AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Physics
Calculate the period and frequency for
the second hand, minute hand, and hour
hand of a clock.
A. For second hand, period \( =1 \min =60 \mathrm{s} ; \) frequency \( =0 \)
For minute hand, period \( =1 \mathrm{hr}=3600 \mathrm{s} ; \) frequency \( =2 \)
\( 10^{-4} \mathrm{Hz} \)
For hour hand, period \( =12 \mathrm{hrs}=43200 \mathrm{s} ; \) frequency \( =2 \)
\( 10^{-5} \mathrm{Hz} \)
B. For second hand, period \( =1 \min =360 \) s; frequency \( =0 \)
For minute hand, period \( =1 \mathrm{hr}=600 \mathrm{s} ; \) frequency \( =2.7 \)
\( 10^{-4} \mathrm{Hz} \)
For hour hand, period \( =12 \mathrm{hrs}=3200 \mathrm{s} ; \) frequency \( =2 . \) \( 10^{-5} \mathrm{Hz} \)
C. For second hand, period \( =1 \min =0 \) s; frequency \( =0.0 \)
For minute hand, period \( =1 \mathrm{hr}=36 \mathrm{s} ; \) frequency \( =2.7^{\circ} \)
\( 10^{-4} \mathrm{Hz} \)
For hour hand, period \( =12 \mathrm{hrs}=43200 \mathrm{s} ; \) frequency \( =2 \)
\( 10^{-5} \mathrm{Hz} \)
D. For second hand, period \( =1 \) min \( =3660 \) s; frequency \( = \)
For minute hand, period \( =1 \mathrm{hr}=3600 \mathrm{s} ; \) frequency \( =2 \)
\( 10^{-4} \mathrm{Hz} \)
For hour hand, period \( =12 \mathrm{hrs}=4300 \mathrm{s} ; \) frequency \( =2 \)
\( 10^{-5} \mathrm{Hz} \)
Subject: Chemistry
What is wrong with the Lewis dot
structure for \( I O^{-} ? \)
\[
[\because \dot{I}: \dot{O}:]^{-}
\]
A. The bond between \( I \) and \( O \) should be represented with single line
B. The negative symbol should be on the inside of the brackets
c. oxygen is not satisfied according to the octet rule
D. There are not enough electrons
Subject: Maths
If the rate of change in the circumference of a circle of \( 0.3 \mathrm{cm} / \mathrm{s} \) then the rate of change in the area of the circle when the radius is \( 5 \mathrm{cm}, \) is:
A. \( 1.5 \mathrm{sq} \mathrm{cm} / \mathrm{s} \)
B. \( 0.5 \mathrm{sq} \mathrm{cm} / \mathrm{s} \)
c. \( 5 \mathrm{sq} \mathrm{cm} / \mathrm{s} \)
D. 3 sq cm/s
Subject: Maths
The function \( \boldsymbol{f}(\boldsymbol{x})=-\frac{\boldsymbol{x}}{\mathbf{2}}+\sin \boldsymbol{x} \)
defined on \( \left[-\frac{\pi}{3}, \frac{\pi}{3}\right] \) is
A. increasing
B. decreasing
c. constant
D. none of these
Subject: Maths
Let \( h \) be a twice continuously differentiable positive function on an open interval \( J . \) Let \( g(x)=n(h(x)) \) for
\( \operatorname{each} x \epsilon J \)
\( A \cdot g \) is increasing on \( J \)
B. \( g \) is decreasing on \( J \)
c. \( g \) is concave up on \( J \)
D. \( g \) is concave down on \( J \)
Subject: Maths
Which of the following are correct regarding normal distribution curve?
