by the wall on mass m at a
distance \( x \) from the centre of the tunnel
\( \mathbf{A} \)
B. \( \frac{m g x}{\sqrt{R^{2} / a+x^{2}}} \)
\( c \cdot \frac{m g}{3} \)
D. \( \frac{m g x}{R} \) | 3 | Physics |
The substance that will be flattened on
beating with a hammer is :
A. crystal of iodine
B. lump of sulphur
c. piece of coal
D. zinc granule | 1 | Chemistry |
\( 45 g \) of water at \( 50^{\circ} C \) in a beaker is cooled when \( 50 g \) of copper at \( 18^{\circ} C \) is added to it. The contents are stirred till
final constant temperature is reached. Calculate the final temperature. The specific heat capacity of copper is \( 0.39 J g^{-1} K^{-1} \) and that of water is
\( 4.2 J g^{-1} K^{-1} . \) State the assumption used. | 3 | Physics |
In Nepenthes, the pitcher is modified
A. Whole leaf
B. Leaf apex
c. Lamina
D. Petiole
E. Leaf base | 0 | Biology |
Bohr's atomic model couldn't explain
A. the fine spectrum of hydrogen
B. the spectra of single electron species
c. the stability of atom
D. Both \( A \) and \( C \) | 1 | Chemistry |
The magnetic flux linked with a coil
satisfies the relation \( \phi=4 t^{2}+6 t+9 \)
Wh, where t is the time in second. The emf induced in the coil at \( t=2 s \) is
A 22 V V \( V \) ) 22
в. \( 18 V \)
\( \mathrm{c} .16 \mathrm{V} \)
D. \( 40 V \) | 3 | Physics |
Let \( f \) and \( g \) be real-valued functions
such that
\( \boldsymbol{f}(\boldsymbol{x}+\boldsymbol{y})+\boldsymbol{f}(\boldsymbol{x}-\boldsymbol{y})=2 \boldsymbol{f}(\boldsymbol{x}) \)
\( \boldsymbol{g}(\boldsymbol{y}) \forall \boldsymbol{x}, \boldsymbol{y} \boldsymbol{\epsilon} \boldsymbol{R} \)
if \( f \) is not identically zero and \( f|(x)| \leq \)
\( \mathbf{1}, \forall \boldsymbol{x} \epsilon \boldsymbol{R}, \) then \( |\boldsymbol{g}(\boldsymbol{y})| \leq \mathbf{1}, \forall \boldsymbol{y} \boldsymbol{\epsilon} \boldsymbol{R} \)
If true enter 1 else enter 0
A. True
B. False | 2 | Maths |
The temperature of a substance
increases by \( 27^{\circ} \mathrm{C} \). On the Kelvin scale
this increase is equal to
\( \mathbf{A} \cdot 300 K \)
в. \( 2.46 K \)
c. \( 27 K \)
D. \( 7 K \) | 3 | Physics |
The volume of an air bubble is doubled
as it rises from the bottom of a lake to
its surface. The atmospheric pressure is \( 75 \mathrm{cm} \) of mercury and the ratio of the density of mercury to that of lake water is \( 40 / 3, \) the depth of the lake is | 3 | Physics |
The volume of the \( y= \) tethradron formed by the coterminous edges \( \bar{a}, \bar{b}, \bar{c} \) is 3 Then the volume of the parallelepiped
formed by the coterminous edges \( \overline{\boldsymbol{a}}+ \) \( \bar{b}, \bar{b}+\bar{c}, \bar{c}+\bar{a} \) is
\( \mathbf{A} \cdot \mathbf{6} \)
B. 18
\( c .36 \)
D. | 3 | Physics |
What will be the ratio of \( C l^{35} \) and \( C l^{37} \)
respectively in chlorine if the average atomic mass of chlorine is \( 35.5 ? \)
A . 1:
B. 2:1
c. 3: 1
D. 3:2 | 1 | Chemistry |
During the meiotic division, the
A. Homologous chromosomes are separated
B. Linkage is disturbed
C. Homologous chromosomes do not segregate
D. All of the above | 0 | Biology |
The current through the \( 8 \Omega \) resistor is
\( A \cdot 4 A \)
B. 2 A
c. zero
D. 2.5 A | 3 | Physics |
A small object of linear dimension \( x \) lies on the axis of an optical mirror of local length \( f \) at a distance \( a \) from mirror
The linear dimension of image:
\( ^{A} \cdot_{x}\left(\frac{f}{f-a}\right)^{2} \)
B. \( x\left(\frac{f}{f-a}\right) \)
c. \( x\left(\frac{f}{a-f}\right)^{1 / 2} \)
D. \( x\left(\frac{a-f}{f}\right)^{1 / 2} \) | 3 | Physics |
Find the mode for the following table.
