AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Physics
A coin is released inside a lift at a
height of \( 2 \mathrm{m} \) from the floor of the lift. The height of the lift is 10 m. The lift is
moving with an acceleration of \( 9 m / s^{2} \) downwards. The time after which the
coin will strike the lift is :
\( A \cdot 4 s \)
B. 2 s
c. \( \frac{4}{\sqrt{21}} s \)
D. \( \frac{2}{\sqrt{11}} s \)
Subject: Maths
A random variable \( \boldsymbol{X} \) has the following probability distribution:
\[
\begin{array}{lcccc}
\begin{array}{l}
\text { Values } \\
\text { of } \mathbf{X}:
\end{array} & -2 & -1 & 0 & 1 \\
\hline P(x): & 0.1 & \mathrm{k} & 0.2 & 2 \mathrm{k} \\
& & & & \\
& P(x): & & &
\end{array}
\]
Find the value of \( a, \) if \( k=\frac{1}{a} \)
Subject: Maths
\( A B C \) is an isosceles triangle, If the
coordinates of the base are \( B(1,3) \) and
\( C(-2,7), \) the coordinates of vertex \( A, \) is
\( ^{\mathbf{A}} \cdot\left(-\frac{1}{2},-4\right) \)
в. (1,6)
\( ^{c} \cdot\left(\frac{5}{6}, 6\right) \)
D. None of these
Subject: Maths
f \( x \) \& y are in direct proportion then find the value of a
\( \boldsymbol{x} \mathbf{2} \mathbf{3} \mathbf{5} \)
\( \boldsymbol{y} \boldsymbol{4} \boldsymbol{6} \boldsymbol{a} \mathbf{1 4} \)
A . 8
B. 10
c. 15
D. 20
Subject: Chemistry
Maximum boiling point would be shown by:
A. \( C H_{3}-O-C H_{3} \)
в. \( C_{2} H_{5}-O-C_{2} H_{5} \)
c. \( C H_{3}-C H_{2}-C H_{2}-O H \)
D. \( \left(C H_{3}\right)_{2} C H-O H \)
Subject: Maths
Value of \( \int \frac{d x}{x^{2}\left(x^{4}+1\right)^{3 / 4}} \) is :
A \( -\left(1+\frac{1}{x^{4}}\right)^{\frac{1}{4}}+c \)
B. \( \quad\left(1+\frac{1}{x^{4}}\right)^{\frac{1}{4}}+c \)
c. \( \quad-\left(1-\frac{1}{x^{4}}\right)^{\frac{1}{4}}+c \)
D. None of these
Subject: Maths
If the sum of \( m \) terms of an arithmetical
progression is equal to the sum of
either the next \( n \) terms or the next \( p \) terms, then \( \left(\frac{n+m}{n-m}\right)\left(\frac{p-m}{p+m}\right) \) is
A \( \cdot \frac{n}{p} \)
в. \( \frac{p}{n} \)
c. \( n p \)
D. \( \frac{p}{m} \)
Subject: Chemistry
\( 25 \mathrm{mL} \) samples of distilled water, tap
water and boiled water required,
respectively, \( 1 \mathrm{mL}, 13 \mathrm{mL} \) and \( 5 \mathrm{mL} \) of soap solution to form a permanent
lather. The ratio of temporary to permanent hardness in the tap water is :
A .3: 2
B . 2: 3
\( c \cdot 1: 2 \)
D. 2: 1
Subject: Maths
\( \int e^{x} \frac{x-1}{(x+1)^{3}} d x \) is equal to
A \( \cdot \frac{e^{x}}{x+1}+C \)
в. \( \frac{e^{x}}{(x+1)^{2}}+C \)
c. \( -\frac{e^{x}}{x+1}+C \)
D. \( -\frac{e^{x}}{(x+1)^{2}}+C \)
Subject: Physics
A step-up transformer operates on a \( 230 \mathrm{V} \) line and supplies aload of 2 amp. The ratio of the primary and secondary windings is \( 1: 25 . \) The current in the primary is
\( A \cdot 15 A \)
B. 12.5 A
\( c \cdot 25 A \)
D. 50 A
Subject: Physics
A rocket of mass \( 4000 \mathrm{kg} \) is set for
