AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Chemistry
What are the coefficients of all in lowest
term after balancing the reaction?
\( \ldots \boldsymbol{C}_{4} \boldsymbol{H}_{10}+\ldots . \boldsymbol{O}_{2} \rightarrow \ldots \boldsymbol{C} \boldsymbol{O}_{2}+\ldots . \boldsymbol{H}_{2} \boldsymbol{O} \)
B. 2,13,8,10
c. 1,6,1,5
D. 3,10,16,20
E .4,26,16,20
Subject: Maths
The radius of a cylinder is increasing at the rate of \( 5 \mathrm{cm} / \mathrm{min} \) so that its volume
is constant. When its radius is \( 5 \mathrm{cm} \) and
height is \( 3 \mathrm{cm}, \) then the rate of decreasing of its height is
\( \mathbf{A} \cdot 6 \mathrm{cm} / \mathrm{min} \)
B. \( 3 \mathrm{cm} / \mathrm{min} \)
c. \( 4 \mathrm{cm} / \mathrm{min} \)
\( \mathbf{D} \cdot 5 \mathrm{cm} / \mathrm{min} \)
E . \( 2 \mathrm{cm} / \mathrm{min} \)
Subject: Chemistry
The root mean square speed at \( N T P \)
for the \( \operatorname{gases} C H_{4}, H_{2}, H e \) and \( F_{2} \) are
in the order
A \( \cdot C H_{4}<H_{2}<H e<F_{2} \)
B. \( H_{2}<H e<C H_{4}<F_{2} \)
c. \( H_{2}<H e<F_{2}<C H_{4} \)
D. \( F_{2}<C H_{4}<H_{2}<H e \)
Subject: Maths
A trader buys an unfinished article for
Rs. 1,800 and spends Rs. 600 on its finishing, parking transportation, etc. He marks the article at such a price that will give him \( 20 \% \) profit. How much will a customer pay for he article including \( 12 \% \) sales tax.
A . \( R s .3,165.60 \)
в. \( R s .3,788.60 \)
c. \( R s .3,225.60 \)
D. Rs.3, 338.60
Subject: Chemistry
Calculate the mole fraction of \( N_{2} \) gas in
a mixture of \( N_{2} \) and \( O_{2} \). If the partial
pressure of \( \boldsymbol{O}_{2} \) is \( 63 \mathrm{cm} \) of \( \mathrm{Hg} \) and the
total pressure of the mixture is \( 90 \mathrm{cm} \) of Hg.
Subject: Maths
\( \lim _{\boldsymbol{n} \rightarrow \infty} \frac{\mathbf{1}^{\boldsymbol{p}}+\boldsymbol{2}^{\boldsymbol{p}}+\ldots+\boldsymbol{n}^{\boldsymbol{p}}}{\boldsymbol{n}^{\boldsymbol{p}+1}} \) is
A. \( \frac{1}{p+1} \)
B. \( \frac{1}{1-p} \)
c. \( \frac{1}{p}-\frac{1}{p-1} \)
D. \( \frac{1}{p+2} \)
Subject: Maths
A diet is to contain at least 80 units of
vitamin \( A \) and 100 units of minerals.
Two foods \( F_{1} \) and \( F_{2} \) are available. Food
\( F_{1} \operatorname{costs} \) Rs. 4 per unit food and \( F_{2} s \)
costs Rs.6 per unit. One unit of food \( \boldsymbol{F}_{1} \)
contains 3 units of vitamin \( A \) and 4
units of minerals. One unit of food \( \boldsymbol{F}_{2} \)
contains 6 units of vitamin \( A \) and 3
units of minerals. Formulate this as a
linear programming problem. Find the minimum cost for diet that consists of
mixture of these two foods and also
meets the mineral nutritional
requirements?
