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Ancestor of man, who first time showed
bipedal movement is
A. Cro-Magnon
B. Australopithecus
c. Java ape man
D. Peking man
| 0 |
Biology
|
Find the area of the shaded region
\( (\boldsymbol{\pi}=\mathbf{3 . 1 4}, \sqrt{\mathbf{3}}=\mathbf{1 . 7 3}) \)
| 2 |
Maths
|
toppr
Q Type your question_
given data?
Times \( 0 \quad 10 \)
20
30
\( (s) \)
stanc \( \begin{array}{llll}\text { 0 } & \text { 40 } & \text { 80 } & \text { 120 }\end{array} \) \( (m) \) ne 0
\( A \)
B.
\( c \)
\( D \)
| 3 |
Physics
|
Find the amount of water displaced by a solid spherical ball of diameter
\( 0.21 \mathrm{cm} \)
| 2 |
Maths
|
The time taken (in hours) by a car to
travel \( 900 k m \) if it travels \( 600 k m \) in
\( 12 h r s \)
\( A \cdot 18 \)
B. 16
\( c \cdot 15 \)
D. None of these
| 2 |
Maths
|
If \( X \) is a point on the line \( A B . Y \) and \( Z \)
are points outside such that \( \angle A X Y= \)
\( 45^{\circ} \) and \( \angle Y X Z=150^{\circ}, \) then \( \angle A X Z \) is
equal to:
A \( \cdot 120^{\circ} \)
B. \( 135^{\circ} \)
\( c \cdot 150^{\circ} \)
D. \( 165^{\circ} \)
| 2 |
Maths
|
ldentify the correct order of various stages in the manufacture of usable form of iron:
\( \mathbf{A} \)
B.
\( \mathbf{c} \)
D. Iron ore \( \rightarrow \) Cast iron \( \rightarrow \) Pig iron
| 1 |
Chemistry
|
a Q Type your question 3
\( A \)
C- \( 4, B-1, A-2 \) \( \mathrm{H}-7, \mathrm{G}-8, \mathrm{F}-6, \mathrm{E}-5, \mathrm{D}-3 \)
B. \( \mathrm{H}-6, \mathrm{G}-8, \mathrm{F}-7, \mathrm{E}-5, \mathrm{D}-3, \mathrm{C}-4, \mathrm{B}-1, \mathrm{A}-2 \)
\( c \)
\( \mathrm{H}-6 \) , \( \mathrm{G}-8, \mathrm{F}-7, \mathrm{E}-4, \mathrm{D}-3, \mathrm{C}-2, \mathrm{B}-1, \mathrm{A}-5 \)
D. \( \mathrm{G}-8, \mathrm{F}-7, \mathrm{E}-4, \mathrm{D}-2, \mathrm{C}-2, \mathrm{B}-1, \mathrm{A}-5 \) \( \mathrm{H}-6 \)
| 0 |
Biology
|
A uniform metallic wire has a
resistance of \( 18 \Omega \) and is bent into an equilateral triangle. Then, the resistance between any two vertices of the triangle is
\( A \cdot 8 \Omega \)
B. \( 12 \Omega \)
c. \( 4 \Omega \)
D. 2\Omega
| 3 |
Physics
|
The wavefront is a surface in which
A. all points are in the same phase
B. there is a pair of points in opposite phase
C \cdot there is a pair of points with phase difference \( \left(\frac{\pi}{2}\right) \)
D. there is no relation between the phases
| 3 |
Physics
|
List three main differences between
DNA and RNA?
| 0 |
Biology
|
A function \( f \) is defined as follows:
\( \boldsymbol{f}(\boldsymbol{x})= \)
\( \left\{\begin{array}{ll}1 & \text { for }-\infty< \\ 1+\sin x & \text { for } 0 \leq x<\frac{\pi}{2} \\ 2+\left(x-\frac{\pi}{2}\right)^{2} & \text { for } \frac{\pi}{2} \leq x<+\infty\end{array}\right. \)
Discuss the continunity and
differentiability at \( \boldsymbol{x}=\mathbf{0} \& \boldsymbol{x}=\boldsymbol{\pi} / \mathbf{2} \)
This question has multiple correct options
A. continuous but not differentiable at \( x=0 \)
B. differentiable and continuous at \( x=\pi / 2 \)
c. neither continuous but nor differentiable at \( x=0 \)
D. continuous but not differentiable at \( x=\pi / 2 \)
| 2 |
Maths
|
A thin circular ring first slip down a
smooth incline then rolls down a rough
incline of identical geometry from the same height. The ratio of time taken in the two motion is :
A \( \cdot \frac{1}{2} \)
B.
c. \( \frac{1}{\sqrt{2}} \)
D.
| 3 |
Physics
|
form oxocations.
