AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Chemistry
Identify \( \boldsymbol{A}, \boldsymbol{B}, \boldsymbol{C}, \boldsymbol{D}, \boldsymbol{E}, \boldsymbol{F}, \boldsymbol{G} \)
\( \mathbf{K}_{2} \mathbf{C r}_{2} \mathbf{O}_{7} \stackrel{\mathbf{K O H}}{\longrightarrow}(\mathbf{A}) \frac{\mathbf{P} \mathbf{b}\left(\mathbf{C H}_{3} \mathbf{C O O}\right)_{2}}{\mathbf{C H}_{3} \mathbf{C O O H}}>(\mathbf{B}) \)
\( \mathbf{N H}_{4} \mathbf{C l} \)
\( (\mathrm{C}) \stackrel{\Delta}{\longrightarrow}(\mathrm{D})+(\mathrm{E}) \)
(gas) (green) \( \frac{|\mathbf{A}|, \Delta}{\mid} \)
(F) (metal) \( +(G) \) oxide
Subject: Physics
The instantaneous value of current at a
given instant is1 \( A \) and peak value of current is \( \frac{5}{3} A . \) The potential difference between \( P \) and \( Q \) at the same instant is
A \( \cdot \frac{23}{3} V \)
B. \( 7 V \)
\( c .3 V \)
D. \( 4 V \)
Subject: Maths
If \( \int \frac{2 x^{2}+3}{\left(x^{2}-1\right)\left(x^{2}+4\right)} d x= \)
\( \operatorname{Alog}\left(\frac{\boldsymbol{x}+\mathbf{1}}{\boldsymbol{x}-\mathbf{1}}\right)+\boldsymbol{B} \tan ^{-1}\left(\frac{\boldsymbol{x}}{\mathbf{2}}\right)+\boldsymbol{C} \) then
\( (A, B) \) is
A \( \cdot\left(-\frac{1}{2}, \frac{1}{2}\right) \)
B \( \cdot\left(\frac{1}{2},-\frac{1}{2}\right) \)
\( \left(\frac{1}{2}, \frac{1}{2}\right) \)
D. (1,-1)
Subject: Maths
Let \( n \) be a positive integer. Call a non-
empty subset \( S \) of \( \{1,2, \ldots, n\} \) good, if
the arithmetic mean of the elements of
\( S, \) is also an integer. Further let \( t_{n} \) denote the number of good subsets of
\( \{1,2, \ldots, n\} . \) Prove that \( t_{n} \) and \( n \) are both
odd or both even
Subject: Maths
One angle of a seven-sided polygon is
\( 114^{\circ} \) and each of the other six angles is
\( x^{\circ} . \) The value of \( x \) is?
A \( \cdot 114^{\circ} \)
B. 121
\( c \cdot 131^{\circ} \)
D. \( 151^{\circ} \)
Subject: Chemistry
Positive deviation from ideal behaviour
takes place because of :
A . molecular interaction between atoms and \( \frac{P V}{n R T}>1 \)
B. molecular interaction between atoms and \( \frac{P V}{n R T}<1 \)
C ' finite size of atoms and \( \frac{P V}{n R T}>1 \)
D tinite size of atoms and \( \frac{P V}{n R T}<1 \)
Subject: Chemistry
The ionisation constants of formic acid
and ammonium hydroxide are \( 2 \times 10^{-4} \)
and \( 2 \times 10^{-5} \) respectively. The pH of
aqueous solution of ammonium formate is :
\( A \cdot 7 \)
B. 6.
c. 11.5
D. 8
Subject: Maths
The distance between the lines \( y= \)
\( 2 x+4 \) and \( 3 y=6 x-5 \) is equal to
A .
B. \( 3 / \sqrt{5} \)
c. \( \frac{17 \sqrt{5}}{15} \)
D. \( \frac{17}{\sqrt{3}} \)
Subject: Chemistry
Select the correct statement(s) for
double salt:
This question has multiple correct options
A. Double salts are stable in solid state but loose their
identity in aqueous solution.