vertical firing. How much gas must be ejected per second so that the rocket may have initial upwards acceleration of magnitude \( 19.6 ~ m / s^{2} ? \) [Exhaust speed of fuel \( =\mathbf{9 8 0 m / s} \)
A. \( 240 \mathrm{kg} / \mathrm{s} \)
в. \( 80 \mathrm{kg} / \mathrm{s} \)
c. \( 120 \mathrm{kg} / \mathrm{s} \)
D. None
Subject: Chemistry
If \( \boldsymbol{E}^{o}_{\boldsymbol{F} e^{2+} / \boldsymbol{F} e}=\boldsymbol{x}_{1} \boldsymbol{V} \) and \( \boldsymbol{E}^{o}_{\boldsymbol{F} e^{3+} / \boldsymbol{F} e^{2+}}= \)
\( \boldsymbol{x}_{2} \boldsymbol{V}, \) then \( \boldsymbol{E}^{o} \boldsymbol{F e}^{3+} / \boldsymbol{F} e \) will be :
A \( \cdot\left(2 x_{1}+x_{2}\right) V \)
В . \( \left(3 x_{2}-x_{1}\right) V \)
\( \mathbf{c} \cdot\left(2 x_{1}+x_{2}\right) / 3 V \)
\( \mathbf{D} \cdot\left(x_{1}+2 x_{2}\right) / 3 V \)
Subject: Maths
If \( \boldsymbol{y}=\boldsymbol{4}^{l o g_{2} \sec x}-\boldsymbol{9}^{l o g_{3} t a n x}, \) then \( \frac{\boldsymbol{d} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}}= \)
\( \mathbf{A} \cdot \mathbf{0} \)
B.
c. 2
D. 3
Subject: Maths
Find the values of \( c \) that satisfy the MVT for integrals on \( [\mathbf{0}, \mathbf{1}] \) \( \boldsymbol{f}(\boldsymbol{x})=\boldsymbol{x}(\mathbf{1}-\boldsymbol{x}) \)
A \( c_{c}=\frac{1}{2} \)
B. \( c=-\frac{1}{2} \)
c. \( _{c=\frac{2}{3}} \)
D. \( c=-\frac{1}{3} \)
Subject: Chemistry
Choose the correct oxidation states of
Chlorine in species:
This question has multiple correct options
\( \mathbf{A} \cdot(\mathrm{a}) \mathrm{HOCl}-+1 \)
B. (b) \( H O C l O-+3 \)
\( \mathbf{c} \cdot(\mathrm{c}) H O B r-+3 \)
D. (d) \( H O B r O_{2}-+5 \)
E \( \cdot(\text { e }) H O I O_{3}-+7 \)
\( F \cdot(f) H O C l O_{3}-+5 \)
G. None of the above
Subject: Physics
A man \( m=80 k g \) is standing on a
trolley of mass \( 320 \mathrm{kg} \) on a smooth surface. If man starts walking on trolley along rails at a speed of \( 1 \boldsymbol{m} / \boldsymbol{s}, \) then
after 4 sec, his displacement relative to
ground is
A . \( 4 m \)
B. \( 4.8 m \)
c. \( 3.2 m \)
D. \( 6 m \)
Subject: Physics
The electric field between the inside
and outside layers is:
A \( \cdot 10^{6} V m^{-1} \)
В. \( 5 \times 10^{6} V m^{-1} \)
c. \( 0.2 \times 10^{7} V m^{-1} \)
D. \( 10^{7} V m^{-1} \)
Subject: Physics
The length,breadth and thickness of a rectangular copper sheet are \( 4 c m, 2.5 c m \) and \( 1.56 c m \) respectively.
Find the area of the sheet to corrected
significant figures.
A \( \cdot 40.3 \mathrm{cm}^{2} \)
B . \( 40.28 \mathrm{cm}^{2} \)
c. \( 40 \times 10^{2} \mathrm{cm}^{2} \)
D. \( 0.4 \times 10^{2} \mathrm{cm}^{2} \)
Subject: Maths
Find the cube of \( 3 a-2 b \)
B . \( a^{3}-54 a^{2} b+6 a b^{2}-b^{3} \)
\( \mathbf{c} \cdot 27 a^{3}-54 a^{2} b+6 a b^{2}-8 b^{3} \)
D. \( a^{3}-54 a^{2} b-36 a b^{2}-8 b^{3} \)
Subject: Chemistry
ASSERTION: In froth floatation process,
sodium ethyl xanthate is used as a collector.