A. Lanthanides
B. Actinides
c. Noble gas
D. Alkali metalss
| 1 |
Chemistry
|
The given diagram represents a dividing cell stained with giemsa. From the options given below, identify the correct stage of cell division.
A. Leptotene
B. Zygotene
c. Pachytene
D. Diakinesis
| 0 |
Biology
|
When a transverse wave on a string is reflected from the free end, the phase change produced is
A. Zero rad
в. \( \frac{\pi}{2} \) rad
c. \( \frac{3 \pi}{4} \) rao
D. \( \pi \) rad
| 3 |
Physics
|
\( A B \| C D \) and \( A C M \) is a straight line
\( \angle B A C \) is equal to:
A \( \cdot 106^{\circ} \)
B. \( 108^{\circ} \)
\( \mathrm{c} \cdot 110^{\circ} \)
D. \( 109^{\circ} \)
| 2 |
Maths
|
Motion of wheel of a bicycle is (projectile, circular)
motion.
| 3 |
Physics
|
Tranquilizers are used to:
A. reduce tension
B. reduce blood pressure
C . reduce body pain
D. reduce cholesterol
| 1 |
Chemistry
|
What is the nature of carbon atom
marked with asterisk \( (*) \) sign in the
given compounds?
\[
\mathrm{CH}_{3}-\mathrm{CH}_{2}-\dot{\mathrm{C}} \mathrm{H}_{2}-\mathrm{CH}_{3}
\]
| 1 |
Chemistry
|
Which one of the following is correctly matched?
A. Emulsion-curd
B. Foam-mist
c. Aerosol-smoke
D. Solid sol-cake
| 1 |
Chemistry
|
What is preservative? Give the name
and formula of any two preservatives.
| 1 |
Chemistry
|
Given are the isomers \( C_{8} H_{8} O_{2} \)
Which isomer reacts with \( N a H C O_{3} ? \)
\( A \)
B.
\( c \)
\( D \)
| 1 |
Chemistry
|
Write the complete nuclear reactions:
(a) \( _{4}^{9} B e+_{2}^{4} H e \longrightarrow_{6}^{12} C+ \)
\( (b)_{1}^{3} H \longrightarrow_{2}^{3} H e+_{-} \)
\( (c) \frac{14}{7} N+_{2}^{4} H e \longrightarrow_{8}^{17} O+ \)
(d) \( _{92}^{235} U+_{0}^{1} n \longrightarrow_{38}^{92} S r+X e+3_{0}^{1} n \)
\( (\mathrm{e})_{3}^{7} L i+_{0}^{1} n \longrightarrow 2_{2}^{4} H e+ \)
\( (f)_{92}^{238} U+_{-\perp-}----\longrightarrow_{92}^{239} U \longrightarrow_{93}^{239} \)
\( N p+ \)
\( (g)_{7}^{14} N+_{0}^{1} n \longrightarrow_{-}-\ldots---+_{1}^{3} H \)
(h) \( _{3}^{7} L i+_{-} \) \( \longrightarrow_{4}^{8} B e+\gamma \)
radiations
(i) \( _{1}^{2} \boldsymbol{H}+_{\text {一一一一一一一 }}_{2}^{4} \boldsymbol{H} e+_{0}^{1} \boldsymbol{n} \)
\( (j)_{13}^{27} A l+_{0}^{1} n \longrightarrow_{11}^{24} N a+ \)
\( (\mathrm{k})_{13}^{27} A l+_{2}^{4} H e \longrightarrow_{-}------+_{1}^{1} H \)
(I) \( \frac{235}{92} \boldsymbol{U}+_{0}^{1} \boldsymbol{n} \longrightarrow \)
\( +_{52}^{137} \boldsymbol{T} \boldsymbol{e}+_{40}^{97} \boldsymbol{Z} \boldsymbol{r} \)
\( (\mathrm{m})_{34}^{86} \mathrm{Se} \longrightarrow_{-1}-\mathrm{-}_{-1} \mathrm{e} \)
| 3 |
Physics
|
Depending on the magnetic property
the materials are classified in to
diamagnetic, paramagnetic and ferro magnetic. The behaviour of magnetic field lines near a magnetic substance is shown in the figure. Which material corresponds to the figure.
