AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Chemistry
Assertion: The addition of acid to a
solution buffered to pH 7 slightly lowest the pH.
Reason: \( \mathrm{pH} \) of any neutral solution always lowers on the addition of acids.
A. Both Assertion and Reason are true and Reason is the correct explanation of Assertion
B. Both Assertion and Reason are true but Reason is not the correct explanation of Assertion
c. Assertion is true but Reason is false
D. Assertion is false but Reason is true
E. Both Assertion and Reason are false
Subject: Physics
A student measures the terminal
potential difference (V) of a cell (of emf
\( \varepsilon \) and internal) resistance \( r \) as a
function of the current (I) flowing
through it. The slope and intercept of
the graph between \( V \) and \( I \), then respectively equal to:
\( \mathbf{A} \cdot-\in \) and \( r \)
B. \( \in \) and \( -r \)
c. \( -r \) and \( \epsilon \)
D. \( r \) and \( -\epsilon \)
Subject: Physics
A force \( \overrightarrow{\boldsymbol{F}}=(2 \hat{\boldsymbol{i}}+\boldsymbol{3} \hat{\boldsymbol{j}}-\boldsymbol{5} \hat{\boldsymbol{k}}) \boldsymbol{N} \) acts at a
point \( \vec{r}_{1}=(2 \hat{i}+4 \hat{j}+7 \hat{k}) m . \) The
torque of the force about the point \( \vec{r}_{2}= \) \( (\hat{\mathbf{i}}+\mathbf{2} \hat{\mathbf{j}}+\mathbf{3} \hat{\boldsymbol{k}}) \boldsymbol{m} \) is :
A \( .17 \hat{j}+5 \hat{k}-3 \hat{i}) N m \)
B . \( 2 \hat{i}+4 \hat{j}-6 \hat{k}) N m \)
c. \( 12 \hat{i}-5 \hat{k}+7 \hat{k}) N m \)
D. \( 13 \hat{j}-22 \hat{i}-\hat{k}) N m \)
Subject: Physics
1)
\( I, \) is placed in a horizontal plane near a
long straight conductor carrying steady
current \( I_{1} \) at a distance \( d \) from the
conductor as shown in figure. The loop
will experience
A. A net repulsive force away from the conductor
B. A net torque acting upward perpendicular to the horizontal plane
c. A net torque acting downward normal to the horizontal plane
D. A net attractive force towards the conductor
Subject: Maths
Rakesh consumes an average of 1680 calories per day.On the day of his finals, Rakesh consumes \( 12 \% \) more calories
per day than he usually does. During the last day of finals, he celebrates by consuming an additional 900 calories. Which of the following represents the total number of calories Rakesh
consumes during d days of finals?
A. \( 1.12(1680 d+900) \)
в. \( 1.12(1680 d)+900 \)
c. \( 1.12(1680+900) d \)
D. \( (180+0.12 d)+900 \)
Subject: Maths
If \( \boldsymbol{y}=\boldsymbol{a}^{\boldsymbol{x}}+\log \boldsymbol{x}+\boldsymbol{3} \boldsymbol{x}^{2}, \) find \( \frac{\boldsymbol{d} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}} \)
Subject: Maths
toppr
Q Type your question_
or \( x \) between the oralnates \( x=a \) メ \( x= \)
\( b, \) is given by definite integral
\( \int_{a}^{b} y d x \) or \( \int_{a}^{b} f(x) d x \) and the area
bounded by the curve \( x=f(y), \) the axis
of \( y \& \) two abscissae \( y=c \& y=d \) is
given by \( \int_{c}^{d} x d y \) or \( \int_{c}^{d} f(x) d y . \) Again if
we consider two curves \( \boldsymbol{y}=\boldsymbol{f}(\boldsymbol{x}), \boldsymbol{y}= \)
\( g(x) \) where \( f(x) \geq g(x) \) in the interval
\( [a, b] \) where \( x=a \& x=b \) are the
points of intersection of these two
curves Shown by the graph given
Then area bounded by these two curves
is given by
\( \int_{a}^{b}[\boldsymbol{f}(\boldsymbol{x})-\boldsymbol{g}(\boldsymbol{x})] \boldsymbol{d} \boldsymbol{x} \)
On the basis of above information
answer the following questions.