Subject: Chemistry
Which of the following will have highest
value of \( p K a ? \)
A. \( F C H_{2} C H_{2} \) СООН
в. \( C H_{3} C H(F)- \) СООН
c. \( C H_{3} C H(B r)-C O O H \)
D. \( C H_{3} C H_{2} C O O H \)
Subject: Chemistry
The specific conductance of \( 0.1 N K C l \) solution at \( 23^{\circ} C \) is 0.012 oh \( m^{-1} c m^{-1} \)
The resistance of cell containing the solution at the same temperature was
found to be 55 ohm. The cell constant
will be:
A \( \cdot 0.142 \mathrm{cm}^{-1} \)
B. \( 0.66 \mathrm{cm}^{-1} \)
D. \( 1.12 \mathrm{cm}^{-1} \)
Subject: Maths
A hemispherical tank of radius \( \boldsymbol{R} \) is
completely filled with water. Now an orifice of small area 'a' is made at the
bottom of tank. The time required to
empty the tank is
\( ^{\mathrm{A}} \cdot \frac{14 \pi R^{\frac{5}{2}}}{15 \sqrt{2} a \sqrt{g}} \)
\( ^{\mathrm{B}} \cdot \frac{14 \pi R^{\frac{3}{2}}}{\sqrt{2} a \sqrt{g}} \)
c. \( \frac{14 \pi R^{\frac{5}{2}}}{5 \sqrt{2} a \sqrt{g}} \)
\( \frac{4 \pi R^{\frac{5}{2}}}{15 \sqrt{2} a \sqrt{g}} \)
Subject: Physics
A heavy particle hanging from a string of length/ is projected horizontally with speed \( \sqrt{g l} . \) The speed of particle at the point where the tension in the string equals weight of the particle is
A \( \cdot \sqrt{2 g l} \)
B. \( \sqrt{3 g l} \)
c. \( \sqrt{g l l 2} \)
D. \( \sqrt{g l / 3} \)
Subject: Physics
A beam of protons enters a uniform
magnetic field of \( 0.3 T \) with a velocity of
\( 4 \times 10^{5} \mathrm{m} / \mathrm{s} \) in a direction making an
angle of \( 60^{\circ} \) with the direction of
magnetic field. The path of motion of the particle will be :
A . circular
B. straight line
c. parabolic
D. helical
Subject: Maths
What should be added to \( 6 x^{2}-3 x y+ \)
\( 4 y^{2} \) to get \( 2 y^{2}+x y-4 x^{2} ? \)
A. \( -x^{2}-y^{2}+4 y \)
B . \( -10 x^{2}-y^{2}+4 x y \)
c. \( x^{2}-2 y^{2}+4 x \)
D. \( -10 x^{2}-2 y^{2}+4 x y \)
Subject: Biology
Given below are four statements (a-d)
regarding human blood circulatory
system.
(a) Arteries are thick-walled and have
narrow lumen as compared to veins.
(b) Angina is acute chest pain when the blood circulation of the brain is
reduced.
(c) Persons with blood group \( A B \) can
donate blood to any person with any blood group under ABO system.
(d) Calcium ions play a very important
role in blood clotting.

Which two of the above statements are
correct?
\( A \cdot(c) \) and (d)
B. (a) and (d)
c. (a) and (b)
D. (b) and (c)
Subject: Chemistry
Which of the following is correct
statement?
A. Conductivity \& molar conductivity of solution increase on dilution
B. Voltage of button cell remain unchanged through out its life time
C. On electrolysis of aqueous \( C u S O_{4} \) using platinum
electrode its concentration \( \left[C u^{2+}\right] \) remain constant
D. On electrolysis of aqueous \( N a C l \), solution becomes acidic
Subject: Physics
Which of the following is used in cancer treatment?
\( \mathbf{A} \cdot \frac{1331}{51} \)
B . \( _{15}^{22} P \)
\( \mathrm{c} \cdot_{27}^{60} \mathrm{Co} \)
\( \mathrm{D} \cdot_{1}^{2} \mathrm{H} \)
Subject: Chemistry
What is the sum of oxidation numbers
of all the carbon atoms except that
attached to \( -C H O \) group in
\( \boldsymbol{C}_{\boldsymbol{6}} \boldsymbol{H}_{\boldsymbol{5}} \boldsymbol{C} \boldsymbol{H} \boldsymbol{O} ? \)
A . -6
B. -5
c. -4
D. - -
Subject: Chemistry
Calculate pH of a buffer prepared by adding \( 10 m L \) of \( 0.10 M \) acetic acid to
\( 20 m L \) of \( 0.1 M \) sodium acetate
\( \left[\boldsymbol{p} \boldsymbol{K}_{\boldsymbol{a}}\left(\boldsymbol{C H}_{3} \boldsymbol{C O O H}\right)=\boldsymbol{4 . 7 4}\right] \)
A . 3.00
в. 4.44
c. 4.74
D. 5.04
Subject: Maths
Suppose a manufacturer of printed circuits has a stock of 200 resistors,
120 transistors and 150 capacitors and is required to produce two types of circuits.