(i) Symmetrical about the line \( \boldsymbol{X}=\boldsymbol{\mu} \) (Mean)
(ii) Mean \( = \) Median \( = \) Mode
(iii) Unimodal
(iv) Points of inflexion are at \( \boldsymbol{X}=\boldsymbol{\mu} \pm \boldsymbol{\sigma} \)
A . (i), (ii)
B. (ii), (iv)
c. (i), (ii), (iii)
D. All of these
Subject: Physics
Three charges \( -\mathbf{q}_{1},+\mathbf{q}_{2} \) and \( -\mathbf{q}_{3} \) are
placed as shown in the figure. The \( x \)
component of the force on \( -q_{1} \) is proportional to:
A \( \cdot \frac{\mathrm{q}_{2}}{\mathrm{b}^{2}}-\frac{\mathrm{q}_{3}}{\mathrm{a}^{2}} \cos \theta \)
B. \( \frac{\mathrm{q}_{2}}{\mathrm{b}^{2}}+\frac{\mathrm{q}_{3}}{\mathrm{a}^{2}} \sin \theta \)
c. \( \frac{\mathrm{q}_{2}}{\mathrm{b}^{2}}+\frac{\mathrm{q}_{3}}{\mathrm{a}^{2}} \cos \theta \)
D. \( \frac{\mathrm{q}_{2}}{\mathrm{b}^{2}}-\frac{\mathrm{q}_{3}}{\mathrm{a}^{2}} \sin \theta \)
Subject: Chemistry
toppr LoGin Jolv now
Q Type your question reacivul with
Phenolphthalien
solution Solution \( \begin{array}{ll}\text { pH } & \text { ne } \\ \text { Vlaue } & \begin{array}{l}\text { Phe } \\ \text { so }\end{array}\end{array} \)
1 нС।
A 7 Distilled
water No colour
change.
13 Naoн Turns into pink
colour.
Lemon
juice \( 2.5 \quad \) No colour
change. .
Nacı 7 \( c \) No colour
change.
Baking
Soda Tu Turns into pink
colour. into
yell
colo
(a) List out the acids in the above table.
(b) What is the nature of the solution
which gives pink colour with Phenolphthalein solution?
(c) List out the neutral solutions in the
above table.
(d) Name the strongest acid and the
strongest base among the given
solutions.
Subject: Physics
If the extension of the spring is \( x_{0} \) at
time \( t, \) then the displacement of the
first block at this instant is :
\( ^{\mathbf{A}} \cdot \frac{1}{2}\left(\frac{F t^{2}}{2 m}+x_{0}\right) \)
B \( \cdot-\frac{1}{2}\left(\frac{F t^{2}}{2 m}+x_{0}\right) \)
c. \( \frac{1}{2}\left(\frac{F t^{2}}{2 m}-x_{0}\right) \)
D. \( \frac{F t^{2}}{2 m}+x_{0} \)
Subject: Chemistry
Match list I with list II and select the
correct answer using the codes given
below the lists.
List I List II
I. Cyanide e Ge and e process
A. Ultrapure
\( \| \)
Floatation process Pine oil
B.
III. Electrolytic reduction
C. Extraction of \( A l \)
Iv. Zone refining
D. Extraction of f \( A u \)
\( \mathbf{A} \cdot I-C, I I-A, I I I-D, I V-B \)
B . \( I-D, I I-B, I I I-C, I V-A \)
\( \mathbf{c} \cdot I-C, I I-B, I I I-D, I V-A \)
D . \( I-D, I I-A, I I I-C, I V-B \)
Subject: Physics
The number of electric lines of force that
radiate outwards from \( 8.85 \mu \mathrm{C} \) of charges
in a vacuum is:
A \( \cdot 10^{-6} \)
- \( ^{-6}-10 \)
B. \( 10^{-12} \)
\( c \cdot 10^{12} \)
D. \( 10^{\circ} \)
Subject: Maths
A fair coin is tossed at a fixed number
of times. If the probability of getting exactly 3 heads equals the probability
of getting exactly 5 heads, then the probability of getting exactly one head
is
A \( \cdot \frac{1}{64} \)
в. \( \frac{1}{32} \)
c. \( \frac{1}{16} \)
D.
