AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Physics
Three substances are added to a mug to
make coffee : Coffee is at \( 65^{\circ} \mathrm{C} \), Milk at
\( 65^{\circ} \mathrm{C} \) and Sugar, which is in thermal
equilibrium with coffee. Then This question has multiple correct options
A. Heat will be transferred from sugar to coffee to reach equilibrium
B. The sugar is in equilibrium with the milk
c. Heat will be transferred from the coffee to the sugar to reach equilibrium
D. None of these conclusions are valid
Subject: Physics
Calculate the electric potential at the
center of the square:
\( A \)
в. \( k \frac{29}{x^{2}} \)
\( c \cdot_{k} \frac{4 q}{c^{2}} \)
D. \( k \frac{49}{6} \)
\( E \)
\[
k \frac{(4 \sqrt{2})}{s}
\]
Subject: Physics
Find the \( Q \) -value and the kinetic energy
of the emitted \( \alpha \) - Particle in the \( \alpha \) -decay of \( (a)_{86}^{220} R n \) and
(b) 226
88 Ra.
Given:
\( \boldsymbol{m}\left(_{\mathbf{8 8}}^{226} \boldsymbol{R} \boldsymbol{a}\right)=\mathbf{2 2 6 . 0 2 5 4 0} \boldsymbol{u} \)
\( \boldsymbol{m}\left(_{86}^{222} \boldsymbol{R} \boldsymbol{n}\right)=\mathbf{2 2 2 . 0 1 7 5 0} \boldsymbol{u} \)
\( \boldsymbol{m}\left(_{84}^{216} \boldsymbol{P o}\right)=\mathbf{2 1 6 . 0 0 1 8 9} \boldsymbol{u} \)
Subject: Maths
n Fig. \( 2, \) 'O' is the centre of the circle,
find \( \angle A O C, \operatorname{given} \angle B A O=30^{\circ} \) and
\( \angle B C O=40^{\circ} \)
\( A \cdot 35 \)
В. 140
\( c \cdot 70 \)
D. Cannot be determined
Subject: Maths
Compute the age specific death rate for the following data:
Number of
deaths \( \begin{array}{ll}\text { Age } & \text { Population (in } \\ \text { Group } & \text { thousands) } \\ \text { (years) } & \text { thousands) }\end{array} \)
5 Below
5 360
\( _{5}-30 \) na
\begin{tabular}{l|l} 
Above & \\
30 & 10
\end{tabular} 280
Subject: Maths
\( \int \frac{\tan 2 \theta d \theta}{\sqrt{\cos ^{6} \theta+\sin ^{6} \theta}} \) is equal to
\( \mathbf{A} \cdot \ln \left|\frac{1+\sqrt{1+3 \cos ^{2} 2 \theta}}{\cos 2 \theta}\right|+c \)
B \( \cdot \ln \left|\frac{\sqrt{1+3 \cos ^{2} 2 \theta}}{\cos 2 \theta}\right|+c \)
\( \mathrm{c} \cdot \ln \left|\frac{1+\sqrt{2+3 \cos ^{2} 2 \theta}}{\sin 2 \theta}\right|+c \)
D. None of these
Subject: Maths
The common ratio for the term \( \boldsymbol{a}_{n}= \)
\( 2 \times\left(\frac{1}{4}\right)^{n-1} \) is
A \( \cdot \frac{1}{2} \)
в. \( \frac{1}{3} \)
\( c \cdot \frac{1}{4} \)
D.
Subject: Chemistry
(a) Write IUPAC names of the following
compounds:
(i) \( \boldsymbol{C H}_{2}=\boldsymbol{C H}-\boldsymbol{C H}_{2}-\boldsymbol{O H} \)
(ii) \( \boldsymbol{C H}_{2}-\boldsymbol{C H}-\boldsymbol{C H}_{2} \)
\( \begin{array}{ccc}1 & 1 & 1 \\ o_{H} & o_{H} & o_{H}\end{array} \)
(b) Write equations of the following chemical reactions:
(i) Phenol reacts with \( B r_{2} \) in
presence of \( \boldsymbol{C S}_{\mathbf{2}} \)
(ii) Ethanol is heated at \( 573 \mathrm{K} \) in
presence of Cu.