Type A requires 20 resistors, 10 transistors and 10 capacitors
Type B requires 10 resistors, 20 transistors and 30 capacitors. If the profit on type \( A \) circuits is \( E 5 \) and
that on type \( B \) circuits is \( E 12 \), how
many of each circuit should be
produced in order to maximize profit?
Subject: Maths
Let \( \boldsymbol{E} \) and \( \boldsymbol{F} \) be events with \( \boldsymbol{P}(\boldsymbol{E})= \)
\( \frac{3}{5}, P(F)=\frac{3}{10} \) and \( P(E \cap F)=\frac{1}{5} . \) Are
\( E \) and \( F \) independent?
A. True
B. False
Subject: Chemistry
Which kind of isomerism is exhibited
by octahedral complex \( \left[\mathrm{Co}\left(\mathrm{NH}_{3}\right)_{4}\right. \)
\( \left.\boldsymbol{B} \boldsymbol{r}_{2}\right] \boldsymbol{C l} ? \)
A. Geometrical and ionization
B. Geometrical and optical
c. optical and ionization
D. Geometrical only
Subject: Maths
Match the entries of Column- I and
Column - II.
A . a-4, b-3, c-2, d-
B. \( a-1, b-3, c-2, d-4 \)
C. \( a-4, b-3, c-1, d-2 \)
D. \( a-3, b-4, c-2, d-1 \)
Subject: Maths
If the functions \( f(x) \) and \( g(x) \) are continuous on \( [a, b] \) and differentiable on \( (a, b), \) then in the interval \( (a, b), \) the
equation \( \left|\begin{array}{ll}\boldsymbol{f}^{\prime}(\boldsymbol{x}) & \boldsymbol{f}(\boldsymbol{a}) \\ \boldsymbol{g}^{\prime}(\boldsymbol{x}) & \boldsymbol{g}(\boldsymbol{a})\end{array}\right|=\frac{1}{\boldsymbol{a}-\boldsymbol{b}}\left|\begin{array}{ll}\boldsymbol{f}(\boldsymbol{a}) & \boldsymbol{f}(\boldsymbol{b}) \\ \boldsymbol{g}(\boldsymbol{a}) & \boldsymbol{g}(\boldsymbol{b})\end{array}\right| \)
A. has at least one root
B. has exactly one root
c. has at most one root
D. no root
Subject: Maths
A fair coin is tossed four times. The
probability that the tails exceed the heads in number is
\( ^{\mathbf{A}} \cdot_{\frac{4}{3} C}\left(\frac{1}{2}\right)^{4} \)
\( ^{\mathbf{B}} \cdot_{3}^{4} C\left(\frac{1}{2}\right)^{4}+\left(\frac{1}{2}\right)^{4} \)
\( ^{c} \cdot\left(\frac{1}{2}\right)^{4} \)
\( ^{\mathrm{D}} \cdot_{3}^{4} C\left(\frac{1}{3}\right)^{2}\left(\frac{2}{3}\right)^{1} \)
Subject: Physics
A charge 'q' moves in a region where electric field and magnetic field both exist, then force on it is : -
\( \mathbf{A} \cdot q(\vec{V} \times \vec{B}) \)
B \( \cdot q \vec{E}+q(\vec{V} \times \vec{B}) \)
\( \mathbf{c} \cdot q \vec{E}+q(\vec{B} \times \vec{V}) \)
\( \mathbf{D} \cdot q \vec{B}+q(\vec{E} \times \vec{V}) \)
Subject: Maths
If a vector \( \vec{A} \) makes angles \( \alpha, \beta \) and \( \gamma \)
with \( X, Y \) and \( Z \) axes respectively then \( \sin ^{2} \alpha+\sin ^{2} \beta+\sin ^{2} \gamma= \)
A .
B.
\( c \cdot 2 \)
D. 3
Subject: Chemistry
\( \boldsymbol{C H}_{3} \boldsymbol{C H}=\boldsymbol{C H} \boldsymbol{C H O} \frac{O \boldsymbol{H}^{-}}{A l d o l} \boldsymbol{A}, \boldsymbol{A} \) is?