B. In double salt the properties of constituent ions are not changed in their aqueous solution.
C. Double salts are stable in solid-state and do not lose their identity in aqueous solution.
D. In double salt the properties of constituent ions are changed in their aqueous solution.
Subject: Chemistry
Mark the correct statement(s) based on
the phase diagram of \( C O_{2} \) shown in the graph.
rhis question has multiple correct options
A \( \cdot 298 \mathrm{K} \) is the normal boiling point of liquid \( C O_{2} \)
B. At 1 atm \& 190 K \( C O_{2} \) will exist as gas.
\( \mathrm{c} \cdot \mathrm{CO}_{2}(s) \) will sublime above \( 195 \mathrm{K} \) under norma atmospheric pressure
D. Melting point \& boiling point of \( C O_{2} \) will increase on increasing pressure.
Subject: Chemistry
The complete balanced equation is:
\( \boldsymbol{C u}+\boldsymbol{N} \boldsymbol{O}_{3}^{-}+\ldots . \rightarrow \boldsymbol{C u}^{2+}+\boldsymbol{N} \boldsymbol{O}_{2}+ \)
A \( \cdot C u+4 H^{+}+2 N O_{3}^{-} \rightarrow C u^{2+}+2 N O_{2}+2 H_{2} O \)
B . \( C u+6 H^{+}+N O_{3}^{-} \rightarrow C u^{2+}+2 N O_{2}+2 H_{2} O \)
c. \( C u+4 H^{+}+2 N O_{3}^{-} \rightarrow 2 C u^{2+}+N O_{2}+2 H_{2} O \)
D. none of these
Subject: Maths
Make \( r \) the subject of formula.
A \( \cdot_{r}=\sqrt{\frac{\pi R^{2} l+V}{\pi l}} \)
в. \( r=\sqrt{\frac{\pi R^{2} l-V}{\pi l}} \)
c. \( _{r}=\sqrt{\frac{\pi R^{2} l+V}{2 \pi l}} \)
D. none of the above
Subject: Biology
Column I contains some terms and
column II contains their meanings.
Match the properly and choose the right
answer.
Colum Column II
1. Conversion of glycogen to
A. Glycogenesis
2. Conversion of glucose to
B. Glycosuria \( \quad \) glycogen
C. \( \quad \) 3. Excretion of glucose in urine Glyconeogenesis
4. Conversion of non-
D. \( \quad \) carbohydrate sources to Glycogenolysis
5. Conversion of glucose to starch
\( A \cdot A-1, B-2, C-3, D-4 \)
B. A-2, B-3, C-4, D-1
C \( . \) A- \( 2, \) B-1, C-3, D-4
D. \( A-1, B-5, C-2, D-4 \)
Subject: Maths
If an equilateral triangle, having centroid at the origin, has a side along
the line, \( x+y=2 \), then the area (in
sq.units) of this triangle is:
\( \mathbf{A} \cdot \mathbf{6} \)
B. \( 6 \sqrt{3} \)
c. \( \frac{9}{2} \sqrt{3} \)
D. \( 3 \sqrt{6} \)
Subject: Chemistry
For the pressure-volume work
expression, the term pressure in the
expression refers to
gas pressure.
\( \mathbf{A} \cdot W=-P_{e x} \cdot \Delta P \)
\( \mathbf{B} \cdot W=-P_{e x} \cdot \Delta V \)
\( \mathbf{C} \cdot W=-P_{e x} \cdot \Delta C \)
\( \mathbf{D} \cdot W=-P_{e x} \cdot \Delta D \)
Subject: Physics
Two long parallel wires are at a distance of 1 metre. Both of them carry one
ampere of current. the force of
attraction per unit length between the two wires is
A \( \cdot 2 \times 10^{-7} \mathrm{Nm}^{-1} \)
В. \( 2 \times 10^{-8} N m^{-1} \)
c. \( 5 \times 10^{-8} \mathrm{Nm}^{-1} \)
D. \( 10^{-7} N m^{-1} \)
Subject: Physics
Assertion
In its rest position the clapper is held away from the bell a short distance by
its springy arm.