The area bounded by parabolas \( \boldsymbol{y}= \)
\( x^{2}+2 x+1 \& y=x^{2}-2 x+1 \) and the
line \( y=\frac{1}{4} \) is equal to
\( \mathbf{A} \)
square unit
B. \( \overline{3} \) square unit
\( c \)
\( \overline{2} \) square unit
D. 2 square unit
Subject: Physics
If in Bohr's atomic model, it is assumed that force between electron the proton
varies inversely as \( r^{4}, \) b energy of the system will be proportional to:
\( \mathbf{A} \cdot n^{2} \)
B . \( n^{4} \)
\( c \cdot n^{6} \)
D. \( n^{8} \)
Subject: Physics
Three identical. spheres of mass in each are placed at the corners of an equilateral triangle of side 2 in. Taking one of the corner as the origin, the
position vector of the centre of mass is
\( \mathbf{A} \cdot \sqrt{3}(\hat{i}-\hat{j}) \)
B. \( \frac{i}{\sqrt{3}}+\hat{j} \)
\( c \cdot \frac{i+3}{3} \)
D. \( \hat{i}+\frac{j}{\sqrt{3}} \)
Subject: Maths
\( \boldsymbol{A}=\left[\begin{array}{cc}\boldsymbol{a} & \boldsymbol{b} \\ \mathbf{0} & \boldsymbol{c}\end{array}\right] \) then \( \boldsymbol{A}^{-1}+(\boldsymbol{A}-\boldsymbol{a} \boldsymbol{I})(\boldsymbol{A}-1) \)
\( \boldsymbol{c} \boldsymbol{I})= \)
A \( \cdot \frac{1}{a c}\left[\begin{array}{cc}a & b \\ 0 & -c\end{array}\right] \)
в. \( \frac{1}{a c}\left[\begin{array}{cc}-a & b \\ 0 & c\end{array}\right] \)
c. \( \frac{1}{a c}\left[\begin{array}{cc}c & -b \\ 0 & a\end{array}\right] \)
D \( \cdot \frac{1}{a c}\left[\begin{array}{cc}c & b \\ 0 & a\end{array}\right] \)
Subject: Physics
An object is placed upright on the axis of a thin convex lens at a distance of
four focal lengths \( (4 f) \) from the center of the lens. An inverted image appears at a distance of \( \frac{4}{3} f \) on the other side of the lens. What is the ratio of the height of the image of the height of the object?
A . \( 1 / 3 \)
B. \( 3 / 4 \)
c. \( 4 / 3 \)
D. 3/1
Subject: Chemistry
\( \boldsymbol{X}+\boldsymbol{H}_{2} \boldsymbol{O} \rightarrow \boldsymbol{Y} \)
\( Y \) is used to remove grease stains from
woollen clothes. Identify \( \boldsymbol{X} \) and \( \boldsymbol{Y} \)
А. \( X=H C l, Y=N a O H \)
B. \( X=N H_{4} O H, Y=N H_{3} \)
c. \( X=N H_{3}, Y=N H_{4} O H \)
D. None of these
Subject: Chemistry
Select the correct statement:
This question has multiple correct options
A. The value of compressibility factor \( ^{\prime} Z^{\prime} \) for \( H_{2} \) gas is greater than one at room temperature and pressure