A \( \cdot C H_{3}(C H=C H)_{3} C H O \)
B . \( C H_{3} C H_{2} C H_{2}(C H=C H)_{2} C H O \)
c. \( C H_{3}\left(C H_{2} C H_{2}\right) C H=C H-C H O \)
D. None of the above is correct
Subject: Chemistry
Reagent used in Carius method is:
A \( \cdot \) fuming \( H N O_{3} \) with \( A g N O_{3} \)
B. fuming \( H N O_{3} \) with \( A g N O_{2} \)
c. fuming \( H_{2} S O_{4} \) with \( A g N O_{3} \)
D. fuming \( H_{2} S O_{4} \) with \( A g N O_{2} \)
Subject: Physics
If a ball is thrown vertically upwards with speed \( u, \) the distance covered during the last \( t \) seconds of its ascent is
\( \mathbf{A} \cdot u \)
в. \( \frac{1}{2} g t^{2} \)
c. \( u t-\frac{1}{2} g t^{2} \)
D. \( (u+g t) t \)
Subject: Chemistry
\( H_{2} O \) has a higher boiling point than
HF because:
A. \( H_{2} O \) is more polar than \( H F \)
B. \( H_{2} O \) can form more hydrogen bonds
C. \( H_{2} O \) has a higher molecular weight
D. \( H_{2} O \) has more atoms
E. \( H_{2} O \) does not have a higher boiling point that \( H F \)
Subject: Physics
A proton, a deutron and an \( \alpha \) particle
accelerated through the same potential difference enter a region of uniform magnetic field, moving at right angles
to \( B \). What is the ratio of their radii.?
A .2: 1: 1
B. \( 1: \sqrt{2}: \sqrt{2} \)
c. 1: 2: 1
D. 1: 1: 2
Subject: Maths
\( \boldsymbol{P}(\boldsymbol{A})=\frac{1}{\boldsymbol{Z}} \)
\( \boldsymbol{P}(\boldsymbol{B})=\frac{1}{\boldsymbol{4}} \)
\( \boldsymbol{P}(\boldsymbol{A} \cap \boldsymbol{B})=\frac{1}{\mathbf{5}} \)
\( \boldsymbol{P}(\boldsymbol{A} / \boldsymbol{B})=? \)
Subject: Physics
A small disc of radius \( 2 \mathrm{cm} \) is cut from
a disc of radius \( 6 \mathrm{cm} \). If the distance
between their centres is \( 3.2 \mathrm{cm}, \) what is
the shift in the centre of mass of the
disc?
A. \( 0.4 \mathrm{cm} \)
B. 2.4 \( \mathrm{cm} \)
c. \( 1.8 \mathrm{cm} \)
D. \( 1.2 \mathrm{cm} \)
Subject: Maths
Find variance for following data:
\( \begin{array}{lllll}\text { Class } & \mathbf{3 0}- & \mathbf{4 0}- & \mathbf{5 0 -} & \mathbf{6} \\ \text { interval } & \mathbf{4 0} & \mathbf{5 0} & \mathbf{6 0} & \mathbf{7}\end{array} \)
Frequency \( \quad 3 \) What is and 12
A. 14.17
B. 18.17
c. 16.17
D. 15.17
Subject: Physics
The amount of work done is pumping water out of a cubical vessel of height
\( \mathrm{m} \) is nearly (Given \( \rho_{w a t e r}=1000 \mathrm{kg} / \mathrm{m}^{3} \)
A . 5,000
в. 10,000
c. 5 J
D. 10 J
Subject: Chemistry
The IUPAC name of \( \boldsymbol{C H}_{3}-\boldsymbol{C H}= \)
\( \boldsymbol{C H}-\boldsymbol{C O O H} \) is:
A. but-2-ene-1-oic acid
B. but-1-ene-1-oic acid
c. but-2-ene-1-carboxylic acid
D. propene-1-carboxylic acid
Subject: Chemistry
Which of the following statements
is/are correct regarding inter-halogen
compounds of ABX types?