REASON: Sulphide ores are water soluble.
A. If both assertion and reason are CORRECT, and the reason is the CORRECT explanation of the assertion
B. If both assertion and reason are CORRECT, but the reason is NOT the CORRECT explanation of the assertion
C. If assertion is CORRECT but reason is INCORRECT.
D. If assertion is INCORRECT but reason is CORRECT.
Subject: Chemistry
The I.U.P.A.C name for \( \boldsymbol{K}_{\mathbf{3}}\left[\boldsymbol{C o}\left(\boldsymbol{N} \boldsymbol{O}_{2}\right)_{\boldsymbol{6}}\right] \) is
A. Potassium(I) hexanitrocobaltate (II)
B. Potassium(I) hexanitrocobaltate (IV)
c. Potassium hexanitrocobalt (0)
D. Potassium hexanitritocobaltate (III)
Subject: Chemistry
Boiling point of an organic compound is \( 310 K . \) Its enthalpy of vaporisation per mole \( \Delta_{v a p} H \) is \( 27.9 k J m o l^{-1} . \) If the
entropy of vaporisation \( \Delta_{v a p} S \) of organic compound is \( X \) then find out the value of \( X \)
A \( \cdot X=0.09 k J K^{-1} m o l^{-1} \)
B. \( X=-0.09 k J K^{-1} m o l^{-1} \)
c. \( X=0.18 k J K^{-1} m o l^{-1} \)
D. None of these
Subject: Maths
Find the volume of a cube of edge \( 6 \mathrm{cm} \)
\( \mathbf{A} \cdot 64 \mathrm{cm}^{3} \)
В. \( 125 \mathrm{cm}^{3} \)
\( c \cdot 216 c m^{3} \)
D. \( 343 \mathrm{cm}^{3} \)
Subject: Chemistry
Out of the following reduction process-
\( \boldsymbol{A}: \boldsymbol{F} \boldsymbol{e}_{2} \boldsymbol{O}_{3}+\boldsymbol{C} \longrightarrow \boldsymbol{F} \boldsymbol{e}+\boldsymbol{C} \boldsymbol{O}_{2} \)
\( \boldsymbol{B}: \boldsymbol{Z} \boldsymbol{n} \boldsymbol{O}+\boldsymbol{C} \longrightarrow \boldsymbol{Z} \boldsymbol{n}+\boldsymbol{C} \boldsymbol{O}_{2} \)
\( \boldsymbol{C}: \boldsymbol{S} \boldsymbol{n} \boldsymbol{O}_{2}+\boldsymbol{C} \longrightarrow \boldsymbol{S} \boldsymbol{n}+\boldsymbol{C} \boldsymbol{O}_{2} \)
\( \boldsymbol{D}: \boldsymbol{P b O}+\boldsymbol{C} \longrightarrow \boldsymbol{P b}+\boldsymbol{C O}_{2} \)
Correct processes are:
в. \( A, B, D \)
c. \( A, B, C \)
D. \( B, D \)
Subject: Maths
Let \( \triangle_{1}, \triangle_{2}, \triangle_{3}, \dots, \triangle_{k} \) be the set of
third-order determinants that can be
made with the distinct nonzero real
numbers \( a_{1}, a_{2}, a_{3}, \dots a_{9}, \) and \( \Sigma a_{i}=0 \)
Then
This question has multiple correct options
\( \mathbf{A} \cdot k=9 ! \)
B . \( \sum_{i=1}^{k} \Delta_{i}=0 \)
C . at least one \( \Delta_{i}=0 \)
D. none of these
Subject: Biology
E. coli cells with a mutated Z gene of the
lac operon cannot grow in medium containing only lactose as the source of energy because
A. In the presence of glucose, E. coli cells do not utilize lactose
B. They cannot transport lactose from the medium into the cell.
c. The lac operon is constitutively active in these cells.