B. The real gas behaves as an ideal gas at Boyle's temperature.
C. For a real gas following van der Waals' equation of state, the expression of critical temperature is \( \frac{8 a}{27 R . b} \)
D. At low pressure, the compressibility factor \( ^{\prime} Z^{\prime}=1+ \)
\( \frac{P . b}{R T} \) for a van der Waals' gas
Subject: Chemistry
For this reaction relate \( \Delta \boldsymbol{H} \) and \( \boldsymbol{\Delta} \boldsymbol{U} \)
\( \mathbf{2} N \boldsymbol{O}_{2}(\boldsymbol{g}) \quad \longrightarrow \boldsymbol{N}_{2} \boldsymbol{O}_{4}(\boldsymbol{g}) \)
A. \( \Delta H=\Delta U \)
в. \( \Delta H>\Delta U \)
\( \mathbf{c} \cdot \Delta H<\Delta U \)
D. None of these
Subject: Chemistry
The precipitate of \( M_{2} S_{3} \) obtained on
mixing equal volumes of solutions \( \boldsymbol{S}_{1} \)
having \( \left[M^{3+}\right]=4 \times 10^{-5} M \) and \( S_{2} \)
having \( \left[S^{2-}\right]=2 \times 10^{-3} M . \) Calculate
its solubility product.
Subject: Physics
An isotropic point source emits light with wavelength 500nm. The radiation
power of the source is \( \boldsymbol{P}=\mathbf{1 0} \boldsymbol{W} \). Find
the number of photons passing through unit area per second at a distance of
\( 3 m \) from the source
A \( .5 .92 \times 10^{17} / m^{2} s \)
B . \( 2.23 \times 10^{17} / m^{2} s \)
c. \( 2.23 \times 10^{18} / m^{2} s \)
D. \( 5.92 \times 10^{18} / m^{2} s \)
Subject: Chemistry
For the reaction between \( M n O_{4}^{-} \) and
\( C_{2} O_{4}^{-} \) in basic solution, the unbalanced equation is as follows:
\( M n O_{4}^{-}+C_{2} O_{4}^{2-} \longrightarrow M n O_{2}(s)+ \)
\( \boldsymbol{C O}_{3}^{2-} \)
In a balanced equation, the number of
\( O H^{-} \) ions on the right is :
Subject: Maths
A man running round a race course notes that the sum of the distance of
two flag posts from him is always \( 10 m \) and the distance between the flag posts
is 8 m. The area of the path he encloses
in square metres is:
A . \( 15 \pi \)
в. \( 20 \pi \)
c. \( 27 \pi \)
D. \( 30 \pi \)
Subject: Physics
For a body starting from rest, what will be the ratio of the distance travelled by
the body the 4 th and 3 rd second during its journey?
A \( \cdot \frac{7}{5} \)
в. \( \frac{7}{3} \)
\( c \cdot \frac{5}{7} \)
D. \( \frac{3}{7} \)
Subject: Biology
Match the items given in Column I with
those in Column II and select the correct
options given below:
Column I
Fibrinogen osmotic balance
Globulin 2 Blood clotting
Defence Albumin \( \quad 3 \quad \) mechanism
A. \( A-1, B-3, C-2 \)
B. \( A-3, B-2, C-1 \)
c. \( A-2, B-3, C-1 \)
D. \( A-1, B-2, C-3 \)
Subject: Chemistry
Which of the following statements is
correct for \( \boldsymbol{C} \boldsymbol{s} \boldsymbol{B} \boldsymbol{r}_{3} \)
A. It is covalent compound
B. It contains \( C s^{3+} \) and \( B r \)
c. It contains \( C s^{+} \) and \( B r_{3}^{-} \)
D. It contains \( C s^{+} \) and \( B r^{-} \) and lattice \( B r_{2} \) molecule
Subject: Maths
Find the value of \( \tan ^{-1}\left(\frac{1}{2} \tan 2 A\right)+ \)
\( \tan ^{-1}(\cot A)+\tan ^{-1}\left(\cot ^{3} A\right), \) for \( 0< \)
\( \boldsymbol{A}<\frac{\boldsymbol{\pi}}{\boldsymbol{4}} \)
\( \mathbf{A} \cdot-\pi / 2 \)
в. \( +\pi / 2 \)
c. \( -\pi \)
D. \( +\pi \)
Subject: Chemistry
Select the correct statements.