This question has multiple correct options
\( A \cdot X \) may be 1,3,5 and 7
B. A is a more-electronegative halogen than B
\( \mathrm{C} \cdot F B r_{3} \) is a stable inter-halogen compound
D. the structures of \( C I F_{3} \) and \( I F_{2} \) show deviation from
normal structures and could be explained on the basis of VSEPR theory
Subject: Physics
The half-life of \( ^{215} A t \) is \( 100 \mu \) s. The time
taken for the radioactivity of a sample of \( ^{215} A t \) to decay to \( 1 / 16 \) th of its initial value is
A. \( 400 \mu s \)
B. \( 6.3 \mu s \)
c. \( 40 \mu s \)
D. 300\mus
Subject: Chemistry
The experimental data for
decomposition of \( N_{2} O_{5}\left[2 N_{2} O_{5} \rightarrow\right. \)
\( \left.4 N O_{2}+O_{2}\right] \) in gas phase at \( 318 K \) are
given below:
\[
\text { t/s } \quad \mathbf{0} \quad \mathbf{4 0 0} \quad \mathbf{8 0 0}
\]
\[
10^{2}
\]
\[
\left[N_{2} O_{5}\right] / m o l L^{-1}
\]
(i) Plot \( \left[N_{2} O_{5}\right] \) against t.
(ii) Find the half-life period for the
reaction.
(iii) Draw a graph between \( \log \left[N_{2} O_{5}\right] \)
and t.
(iv) What is the rate law?
(v) Calculate the rate constant.
(vi) Calculate the half-life period from \( \mathbf{k} \) and compare it with (ii)
Subject: Physics
A proton is projected with a speed of
\( 3 \times 10^{6} m / s \) horizontally from east to
west. A uniform magnetic field B of strength \( 2 \times 10^{-3} T \) exists in the
vertically upward direction the magnitude of magnetic force on proton is \( \boldsymbol{F} \times \mathbf{1 0}^{-16} \boldsymbol{N} \). What is the value of \( \boldsymbol{F} \) ?
Subject: Physics
Two plane mirrors are inclined at an
angle \( \theta . \) A ray of light is reflected from the first mirror and is then incident on
the second mirror from which it is again
reflected. What is deviation of incident
ray?
A \( \cdot 360^{\circ}+2 \theta \)
В. \( 360^{\circ}-\theta \)
\( \mathbf{c} \cdot 360^{\circ}-2 \theta \)
D. \( 360^{\circ}+\theta \)
Subject: Physics
A bullet of mass \( A \) and velocity \( B \) is fired into a block of wood of mass \( C . \) If loss of
any mass and friction be neglected, then velocity of the system must be
\( ^{\text {A }} \cdot \frac{A B}{A+C} \)
в. \( \frac{A+C}{B+C} \)
c. \( \frac{A C}{B+C} \)
D. \( \frac{A+B}{A C} \)
Subject: Chemistry
Anhydrous borax is:
\( \mathbf{A} \cdot N a_{2} B_{4} O_{7} \)
B. \( N a_{2} B_{4} O_{7} .5 H_{2} O \)
\( \mathbf{c} \cdot N a_{2} B_{4} O_{7} \cdot 10 H_{2} O \)
D. \( N a_{2} B_{4} O_{7} .8 H_{2} O \)
Subject: Chemistry
Assertion
The number of unpaired electrons in the
following gaseous ions:
\( M n^{3+}, C r^{3+}, V^{3+} \) and \( T i^{3+} \) are 4,3,2
and 1 respectively.
Reason
Among these \( \mathrm{Cr}^{3+} \) is most stable in
aqueous solution.
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: Chemistry
100ml of \( 0.01 \mathrm{M} C H_{3} \) COOH reacts
with \( 40 \mathrm{ml}, 0.01 \mathrm{M} N a O H\left(K_{a}=10^{-5}\right) \)
Find \( p H \) when \( 1 \mathrm{ml} \) of \( 0.01 \mathrm{M} \) HCl is
added.
Subject: Physics
A solenoid of length \( 1.5 \mathrm{m} \) and \( 4 \mathrm{cm} \)
diameter possesses 10 turns per \( \mathrm{cm} . \) A current of \( 5 \mathrm{A} \) is flowing through it, the magnetic induction at axis inside the
solenoid is \( \left(\mu_{0}=4 \pi \times\right. \)
\( \left.10^{-7} w e b e r a m p^{-1} m^{-1}\right) \)
A \( \cdot 4 \pi \times 10^{-5} \) gauss
В . \( 2 \pi \times 10^{-5} \) gauss
c. \( 4 \pi \times 10^{-5} \) tesla
D. \( 2 \pi \times 10^{-5} \) tesla
Subject: Maths
How many terms are there in the G.P \( \mathbf{3}, \mathbf{6}, \mathbf{1 2}, \mathbf{2 4}, \dots \dots \dots, \mathbf{3 8 4} ? \)
\( \mathbf{A} \cdot \mathbf{8} \)
B. 9
c. 10
D. 11
E. 7
Subject: Maths
Consider the plane \( (\boldsymbol{x}, \boldsymbol{y}, \boldsymbol{z})= \)
\( (0,1,1)+\lambda(1,-1,1)+\mu(2,-1,0) . \) The
distance of this plane from the origin is:
A \( \cdot \frac{1}{3} \)
B. \( \frac{\sqrt{3}}{2} \)
\( c \cdot \sqrt{\frac{3}{2}} \)
D. \( \frac{2}{\sqrt{3}} \)
Subject: Chemistry
Why is sulphur dioxide considered as
an air pollutant?