Subject: Chemistry
Which of the following changes will cause the free energy of the cell reaction to decrease:
\( \boldsymbol{Z} \boldsymbol{n}\left|\boldsymbol{Z n} \boldsymbol{S} \boldsymbol{O}_{4(\boldsymbol{a q})}(\boldsymbol{x}, \boldsymbol{M}) \| \boldsymbol{H} \boldsymbol{C l}_{(\boldsymbol{a q})}\left(\boldsymbol{x}_{\boldsymbol{2}} \boldsymbol{M}\right)\right| \boldsymbol{H} \)
This question has multiple correct options
\( 200 \mathrm{m} \)
B. Increase in pressure of hydrogen from 1 atm to 2 atm
c. Increase in molarity \( x_{2} \) from 0.1 to 1 M
D. Decrease in molarity \( x_{1} \) from 1 M to 0.1 M
Subject: Physics
A battery of \( 10 \mathrm{V} \) and internal resistance
\( 0.5 \Omega \) is connected across a variable
resistance R. The value of \( R \) for which
the power delivered in its maximum state, is equal to :-
A \( .0 .5 \Omega \)
в. \( 1 \Omega \)
c. \( 1.5 \Omega \)
D. \( 2.0 \Omega \)
Subject: Physics
In the half wave rectifier circuit
operating from 50 \( \boldsymbol{H} \boldsymbol{z} \) mains frequency, the fundamental frequency in the ripple would be
\( \mathbf{A} \cdot 2.5 H z \)
B. \( 50 \mathrm{Hz} \)
c. \( 70.7 H z \)
D. \( 100 H z \)
Subject: Maths
On the interval \( \boldsymbol{I}=[-2,2] \),for the
function \( \left\{\begin{array}{ll}(x+1) e^{-\left[\frac{1}{[x]}+\frac{1}{x}\right]} & (x \neq 0) \\ 0 & (x=0)\end{array}\right. \)
(where []\( \text { is } G I F) \) which one of the
following hold good?
This question has multiple correct options
A. is continuous for all values of \( x \in I \)
B. is continuous for all values of \( x \in I-(0) \)
c. assumes all intermediate values from \( f(-2) \) \& \( f(2) \)
D. has a maximum value equal to
Subject: Physics
When the tension in a metal wire is \( T_{1} \)
its length is \( l_{t} \). When the tension is \( T_{2} \)
its length is \( l_{2} \). The natural length of
wire is
\( ^{\mathbf{A}} \cdot \frac{T_{2}}{T_{1}}\left(l_{1}+l_{2}\right) \)
в. \( T_{1} l_{1}+i_{2} l_{2} \)
c. \( \frac{l_{1} T_{2}-l_{2} T_{1}}{T_{2}-T_{1}} \)
D. \( \frac{l_{T_{2}-l_{2} T_{1}}}{T_{2}+T_{1}} \)
Subject: Physics
A biconvex lens of focal length \( \boldsymbol{f} \) and
radii of curvature of both the surfaces \( \boldsymbol{R} \)
is made of a material of refractive index
\( \boldsymbol{n}_{1} . \) This lens is placed in a liquid of
refractive index \( n_{2} . \) Now this lens will
behave like:
This question has multiple correct options
A. either as convex or as a concave lens depending solely on \( R \)
B. a convex lends depending on \( n_{1} \) and \( n_{2} \)
C . a concave lends depending on \( n_{1} \) and \( n_{2} \)
D. a convex lens of same focal length irrespective of
\( R, n_{1} \) and \( n_{2} \)
Subject: Chemistry
At \( 283 \mathrm{K} \) a saturated solution of solid \( \mathrm{X} \)
can be prepared by dissolving 21.0 g of it in 100 g of water. The maximum amount of \( X \) which can be dissolved in 100 g of water at \( 313 \mathrm{K} \) is \( 62.0 \mathrm{g} \). An attempt is made to dissolve 50.0 g of \( X \) in 100 g of water at \( 313 \mathrm{K} \)
. All the 50.0 g of \( X \) will dissolve at 313 K.