D. They cannot synthesize functional \( \beta \) -galactosidase.
Subject: Maths
Assertion
The equation \( a \sin x+\cos 2 x=2 a-7 \)
possesses a solution if \( \boldsymbol{a} \in[\mathbf{2}, \mathbf{6}] \)
Reason
\( -1 \leq \sin x \leq 1 \forall x \in R \)
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
For the reaction
\( \boldsymbol{C u} \boldsymbol{S O}_{4} \cdot \boldsymbol{5} \boldsymbol{H}_{2} \boldsymbol{O}(\boldsymbol{s}) \rightleftharpoons \)
\( \boldsymbol{C u} \boldsymbol{S O}_{4} \cdot \boldsymbol{3} \boldsymbol{H}_{2} \boldsymbol{O}(\boldsymbol{s})+\boldsymbol{2} \boldsymbol{H}_{2} \boldsymbol{O}(\boldsymbol{g}) \)
which one is correct representation:
A \( \cdot K_{P}=\left(P_{H_{2}} \partial\right)^{2} \)
в. \( K_{C}=\left[H_{2} O\right]^{2} \)
\( \mathbf{c} \cdot K_{p}=K_{c}(R T)^{2} \)
D. all of these
Subject: Maths
Consider the curves \( y=\sin x \) and \( y= \)
\( \cos x \)
What is the area of the region bounded by the above two curves and the lines \( x=\frac{\pi}{4} \) and \( x=\frac{\pi}{2} ? \)
B. \( \sqrt{2}+1 \)
\( c \cdot 2 \sqrt{2} \)
\( D \)
Subject: Chemistry
Calcium imide on hydrolysis will give gas (B) which on oxidation by bleaching powder gives gas \( (\mathrm{C}) . \) Gas \( (\mathrm{C}) \) on reaction with magnesium gives compound (D). (D) on hydrolysis gives again gas \( (\mathrm{B}) .(\mathrm{B}),(\mathrm{C}) \) and \( (\mathrm{D}) \)
respectively are:
A. \( N H_{3}, N_{2}, M g_{3} N_{2} \)
B. \( N_{2}, N H_{3}, M g_{3} N_{2} \)
c. \( N_{2}, N_{2} O_{5}, M g\left(N O_{3}\right)_{2} \)
D. \( N H_{3}, N O_{2}, M g\left(N O_{2}\right)_{2} \)
Subject: Chemistry
Among the following outermost configuration of metals, which shows the highest oxidation state:
A \( \cdot 3 d^{3} 3 s^{2} \)
B . \( 3 d^{5} 4 s^{1} \)
\( \mathbf{c} \cdot 3 d^{5} \mathbf{f} s^{2} \)
D. \( 3 d^{6} 4 s^{2} \)
Subject: Physics
The average depth of Indian Ocean is about \( 3000 m \). The fractional
compression, \( \frac{\Delta V}{V} \) of water at the
bottom of the ocean is then
(Given: Bulk modulus of the water=
\( 2.2 \times 10^{9} N m^{-2} \) and \( g=10 m s^{-2} \)
\( \mathbf{A} \cdot 0.82 \% \)
B . \( 0.91 \% \)
c. \( 1.36 \% \)
D. 1.24\%
Subject: Chemistry
The oxidation states of metal in the
compounds \( F e_{0.94} O \) and
\( \left[\boldsymbol{C r}\left(\boldsymbol{P P h}_{3}\right)_{3}(\boldsymbol{C O})_{3}\right] \) respectively are:
A \( \cdot \frac{200}{94}, 0 \)
в. \( 0, \frac{94}{200} \)
\( c \cdot 2,1 \)
D. \( 1, \frac{200}{94} \)
Subject: Chemistry
Which option is correct?
\[
\mathrm{HC} \equiv^{2}-\mathrm{CH}_{2}-\mathrm{CH}=\mathrm{CH}_{2}
\]
\( A \)
\[
\stackrel{1}{\mathrm{C}} \Rightarrow \text { sp hybridised }
\]
в.
\[
\stackrel{5}{\mathrm{C}} \Rightarrow \mathrm{sp}^{2} \text { hybridised }
\]
\( c \)
\( \stackrel{3}{\mathrm{C}} \Rightarrow \) sp \( ^{3} \) hybridised
D. A
Subject: Chemistry
The coordination of \( P t \) in the complex
\( \operatorname{ion}\left[\boldsymbol{P t}(\boldsymbol{e n})_{2} \boldsymbol{C l}_{2}\right]^{2+} \) is:
\( A \cdot 3 \)
B. 4
\( c \cdot 5 \)
D. 6
Subject: Maths
Solve the following system of equations by using Matrix inversion method.