(I) Increase in relative humidity decreases the density of air
(II) Increase in relative humidity decreases the rate of evaporation of
water
(III) Increase in relative humidity
decreases the velocity of sound
(IV) Increase in relative humidity increases the velocity of sound
A . ।, ॥, । v
в. ।, и, III
\( c \cdot 1,1 \)
D. I, IV
Subject: Physics
An object of mass \( \mathrm{m} \) rests on a plane
inclined at an angle of \( \theta . \) What is the
maximum value for the coefficient
of static friction at which the object will slide down the incline?
A \( . \sin \theta-\cos \theta \)
B. \( \cos \theta-\sin \theta \)
c. mgsint
D. \( \sin \theta / \cos \theta \)
E. \( \sin \theta+\cos \theta \)
Subject: Chemistry
In cyanide method, silver metal is
obtained as given in the following
reaction:
\( \mathbf{2} \boldsymbol{K}\left[\boldsymbol{A} \boldsymbol{g}(\boldsymbol{C} \boldsymbol{N})_{2}\right]+\boldsymbol{Z} \boldsymbol{n} \longrightarrow \)
\( \boldsymbol{K}_{2}\left[\boldsymbol{Z} \boldsymbol{n}(\boldsymbol{C} \boldsymbol{N})_{4}\right]+\boldsymbol{2} \boldsymbol{A} \boldsymbol{g} \)
In this :
A. \( A g \) has been oxidised and \( Z n \) has been reduced
B. \( A g^{+} \) has been reduced and \( Z n \) has been oxidised
c. both the metals have been oxidised
D. both the metals have been reduced
Subject: Physics
The potential energy function associated with the force \( \overrightarrow{\boldsymbol{F}}=\mathbf{4 x y} \hat{\mathbf{i}}+ \)
\( 2 x^{2} \hat{j} \) is
A \( \cdot U=-x^{2} y \)
B . \( U=-2 x^{2} y+ \) constant
C. \( U=2 x^{2} y+ \) constant
D. Not defined
Subject: Maths
If \( n \) is a positive integer and \( (5 \sqrt{5}+ \)
\( \mathbf{1 1})^{2 n+1}=I+f \) where I is an integer
and \( 0<f<1 \) then
This question has multiple correct options
A. I is an even integer
B. \( (I+f)^{2} \) is divisible by \( 2^{2 n+1} \)
c. lis divisible by 22
D. None of these
Subject: Chemistry
Assertion
The para-isomers have higher melting point as compared to their ortho and meta-isomers.
Reason
It is due to symmetry of para-isomers that fits in crystal lattice better as
compared to ortho- and meta-isomers.
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
The degree measure of 1 radian (taking \( \left.\boldsymbol{\pi}=\frac{\boldsymbol{2} \boldsymbol{2}}{\boldsymbol{7}}\right) \) is
A \( \cdot 55^{\circ} 61^{\prime} 22^{\prime \prime} \) (approx.)
В \( \cdot 57^{\circ} 16^{\prime} 22^{\prime \prime} \) (approx.)
c. \( 57^{\circ} 22^{\prime} 16^{\text {" }} \) (approx.)