2. At \( 313 \mathrm{K} 29.0 \mathrm{g} \) of \( \mathrm{X} \) will remain undissolved.
3. Solubility of X decreases with an
increase in temperature.
4. On cooling the solution of \( X \) from 313 \( \mathrm{K} \) to \( 283 \mathrm{K} \) more than \( 21.0 \mathrm{g} \) of \( \mathrm{X} \) will crystallize out.

Which of the following statement are
correct?
A \( . \) and 2
B. 1 and 4
\( c \cdot 2 \) and 3
D. 1,3 and 4
Subject: Chemistry
An organic compound
(A) (molecular
formula \( C_{8} H_{16} O_{2} \) ) was hydrolysed with dilute sulphuric acid to give a carboxylic acid (B) and an alcohol (C). Oxidationof
(C) with chromic acid
produced (B).
(C) on dehydration gives but-1-ene.Write equations for the reactions involved.
Subject: Physics
A solid of mass 250 g at \( 90^{0} C \) is dropped in a calorimeter containing 100
\( g \) of water at \( 15^{0} C . \) The resulting
temperature of mixture becomes \( 40^{0} C \) The mass of calorimeter is 100 g and its specific heat capacity is \( 0.1 \mathrm{cal} / \mathrm{g}^{0} \mathrm{C} \) Find the specific heat capacity of the
solid.
Subject: Physics
Three different circuits(I, II and III) are
constructed using identical batteries
and resistors of \( \mathrm{R} \) and \( 2 R \) ohm. What
can be said about current lin arm AB of
each circuit?
A \( \cdot I_{I I}<I_{I}<I_{I I} \)
в. \( I_{I}<I_{I I}<I_{I I} \)
c. \( I_{I}=I_{I I}=I_{I I} \)
D \( \cdot I_{I}>I_{I I}=I_{I I} \)
Subject: Physics
A person has a \( 15 \mathrm{cm} \) wide face and his
two eyes are separated by \( 9 \mathrm{cm} . \) The minimum width of a mirror required for
the person to view his complete face literally is
\( \mathbf{A} \cdot 15 \mathrm{cm} \)
в. 9 ст
\( c .6 c m \)
D. 3 cm
Subject: Physics
Two conducting plates \( A \) and \( B \) are
parallel. A is given a charge \( Q_{1} \) and \( B \) is
given a charge \( Q_{2} \). The charge on inner
side of B is :
\( A \)
\[
\frac{Q_{2}-Q_{1}}{2}
\]
в.
\[
\frac{\left(Q_{1}-Q_{2}\right)}{2}
\]
\( c \)
\[
\frac{\left(Q_{1}+Q_{2}\right)}{2}
\]
\( D \)
\[
\frac{-\left(Q_{1}+Q_{2}\right)}{2}
\]
Subject: Chemistry
\( p K_{a} \) for the acid \( H A \) is \( 6 . \) The value of
\( \boldsymbol{K} \) for the reaction \( \boldsymbol{A}^{-}+\boldsymbol{H}_{3} \boldsymbol{O}^{+} \rightleftharpoons \)
\( \boldsymbol{H} \boldsymbol{A}+\boldsymbol{H}_{2} \boldsymbol{O} \) is:
A \( \cdot 1 \times 10^{-6} \)
B. \( 1 \times 10^{8} \)
c. \( 1 \times 10^{-8} \)
D. \( 1 \times 10^{6} \)
Subject: Maths
If \( A \) and \( B \) are two events. The probability
that at most one of \( A, B \) occurs is
A \( .1-P(A \cap B) \)
в. \( P(\bar{A})+P(\bar{B})-P(\bar{A} \cap B) \)
c. \( P(\bar{A})+P(\bar{B})+P(\bar{A} \cap \bar{B}) \)
D. All of the above
Subject: Chemistry
Which of the following correctly
represents Dalton's symbols?