| 3 |
Physics
|
Intercellular communication in
multicellular organisms occur through
A. Digestive system only
B. Nervous system only
c. Both nervous and endocrine system
D. Respiratory system only
| 0 |
Biology
|
An iron ball at \( 50^{\circ} C \) is dropped in a
beaker of water at \( 50^{\circ} C . \) The heat will
A. Not flow from iron ball to water
B. Not not flow from iron ball to water or from water to iron ball
c. Not flow from water to iron ball
D. Increase the temperature of both
| 1 |
Chemistry
|
What are chelates? Giving one example and write the importance of chelate?
| 1 |
Chemistry
|
Select the correct order of density.
This question has multiple correct options
\( A \cdot N a>K \)
B. Na<K
c. \( \mathrm{Mg}>\mathrm{ca} \)
D. Mg<ca
| 1 |
Chemistry
|
The single electrode potential of metal \( E \)
of \( 0.1 \mathrm{M} \) solution of \( \mathrm{M}^{+} / \)Mions\( \left[E^{0}=\right. \)
\( -2.36 V] \) is nearly:
A . \( +2.41 V \)
в. \( -2.41 V \)
c. \( 4.82 V \)
D. \( +4.82 V \)
| 1 |
Chemistry
|
From the following equations, pick out the possible nuclear reactions.
This question has multiple correct options
\( \begin{array}{lllllll}\mathbf{C} \cdot_{7} N^{14} & + & _{1} H^{1} & \rightarrow & 8 & O^{15} & + & 7.3 & M e V\end{array} \)
D・ \( _{92} U^{235}+_{0} n^{1} \rightarrow_{54} X^{140}+_{38} S i^{94}+ \)
\( 20 n^{1}+\gamma+200 \mathrm{MeV} \)
| 3 |
Physics
|
In the experiment of verification of Ohms law the error in the current measurement
is \( 1 \% \), while that in the voltage
measurement is \( 2 \% \). The error in the
resistance has a maximum value of
A . 1\%
B. 2\%
c. 3\%
D. none of these
| 3 |
Physics
|
Use Kirchhoff's rule to obtain conditions
for the balance condition in a
Wheatstone bridge.
| 3 |
Physics
|
Synthetic testosterone promotes
A. menstrual cycle
B. muscle growth
c. respiration
D. birth control agents
| 1 |
Chemistry
|
A train of mass \( M \) is moving on a
circular track of radius \( R \) with a
constant speed \( v \). The length of the train is half of the perimeter of the track. The linear momentum of the train will be
A . zero
в. \( \frac{2 M v}{\pi} \)
c. \( M v R \)
D. \( M v \)
| 3 |
Physics
|
The frequency of a particle executing SHM is 10 Hz. The particle is suspended from a vertical spring. At the highest point of its oscillation, the spring is unstretched. Maximum speed of the
particle is \( (\boldsymbol{g}=\mathbf{1 0 m} / \boldsymbol{s} \mathbf{2}) \)
\( ^{\text {A }} \cdot \frac{1}{2 \pi} m s \)
в. \( \frac{7}{2 \pi} m s \)
c. \( \frac{5}{2 \pi} m s \)
D. \( \frac{1}{3 \pi} m s \)
| 3 |
Physics
|
A car can finish a certain journey in 10 hours at the speed of \( 48 \mathrm{km} / \mathrm{hr} \). By how much should its speed be increased so that it may take only 8 hours to cover
the same distance ? (in km/hr)
| 2 |
Maths
|
Assertion
Competitive inhibitors compete with the natural substrate for their
attachment on the active sites of
enzymes.
Reason
In competitive inhibition, inhibitor binds to allosteric site of the enzyme.
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 particle \( X \) in the following nuclear
reaction is \( \frac{13}{7} \mathrm{N} \longrightarrow_{6}^{13} \mathrm{C}+_{1}^{0} \mathrm{e}+X \)
A. \( P \)
B.