D. \( 57^{\circ} 22^{\prime} 22^{\prime \prime} \) (approx.)
Subject: Chemistry
\( 10 \mathrm{mL} \) of a gaseous hydrocarbon is exploded with 100 mL of oxygen. The residual gas on cooling is found to
measure \( 95 \mathrm{mL} \) of which \( 20 \mathrm{mL} \) is
absorbed by caustic soda and the remainder by alkaline pyrogallol. The
formula of the hydrocarbon is :
A \( . C H_{4} \)
в. \( C_{2} H_{6} \)
\( \mathbf{c} \cdot C_{2} H_{4} \)
D. \( C_{2} H_{2} \)
Subject: Maths
The length of the latusrectum of an ellipse is equal to one-half of its minor axis. Then the eccentricity of the ellipse is :
A \( \cdot \frac{\sqrt{3}}{2} \)
B. \( \frac{\sqrt{2}}{3} \)
c. \( \frac{1}{\sqrt{3}} \)
D. \( \frac{1}{\sqrt{2}} \)
Subject: Physics
A charged particle \( q \) is shot from a large
distance towards another charged particle \( Q \) which is fixed, with a speed \( v \)
t approaches \( Q \) up to a closest distance \( r \) and then returns. If \( q \) were
given a speed \( 2 v, \) the distance of
approach would be
\( A \)
B. \( 2 r \)
c. \( r / 2 \)
D. \( r / 4 \)
Subject: Maths
Examine whether the given function \( f(x) \) is continuous at \( x=3 \)
\[
\begin{array}{c}
\boldsymbol{f}(\boldsymbol{x})= \\
\frac{\boldsymbol{x}^{4}-\boldsymbol{8} \boldsymbol{x}}{\sqrt{\boldsymbol{x}^{2}+\mathbf{5}}-\mathbf{3}}, \quad \text { for } \quad \boldsymbol{x} \neq \boldsymbol{3} \\
\boldsymbol{3} \quad \text { for } \quad \boldsymbol{x}=\mathbf{3}
\end{array}
\]
\[
\boldsymbol{f}(\boldsymbol{x})=\mathbf{3}
\]
Subject: Chemistry
A flask has a volume of \( 0.25 d m^{3} . \) What
volume of air will be displaced from the
flask if it is heated from \( 300 K \) to
\( \mathbf{3 6 0} \boldsymbol{K} ? \)
\( \mathbf{A} \cdot 0.25 d m^{3} \)
в. \( 0.5 d m^{3} \)
c. \( 0.05 d m^{3} \)
D. None of these
Subject: Chemistry
Consider the following properties of the
noble gases:
I: they readily from compounds
which are colourless.
II : they generally do not form ionic
compounds. III : they have variable oxidation states
in their compounds. \( I V: \) they generally do not form covalent compounds.
Select the the correct properties.
A. \( I, I I \) and \( I I I \) only
B. II and III only
C. \( I \) and \( I I I \) only
D. I only
Subject: Chemistry
An element with the electron
configuration \( [\boldsymbol{X} \boldsymbol{e}] \boldsymbol{4} \boldsymbol{f}^{14} \boldsymbol{5} \boldsymbol{d}^{7} \boldsymbol{6} \boldsymbol{s}^{2} \) is:
A. an alkaline earth element
B. a transition element
c. an inertgas
D. a rare earth
Subject: Chemistry
Addition of ethylene glycol (non-volatile) to water lowers the freezing point of water and hence it is used as antifreeze.
Addition of any substance to water
lowers its freezings point of water.
A. Statement-1 is true, statement-2 is true and statement-2 is correct explanation for statement-
B. Statement-1 is true, statement-2 is true and statement-2 is NOT the correct explanation for statement-1
C. Statement-1 is true, statement-2 is false
D. Statement-1 is false, statement-2 is true
Subject: Maths
Consider an ellipse \( \frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}=1 \) What is the area included between the ellipse and the greatest rectangle inscribed in the ellipse?
A \( . a b(\pi-1) \)
B. \( 2 a b(\pi-1) \)
c. \( a b(\pi-2) \)
D. None of the above
Subject: Physics
In an experiment, setup \( A \) consists of two parallel wires which carry currents
in opposite directions as shown in the figure. \( A \) second setup \( B \) is identical to
setup \( A \), except that there is a metal
plate between the wires.