1
2
3
4
0
0
A. 1: oxygen, 2: hydrogen, 3 : nitrogen, 4: carbon and 5 sulphur
B. 1: hydrogen, 2: nitrogen, 3 : oxygen, 4: carbon and 5 sulphur
C. 1: hydrogen, 2 : nitrogen, 3: oxygen, 4 : sulphur and 5 carbon
D. 1: hydrogen, 2: carbon, 3 : oxygen, 4 : sulphur and 5 nitrogen
Subject: Chemistry
litre of a sample of \( H_{2} \) is at \( 0^{\circ} C \) and 1
atm pressure.1 litre of another sample
of hydrogen is at \( 0^{\circ} \mathrm{C} \) and 2 atm
pressure. Kinetic energies of the gases are in the ratio of:
A \( \cdot 1: 2 \)
B. 2:1
c. 3:
D. 1:
Subject: Physics
Find the new position of the balance point when \( 5 \omega \) resistor is changed by 4
\( \omega \) resistor
A. \( 26.5 \mathrm{cm} \)
B. 52 \( \mathrm{cm} \)
c. 67.2 \( \mathrm{cm} \)
D. \( 83.3 \mathrm{cm} \)
Subject: Physics
A particle execute S.H.M from the mean position. its amplitude is \( A \), its time period is "T.' At what displacement,its speed is half of its maximum speed.
A \( \cdot \frac{\sqrt{3} A}{2} \)
в. \( \frac{\sqrt{2}}{3} A \)
c. \( \frac{2 A}{\sqrt{3}} \)
D. \( \frac{3 A}{\sqrt{A}} \)
Subject: Physics
A man with normal near point \( (25 \mathrm{cm}) \) reads a book with small print using a magnifying glass: a thin convex lens of focal length \( 5 \mathrm{cm} \)
(a) What is the closest and the farthest
distance at which he should keep the lens from the page so that he can read the book when viewing through the magnifying glass?
(b) What is the maximum and the minimum angular magnification (magnifying power) possible using the above simple microscope?
Subject: Maths
What is the degree of the following polynomial expression:
\( \boldsymbol{u}^{\frac{-1}{2}}+\boldsymbol{3} \boldsymbol{u}+\boldsymbol{2} \)
\( \mathbf{A} \cdot \mathbf{1} \)
B. 0
\( c \cdot \frac{-1}{2} \)
D. Not Defined
Subject: Maths
Two forces act at the vertex \( \mathbf{A} \) of
quadrilateral ABCD represented by \( A B, \overline{A D} \) and two at \( C \) represented by \( C D \) and \( \overline{C B} . \) If \( \mathrm{E}, \mathrm{F} \) are mid points of \( A C \) and \( \overline{B D} \) respectively, then their resultant is
A. \( \overline{E F} \)
в. \( 2 \overline{E F} \)
c. \( \frac{3}{2} \overline{E F} \)
D. \( 4 \overline{E F} \)
Subject: Physics
Shown in the figure is a very long semicylindrical conducting shell of radius \( \mathrm{R} \) and carrying a current i. An infinitely
long straight current carrying conductor lies along the axis of the semi - cylinder. If the current flowing
through the straight wire be \( i_{0} \), then the
force per unit length on the conducting
wire is :
A \( \cdot \frac{\mu_{0} i \times i_{0}}{\pi^{2} R} \)
В \( \cdot \frac{\mu_{0} i \times i_{0}}{\pi R^{2}} \)
c. \( \frac{\mu_{0} i_{o}^{2} \times i}{\pi^{2} R} \)
D. None of these
Subject: Maths
\( X, Y \subset \mathrm{R}, f: X \rightarrow Y \) is a function and
\( f(x)=x^{2} \forall x \in X \) then the condition
for it to be one-one but not onto is
A \( . X=Y=R^{+} \)
B . \( X=R, Y=R^{+} \)
c. \( X=R^{+}, Y=R \)
D. \( X=Y=R \)
\( R \)
Subject: Biology
Correct sequence of stages of
succession on a bare rock is?