Temperature
in \( ^{o} \boldsymbol{C} \)
\[
\begin{array}{ll}
\text { 3) } 3.4 & \text { 34.6 }
\end{array}
\]
\( \mathbf{2 9} \)
Number of
days 7 6 | 2 | Maths |
To get an output \( Y=1 \) in given circuit
which of the following input will be
correct.
\( \mathbf{A} \cdot A=1 ; B=0 ; C=1 \)
В. \( A=1 ; B=1 ; C=0 \)
c. \( A=0 ; B=1 ; C=0 \)
D. \( A=1 ; B=0 ; C=0 \) | 3 | Physics |
Make an outline of the classification.
What are the advantages and disadvantage of this classification? | 0 | Biology |
A ball strikes a smooth horizontal
ground at an angle of \( 45^{\circ} \) with the vertical. What cannot be the possible angle of its velocity with vertical after the collision? (Assume \( e \leq 1 \) )
A . \( 45^{\circ} \)
B. \( 30^{\circ} \)
\( c \cdot 53^{\circ} \)
D. \( 60^{\circ} \) | 3 | Physics |
The area of \( \square O A P B \) is:
A \( .24 \mathrm{cm}^{2} \)
B. \( 36 \mathrm{cm}^{2} \)
c. \( 48 \mathrm{cm}^{2} \)
D. \( 60 \mathrm{cm}^{2} \) | 2 | Maths |
(i) Why does a current carrying, freely suspended solenoid rest along a particular direction?
(ii) State the direction in which it rests. | 3 | Physics |
If a conductor has \( 10^{8} \) number of
electrons, then the total charge of the conductor is:
A. \( +1.6 \times 10^{-19} \mathrm{C} \)
В. \( -1.6 \times 10^{-19} \mathrm{c} \)
c. \( +1.6 \times 10^{-11} \mathrm{c} \)
D. \( -1.6 \times 10^{-11} \mathrm{C} \) | 3 | Physics |
Which was not proposed by Darwin?
A. Struggle for existence
B. Natural selection
C . Genetic drift
D. Survival of the fittest | 0 | Biology |
The ground state energy of hydrogen atom is \( -13.6 e V . \) What is the potential
energy of the electron in this state?
A \( .0 \mathrm{eV} \)
B . -27.2 eV
\( \mathrm{c} \cdot 1 \mathrm{eV} \)
D. 2 eV | 1 | Chemistry |
Find the cube root of
\( 99-70 \sqrt{2} \) | 2 | Maths |
\( N a C l \) is less soluble in \( D_{2} O \) than \( H_{2} O \)
why? | 1 | Chemistry |
A satellite is launched into a circular
orbit of radius r around the earth. \( \mathbf{A} \)
second satellite is launched into an
orbit of radius \( 1.01 \mathrm{r} \). The period of the second satellite is larger than that of
first one by approximately.
\( A \cdot 0.5 \% \)
B . 1.0 \%
c. \( 1.5 \% \)
D. 3.0 \% | 3 | Physics |
What is the value of \( \int_{0}^{a} \frac{x-a}{x+a} d x ? \)
A. \( a+2 a \log 2 \)
в. \( a-2 a \log 2 \)
c. \( 2 a \log 2-a \)
D. \( 2 a \log 2 \) | 2 | Maths |
A \( 2 M e V \) neutron is emitted in a fission
reactor. If it looses half of its kinetic
energy in each collision with a
moderator atom, how many collisions must it undergo to achieve thermal energy of \( 0.039 e V ? \)
A . 20
B. 26
c. 30
D. 42
E . 48 | 3 | Physics |
If the standard deviation of the numbers
\( 2,3, a \) and 11 is \( 3.5, \) then which of the
following is true?
A \( \cdot 3 a^{2}-32 a+84=0 \)
B . \( 3 a^{2}-34 a+91=0 \)
c. \( 3 a^{2}-23 a+44=0 \)
D. \( 3 a^{2}-26 a+55=0 \) | 2 | Maths |
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