Reason
The spring constant of spring must be such that clapper should be able to give
reaction to the magnetic force of
attraction upto a certain extent
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
A particle has an initial velocity of \( 3 \hat{i}+4 \hat{j}) \mathrm{m} / \mathrm{s} \) and a constant
acceleration of \( (4 \hat{i}-3 \hat{j}) m / s^{2} . \) Its
speed after one second will be equal to:
A. 0
B. \( 7 \sqrt{2} \frac{m}{s} \)
c. \( \sqrt{50} \frac{m}{s} \)
D. 25 m/sec
Subject: Chemistry
Assertion
0.2 per cent solution of phenol is an
antiseptic while its one percent solution is disinfectant.
Reason
Antiseptics are also called disinfectant.
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
Pyrophosphoric acid is the mixture of :
A. \( \mathrm{H}_{3} \mathrm{PO}_{3}+\mathrm{HPO}_{3} \)
в. \( \mathrm{H}_{3} \mathrm{PO}_{4}+\mathrm{H}_{3} \mathrm{PO}_{3} \)
c. \( \mathrm{H}_{3} \mathrm{PO}_{4}+\mathrm{HPO}_{3} \)
D. none of these
Subject: Physics
A rubber ball drops from a height h. If the ball rises to h / 2 after rebounding three times coefficient of restitution \( e \)
is
A \( \cdot \frac{1}{2} \)
в. \( \quad\left(\frac{1}{2}\right)^{\frac{1}{2}} \)
c. \( \quad\left(\frac{1}{2}\right)^{\frac{1}{4}} \)
D.
Subject: Physics
Three men \( A, B \) and \( C \) of masses
\( 40 k g, 50 k g \) and \( 60 k g \) are standing on
a plank of mass \( 90 \mathrm{kg} \), which is kept on
a smooth horizontal plane. If \( A \) and \( C \)
exchange their positions then mass \( B \)
will shift
A. \( 1 / 3 m \) towards left
B. \( 1 / 3 m \) towards right
c. will not move w.r.tground
D. \( 5 / 3 m \) towards left
Subject: Physics
A drop of water of radius \( 0.0015 \mathrm{mm} \) is falling in air. If the coefficient of
viscosity of air is \( 1.8 \times 10^{-5} k g / m s \)
what will be the terminal velocity of the drop? (density of water \( =1.0 \times \) \( 10^{3} k g / m^{2} \) and \( g=9.8 \mathrm{N} / \mathrm{kg} \) ). The
density of air can be neglected
A \( .2 .72 \times 10^{-4} \mathrm{m} / \mathrm{s} \)
B . \( 3.72 \times 10^{-4} \mathrm{m} / \mathrm{s} \)
c. \( 0.72 \times 10^{-4} \mathrm{m} / \mathrm{s} \)
D. \( 12.72 \times 10^{-4} \mathrm{m} / \mathrm{s} \)
Subject: Chemistry
"While comparison of \( L i^{+} \) and \( N a^{+} \)
salts in terms of property of complex
formation we found that \( \left[\boldsymbol{L} \boldsymbol{i}\left(\boldsymbol{N} \boldsymbol{H}_{3}\right)_{4}\right] \)
exists and \( N a \) does not form any
complex." Answer whether the above statement is
true or false.
If true enter 1 , else 0
Subject: Maths
\( 25 x^{2}-\left(x^{2}-36\right)^{2}= \)
A \( \cdot(x-4)(x+4)(x+9)(x-9) \)
B \( \cdot(x-4)(4+x)(x+9)(9-x) \)
\( \mathbf{c} \cdot(x+4)(x+4)(x-9)(x-9) \)
D \( \cdot(x-4)(4-x)(x+9)(9+x) \)
Subject: Maths
\( P, Q \) and \( R \) are three sets and \( \xi=P \cup \)
\( Q \cup R \) Given that \( n(\xi)=60, n(P \cap \)
\( Q)=5, n(Q \cap R)=10, n(P)=20 \) and
\( \boldsymbol{n}(\boldsymbol{Q})=23, \) find \( \boldsymbol{n}(\boldsymbol{P} \cup \boldsymbol{R}) \)
A . 37
B . 38
c. 45
D. 52
Subject: Physics
Light of intensity \( =3 W / m^{2} \) is incident
on a perfectly absorbing metal surface of area \( 1 m^{2} \) making an angle of \( 60^{\circ} \) with the normal. If the force exerted by
the photons on the surface is \( \boldsymbol{p} \times 10^{-9} \)
(in Newton), then the value of p is :
A. 5
B. 2
\( c \)
\( D .3 \)
Subject: Biology
Which of the following statement is
true?