\( \mathbf{c} \cdot e^{-} \)
\( D \)
| 3 |
Physics
|
The general solution of differentia
equation is \( (y+c)^{2}=c x \) where \( c \) is an
arbitrary constant. The order and degree of the differential equation are respectively:
A .1,2
в. 2,2
c. 1,1
D. 2,1
| 2 |
Maths
|
In the air brake, air pressure is supplied
by
A. Engine manifold
B. A compressor
c. The diaphragm valve
D. pump
| 3 |
Physics
|
One kilogramme force is the force due to gravity on a mass of
A . \( 1 g \)
B. \( 10 g \)
\( c .100 g \)
D. \( 1000 g \)
| 3 |
Physics
|
Correct form of gravitational law is:
A \( \cdot \vec{F}=-\frac{G m_{1} m_{2}}{r^{2}} \)
В \( \cdot \vec{F}=-\frac{G m_{2} m_{1}}{r^{2}} \)
c. \( \vec{F}=-\frac{G m_{1} m_{2}}{r^{2}} \hat{r} \)
D・ \( \vec{F}=-\frac{G m_{1} m_{2}}{r^{3}} \vec{r} \)
| 3 |
Physics
|
Anaerobic respiration is
A. Complete oxidation
B. Incomplete oxidation
c. Anabolic reaction
D. Fermentation
| 0 |
Biology
|
Which molecule is a meso compound?
\( \mathbf{A} \cdot V I \) and \( I I \)
B. \( I V \) and \( V \)
c. \( I, I I \) and \( I I I \)
D. none of these
| 1 |
Chemistry
|
A weightless ladder 20 ft long assets
against a frictionless wall at an angle
\( 60^{\circ} \) from the horizontal. A 150 pound
man is 4 ft from the top of the ladder. A horizontal force is needed to keep it from slipping. Choose the correct magnitude from the following.
A . \( 175 ~ l b \)
B. \( 100 l b \)
c. \( 120 l b \)
D. 17.3 lb
| 3 |
Physics
|
For \( \boldsymbol{C u}(\boldsymbol{s})+\boldsymbol{N O}_{3}^{-}(\boldsymbol{a} \boldsymbol{q})+\boldsymbol{H}^{+}(\boldsymbol{a} \boldsymbol{q}) \rightarrow \)
\( \boldsymbol{C u}^{2+}(\boldsymbol{a q})+\boldsymbol{N O}_{2}(\boldsymbol{g})+\boldsymbol{H}_{2} \boldsymbol{O}(l), \) which
of the following takes place?
A. \( C u(s) \) is oxidized
B . \( H^{+}(a q) \) is oxidized
c. \( C u(s) \) is reduced
D. \( H^{+}(a q) \) is reduced
E . \( N O_{3}^{-} \) is oxidized
| 1 |
Chemistry
|
A bird is flying due east with a velocity of \( 4 m s^{-1} . \) The wind starts to blow with a
velocity of \( 3 m s^{-1} \) due north. What is the
magnitude of relative velocity of bird
w.r.t. wind? Find out.its direction also.
| 3 |
Physics
|
A circular garden has an area of \( 314 m^{2} \)
A sprinkle at the centre of garden can
cover an area that has a radius of \( 12 \mathrm{m} \)
Will the sprinkle water the entire
garden?