Let \( F_{A} \) and \( F_{B} \) be the magnitude of the
force between the two wires in setup \( \boldsymbol{A} \)
and \( B, \) respectively, then which of the following condition is correct:
\( \mathbf{A} \cdot F_{A}>F_{B} \neq 0 \)
B . \( F_{A}<F_{B} \)
c. \( F_{A}=F_{B} \neq 0 \)
D. \( F_{A}>F_{B}=0 \)
Subject: Chemistry
An unknown chlorohydrocarbon as 3.55 \( \% \) of chlorine. If each molecule of the
hydrocarbon has one chlorine atom only
chlorine atoms present in \( 1 g \) of
chlorohydrocarbon are: (Atomic wt. of \( C l=35.5 u ; \) Avogadro constant \( = \)
\( 6.023 \times 10^{23} m o l^{-1} \)
A. \( 6.032 \times 10^{9} \)
В. \( 6.032 \times 10^{23} \)
c. \( 6.032 \times 10^{2} \)
D. \( 6.032 \times 10^{20} \)
Subject: Physics
Which of the following statements is
true?
A. A convex lens has 4 dioptre power having a focal length \( 0.25 \mathrm{m} \)
B. A convex lens has 4 dioptre power having a focal length \( 0.125 \mathrm{m} \)
C. A concave lens has 4 dioptre power having a focal length \( 0.25 \mathrm{m} \)
D. A concave lens has 4 dioptre power having a focal length \( 0.125 \mathrm{m} \)
Subject: Maths
A circle has the equation \( (x+1)^{2}+ \)
\( (y-3)^{2}=16 \) What are the coordinates
of its center and the length of its
radius?
A. (-1,3) and 4
B. (1,-3) and 4
c. (-1,3) and 16
D. (1,-3) and 16
Subject: Maths
A particle's velocity \( v \) at time \( t \) is given by \( v=2 e^{2 t} \cos \frac{\pi t}{3} . \) The least value of \( t \) at
which the acceleration becomes zero is
\( \mathbf{A} \cdot \mathbf{0} \)
в. \( \frac{3}{2} \)
\( ^{\mathrm{c}} \cdot \frac{3}{\pi} \tan ^{-1}\left(\frac{6}{\pi}\right) \)
D. \( \frac{3}{\pi} \cot ^{-1}\left(\frac{6}{\pi}\right) \)
Subject: Physics
Each wire in Fig. has cross-section area
\( 5 \times 10^{-3} c m^{2} \) and \( Y=2 \times 10^{11} P a . P, Q \)
and R have mass \( 3 k g \) each. Find the
strain developed in A. Assume surface
to be smooth.
A \( \cdot 10^{-5} \)
B. \( 10^{-6} \)
c. \( 10^{-4} \)
D. none
Subject: Maths
Factorise the expression: \( (x-2 y+ \)
\( 3 z)^{2} \)
\( \mathbf{A} \cdot x^{2}+y^{2}+9 z^{2}-4 x y+12 y z+6 z x \)
B . \( x^{2}+y^{2}+9 z^{2}-4 y-12 y z+6 z x \)
\( \mathbf{c} \cdot x^{2}+4 y^{2}+9 z^{2}-4 x y-12 y z+5 z x \)
D. \( x^{2}+4 y^{2}+9 z^{2}-4 x y-12 y z+6 z x \)
Subject: Chemistry
Which of the following will yield a mixture of 2-chlorobutene and 3
chlorobutene on treatment with \( \boldsymbol{H} \boldsymbol{C l} \) ?