Subject: Maths
\( A \) is a \( 3 \times 3 \) diagonal matrix having integral entries such that \( \operatorname{det}(A)=120 \)
number of such matrices is \( 10 n \), then
\( \boldsymbol{n} \) is
A . 36
B . 38
\( c \cdot 34 \)
D. 30
Subject: Chemistry
Assertion
\( \left(C_{2} H_{5}\right)_{3} N \) is less basic than
trimethylaine \( \left(\boldsymbol{C H}_{\mathbf{3}}\right)_{\mathbf{3}} \boldsymbol{N} \)
Reason
Due to hyperconjugation of \( C_{2} H_{5} \) is
less than methyl.
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
Subject: Maths
Addition Theorem of Probability states
that for any two events \( A \) and \( B \)
\( \mathbf{A} \cdot P(A \cup B)=P(A)+P(B) \)
B \( \cdot P(A \cup B)=P(A)+P(B)+P(A \cap B) \)
\( \mathbf{c} \cdot P(A \cup B)=P(A)+P(B)-P(A \cap B) \)
D \( . P(A \cup B)=P(A) \times P(B) \)
Subject: Physics
The following three objects (1) a metal
tray,
(2) a block of wood, and (3) a
wooden cap are left in a closed room
overnight. Next day the temperature of
each is recorded as \( T_{1}, T_{2}, \) and \( T_{3} \)
respectively. The likely situation is :
A. \( T_{1}=T_{2}=T_{3} \)
в. \( T_{3}>T_{2}>T_{1} \)
c. \( T_{3}=T_{2}>T_{1} \)
D. \( T_{3}>T_{2}=T_{1} \)
Subject: Maths
Find the rate of change of the area of a
circle with respect to its radius \( r \) when
(i) \( r=3 \mathrm{cm} \)
(ii) \( r=4 \mathrm{cm} \)
\( \mathbf{A} \cdot 6 \pi, 8 \pi \)
B . \( 5 \pi, 8 \pi \)
\( \mathbf{c} .4 \pi, 10 \pi \)
D . \( 2 \pi, 8 \pi \)
Subject: Chemistry
\( H_{2} O_{2} \) oxidises \( M n O_{2} \) to \( M n O_{4}^{-} \) in
basic medium. \( \boldsymbol{H}_{2} \boldsymbol{O}_{2} \) and \( \boldsymbol{M} \boldsymbol{n} \boldsymbol{O}_{2} \) react
in the molar ratio of \( x: y . \) What is the
value of \( \boldsymbol{x}+\boldsymbol{y} ? \)
Subject: Chemistry
The threshold wavelength for ejection of an electron from metal is 310 nm. The
kinetic energy of emitted photoelectron is \( 36 \times 10^{-20} J . \) Then the frequency of
incident light is:
A \( \cdot 1.5 \times 10^{15} \mathrm{Hz} \)
B . \( 2.5 \times 10^{18} \mathrm{Hz} \)
c. \( 1 \times 10^{22} H z \)
D. 2.5 \( \times 10^{12} \mathrm{Hz} \)
Subject: Chemistry
Assertion
Cu doesn't give \( \boldsymbol{H}_{2} \) when treated with
dil. \( \boldsymbol{H}_{2} \boldsymbol{S} \boldsymbol{O}_{4} \) or dil. \( \boldsymbol{H} \boldsymbol{C l} \)
Reason
Less active metals like \( C u \) do not give
\( \boldsymbol{H}_{2} \)
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
Subject: Maths
Prove the following:
\( \left|\begin{array}{lll}\boldsymbol{b}+\boldsymbol{c} & \boldsymbol{c}+\boldsymbol{a} & \boldsymbol{a}+\boldsymbol{b} \\ \boldsymbol{a}+\boldsymbol{b} & \boldsymbol{b}+\boldsymbol{c} & \boldsymbol{c}+\boldsymbol{a} \\ \boldsymbol{c}+\boldsymbol{a} & \boldsymbol{a}+\boldsymbol{b} & \boldsymbol{b}+\boldsymbol{c}\end{array}\right|=\mathbf{2}\left|\begin{array}{lll}\boldsymbol{a} & \boldsymbol{b} & \boldsymbol{c} \\ \boldsymbol{c} & \boldsymbol{a} & \boldsymbol{b} \\ \boldsymbol{b} & \boldsymbol{c} & \boldsymbol{a}\end{array}\right| \)
Subject: Chemistry
What is the molecular formula of
Magnesium Pyrophosphate formed during Carius method for estimation of
phosphorous in organic compound?