A. The collenchyma occurs in layers below the epidermis in monocotyledonous plants
B. Sclerenchyma cells are usually dead and without protoplasts.
c. xylem parenchyma cells are living and thin walled and their cell walls are made up of lignin.
D. The companion cells are specialized sclerenchymatous cells.
E. Phloem fibres are generally present in the primary phloem.
Subject: Maths
Degree of \( \left[\frac{d^{2} y}{d x^{2}}+\left(\frac{d y}{d x}\right)^{2}\right]^{3 / 2}=k \frac{d^{2} y}{d x^{2}} \)
is:
\( A \cdot 4 \)
B.
\( c \cdot 2 \)
\( D \)
Subject: Physics
A metal rod moves at a constant
velocity in a direction perpendicular to its length. A constant uniform magnetic field exists in space in a direction perpendicular to the rod as well as its velocity. Select the correct statement(s) from the following:
A. The entire rod is at the same electric potentia
B. There is an electric field in the rod
c. The electric potential is highest at the center of the rod and decrease toward its ends
D. The electric potential is lowest at the center of the rod and increases toward its ends
Subject: Chemistry
\( ?+\boldsymbol{H}_{2} \boldsymbol{S} \boldsymbol{O}_{4} \rightarrow \boldsymbol{C} \boldsymbol{u} \boldsymbol{S} \boldsymbol{O}_{4}+\boldsymbol{H}_{2} \boldsymbol{O} \)
A \( \cdot \) CuSO \( _{4} \)
в. \( C u C l_{2} \)
c. \( C u \)
D. \( C u O \)
Subject: Maths
If \( e \) and \( e^{\prime} \) be the eccentricities of two
conics \( S \) and \( S^{\prime} \) such that \( e^{2}+\left(e^{\prime}\right)^{2}= \)
\( 3, \) then both \( S \) and \( S^{\prime} \) are
A. Ellipses
B. Parabolas
c. Hyperbolas
D. None of these
Subject: Chemistry
For the reaction \( 2 A+3 B \rightarrow \) products,
\( A \) is taken in excess and on changing the concentration of \( \mathrm{B} \) from \( 0.1 \mathrm{M} \) to 0.4
M, the rate becomes doubled. Thus, the rate law of the reaction is:
A \( \cdot \frac{d x}{d t}=k[A]^{2}[B]^{2} \)
в. \( \frac{d x}{d t}=k[A][B] \)
\( \stackrel{d x}{d t}=k[A]^{0}[B]^{2} \)
D. \( \frac{d x}{d t}=k[B]^{1 / 2} \)
Subject: Chemistry
In the cyanide extraction process of
silver from argentite ore, the oxidizing
and reducing agents used are:
A. \( O_{2} \) and \( C O, \) respectively
B. \( O_{2} \) and \( Z n \) dust, respectively
c. \( H N O_{3} \) and \( Z n \) dust, respectively
D. \( H N O_{3} \) and \( C O, \) respectively
Subject: Maths
Arrange the eccentricities of the following ellipses in particular order.
A- Ellipse whose Latus rectum is half of its major axis.
B- Ellipse whose distance between the foci is equal to the distance between a focus and one end of minor axis
C- Ellipse whose major axis is double the minor axis.