\( \mathbf{2} \boldsymbol{x}-\boldsymbol{y}+\mathbf{3} \boldsymbol{z}=\mathbf{9}, \boldsymbol{x}+\boldsymbol{y}+\boldsymbol{z}=\mathbf{6}, \boldsymbol{x}- \)
\( \boldsymbol{y}+\boldsymbol{z}=\mathbf{2} \)
Subject: Physics
Two co-axial lenses of power \( +4 D \) and \( -2 D \) are placed in contact. The focal length of combination is
\( \mathbf{A} \cdot 0.5 m \)
B. \( 0.25 \mathrm{m} \)
c. \( 0.16 m \)
D. \( -0.5 m \)
Subject: Physics
The pulley and string are shown in Fig. smooth and of negligible mass. For the
system to remain in equilibrium, the
angle \( \theta \) should be
\( A \cdot 0^{0} \)
B. \( 30^{\circ} \)
\( c \cdot 45^{\circ} \)
D. \( 60^{\circ} \)
Subject: Maths
The minimum value of \( \mathbf{a}^{2} \sec ^{2} \boldsymbol{\theta}+ \)
\( \mathbf{b}^{2} \cos \mathbf{e c}^{2} \boldsymbol{\theta} \) is
\( A \cdot a^{2}-b^{2} \)
B. \( 2\left(a^{2}+b^{2}\right) \)
\( c \cdot(a-b)^{2} \)
D. \( (a+b)^{2} \)
Subject: Chemistry
The diagram below shows the set up for
the laboratory preparation of a pungent alkaline gas.
The balanced equation for the above
preparation is :
A \( \cdot 2 C a O+2 N H_{4} C l \rightarrow 2 C a C l_{2}+H_{2} O+2 N H_{3} \)
в. \( C a O+N H_{4} C l \rightarrow C a C l_{2}+H_{2} O+N H \)
\( \mathrm{c} \cdot \mathrm{CaO}+2 \mathrm{NH}_{4} \mathrm{Cl} \rightarrow \mathrm{CaCl}_{2}+\mathrm{H}_{2} \mathrm{O}+2 \mathrm{NH} \)
D. 2 CaO \( +N H_{4} C l \rightarrow 2 C a C l_{2}+H_{2} O+2 N H \)
Subject: Maths
\( \boldsymbol{A}=\left(\begin{array}{cc}\mathbf{5} & \mathbf{2} \\ \mathbf{7} & \mathbf{3}\end{array}\right) \) and \( \boldsymbol{B}=\left(\begin{array}{cc}\mathbf{2} & \mathbf{- 1} \\ \mathbf{- 1} & \mathbf{1}\end{array}\right) \)
verify that \( (\boldsymbol{A B})^{\boldsymbol{T}}=\boldsymbol{B}^{\boldsymbol{T}} \boldsymbol{A}^{\boldsymbol{T}} \)
Subject: Chemistry
Assertion
Nitrous oxide is also known as laughing
gas.
Reason
It is a colourless gas having a faint
sweet odour.
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
What is the vapour pressure of the solution containing \( 34.2 \mathrm{g} \) of sucrose per 100 g of water at \( 25^{\circ} \mathrm{C} \) ? The vapour
pressure of water at \( 25^{\circ} \mathrm{C} \) is \( 23.75 \mathrm{mm} \)
\( A \cdot 20.3 \mathrm{mm} \)
B. 23.10 mm
c. Unpredictable
D. 23.33 mm
Subject: Chemistry
Which of the following compounds does not give nitrogen on heating?
A. \( N a N_{3} \)
B \( \cdot\left(N H_{4}\right)_{2} S O_{4} \)
c. \( N H_{4} N O_{2} \)
D. \( \left(N H_{4}\right)_{2} C r_{2} O_{7} \)
Subject: Physics
The shape of the string is drawn at \( t=0 \) and the area of the pulse enclosed by the string and the \( x \) -axis ismeasured. it
will be equal to
\( A \cdot 2 c m^{2} \)
B. \( 2.5 \mathrm{cm}^{2} \)
c. \( 4 c m^{2} \)
\( D \cdot 5 c m^{2} \)
Subject: Maths
If \( \vec{u}, \vec{v} \) and \( \vec{w} \) are three non-coplanar vectors, then \( (\overrightarrow{\boldsymbol{u}}+\overrightarrow{\boldsymbol{v}}-\overrightarrow{\boldsymbol{w}}) \cdot(\overrightarrow{\boldsymbol{u}}-\overrightarrow{\boldsymbol{v}}) \times \)
\( (\vec{v}-\vec{w}) \) equals
A \( . \vec{u} .(\vec{v} \times \vec{w}) \)
B.
c. \( 2 \vec{u} \cdot(\vec{v} \times \vec{w}) \)
D. \( \vec{u} .(\vec{w} \times \vec{v}) \)
Subject: Chemistry
What will be standard cell potential of galvanic cell with the following
reaction?