A. It increases the temperature of the atmosphere.
B. It is used as insecticide which causes air pollution.
C. It causes acid rain due to formation of sulphuric acid on combining with \( O_{2} \) and \( H_{2} O \)
D. It is a strong oxidising agent hence oxidises the other components of air.
Subject: Physics
A pendulum bob is held stationary by a horizontal force H. The three forces
acting on the bob are shown in the
diagram.
The tension in the string of the pendulum is T. The weight of the pendulum bob is W.The string is held at
an angle of \( 30^{\circ} \) to the vertical.
Which statement is correct?
A. \( H=T \cos 30 \)
B. \( T=H \sin 30 \)
c. \( W=T \sin 30 \)
D. \( W=T \cos 30 \)
Subject: Maths
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 \( \left(f_{1}\right) \)
Subject: Maths
For the function \( f(x)=e^{x}, a=0, b=1 \)
the value of \( c \) in mean value theorem
will be
\( \mathbf{A} \cdot \mathbf{0} \)
B. \( \log (e-1) \)
\( c \cdot \log x \)
\( D \)
Subject: Maths
Let \( S \) be a relation on the set \( R \) of all
real numbers defined by \( \boldsymbol{S}= \)
\( \left\{(a, b) \in R \times R: a^{2}+b^{2}=1\right\} . \) Prove
that \( S \) is not an equivalence relation on
\( \boldsymbol{R} \)
Subject: Chemistry
The correct order of strength of acidity
of the following compounds is:
A \( . \) (ii) \( >(\mathrm{i})>(\text { iii })>(\text { iv }) \)
B. (i) > (ii) > (iii) > (iv)
\( c \cdot(\text { iv })>(\text { iii })>(\text { ii })>(i \)
\( D \cdot(\text { iv })>(\text { iii })>(i)>(\text { ii }) \)
Subject: Maths
Evaluate: \( \int \frac{1}{x^{2}\left(x^{4}+1\right)^{\frac{3}{4}}} d x ; x=0 \)
\( ^{\mathrm{A}} \frac{\left(x^{4}-1\right)^{\frac{1}{4}}}{x}+c \)
B. \( -\frac{\left(x^{4}+1\right)^{\frac{1}{4}}}{x}+c \)
c. \( \frac{\sqrt{x^{4}+1}}{x}+c \)
D. None of these
Subject: Physics
The dimensional formula of electric
potential is given by
\( \mathbf{A} \cdot\left[M L^{2} T^{-3} A^{-1}\right] \)
B. \( \left[M L^{2} T^{-2} A^{-1}\right] \)
\( \mathbf{c} \cdot\left[M L^{2} T^{-1} A^{-1}\right] \)
D. \( \left[M L^{2} T^{-2}\right] \)
Subject: Maths
Solve \( \left.\boldsymbol{D}=\mid \begin{array}{ccc}\mathbf{1} & -\mathbf{2} & \mathbf{1} \\ \mathbf{2} & \mathbf{1} & -\mathbf{1} \\ \mathbf{1} & \mathbf{3} & \mathbf{1}\end{array}\right] \)
Subject: Physics
During an experiment, an ideal gas is found to obey a condition \( \frac{\boldsymbol{P}^{2}}{\boldsymbol{\rho}}= \)
constant \( [\rho=\text { density of the gas }] \) The gas is initially at temperature \( T \) pressure \( P \) and density \( \rho . \) The gas expands such that density changes to
\( \frac{\rho}{2} \)
This question has multiple correct options
A. The pressure of the gas changes to \( \sqrt{2} P \)
B. The temperature of the gas changes to \( \sqrt{2} T \)
C. The graph of the above process on the P-T diagram is parabola.
D. The graph of the above process on the P-T diagram is hyperbola.
Subject: Chemistry
The boiling point of liquid \( A, B, C \) and \( D \) \( \operatorname{are} 80^{\circ} C, 60^{\circ} C, 90^{\circ} C \) and \( 100^{\circ} C \)
respectively. Which will show highest vapour pressure at room temperature?