D- Ellipse whose distance between the foci is 6 and the length of minor axis is
8
\( A \)
\[
(A)=(C)>(D)>(B)
\]
B. \( (A)=(C)<(D)<(B) \)
\( c \)
\[
(A)>(C)>(D)>(B)
\]
D. none of these
Subject: Physics
The molar specific heat of oxygen at
constant pressure \( \boldsymbol{C}_{\boldsymbol{P}}= \)
\( \mathbf{7 . 0 3} \mathbf{c a l} / \mathbf{m o l}^{\circ} \mathbf{C} \) and \( \boldsymbol{R}= \)
\( 8.32 J / \) mol \( ^{\circ} \mathrm{C} \). The amount of heat
taken by 5 moles of oxygen when heated
at constant volume from \( 10^{\circ} \mathrm{C} \) to \( 20^{\circ} \mathrm{C} \)
will be approximately.
\( \mathbf{A} \cdot 25 \) cal
в. 50 cal
c. 253 call \( l \)
D. 500 call
Subject: Physics
Wo are
kept in two identical vessels, which are
placed in a freezer that extracts heat from them at the same rate causing each liquid to transform into a solid. The schematic figure shows the temperature T vs time \( t \) plot for the two
material. We denote the specific heat of materials in the liquid(solid) states to
be \( C_{L 1}\left(C_{S 1}\right) \) and \( C_{L 2}\left(C_{S 2}\right) \) respectively. Choose the correct option.
A \( \cdot C_{L 1}<C_{L 2} \) and \( C_{S 1}<C_{S 2} \)
B . \( C_{L 1}>C_{L 2} \) and \( C_{S 1}<C_{S 2} \)
C. \( C_{L 1}>C_{L 2} \) and \( C_{S 1}>C_{S 2} \)
D. \( C_{L 1}<C_{L 2} \) and \( C_{S 1}>C_{S 2} \)
Subject: Physics
A metallic shpere of radius \( 1.0 \times \) \( 10^{-3} m \) and density \( 1.0 \times 10^{4} k g / m^{3} \)
enters a tank of water after a free fall,
falling through a distance of h in the earth's gravitational field. If its velocity remains unchanged after entering water, determine the value of \( h \)
[Given : coefficient of viscosity of water
\( =1.0 \times 10^{-3} N-s / m^{2}, g=10 m / s^{2} \)
and density of water \( \left.=1.0 \times 10^{3} k g / m^{3}\right] \)
A. 20 \( m \)
B. 40 \( m \)
\( c \cdot 80 m \)
D. \( 10 \mathrm{m} \)
Subject: Physics
Which of the following expressions are applicable to the moving coil galvanometer?
A \( \cdot \overrightarrow{F_{m}}=q(\vec{V} \times \vec{B}) \)
в. \( B=B_{0} \tan \theta \)
c. \( \vec{\tau}=\vec{M} \times \vec{B} \)
D. none of these
Subject: Physics
Two identical blocks of weight W are placed one on top of the other as shown in figure. The upper block is tied to the
wall. The lower block is pulled to the right with a force F. The coefficient of static friction between all surfaces in
contact is \( \mu . \) What is the largest force
that can be exerted before the lower
block starts to slip?
A \( \cdot \mu W \)
в. \( 2 \mu W \)
\( c \cdot 3 \mu W \)
D. \( 4 \mu W \)
Subject: Physics
A capacitor of capacitance \( C \) is charged to a potential difference V from a cell and
then disconnected from it. A charge +Q is now given to its positive plate. The potential difference across the capacitor
is now:
A. \( V \)
B. \( V+\frac{Q}{C} \)
\( c \cdot V+\frac{Q}{2 C} \)
D. \( V-\frac{Q}{C}, \) if \( V<C V \)
Subject: Physics
The figure shows a ray incident at angle
\( i=\frac{\pi}{3} . \) If the plot drawn show the
variation of \( |r-i| \) versus \( \frac{\mu_{1}}{\mu_{2}}=k,(r= \)
angle of refraction)
A \( \cdot \) the value of \( k_{1} i s \frac{2}{\sqrt{3}} \)
B. the value of \( \theta_{1}=\frac{\pi}{6} \)
C. the value of \( \theta_{2}=\frac{\pi}{3} \)
D. the value of \( k_{2} \) is 1