A. \( M g_{2} P_{2} O_{7} \)
в. \( M g_{2} P_{2} O_{5} \)
\( \mathrm{c} \cdot M g_{2} P O_{4} \)
D. \( M g P_{2} O_{5} \)
Subject: Physics
Assertion
Swimming is possible due to third law
of motion
Reason
Rebounding of rubber ball takes place
due to third law of motion.
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
Subject: Maths
Subtract \( 4 p^{2} q-3 p q+5 p q^{2}-8 p+ \)
\( 7 q-10 \) from \( 18-3 p-11 q+5 p q \)
\( 2 q^{2}+5 p^{2} q \)
A \( \cdot 28+5 p-18 q+8 p q-2 q^{2}+p^{2} q-5 p q^{2} \)
B . \( 8+11 p-18 q+8 p q-2 q^{2}+p^{2} q-5 p q^{2} \)
C. \( 28-5 p+18 q-8 p q+2 q^{2}-p^{2} q+5 p q^{2} \)
D. none
Subject: Chemistry
Naphthalene balls used to repel moths and other insects are obtained from \( X \)
These days \( Y \), a petroleum product, is used in place of \( X \) for metalling the roads. What are \( X \) and \( Y \) respectably?
A. Coke, coal
B. Coal, coke
c. Bitumen, coal tar
D. Coal tar, bitumen
Subject: Chemistry
Which of the following method(s) does work for the preparation of secondary amine?
A \( \cdot R_{3} N \frac{(i) B r-C N}{(i i) H_{3} O^{+}} ? \)
\( (i i i) \Delta \)
c. \( R N C \frac{N l / H_{2}}{\Delta} ? \)
D. All of these
Subject: Chemistry
Assertion
\( H N O_{3} \) oxidises sulphur to \( H_{2} S O_{4} \) acid (S+VI) but only oxidises selenium to
\( \boldsymbol{H}_{2} \boldsymbol{S} \boldsymbol{e} \boldsymbol{O}_{3}(\boldsymbol{S} \mathbf{e}+1 \mathbf{V}) \)
Reason
In selenium atoms, the electrons are more tightly held by the nucleus on account of increased nuclear charge.