| 2 |
Maths
|
\( \frac{-}{\infty} \)
of
\( \frac{\delta}{2} \)
| 1 |
Chemistry
|
The IUPAC name for the coordination
compound \( \mathbf{B a}\left[\mathbf{B r} \mathbf{F}_{4}\right] \) is
A. Barium tetrafluorobromate (v)
B. Barium tetrafluorobromate (III)
c. Barium bis (tetrafluorobromate) (III)
D. Nne of these
| 1 |
Chemistry
|
Activation energy \( \left(\boldsymbol{E}_{\boldsymbol{a}}\right) \) and rate
constants \( \left(k_{1} \text { and } k_{2}\right) \) of a chemical reaction at two different temperature
\( T_{1} \) and \( T_{2} \) ) are related by:
\( ^{\mathbf{A}} \cdot \ln \frac{k_{2}}{k_{1}}=-\frac{E_{a}}{R}\left[\frac{1}{T_{1}}-\frac{1}{T_{2}}\right] \)
в. \( \ln \frac{k_{2}}{k_{1}}=-\frac{E_{a}}{R}\left[\frac{1}{T_{2}}-\frac{1}{T_{1}}\right] \)
\( ^{\mathrm{c}} \cdot \ln \frac{k_{2}}{k_{1}}=-\frac{E_{a}}{R}\left[\frac{1}{T_{2}}+\frac{1}{T_{1}}\right] \)
D \( \cdot \ln \frac{k_{2}}{k_{1}}=\frac{E_{a}}{R}\left[\frac{1}{T_{1}}-\frac{1}{T_{2}}\right] \)
| 1 |
Chemistry
|
If \( A=\left[\begin{array}{ll}1 & 2 \\ 3 & 4\end{array}\right], B\left[\begin{array}{ll}3 & 8 \\ 7 & 2\end{array}\right] \) and \( 2 x+ \)
\( A=B \) then find \( x \)
| 2 |
Maths
|
A body of mass \( M \) is attached to one
end of a rod of mass \( M \) and length \( L \)
The entire system is rotated about an axis passing through the other end of
the rod. The \( M . I . \) of the system about die given axis of rotation is:
\( ^{\mathrm{A}} \cdot \frac{M L^{2}}{3} \)
B. \( \frac{4}{3} M L^{2} \)
\( \mathbf{c} \cdot 2 M L^{2} \)
D. \( 3 M L^{2} \)
| 3 |
Physics
|
Select the correct option:
Vascular cambium and cork cambium
are the examples of
A. Apical meristem
B. Lateral meristem
c. Intercalary meristem
D. Promeristem
| 0 |
Biology
|
What is the probability that a two digit number selected at random will be a
multiple of 3 and not a multiple of \( 5 ? \)
A \( \cdot \frac{1}{15} \)
в. \( \frac{3}{15} \)
c. \( \frac{4}{15} \)
D. \( \frac{5}{15} \)
| 2 |
Maths
|
A solenoid has a core of a substance
with relative permeability \( 600 . \) What is the magnetic permeability of the given substance?
A \( \cdot 20 \pi \times 10^{-5} N A^{-2} \)
B. \( 21 \pi \times 10^{-5} N A^{-2} \)
c. \( 22 \pi \times 10^{-5} N A^{-2} \)
D. \( 24 \pi \times 10^{-5} N A^{-2} \)
| 3 |
Physics
|
Alary muscles in cockroach are associated or connected with
A. Trachea
B. Heart
c. Legs
D. Alimentary canal
| 0 |
Biology
|
A large positive value of \( \Delta G \) corresponds to which of these?
A. Small positive \( K \)
B. Small negative \( K \)
c. Large positive \( K \)
D. Large negative \( K \)
| 1 |
Chemistry
|
Which of the following is not a characteristic feature during mitosis in somatic cells?
A. Spindle fibres
B. Disappearance of nucleolus
c. chromosome movement
D. Synapsis
| 0 |
Biology
|
What is biasing a diode? Write two differences between the two kinds of
biasing.
| 3 |
Physics
|
A car travelling at \( 60 k m / h \) overtakes another car travelling at \( 42 k m / h \) Assuming each car to be \( 5.0 m \) long, the time taken for the over taking is
\( \mathbf{A} \cdot 6 s \)
B . \( 4 s \)
c. \( 3 s \)
D. \( 2 s \)
| 3 |
Physics
|
Let [.] denote the greatest integer
function and \( f(x)=\left[\tan ^{2} x\right] . \) Then
\( \mathbf{A} \cdot \lim _{x \rightarrow 0} f(x) \) does not exis
B. \( f(x) \) is continuous at \( x=0 \)
c. \( f(x) \) is not differentiable at \( x=0 \)
| 2 |
Maths
|
Write the formula to find the magnitude of the gravitational force between the
earth and an object on the surface of the earth.
| 3 |
Physics
|
Using the property of determinants and with out expanding prove that \( \left|\begin{array}{lll}\boldsymbol{a}-\boldsymbol{b} & \boldsymbol{b}-\boldsymbol{c} & \boldsymbol{c}-\boldsymbol{a} \\ \boldsymbol{b}-\boldsymbol{c} & \boldsymbol{c}-\boldsymbol{a} & \boldsymbol{a}-\boldsymbol{b} \\ \boldsymbol{c}-\boldsymbol{a} & \boldsymbol{a}-\boldsymbol{b} & \boldsymbol{b}-\boldsymbol{c}\end{array}\right|=\mathbf{0} \)
| 2 |
Maths
|
A uniformly wound solenoidal coil of
self-inductance \( 1.8 \times 10^{-4} \mathrm{H} \) and
resistance \( 6 \Omega \) is cut into two identical
coils. They are now connected in parallel across a 12 volt battery of negligible resistance. Find the current drawn by the circuit in amp.