A. Lichens \( \rightarrow \) Mosses \( \rightarrow \) Grasses \( \rightarrow \) Shrubs \( \rightarrow \) Trees
B. Trees \( \rightarrow \) Shrubs \( \rightarrow \) Lichens \( \rightarrow \) Mosses \( \rightarrow \) Grasses
C. Mosses \( \rightarrow \) Shrubs \( \rightarrow \) Trees \( \rightarrow \) Lichens \( \rightarrow \) Grasses
D. Mosses \( \rightarrow \) Lichens \( \rightarrow \) Grasses \( \rightarrow \) Shrubs \( \rightarrow \) Trees
Subject: Maths
Factorise the expression: \( 7 p^{2}+21 q^{2} \)
\( \mathbf{A} \cdot 7\left(p^{2}+q^{2}\right) \)
B. \( \left(p^{2}-3 q^{2}\right) \)
C \( .7\left(p^{2}+3 q^{2}\right) \)
D. \( \left(p q^{2}+3 q^{2}\right) \)
Subject: Physics
Two thin lenses of focal lengths \( 20 \mathrm{cm} \) and \( 25 \mathrm{cm} \) are placed in contact. The effective power of the combination is :
\( A \cdot 1 \)
\( \frac{1}{9} \) diopters
B. 45 diopters
c. 6 diopters
D. 9 diopters
Subject: Chemistry
Solid \( B e\left(N O_{3}\right)_{2} \) is gradually dissolved in a \( 1.0 \times 10^{-4} M N a_{2} C O_{3} \) solution. At
what concentration of \( B a^{2+} \) will a
percipitate begin to form?
\( \left(K_{S P} \text { for } B a C O_{3}=5 \times 10^{-9}\right) \)
A. \( 8.1 \times 10^{-8} M \)
в. \( 8.1 \times 10^{-7} M \)
c. \( 4.1 \times 10^{-5} M \)
D. \( 5.1 \times 10^{-5} M \)
Subject: Maths
Box I contains two white and three black
balls. Box II contains four white and one
black balls and box III contains three
white and four black balls. A dice having
three red, two yellow and one green face,
is thrown to select the box. If red face
turns up, we pick up box I, if a yellow face turns up we pick up box II, otherwise, we pick up box III. Then, we draw a ball from the selected box. If the
ball drawn is white, what is the
probability that the dice had turned up with a red face?
Subject: Maths
Solve the equation \( \sqrt{3} \cos x-\sin x=1 \)
A \( \cdot x=2 n \pi-\frac{\pi}{3} \pm \frac{\pi}{3}, n \in Z \)
В . \( x=2 n \pi-\frac{\pi}{6} \pm \frac{\pi}{3}, n \in Z \)
c. \( x=2 n \pi-\frac{\pi}{6} \pm \frac{\pi}{6}, n \in Z \)
D. None of these
Subject: Maths
If the primitive of \( \frac{x^{5}+x^{4}-8}{x^{3}-4 x} \) is \( \frac{x^{3}}{3}+ \) \( \frac{\boldsymbol{x}^{2}}{2}+\boldsymbol{A} \boldsymbol{x}+|\log \boldsymbol{f}(\boldsymbol{x})|+C \) then
This question has multiple correct options
\( \mathbf{A} \cdot A=1 \)
\( \mathbf{B} \cdot A=4 \)
\( \mathbf{C} \cdot f(x)=x^{2}(x-2)^{5}(x+2)^{-3} \)
D. \( f(x)=x^{2}(x-2)^{3}(x+2)^{-2} \)
Subject: Physics
The two capacitors \( 2 \mu F \) and \( 6 \mu F \) are put in series, the effective capacity of
the system is \( \mu \boldsymbol{F} \) is:
\( A \cdot 8 \mu F \)
в. \( 2 \mu F \)
c. \( 3 / 2 \mu F \)
D. \( 2 / 3 \mu F \)
Subject: Maths
Find the acute angle between the lines \( 3 x+y-7=0 \) and \( x+2 y-9=0 \)
A \( \cdot 45^{\circ} \)
B . \( 135^{\circ} \)
\( c \cdot 60^{\circ} \)
D. \( 120^{\circ} \)
Subject: Chemistry
A certain alkaloid has \( 70.8 \% \) carbon, 6.2
\( \% \) hydrogen, \( 4.1 \% \) nitrogen and the rest oxygen.What is its empirical formula?