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
Subject: Physics
Two particles \( P \) and \( Q \) describe SHM of same amplitude a and frequency along the same straight line. The
maximum distance between the two
particles is \( a \sqrt{2} . \) The initial phase difference between the particle is
\( \mathbf{A} \cdot \pi / 3 \)
в. \( \pi / 2 \)
c. \( \pi / 6 \)
D. zero
Subject: Chemistry
70 cal of heat is required to raise the temperature of a diatomic gas at
constant pressure from 30 to \( 35^{\circ} \) C. The amount of heat required (in cal) to raise
the temperature of the same gas
through the same range \( \left(30 \text { to } 35^{\circ} C\right) \) at constant volume is:
A . 30
B. 60
c. 50
D. 70
Subject: Maths
The Inverse expression of \( x+\frac{1}{x} \) will be:
A \( \frac{x^{2}+1}{x} \)
B. \( \frac{1}{x}-x \)
c. \( \frac{x}{x^{2}+1} \)
D. \( \frac{x}{x^{2}-1} \)
Subject: Chemistry
Assertion
In the acid-base titration involving a strong base and a weak acid, methyl orange can be used as an indicator
Reason
Methyl orange changes its colour in pH range 3 to 5
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
Subject: Maths
Find the value of \( k \) if line PQ is parallel to line RS where \( \boldsymbol{P}(\mathbf{2}, \boldsymbol{4}), \boldsymbol{Q}(\boldsymbol{3}, \boldsymbol{6}), \boldsymbol{R}(\boldsymbol{8}, \boldsymbol{1}) \)
and \( S(10, k) \)
Subject: Chemistry
The heat of combustion of carbon to
\( \boldsymbol{C O}_{2}(\boldsymbol{g}) \) is \( -\boldsymbol{3} \boldsymbol{9} \boldsymbol{3} . \boldsymbol{5} \boldsymbol{k} \boldsymbol{J} \quad \boldsymbol{m} \boldsymbol{o l}^{-1} \)
Calculate the heat released upon
formation of \( 35.2 g \) of \( C O_{2}(g) \) from
carbon and oxygen gas.
\( \mathbf{A} \cdot-315 k J \)
в. \( 315 J \)
c. \( 215 k J \)
D. \( -215 . J \)
Subject: Physics
In Fraunhofer diffraction pattern, slit
width is \( 0.2 m m \) and screen is at \( 2 m \)
away from the lens. If wavelength of light used in \( 5000 A \) then the distance
between the first minimum on either
side of the central maximum is \( (\boldsymbol{\theta} \) is
small and measure in radian):
A \( \cdot 10^{-1} m \)
B. \( 10^{-2} \) m
c. \( 2 \times 10^{-2} m \)
D. \( 2 \times 10^{-1} m \)
Subject: Maths
Fill in the blanks.
(i) The additive identity of the integers is P.
(ii) The integer which is 8 less than -24 is \( \underline{Q}_{-} \)
(iii) Every integer less than zero is \( R \)
\( P \quad Q \quad R \)
\( \begin{array}{lll}A \cdot O & -32 & \text { negative }\end{array} \)
B. \( 1-32 \) positive
c. \( 0-16 \) negative
D. 1 -32 negative
Subject: Chemistry
Balance the following equation by ion electron method.
\( \boldsymbol{C r}_{2} \boldsymbol{O}_{7}^{2-}+\boldsymbol{H}^{+}+\boldsymbol{C}_{2} \boldsymbol{O}_{4}^{2-} \rightarrow \boldsymbol{C r}^{3+}+ \)
\( \boldsymbol{C O}_{2}+\boldsymbol{H}_{2} \boldsymbol{O} \)
Subject: Physics
A uniform rod \( A B \) of mass \( m \) and length is at rest on a smooth horizontal
surface. An impulse J is applied to the end B perpendicular to the rod in horizontal direction. Speed of particle \( P \)
at a distance I/6 from the centre
towards \( A \) of the rod after time \( t=\frac{\pi m l}{12 J} \)
is
A \( \cdot_{2} \frac{J}{m} \)
B. \( \frac{J}{\sqrt{2} m} \)
c. \( \frac{J}{m} \)
D. \( \sqrt{2} \frac{J}{m} \)