\( \boldsymbol{2} \boldsymbol{C r}_{(s)}+\boldsymbol{3} \boldsymbol{C} \boldsymbol{d}_{(a q)}^{2+} \rightarrow \boldsymbol{2} \boldsymbol{C r}_{(a q)}^{3+}+\boldsymbol{3} \boldsymbol{C} \boldsymbol{d}_{(s)} \)
\( \left[\text { Given: } \boldsymbol{E}_{C r^{3+} / C r}^{o}=-\mathbf{0 . 7 4 V} \) and \right.
\( \boldsymbol{E}_{C d^{2+} / C d}^{o}=-\mathbf{0 . 4 0 V} \)
\( \mathbf{A} \cdot 0.74 \mathrm{v} \)
B. \( 1.14 \mathrm{V} \)
c. \( 0.34 v \)
D. \( -0.34 \mathrm{v} \)
Subject: Maths
\( \mathbf{A}=\left[\begin{array}{lll}b^{2} c^{2} & b c & b+c \\ c^{2} a^{2} & c a & c+a \\ a^{2} b^{2} & a b & a+b\end{array}\right] \) then \( |A|=? \)
A \( \cdot a b c \)
B . \( a b c-1 \)
\( c \cdot a b c+1 \)
D.
Subject: Physics
Three masses of \( 500 g, 300 g \) and \( 100 g \)
are suspended at the end of a spring as shown and are in equilibrium. When the
\( 500 g \) mass is removed suddenly, the
system oscillates with a period of 2
second. When the \( 300 g \) mass is also
removed, it will oscillate with a period
\( \mathbf{A} \cdot 2 \sec \)
B. 4 sec
c. 8 sec
D. 1 sec
Subject: Physics
There are two vessels of same
consisting same no of moles of two different gases at same temperature.
One of the gas is \( C H_{4} \& \) the other is
unknown X. Assuming that all the molecules of \( X \) are under random
motion whereas in \( C H_{4} \) except one all
are stationary. Calculate \( Z_{1} \) for \( X \) in
terms of \( Z_{1} \) of \( C H_{4} . \) Given that the collision diameter for both gases are same \( \&\left(U_{r m s}\right)_{x}=\frac{1}{\sqrt{6}}(U a v)_{C H_{4}} \)
A \( \cdot \frac{2 \sqrt{2}}{3 \sqrt{\pi}} Z_{1} \)
B \( \cdot \frac{3 \sqrt{2}}{2 \sqrt{\pi}} Z_{1} \)
c. \( \frac{2 \sqrt{3}}{2 \sqrt{\pi}} Z_{1} \)
D. \( \frac{4 \sqrt{2}}{3 \sqrt{\pi}} Z_{1} \)
Subject: Chemistry
A solution of weak acid \( H A \) was
titrated with base NaOH. The
equivalence point was reached when
\( 36.12 m L \) of \( 0.1 M \) NaOH has been
added. Now \( 18.06 m L \) of \( 0.1 M H C l \)
were added to titrated solution, the \( p H \)
was found to be \( 4.92 . \) What will be the
\( \boldsymbol{p} \boldsymbol{H} \) of the solution obtained by mixing \( 10 m L \) of \( 0.2 M N a O H \) and \( 10 m L \) of
\( 0.2 M H A ? \)
\( \mathbf{A} \cdot p H=3 \)
В. \( p H=4 \)
\( \mathbf{c} \cdot p H=9 \)
D. \( p H=11 \)
Subject: Maths
\( \ln \) an A.P., prove that \( \boldsymbol{d}=\boldsymbol{S}_{\boldsymbol{n}}-\boldsymbol{2} \boldsymbol{S}_{\boldsymbol{n}-\boldsymbol{1}}+ \)
\( \boldsymbol{S}_{\boldsymbol{n}-\boldsymbol{2}} \)
Subject: Physics
Three equal resistors connected in series across a source of e.m.f dissipate
10 watts of power. What will be the power dissipated in watts if the same resistors are connected in parallel
across the same source of e.m.f?