| 3 |
Physics
|
Evaluate the following limits. \( \lim _{x \rightarrow 0} \frac{(a+x)^{2}-a^{2}}{x} \)
| 2 |
Maths
|
Which are two rational number between \( \frac{6}{5} \) and \( \frac{7}{5} \)
| 2 |
Maths
|
Angiosperms have dominated the land flora primarily because of their
A. Domestication by man
B. Power of adaptability in diverse habitat
c. Property of producing large number of seeds
D. Nature of self pollination
| 0 |
Biology
|
Assertion
Standard hydrogen electrode is a half cell having \( 1 M H^{+} \) concentration
bubbled with hydrogen at any pressure
Reason
A hydrogen electrode will always show \( \boldsymbol{E}_{c e l l}=\mathbf{0 . 0 0} \boldsymbol{V} \)
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
|
Find the remainder for given division \( \left(p^{2}+7 p-8\right) \div(p-1) \)
| 2 |
Maths
|
Q Type your question
molecules unite with \( \boldsymbol{H}_{2} \boldsymbol{O} \) to form
\( N H_{4} O H \) molecules. \( N H_{4} O H \) again
dissociates into \( N H_{4}^{+} \) and \( O H^{-} \) ions.
In solution therefore, we have \( \boldsymbol{N} \boldsymbol{H}_{3} \)
molecules, \( N H_{4} O H \) molecules and \( N H_{4}^{+} \) ions and the following equilibrium exist:
\( N H_{3}(g) \) (pressure \( P \) and concentration
\( c \) ) Initially \( \rightleftharpoons N H_{3}(l)+H_{2} O \rightleftharpoons \)
\( N H_{4} O H \rightleftharpoons N H_{4}^{+}+O H^{-} \)
Let \( c_{1} \) mol \( / L \) of \( N H_{3} \) pass in liquid state which on dissolution in water
froms \( c_{2} \) mol \( / L \) of \( N H_{4} O H . \) The
solution contains \( c_{3} \) mol \( / L \) of \( N H_{4}^{+} \) ions. The dissociation constant of
\( N H_{4} O H \) can be given as:
\( ^{\mathrm{A}} \cdot_{K_{b}}=\frac{\left(c_{3}\right)^{2}}{\left(c_{2}-c_{3}\right)} \)
B. \( _{K_{b}}=\frac{\left(c_{3}\right)^{2}}{c_{2}} \)
\( ^{\mathbf{c}} \cdot_{K_{b}}=\frac{c_{3}}{\left(c_{2}-c_{3}\right)} \)
D. \( _{K_{b}}=\frac{c_{3}}{\left(c_{1}-c_{2}\right)} \)
| 1 |
Chemistry
|
An oxyacid of phosphorus has the following properties: The complex
neutralisation of the acid with sodium
hydroxide solution given an aqueous solution of sodium ions and oxy-acid
anions in the ratio 2:1. When a solution
of the acid is warmed with silver nitrate
solution, metallic silver is deposited.