в. \( C_{20} \) Ноо \( \mathrm{NO}_{4} \)
c. \( C_{21} H_{20} N O_{3} \)
D. \( C_{20} \mathrm{H}_{19} \mathrm{NO}_{3} \)
Subject: Maths
\( \mathbf{a}_{r}=\left|\begin{array}{ccc}\mathbf{2}^{r}-\mathbf{1} & \mathbf{2} \mathbf{.} \mathbf{3}^{r}-\mathbf{1} & \mathbf{4} . \mathbf{5}^{r}-\mathbf{1} \\ \boldsymbol{\alpha} & \boldsymbol{\beta} & \boldsymbol{\gamma} \\ \mathbf{2}^{n}-\mathbf{1} & \mathbf{3}^{n}-\mathbf{1} & \mathbf{5}^{n}-\mathbf{1}\end{array}\right| \)
then find the value of \( \sum_{r=1}^{n} \Delta_{r} \)
\( A \)
в. \( \alpha \beta \gamma \)
\( \mathbf{c} \cdot-\alpha \beta \gamma \)
\( D \)
Subject: Physics
Two cells, having emfs of \( 10 V \) and \( 8 V \)
respectively, are connected in series
with a resistance of \( 24 \Omega \) in the external
circuit. If the internal resistances of
each of these cells in ohm are \( 200 \% \) of
the value of their emf's respectively,
find the terminal potential difference
\( \operatorname{across} 8 V \) battery.
A \( .0 .3 A, 3.2 V \)
B. \( 0.5 A, 3.2 V \)
c. \( 0.3 A, 1.2 V \)
D. \( 0.5 A, 2.2 V \)
Subject: Maths
If the mean and S.D. of n observation
\( x_{1}, x_{2}, \dots \dots x_{n} \) are \( \bar{x} \) and \( \sigma \) resp, then the sum of squares of observations is
A \( \cdot n\left(\sigma^{2}+\bar{x}^{2}\right) \)
В \( \cdot n\left(\sigma^{2}-\bar{x}^{2}\right) \)
c. \( n\left(\overline{x^{2}}-\sigma^{2}\right) \)
D. none of these
Subject: Chemistry
4 grams of sodium hydroxide pellets were dissolved in \( 100 \mathrm{cm}^{3} \) of water. The
temperature before adding the sodium hydroxide pellets was 25 degrees \( C \), and after adding the pellets it was 35 degrees C. Calculate the enthalpy change in \( k J / \) mole of the reaction. [Specific heat capacity of water \( = \) \( \mathbf{4} . \mathbf{2} \boldsymbol{J} / \boldsymbol{k} / \boldsymbol{g}] \)
A. \( 42 k J / \) mole
в. \( 4.2 k J / \) mole
c. \( 4200 k J / \) mole
D. None
Subject: Chemistry
\( \boldsymbol{A} \boldsymbol{g}_{2} \boldsymbol{S}+\boldsymbol{N} \boldsymbol{a} \boldsymbol{C} \boldsymbol{N} \rightarrow \boldsymbol{A} \)
\( \boldsymbol{A}+\boldsymbol{Z} \boldsymbol{n} \rightarrow \boldsymbol{B} \)
\( B \) is a metal. Hence, \( A \) and \( B \) are
respectively:
A \( \cdot N a_{2}\left[\operatorname{Zn}(C N)_{4}\right], Z n \)
B. \( \operatorname{Na}\left[A g(C N)_{2}\right], A g \)
c. \( \operatorname{Na}\left[A g(C N)_{4}\right], A g \)
D. \( N a_{3}\left[A g(C N)_{4}\right], A g \)
Subject: Physics
The stable nucleus that has a radius
\( 1 / 3 \) that \( O s^{189} \) is
\( \mathbf{A} \cdot_{3} L i^{7} \)
B \( \cdot_{2} \mathrm{He}^{4} \)
\( \mathbf{c} \cdot_{5} B^{10} \)
\( \mathrm{D} \cdot_{6} C^{12} \)
Subject: Chemistry
Which of the following aqueous solutions will exhibit the highest boiling point?