Subject: Maths
If \( 1.3+2.3^{2}+3.3^{3}+\ldots+n .3^{n}= \)
\( \frac{(2 n-1) 3^{a}+b}{4} \) then \( a \) and \( b \) are respectively
A \( . n, 2 \)
в. \( n, 3 \)
c. \( n+1,2 \)
D. \( n+1,3 \)
Subject: Physics
\( 75 g \) of water at \( 10^{\circ} C \) is heated by supplying \( 25200 J \) of heat energy. If the specific heat capacity of water is
\( 4.2 J / g^{o} C . \) Calculate the final temperature of water
\( \mathbf{A} \cdot 0^{\circ} C \)
B. \( 10^{\circ} \mathrm{C} \)
c. \( 100^{\circ} \mathrm{C} \)
D. \( 90^{\circ} \mathrm{C} \)
Subject: Maths
\( y=\frac{2(x-\sin x)^{\frac{3}{2}}}{\sqrt{x}}, \) find \( \frac{d y}{d x} \)
\( \mathbf{A} \cdot \frac{d y}{d x}=y\left\{\frac{3}{2} \cdot \frac{1-\cos x}{x-\sin x}-\frac{1}{2 x}\right\} \)
B. \( \frac{d y}{d x}=y\left\{\frac{3}{4} \cdot \frac{1-\sin x}{x-\cos x}+\frac{1}{2 x}\right\} \)
\( \mathbf{c} \cdot \frac{d y}{d x}=y\left\{\frac{3}{4} \cdot \frac{1-\cos x}{x-\sin x}-\frac{1}{2 x}\right\} \)
D. \( \frac{d y}{d x}=y\left\{\frac{3}{2} \cdot \frac{1-\sin x}{x-\cos x}-\frac{1}{2 x}\right\} \)
Subject: Maths
The number of employees in companies
\( A, B \) and \( C \) are in the ratio 3: 2: 4
respectively. If the number of employees in the three companies is increased by \( 20 \%, 30 \% \) and \( 15 \% \) respectively, what will be the new ratio of employees working in companies \( A, B \) and \( C \)
respectively?
\( \mathbf{A} \cdot 18: 13: 24 \)
B. 13: 18: 23
\( \mathbf{c} \cdot 17: 13: 23 \)
D. 18: 13: 23
Subject: Chemistry
Statement I: The \( A l^{3+} \) ion needs to be
reduced to form aluminum metal.
Statement II: Reduction is a gain of
electrons.
A. Both Statement I and Statement II are correct and Statement II is the correct explanation of Statement
B. Both Statement I and Statement II are correct, but Statement II is not the correct explanation of Statement I.
c. Statement I is correct, but Statement II is incorrect
D. Statement I is incorrect, but Statement II is correct
Subject: Physics
A light bulb is rated at \( 100 W \) for a
\( 220 V \) supply. Find the rms current through the bulb:
\( \mathbf{A} \cdot 0.25 A \)
в. \( 0.45 A \)
c. \( 0.65 A \)
D. \( 0.85 A \)
Subject: Biology
Match the correct set of scientists in
relation to cell division.
A. Robert Remak
1. Meiosis
\( B \)
I S.R. Pelc
2. Mitosis A.Howard and
\( \mathrm{C} \)
W. Fleming
3. Amitosis
D. Farmer and Moore
4. Cyclins
sand 5. \( \mathrm{G}_{1}, \mathrm{S} \) \( \mathrm{IG}_{2} \) phase
\( A \cdot A-3, B-2, C-1, D-4 \)
B. \( A-3, B-5, C-2, D-1 \)
C. \( A-4, B-2, C-3, D-5 \)
D. \( A-1, B-2, C-3, D-4 \)
Subject: Maths
A pole has to be erected at a point on the boundary of a circular park of
diameter 13 meters in such a way that the difference of its distance from two
diametrically opposite fixed gates \( \boldsymbol{A} \) and \( B \) on the boundary is 7 meters. It is possible to do so? If yes, at what distances from the two gates should the
pole be erected?
A. \( 6.71 m \)
в. \( 0.71 m \)
c. \( 1.51 m \)
D. \( 5.51 \mathrm{m} \)
Subject: Biology
Assertion
Replication and transcription occur in the nucleus but translation occurs in
the cytoplasm.
Reason
mRNA is transferred from the nucleus
into the cytoplasm where ribosomes and amino acids are available for
protein synthesis.
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.