\( p H 0.01 \mathrm{M} \) solution of the sodium salt of
this acid formed (assume \( \boldsymbol{p} \boldsymbol{K}_{\boldsymbol{a}_{1}}=\boldsymbol{2} \boldsymbol{x} \)
is
\( A \cdot 6+2 x \)
B. \( 6-2 x \)
\( c \cdot 6-x \)
D. \( 6+x \)
| 1 |
Chemistry
|
Evaluate:
\( \lim _{x \rightarrow 2} \frac{\sqrt{3-x}-1}{2-x} \)
| 2 |
Maths
|
Integrate the following functions with espect to \( x: \int \frac{d x}{4 x+5} \)
This question has multiple correct options
A \( \cdot \frac{1}{4} \ln (4 x+5)+c \)
B. \( \frac{1}{4} \ln (4 x+5)-c \)
\( ^{\mathbf{c}} \cdot \frac{-1}{4} \ln (4 x+5)-c \)
D. \( 4 \ln (4 x-5)-c \)
| 2 |
Maths
|
Laughing gas is prepared by heating:
A \( . N H_{4} C l \)
B. \( \left(N H_{4}\right)_{2} S O_{4} \)
c. \( N H_{4} C l+N a N O_{3} \)
D. \( N H_{4} N O_{3} \)
| 1 |
Chemistry
|
Calculate equilibrium constant for the equilibrium
\( 2 m n O_{4}^{-}+6 H^{+}+5 H_{2} C_{2} O_{4} \rightleftharpoons \)
\( \mathbf{2} M N^{2+}+\mathbf{8} H_{2} O+\mathbf{1 0} C O_{2} \)
Given that, \( \boldsymbol{E}_{M n O_{4} M n^{2+}}^{0}=\mathbf{1 . 5 1} \quad \boldsymbol{V} \) and
\( \boldsymbol{E}_{\mathrm{CO}_{3} \mathrm{C}_{2} \boldsymbol{O}_{4}^{2-}}^{0}=-\mathbf{0 . 4 9} \boldsymbol{V} \)
| 1 |
Chemistry
|
If \( \vec{b} \) is the vector whose initial point divides the joining \( 5 \hat{i} \) and \( 5 \hat{j} \) in the ratio \( \lambda: 1 \) and terminal point is at origin. If \( |\vec{b}| \leq \sqrt{37}, \) then \( \lambda \in \)
\( ^{\mathbf{A}} \cdot(-\infty,-6] \cup\left[-\frac{1}{6}, \infty\right) \)
B \( \cdot(-\infty,-3) \cup\left[-\frac{1}{4}, \infty\right) \)
\( ^{\mathbf{c}} \cdot(-\infty, 0) \cup\left(\frac{1}{2}, \infty\right) \)
D. \( \left[-6,-\frac{1}{6}\right] \)
| 2 |
Maths
|
The probability of obtaining an even prime number on each die, when a pair of dice is rolled is
\( \mathbf{A} \cdot \mathbf{0} \)
B. \( \frac{1}{3} \)
c. \( \frac{1}{12} \)
D. \( \frac{1}{36} \)
| 2 |
Maths
|
Which statement about molecularity of reaction is not correct?
A. It can be obtained from reaction mechanism
B. It may be either whole number or fractional
C. It depends on elementary step of reaction
D. It is the number of molecules of reactants taking part in a single step reaction
| 1 |
Chemistry
|
Find the magnetic field at P due to the
arrangement shown
A \( \cdot \frac{\mu_{0} i}{\sqrt{2} \pi d}\left(1-\frac{1}{\sqrt{2}}\right) \& \)
B. \( \frac{2 \mu_{0} i}{\sqrt{2} \pi d} \)
c. \( \frac{\mu_{0} i}{\sqrt{2} \pi d} \)
D. \( \frac{\mu_{0} i}{\sqrt{2} \pi d}\left(1+\frac{1}{\sqrt{2}}\right) \)
| 3 |
Physics
|
Solve \( \int_{0}^{\pi / 2} \frac{x \sin x \cos x}{\cos ^{4} x+\sin ^{4} x} d x \)
| 2 |
Maths
|
In an oscillating system, a restoring force is a must. In an \( L-C \) circuit,
restoring force is provide by
A. Capacitor
B. Inductance
c. Resistance
D. Both (A) and (B)
| 3 |
Physics
|
Smoke and fog both are aerosols. In
what way are they different?
| 1 |
Chemistry
|
If the anti-neutrino had a mass of
\( 3 e V / c^{2}(\text { where } c \) is the speed of light) instead of zero mass, what should be
the range of the kinetic energy, K of the electron?
A \( \cdot 0 \leq K \leq 0.8 \times 10^{6} e V \)
B. \( 3.0 e V \leq K \leq 0.8 \times 10^{6} e V \)
c. \( 3.0 e V \leq K<0.8 \times 10^{6} e V \)
D. \( 0 \leq K<0.8 \times 10^{6} e V \)
| 3 |
Physics
|
Two free parallel wires carrying currents
in the opposite directions
A. attract each other
B. repel each other
C. do not affect each other
D. get rotated to be perpendicular to each other
| 3 |
Physics
|
Write down the negations for the
following:
(a) If the diagonals of a parallelogram are perpendicular then it is a rhombus.
(b) Kanchanganga is in India and Everest is in Nepal.