A. \( C H_{2}=C=C H=C H_{3} \)
в. \( H_{2} C=\begin{array}{c}C-C H=C H_{2} \\ C H_{3}\end{array}-C H=C \)
c. \( C H_{2}=C H-C H=C H_{2} \)
D. \( H C \equiv C-C H=C H_{2} \)
Subject: Physics
Complete the table given below:
\( \begin{array}{llll}\text { Element } & \begin{array}{l}\text { Atomic } \\ \text { mass }\end{array} & \begin{array}{l}\text { Molecular } \\ \text { mass }\end{array} & \begin{array}{l}\text { Atomicit } \\ \text { number }\end{array} \\ \text { Chlorine } & 35.5 & 71 & - \\ \text { Ozone } & - & 48 & 3 \\ \text { Sulphur } & 32 & - & 8 \\ \text { Nitrogen } & 14 & - & 2\end{array} \)
Subject: Physics
A nucleus \( z X^{A} \) emits \( 9 \alpha \) -particles and 5 \( p \) particle. The ration of total protons
and neutrons in the final nucleus is:
A \( \frac{(Z-13)}{(A-Z-23)} \)
B. \( \frac{(Z-18)}{(A-36)} \)
c. \( \frac{(Z-23)}{(A-Z-8)} \)
D. \( \frac{(Z-13)}{(A-Z-13)} \)
Subject: Physics
1.0 \( \mathrm{kg} \) of water is contained in a \( 1.25 \mathrm{kW} \) kettle. Calculate the time taken for the
temperature of water to rise from \( 25^{\circ} C \)
to its boiling point \( 100^{\circ} \mathrm{C} \). Specific heat
capacity of water \( =4.2 J g^{-1} K^{-1} \)
Subject: Physics
If the distance travel by a uniformly
accelerated particle in \( p \) th \( , q t \) and \( r t h \) second are \( a, b \) and \( c \) respectively. Then
A \( .(q-r) a+(r-p) b+(p-q) c=1 \)
B. \( (q-r) a+(r-p) b+(p-q) c=-1 \)
c. \( (q-r) a+(r-p) b+(p-q) c=0 \)
D. \( (q+r) a+(r+p) b+(p+q) c=0 \)
Subject: Maths
If a and x represent real numbers for
which \( x^{2}=-a, \) which of the following
statements could be true?
I. \( a>0 \)
II. \( \boldsymbol{a}=\mathbf{0} \)
III. \( \boldsymbol{a}<\mathbf{0} \)
A. None
B. II only
c. ॥ा only
D. I and II only
E. II and III only
Subject: Physics
A ring rolls without slipping on the
ground. Its centre \( C \) moves with a
constant speed \( u . P \) is any point on the
ring. The speed of \( P \) with respect to the
ground is \( \boldsymbol{v} \) This question has multiple correct options
A \( .0 \leq v \leq 2 u \)
B. \( v=u \), if \( C P \) is horizontal
c. \( v=u \), if \( C P \) makes and angle of \( 30^{\circ} \) with horizontal and \( P \) is below the horizontal level of \( C \)
D. \( v=\sqrt{2} u \), if \( C P \) is horizontal
Subject: Physics
A battery of 20 cells (each having e.m.f. 1.8 volt and internal resistance 0.1 ohm
is charged by 220 volts and the charging current is 15 A. The resistance to be put in the circuit is
A . 10.27 ohms
B. 12.27 ohms
c. 8.62 ohms
D. 16.24 ohms
Subject: Maths
Find the value of \( \left(\frac{a}{b-1}\right)+ \) \( \left(\frac{a}{b-1}\right)^{2}+\left(\frac{a}{b-1}\right)^{3} \) if \( a+2 b=2 \)
A . -6
B. 8
c. 10
D. -12
E . 14
Subject: Maths
If \( x_{1}, x_{2}, \dots . . x_{n} \) are \( n \) values of a variable
\( X \) and \( y_{1}, y_{2}, \dots . y_{n} \) are \( n \) values of \( a \)
variable \( \boldsymbol{Y} \) such that \( \boldsymbol{y}_{i}= \)
\( \frac{\boldsymbol{x}_{i}-\boldsymbol{a}}{\boldsymbol{h}} ; \quad \boldsymbol{i}=\mathbf{1}, \boldsymbol{2}, \ldots . ., \boldsymbol{n}, \) then
A. \( \operatorname{Var}(Y)=\operatorname{Var}(X) \)
B. \( \operatorname{Var}(X)=h^{2} \operatorname{Var}(Y) \)
C \( . \operatorname{Var}(Y)=h^{2} \operatorname{Var}(X) \)
D. \( \operatorname{Var}(X)=h^{2} \operatorname{Var}(Y)+a \)
Subject: Physics
In Young's double slit experiment shows
in figure, \( S_{1} \) and \( S_{2} \) are coherent
sources and \( \mathrm{S} \) is the screen having a
hole at a point \( 1.0 \mathrm{mm} \) away from the
central line. White light \( (400 \text { to } 700 \) nm)
is sent through the slits. Which
wavelength passing through the hole
has the strongest intensity?