Subject: Biology
Pick up the correct option
(a) Primary succession begins in areas where natural communities have been
destroyed
(b) Hydrarch succession takes place in
water
(c) Climax community is the community that is near equilibrium with immediate environment
(d) In newly cooled lava secondary succession occurs
\( A \cdot \) a and \( b \)
B. b and c
c. a and \( d \)
D. b only
E. a only
Subject: Physics
After tracing the path of a ray of light
passing through a rectangular glass slab for four different values of the
angle of incidence, a student reported his observations in tabular form as
given below:
\( <\mathrm{e} \) s.No \( \begin{array}{lccc}\text { । } & 30^{0} & 19^{0} & 29^{0} \\ \text { ॥ } & 40^{0} & 28^{0} & 40^{0} \\ \text { ॥। } & 50^{0} & 36^{0} & 50^{0} \\ \text { । } & 60^{0} & 40^{0} & 59^{0}\end{array} \)
The best observation is :
\( A \)
B. II
\( c \)
D. IV
Subject: Maths
The cost of an article including the sales tax is \( R s .616 . \) The rate of sales
\( \operatorname{tax} \) is \( 10 \%, \) if the shopkeeper has made a profit of \( 12 \%, \) then the cost price of the article is?
A. Rs .350
в. \( R s .400 \)
c. \( R s .500 \)
D. Rs .800
Subject: Chemistry
\( \boldsymbol{H} \boldsymbol{B r} \) reacts with \( \boldsymbol{C H}_{2}=\boldsymbol{C H}-\boldsymbol{O C H}_{3} \)
under anhydrous conditions at room temperature to give:
\( \mathbf{A} \cdot C H_{3} C H O \) and \( C H_{3} B r \)
в. \( B r C H_{2} C H O \) and \( C H_{3} O H \)
c. \( B r C H_{2} C H_{2} O C H_{3} \)
D. \( C H_{3}-C H(B r)-O C H_{3} \)
Subject: Maths
Let \( f(x) \) be defined by \( f(x)= \) \( \left\{\begin{array}{cl}\sin 2 x & \text { if } 0<x \leq \frac{\pi}{6} \\ a x+b & \text { if } \frac{\pi}{6}<x \leq 1\end{array} . \text { The values of } a\right. \)
and \( b \) such that \( f \) and \( f^{\prime} \) are
continuous, are
A \( \cdot a=1, b=\frac{1}{\sqrt{2}}+\frac{\pi}{6} \)
в. \( a=\frac{1}{\sqrt{2}}, b=\frac{1}{\sqrt{2}} \)
c. \( _{a=1, b}=\frac{\sqrt{3}}{2}-\frac{\pi}{6} \)
D. None of these
Subject: Chemistry
Four students, \( W, X, Y \) and \( Z, \) made
the following statements about alkanes and alkenes.
\( W \) Bromine reacts with alkanes by
electrophilic substitution. \( X \) Bromine reacts with alkenes by a
free-radical addition mechanism.
\( Y \) Alkenes can be oxidised by acidified
manganate(VII) ions.
\( Z \) Alkenes are formed from alkanes by
cracking. Which two students are correct?
A. \( W \) and \( X \)
B. \( W \) and \( Z \)
c. \( X \) and \( Y \)
D. \( Y \) and \( Z \)
Subject: Physics
Choose the wrong options
This question has multiple correct options
A. Translation kinetic energy of all ideal gases at same temperature is same
B. In one degree of freedom all ideal gases has internal energy \( =\frac{1}{2} R T \)
C. Translational degree of freedom of all ideal gases is three
D. Translational kinetic energy of one mole of all ideal gases is \( \frac{3}{2} R T \)
Subject: Chemistry
Two metals \( M \) and \( N \) have the following values of ionization energies. Find
energy required for formation of \( \boldsymbol{M}^{+} \)
from \( M, M^{+2} \) from \( M^{+}, \) and total
energy required to form \( M^{+2} \) from \( M \)
Do similar calculations for metal \( N \)
\( I E_{1} \quad I E_{2} \)
\[
496 \quad 4560
\]
738 1450
Subject: Physics
Two,weights of \( 5 \mathrm{kg} \) and \( 10 \mathrm{kg} \) are placed on a horizontal table of height \( 1.5 \mathrm{m} \) Which weight will have more potential energy?