A. \( 10 \mathrm{w} \)
B. 30 W
c. \( 90 \mathrm{w} \)
D. \( \frac{10}{3} W \)
Subject: Maths
If \( \left(\begin{array}{lll}1 & 2 & 4 \\ 1 & 3 & 5 \\ 1 & 4 & a\end{array}\right) \) is singular, the value
of \( a \) is
A \( . a=-6 \)
B. \( a=5 \)
c. \( a=-5 \)
\( \mathbf{D} \cdot a=6 \)
Subject: Physics
Four wires made of same material have
different lengths and radii. The wire having more resistance in the following is
A \( .1=100 \mathrm{cm} \mathrm{r}=1 \mathrm{mm} \)
B. \( 1=50 \mathrm{cm} \mathrm{r}=2 \mathrm{mm} \)
c. \( 1=100 \mathrm{cm} \mathrm{r}=1 / 2 \mathrm{mm} \)
D. \( 1=50 \mathrm{cm} \mathrm{r}=1 / 2 \mathrm{mm} \)
Subject: Physics
Maxwell's four equations are written as
(i) \( \oint \overrightarrow{\boldsymbol{E}} \cdot \overrightarrow{\boldsymbol{d}} \boldsymbol{s}=\frac{\boldsymbol{q}_{0}}{\varepsilon_{0}} \)
(ii) \( \oint \vec{B} \cdot \vec{d} s=0 \)
(iii) \( \oint \vec{E} . \overrightarrow{d l}=\frac{d}{d t} \oint \vec{B} \cdot \vec{d} s \)
\( (\text { iv }) \oint \vec{B} \cdot \vec{d} s=\mu_{0} \varepsilon_{0} \frac{d}{d t} \oint \vec{E} \cdot \vec{d} s \)
Out of the four Maxwell's equation above, which one shows the non-
existence of monopoles?
\( A \cdot \) (i) and (iv)
B. (ii) only
c. (iii) only
D. none of these
Subject: Physics
A block is constrained to move along \( x \)
axis under a force \( F=-2 x \). Here, \( F \) is in
newton and \( x \) in metre. Find the work
done by this force when the block is displaced from \( x=2 m \) to \( x=-4 \) m.
A . -4 J
B. -8J
c. -12
D. -16
Subject: Chemistry
Which is the correct order for different
forces?
\( \mathbf{A} \cdot E_{D} \) (Dipole - induced dipole interaction) \( >E_{x} \) (Dipole
induced dipole interaction) \( >E_{L} \) (London force)
B. \( E_{K} \) (Dipole \( _{-} \) dipole interaction) \( >E_{D} \) (Dipole - induce
dipole interaction) \( >E_{L} \) (London force)
C . \( E_{D} \) (Dipole - induced dipole interaction) \( >E_{L} \) (London
force) \( E_{K} \) (Dipole - Dipole interaction)
D. All forces are equally strong.
Subject: Chemistry
Pyrolusite is \( M n O_{2} \stackrel{I}{\rightarrow} M n O_{4}^{2-} \stackrel{I I}{\rightarrow} \)
\( M n O_{4} \)
Steps I and II are respectively:
This question has multiple correct options
A. fuse with KOH / air and electrolytic oxidation.
B. fuse with \( K O H / K N O_{3} \) and electrolytic oxidation.
c. fuse with conc. \( H N O_{3} / a i r \) and electrolytic reduction.
D. dissolve in \( H_{2} O \) and oxidation
Subject: Maths
Let \( \boldsymbol{f}: \boldsymbol{R} \rightarrow \boldsymbol{R} \) be such that \( \boldsymbol{f}(\boldsymbol{x})=\boldsymbol{2}^{\boldsymbol{x}} \)
Determine
(i) Range of \( \boldsymbol{f} \)
(ii) \( \{x: f(x)=1\} \)
(iii) whether \( \boldsymbol{f}(\boldsymbol{x}+\boldsymbol{y})=\boldsymbol{f}(\boldsymbol{x}) \boldsymbol{f}(\boldsymbol{y}) \)
holds.
Subject: Chemistry
Which of the following is an example of oxidation?