\( A \cdot A \)
B. B
\( c \cdot c \)
\( D . \) D
Subject: Biology
Which of the following conditions
correctly describes the manner of
determining the sex in a given
example?
A. \( x \) O condition in humans as found in Klinefelter's
syndrome determines female sex
B. Homozygous sex chromosomes zZ determines female sex in birds
C. \( X O \) type of sex determines male sex in grasshopper
D. Homozygous sex chromosomes \( X X \) produce male in Drosophila
Subject: Physics
Suppose a voltmeter of resistance \( 660 \Omega \) reads the voltage of a very old cell to be
1.32 volt while a potentiometer reads its voltage to be 1.44 volt. The internal resistance of the cell is:
A . \( 30 \Omega \)
B. \( 60 \Omega \)
\( c \cdot 6 \Omega \)
D. \( 0.6 \Omega \)
Subject: Physics
Assertion
In YDSE, if separation between the slits is less than wavelength of light, then no interference pattern can be observed.
Reason

For interference pattern to be observed, light sources have to be coherent.
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: Chemistry
Assertion
Gold sol is hydrophobic and multimolecular.
Reason
Gold sol is prepared by Bredig's arc method.
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: Chemistry
When HCl gas is passed through a
saturated solution of common salt,
pure NaCl is precipitated because
A. HCl is highly ionised in solution
B. HCl is highly soluble in water
C. The solubility product of NaCl is lowered by HC
D. The ionic product of \( \left[N a^{+}\right]\left[C l^{-}\right] \) exceeds the solubility product of NaCl
Subject: Chemistry
Assertion
Emphysema disease is very common in
Kanpur and Kolkata.
Reason
It is a disease of respiratory tract
occuring due to pollution.
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: Chemistry
What are the geometric shape and the oxidation number of the copper atom, respectively, for the complex ion,
\( \left[\boldsymbol{C u}\left(\boldsymbol{N} \boldsymbol{H}_{3}\right)_{4}\left(\boldsymbol{O} \boldsymbol{H}_{2}\right)_{2}\right]^{2+} \)
A. Tetrahedral; +2
B. Square planar; - -
c. Linear; +3
D. Octahedral; +2
Subject: Physics
A block of mass \( M \) with a semicircular
track of radius \( R \) rests on a horizontal
frictionless surface. A uniform cylinder
of radius \( r \) and mass \( m \) is released
from rest from the top point \( \boldsymbol{A} \). The
cylinder steps on the semicircular frictionless track. The distance travelled
by the block when the cylinder reaches
the point \( \boldsymbol{B} \) is :
A \( \cdot \frac{M(R-r)}{M+m} \)
В \( \cdot \frac{m(R-r)}{M+m} \)
c. \( \frac{(M+m) R}{M} \)
D. None of the above
Subject: Maths
The \( 4^{t h} \) term of A.P is equal to 3 times
the first term and the \( 7^{t h} \) term excess
which the third term by 1. Find its \( n^{t h} \) term.
\( \mathbf{A} \cdot n+2 \)
B. \( 3 n+1 \)
c. \( (2 n+1) \)
D. \( 3 n+2 \)
Subject: Physics
A machine gun fires a bullet of mass
\( 40 g \) with a velocity of \( 1200 m s^{-1} . \) The
man holding it can exert a maximum force of \( 144 N \) on the gun. How many
bullets can he fire per second at the
most?
A
B. 3
\( c \cdot 2 \)
\( D \)
Subject: Chemistry
\( A, B, C \) and \( D \) summarize the
properties of sulphuric acid depending on whether it is dilute or concentrated.
\( A= \) Typical acid property \( B= \) Non volatile acid
\( C= \) Oxidizing agent
\( D= \) Dehydrating agent.
Choose the property \( (A, B, C \text { or } D) \) depending on which is relevant to each of the following:
(i) Preparation of Hydrogen chloride gas.
(ii) Preparation of Copper sulphate from copper oxide.
(iii) Action of conc. Sulphuric acid on Sulphur.