\( A \cdot 5 \mathrm{kg} \)
в. \( 10 \mathrm{kg} \)
c. Both will have equal energy
D. None of the above
Subject: Chemistry
Predict \( \Delta H>\Delta U \) or \( \Delta H<\Delta U \)
a. \( C(\text { graphite })+O_{2}(g) \longrightarrow C O_{2}(g) \)
b. \( \boldsymbol{P C l}_{5}(\boldsymbol{g}) \longrightarrow \boldsymbol{P C l}_{3}(\boldsymbol{g})+\boldsymbol{C l}_{2}(\boldsymbol{g}) \)
A. a. \( \Delta H=\Delta U ; \) b. \( \Delta H>\Delta U \)
В. а. \( \Delta H>\Delta U ; \) b. \( \Delta H=\Delta U \)
c. a. \( \Delta H>\Delta U ; \) b. \( \Delta H<\Delta U \)
D. None of these
Subject: Physics
\( \boldsymbol{A}=? \)
\( \boldsymbol{B}=\mathbf{?} \)
A \( . A=2 m, B=7 m \)
В \( . A=7 m, B=5 m \)
\( \mathbf{c} . A=3 m, B=6 m \)
D. \( A=2 m, B=5 m \)
Subject: Maths
\( \frac{\boldsymbol{d}}{\boldsymbol{d} \boldsymbol{x}} \tan ^{-1}\left[\frac{\sqrt{\mathbf{1}+\sin \boldsymbol{x}}-\sqrt{\mathbf{1}-\sin \boldsymbol{x}}}{\sqrt{\mathbf{1}+\sin \boldsymbol{x}}-\sqrt{\mathbf{1}-\sin \boldsymbol{x}}}\right]= \)
\( A \)
B. \( -\frac{1}{2} \)
\( c \cdot \frac{1}{2} \)
\( D \)
Subject: Physics
Three uniform sphere, each having mass \( m \) and radius \( r, \) are kept in such a way that each touches the other two.
The magnitude of the gravitational force on any sphere due to the other two is
A \( \cdot \frac{G m^{2}}{r^{2}} \)
в. \( \frac{G m^{2}}{4 r^{2}} \)
c. \( \frac{\sqrt{3} G m^{2}}{4 r^{2}} \)
D. \( \frac{\sqrt{3} G m^{2}}{r^{2}} \)
Subject: Chemistry
\( \ln \operatorname{areaction} \boldsymbol{A}_{2}(\boldsymbol{g})+\boldsymbol{4} \boldsymbol{B}_{2}(\boldsymbol{g}) \rightleftharpoons \)
\( \mathbf{2} \boldsymbol{A} \boldsymbol{B}_{4}(\boldsymbol{g}), \boldsymbol{\Delta} \boldsymbol{H}<0 . \) The formation of
\( A B_{4} \) is not favoured by :
This question has multiple correct options
A. low temperature and high pressure
B. high temperature and low pressure
c. low temperature and low pressure
D. high temperature and high pressure
Subject: Physics
On a horizontal frictionless frozen lake,
a girl \( (36 \mathrm{kg}) \) and a box \( (9 \mathrm{kg}) \) are connected to each other by means of a rope. Initially they are 20 m apart. The girl exerts a horizontal force on the box, pulling it towards her. How far has the girl traveled when she meets the box?
A . 10
B. since there is no friction, the girl will not move
\( c \cdot 16 m \)
D. \( 4 \mathrm{m} \)