A . \( 0.01 M \) urea
в. \( 0.01 M \) К \( N O_{3} \)
c. \( 0.01 M \) Na\( _{2} \) SO \( _{4} \),
D. \( 0.015 M C_{6} H_{12} O_{6} \)
Subject: Chemistry
Which of the following species are hypervalent? \( 1 . C l O_{4}^{-}, 2 . B F_{3}, 3 . S O_{4}^{2-}, 4 . C O_{3}^{2-} \)
\( \mathbf{A} \cdot 1,2,3 \)
в. 1,3
\( c .3,4 \)
D. 1,2
Subject: Chemistry
Which of the following atoms does the electron configuration \( 1 s^{2} 2 s^{2} 2 p^{6} 3 s^{2} 3 p^{6} 3 d^{2} \) represent?
A. An excited state \( C a \) atom
B. A ground state \( C a \) atom
c. An excited state \( S c \) atom
D. An excited state \( K \) atom
Subject: Chemistry
\( 0.12 \mathrm{g} \) of an organic compound containing phosphorous gave 0.22 g of
\( M g_{2} P_{2} O_{7} \) by usual analysis. Calculate
the percentage of the phosphorous in the organic compound.
A. \( 48.5 \% \)
B . \( 51.2 \% \)
c. \( 63.9 \% \)
D. \( 69.2 \% \)
Subject: Maths
A rectangle DEFG is plotted in \( X Y \) plane. The co-ordinates of D , E , F and G \( \operatorname{are}(2,2),(9,2),(9,10) \) and (2,10)
Find the new co-ordinates of G when
DEFG is rotated \( 270^{\circ} \) around origin. This question has multiple correct options
A \( \cdot(-10,2) \)
B. (10,-2)
c. (10,-1)
D. (10,2)
Subject: Physics
Magnetic flux \( \phi \) linked with a stationary loop of resistance \( R \) vaires with time \( t \)
as \( \phi=a t(T-t) . \) Amount of heat
generated in loop during time interval \( \boldsymbol{T} \)
is
\( ^{\mathbf{A}} \cdot \frac{a T}{3 R} \)
\( ^{\mathbf{B}} \cdot \frac{a^{2} T^{2}}{3 R} \)
c. \( \frac{a^{2} T^{2}}{R} \)
D. \( \frac{a^{2} T^{3}}{3 R} \)
Subject: Maths
Length of the latusrectum of the
hyperbola \( \boldsymbol{x} \boldsymbol{y}-\boldsymbol{3} \boldsymbol{x}-\boldsymbol{4} \boldsymbol{y}+\boldsymbol{8}=\boldsymbol{0} \) is
A .4
B. \( 4 \sqrt{2} \)
\( c \cdot 8 \)
D. None of these
Subject: Maths
A function \( f \) is defined as follows:
\( \boldsymbol{f}(\boldsymbol{x})= \)
\( \left\{\begin{array}{ll}1 & \text { for }-\infty< \\ 1+\sin x & \text { for } 0 \leq x<\frac{\pi}{2} \\ 2+\left(x-\frac{\pi}{2}\right)^{2} & \text { for } \frac{\pi}{2} \leq x<+\infty\end{array}\right. \)
Discuss the continunity and
differentiability at \( \boldsymbol{x}=\mathbf{0} \& \boldsymbol{x}=\boldsymbol{\pi} / \mathbf{2} \)
This question has multiple correct options
A. continuous but not differentiable at \( x=0 \)
B. differentiable and continuous at \( x=\pi / 2 \)
c. neither continuous but nor differentiable at \( x=0 \)
D. continuous but not differentiable at \( x=\pi / 2 \)
Subject: Physics
The temperature of a furnace is \( 2327^{\circ} \mathrm{C} \)
and the intensity of maximum in its spectrum is nearly at 12000 A. If the intensity in the spectrum of a star is maximum nearly at 4800 A, then the surface temperature of the star is
\( \mathbf{A} \cdot 767^{\circ} C \)
в. \( 1040^{\circ} \mathrm{C} \)
c. \( 6500^{\circ} \mathrm{C} \)
D. \( 6227^{\circ} \mathrm{C} \)
Subject: Chemistry
Mendeleev predicted the existence of
certain elements not known at that
time and named two of them as Eka -
silicon and Eka - Aluminium.