A \( \cdot S n^{+2}-2 e^{-} \rightarrow S n^{+} \)
B. \( F e^{+3}+e^{-} \rightarrow F e^{+} \)
c. \( C l_{2}+2 e^{-} \rightarrow 2 C l \)
D. None of the above
Subject: Physics
A sample of HCl is placed in an electric
field of \( 2.5 \times 10^{4} N C^{-1} . \) The dipole
moment of HCl is \( 3.4 \times 10^{-30} \mathrm{Cm} \). Find
the maximum torque that can act on a
molecule.
A \( \cdot 7.6 \times 10^{-26} \mathrm{Nm} \)
В. \( 4.3 \times 10^{-26} \mathrm{Nm} \)
c. \( 6.5 \times 10^{-26} \mathrm{Nm} \)
D. \( 8.5 \times 10^{-26} \mathrm{Nm} \)
Subject: Maths
The mean score of 1000 students for an
examination is 34 and \( S . D . \) is 16
(i) How many candidates can be
expected to obtain marks between 30
and 60 assuming the normality of the distribution and
(ii) determine the limit of the marks of
the central \( 70 \% \) of the candidates:
\( \{\boldsymbol{P}[\mathbf{0}<\boldsymbol{z}<\mathbf{0 . 2 5}]=\mathbf{0 . 0 9 8 7} \boldsymbol{P}[\mathbf{0}<\boldsymbol{z}<\mathbf{1} \)
Subject: Chemistry
The anhydride of orthophosphoric acid is :
A. \( \mathrm{P}_{4} \mathrm{O}_{6} \)
в. \( \mathrm{P}_{2} \mathrm{O}_{4} \)
\( \mathrm{c} \cdot \mathrm{P}_{4} \mathrm{O}_{10} \)
D. \( \mathrm{H}_{2} \mathrm{P}_{2} \mathrm{O}_{6} \)
Subject: Chemistry
The products formed by the complete
hydrolysis of \( \boldsymbol{P} \boldsymbol{C l}_{3} \) are:
A. \( H_{3} P O_{3} \) and \( H C l \)
в. \( P O C l_{3} \) and \( H C l \)
\( \mathbf{c} \cdot H_{3} P O_{4} \) and \( H C l \)
D. \( H_{4} P_{2} O_{7} \) and \( H C l \)
Subject: Physics
A uniform rod of mass \( m=0.5 k g \) and
length \( 90 \mathrm{cm} \) rests on a smooth
horizontal surface. One of the ends of
the rod is stuck with impulse \( J= \)
\( 3.0 N s \) in a horizontal direction
perpendicular to the rod as shown in fig.
As a result the rod obtains momentum
\( \boldsymbol{p}=\mathbf{3 . 0} \boldsymbol{N} \boldsymbol{s} . \) Find
Subject: Chemistry
A solution of saturated \( C a F_{2} \) is found to
contain \( 4.1 \times 10^{-4} M \) fluoride ion.
Calculate the \( \boldsymbol{K}_{s p} \) of \( \boldsymbol{C} \boldsymbol{a} \boldsymbol{F}_{2} . \) Neglect
hydrolysis.
Subject: Maths
Find the area of the region enclosed between the two circles \( x^{2}+y^{2}=1 \& \)
\( (x-1)^{2}+y^{2}=1 \)
A \( \cdot \frac{\pi}{6}-\frac{\sqrt{3}}{2} \) squnits
B. \( \frac{\pi}{3}-\frac{\sqrt{3}}{2} \) sq.units
c. \( \frac{\pi}{6}-\frac{\sqrt{3}}{4} \) sq.units
D. \( \frac{\pi}{3}-\frac{\sqrt{3}}{4} \) sq.units
Subject: Physics
If the binding energy per nuclear in \( L i^{7} \) and \( H e^{4} \) nuclei are respectively
\( \mathbf{5 . 6 0} M e V \) and \( 7.06 M e V, \) then energy of reactor \( L i^{7}+P \rightarrow 2_{2} H e^{4} \) is:
A. \( 19.6 \mathrm{MeV} \)
B. \( 2.4 \mathrm{MeV} \)
c. \( 8.4 \mathrm{MeV} \)
D. \( 17.6 \mathrm{MeV} \)
Subject: Physics
What do you understand by the internal resistance of a cell? The potential difference of a cell becomes \( 1.8 \mathrm{V} \) when
\( 0.5 A \) current is drown and when \( 1.0 A \)
current is drawn, it becomes \( 1.6 \mathrm{V} \). Find
the internal resistance of the cell and
its e.m.f.