(c) The Sun is a star or the Jupiter is a
planet.
| 2 |
Maths
|
Write structure of pyrophosphoric acid.
| 1 |
Chemistry
|
Match the following:
Column II gives the order of resistivity for materials in column I
| 3 |
Physics
|
resting on a smooth horizontal ground
attached to one end of a spring of force
constant \( k \) in natural length. If another
block of same mass and moving with a
velocity u toward right is placed on the
block which stick to it due to friction.
The time it will take to reach its
extreme position. Also find the
amplitude of oscillations of the combined mass \( 2 \mathrm{m} \)
\( ^{\mathbf{A}} \cdot A=\sqrt{\frac{m}{2 k}}, t=\sqrt{\frac{k}{2 m}} \)
В. \( A=u \sqrt{\frac{m}{2 k}}, t=\frac{\pi}{2} \sqrt{\frac{2 m}{k}} \)
c. \( A=\sqrt{\frac{u m}{2 k}}, t=\pi \sqrt{\frac{2 m}{k}} \)
D. none of these
| 3 |
Physics
|
Let \( \mathbf{f}:(-\mathbf{1}, \mathbf{1}) \rightarrow \mathbf{R} \) be a differentiable
function with \( \mathbf{f}(\mathbf{0})=-\mathbf{1} \) and \( \mathbf{f}^{\prime}(\mathbf{0})=\mathbf{1} \)
Let \( \mathbf{g}(\mathbf{x})=[\mathbf{f}(\mathbf{2 f}(\mathbf{x})+\mathbf{2})]^{2} . \) Then \( \mathbf{g}^{\prime}(\mathbf{0})= \)
A . -4
B.
\( c \cdot-2 \)
D. 4
| 2 |
Maths
|
\( p \)
\( \dot{g} \)
\( \dot{q} \)
\( \dot{q} \)
| 1 |
Chemistry
|
State whether given statement is True or False.
Force never exists in pairs.
A. True
B. False
| 3 |
Physics
|
Two straight lines drawn on the same
displacement time graph make angles
\( 45^{\circ} \) and \( 60^{\circ} \) as shown. The ratio of the
two velocities is
4. \( \sqrt{3}: 1 \)
3.1:
\( c \cdot 1: 2 \)
\( \sqrt{3}: 2 \)
| 3 |
Physics
|
In the arrangement shown, a car of
certain mass 'm' is in equilibrium by
applying a force of 25 N. If the density of liquid taken is \( 0.9 \mathrm{cm}^{-3} \), then find the
mass of the car
| 3 |
Physics
|
The following real numbers have decimal expansions as given below. In each case, decide whether they are
rational or not. If they are rational and of
the form \( p \), you say about the prime
factors of \( q ? \)
(i) 43.123456789 (ii)
\( 0.120120012000120000 \ldots \)
\( 43 . \overline{123456789} \)
| 2 |
Maths
|
Given the following six statements:
(1) All women are good drivers
(2) Some women are good drivers
(3) No men are good drivers
(4) All men are bad drivers
(5) At least one man is a bad driver
(6) All men are good drivers. The statement that negates statement
(6) is:
A . (1)
B. (2)
\( c \cdot(3) \)
\( D \cdot(4) \)
E. (5)
| 2 |
Maths
|
On dividing the polynomial \( 9 x^{4}- \) \( 4 x^{2}+5 \) by another polynomial \( 3 x^{2}+ \)
\( x-1, \) the remainder comes out to be
\( a x-b, \) Find \( ^{\prime} a^{\prime} \) and \( ^{\prime} b^{\prime} \)
| 2 |
Maths
|
In the figure shown, a block A moving with velocity \( 10 \mathrm{m} / \mathrm{s} \) on a horizontal
surface collides with another block \( \mathrm{B} \) at
rest initially. The coefficient of restitution is \( \frac{1}{2} . \) Neglect fricition every
where. The distance between the blocks
5s after the collision takes place is \( 5 \times \)
\( (i n \quad m), \) then \( c \) is :
| 3 |
Physics
|
\( \ln L-C \) oscillations
This question has multiple correct options
A \( \cdot \) time period of oscillations is \( \frac{2 \pi}{\sqrt{L C}} \)
B. maximum current is \( \frac{q_{0}}{\sqrt{L C}} \)
C. maximum rate of change of current in circuit is \( \frac{q_{0}}{L C} \)
D. maximum potential difference across the inductor is
\( \frac{q_{0}}{2 C} . \) Here \( q_{0} \) is maximum charge on capacitor.
| 3 |
Physics
|
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