Mention the group of these elements in
the Modern Periodic Table :
A. Group 12 and Group 13.
B. Group 14 and Group 15.
c. Group 14 and Group 13.
D. Group 15 and Group 13
Subject: Maths
\( A B C D \) is a cyclic quadrilateral such
that \( A B \) is a diameter of the circle
circumscribing it and \( \angle A D C=140^{\circ} \)
then \( \angle B A C \) is equal to
\( A \cdot 80 \)
B. \( 50^{\circ} \)
\( c \cdot 40^{\circ} \)
D. \( 30^{\circ} \)
Subject: Physics
A sound source is moving towards stationary listener with \( \frac{1}{10} \) th of the speed of sound. The ratio of apparent to real frequency is:
\( ^{\mathrm{A}} \cdot\left(\frac{9}{10}\right)^{2} \)
в. \( \frac{10}{9} \)
c. \( \frac{11}{10} \)
D \( \cdot\left(\frac{11}{10}\right)^{2} \)
Subject: Maths
ff \( y=\log \left(\sqrt{x}+\frac{1}{\sqrt{x}}\right), \) prove that
\( \frac{\boldsymbol{d} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}}=\frac{\boldsymbol{x}-\mathbf{1}}{\boldsymbol{2} \boldsymbol{x}(\boldsymbol{x}+\mathbf{1})} \)
Subject: Chemistry
When freshly precipitated \( F e(O H)_{3} \) is
boiled with water in the presence of few drops of dil. \( \boldsymbol{H} \boldsymbol{C l} \), a hydrated ferric
oxide sol is obtained. This method is
termed:
A. dialysiss
B. peptization
c. ultrafiltration
D. electro-dispersion
Subject: Chemistry
The equilibrium constant \( K_{C} \) for the reaction,
\( A(g)+2 B(g) \rightleftharpoons 3 C(g) \) is \( 2 \times 10^{-3} \)
What would be the equilibrium partial
pressure of gas \( C \) if initial pressure of \( \operatorname{gas} A \) and \( B \) are 1 and 2
Subject: Physics
A small isolated conductor has a large
positive charge.

What is true of the electric field and the
electric potential inside this conductor?
A . Electric Field inside Conductor - Electric Potential inside Conductor, large and positive - large and positive
B. Electric Field inside Conductor - Electric Potential inside Conductor, zero - zero
C. Electric Field inside Conductor - Electric Potential inside Conductor, zero - large and positive
D. Electric Field inside Conductor - Electric Potential inside Conductor, large and positive - zero
E. Electric Field inside Conductor - Electric Potential inside Conductor, large and positive - large and negative
Subject: Maths
A godown building is in the form as shown in figure. The vertical crosssection parallel to the width side of the building is a rectangle \( 7 m \times 3 m \)
mounted by a semi-circle of radius
\( 3.5 m . \) The inner measurements of the
cuboidal portion of the building are
\( 10 m \times 7 m \times 3 m . \) Find the volume of
the godown and the total interior
surface area excluding the floor (Base) (Take \( \boldsymbol{\pi}=\mathbf{2 2} / \mathbf{7}) \)
Subject: Maths
If the vectors \( 2 \vec{a}-\vec{b}+\vec{c}, \vec{a}+2 \vec{b}- \)
\( \overrightarrow{3} c, 3 \vec{a}+m \vec{b}+5 \vec{c} \) are linearly
dependent, then \( \boldsymbol{m}= \)
\( A \cdot 2 \)
B. -
\( c \cdot 4 \)
D. -4
Subject: Chemistry
If \( X \) represents an element of atomic
number 9 and \( Y \) an element of atomic
number \( 20, \) the compound formed by these elements would be :
A . ionic with formula \( Y X_{2} \)
B. covalent with formula \( Y X_{2} \)
c. ionic with formula \( Y X \)
D. covalent with formula \( Y X \)
Subject: Maths
\( \lim _{x \rightarrow 5} \frac{\sin ^{2}(x-5) \tan (x-5)}{\left(x^{2}-25\right)(x-5)} \) is equal to
A. 1
B. \( \frac{1}{10} \)
\( c \cdot 0 \)
\( D \)