A. \( 400 \mathrm{nm} \)
B. 700 nm
\( c .500 \mathrm{nm} \)
D. 667 nm
Subject: Chemistry
Which among the following equations represents the reduction reaction taking place in lead accumulator at positive electrode, while it is being used as a source of electrical energy?
\( \mathbf{A} \cdot P b \rightarrow P b^{2} \)
B. \( P b^{4+} \rightarrow P b \)
\( \mathbf{c} \cdot P b^{2+} \rightarrow P b \)
D. \( P b^{4+} \rightarrow P b^{2} \)
Subject: Physics
In a Young's double slit experiment, the
intensity at the cetral maximum is \( l_{0-} \)
The intensity ata distance \( \beta / 4 \) from the central maximum is ( \( \beta \) is frige width)
A \( \cdot l_{0} \)
в. \( \frac{l_{0}}{2} \)
c. \( \frac{l_{0}}{\sqrt{2}} \)
D. \( \frac{l_{0}}{4} \)
Subject: Chemistry
A current of \( 4.0 \mathrm{A} \) is passed for 5 hours
through 1L of 2M solution of nitrate using two nickel electrodes. The molarity of the solution at the end of the electrolysis will be:
A . 1.5 м
в. 1.2
c. \( 2.5 \mathrm{M} \)
D. 2.0 M
Subject: Physics
A point object is placed at a distance of
\( 25 \mathrm{cm} \) from a convex lens of focal length
\( 20 \mathrm{cm} . \) If a glass slab of thickness \( t \) and
refractive index 1.5 is inserted between
the lens and the object, the image is formed at infinity. The thickness \( t \) is
\( \mathbf{A} \cdot 10 \mathrm{cm} \)
в. \( 5 \mathrm{cm} \)
\( \mathbf{c} \cdot 20 c m \)
D. \( 15 \mathrm{cm} \)
Subject: Chemistry
Assertion
Chlorine gas disproportionate in hot \( \& \) conc. NaOH solution
Reason
NaCl and NaOCl are formed in the above
reaction.
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: Physics
The magnitude of electric field intensity E, such electron, placed in the field, would experience an electric force equal to its weight is :
A \( \cdot 5.6 \times 10^{-7} N C^{-1} \)
B . \( 5.6 \times 10^{-8} N C^{-1} \)
c. \( 5.6 \times 10^{-10} N C^{-1} \)
D. \( 5.6 \times 10^{-11} \mathrm{NC}^{-1} \)
Subject: Chemistry
The specific conductivity of \( 0.1 \mathrm{N} \) KCl solution is 0.0129 ohm \( ^{-1} \mathrm{cm}^{-1} \). The
resistance of the solution in the cell is
100 \( \Omega \). The cell constant of the cell will
be
A . 1.10
B. 1.29
c. 0.56
D. 2.80
Subject: Maths
Image of point \( \mathrm{P}(1,2,3) \) with respect to plane \( \boldsymbol{x}+\boldsymbol{y}+\boldsymbol{z}=\mathbf{1 2}, \) is
A. (5,4,3)
)
B. (9,6,3)
c. (5,6,7)
D. (3,4,5)