Subject: Chemistry
Consider the following equilibrium:
\( \boldsymbol{x}_{2(g)}+\mathbf{2} \boldsymbol{H}_{2(\boldsymbol{g})} \rightarrow \mathbf{2} \boldsymbol{H}_{2} \boldsymbol{X}_{(\boldsymbol{g})}+\boldsymbol{e n e r g y} \)
Addition of \( X_{2} \) to a system described by the above equilibrium will:
A. Increase the equilibrium concentration of \( \left[H_{2}\right] \)
B. Increase the equilibrium concentration of \( \left[H_{2} X\right] \)
C. Decrease the equilibrium concentration of \( \left[H_{2} X\right] \)
D. Have no effect on the equilibrium concentrations
E. Decrease the amount of heat energy given off by the
Subject: Chemistry
An atom of radium combines with two
atoms of chlorine to form RaCl
molecule. The radioactivity of \( \boldsymbol{R} \boldsymbol{a} \boldsymbol{C l}_{2} \)
will be :
A. zero
B. one-half of the same quantity of Ra
C. one-third of the same quantity of Ra
D. as much as that of the same quantity of Ra
Subject: Maths
Assume that the chances of a patient having a heart attack is \( 40 \% \). It is also assumed that a meditation and yoga
course reduce the risk of heart attack by \( 30 \% \) and prescription of certain drug reduces its chances by \( 25 \% \). At a time a
patient can choose any one of the two options with equal probabilities. It is given that after going through one of the two options the patient selected at random suffers a heart attack. Find the
probability that the patient followed a course of meditation and yoga?
Subject: Chemistry
\( \boldsymbol{E}_{\text {Cell }}^{\ominus} \) of \( \boldsymbol{Z} \boldsymbol{n} / \boldsymbol{Z} \boldsymbol{n}^{2+} \| \boldsymbol{C} \boldsymbol{u}^{2+} / \boldsymbol{C u} \) is \( \mathbf{1 . 1 0} \mathbf{v} \)
at \( 25^{\circ} \mathrm{C}, \) the equilibrium constant for
the reaction, \( Z n+C u^{2+} \rightleftharpoons C u+ \)
\( Z n^{2+} \) is approximately of the order of:
\( \mathbf{A} \cdot 10^{-28} \)
B . \( 10^{+37} \)
\( \mathbf{c} \cdot 10^{-18} \)
D. \( 10^{17} \)
Subject: Maths
If \( A \) and \( B \) are coefficients of \( x^{n} \) in the
expansions of \( (1+x)^{2 n} \) and \( (1+x)^{2 n-1} \)
respectively, then \( \frac{A}{B} \) is equal to
A .4
B . 2
\( c .9 \)
D. 6
Subject: Chemistry
The values of \( \Delta H \) and \( \Delta U \) for the
reversible isothermal evaporation of
\( 90.0 \mathrm{g} \) of water at \( 100^{\circ} \mathrm{C} \) are \( x \) cal \( \& y \) cal. Assume that water vapour behaves
as an ideal gas and heat of evaporation of water is 540 cal \( g^{-1} .(R= \)
\( \left.2 c a l \operatorname{mol}^{-1} K^{-1}\right) . \) The value of \( x+y \) is:
Subject: Maths
The negation of the statement \( (\boldsymbol{p} \rightarrow \)
\( \boldsymbol{q}) \wedge \boldsymbol{r} \) is
\( \mathbf{A} \cdot p \wedge \sim q \vee \sim r \)
В \( .(\sim p \wedge q) \wedge(\sim r) \)
c. \( (p \wedge \sim q) \wedge(r) \)
D. \( (p \wedge \sim q) \wedge(\sim r) \)
Subject: Chemistry
Point out the correct decreasing order of
\( \boldsymbol{p} \boldsymbol{K}_{\boldsymbol{b}} \) values of following amines:
\( \boldsymbol{C}_{2} \boldsymbol{H}_{5} \boldsymbol{N} \boldsymbol{H}_{2}, \boldsymbol{C}_{6} \boldsymbol{H}_{5} \boldsymbol{N} \boldsymbol{H} \boldsymbol{C} \boldsymbol{H}_{3} \)
\( \left(C_{2} H_{5}\right)_{2} N H \) and \( C_{6} H_{5} N H_{2} \)
\( \mathbf{A} \cdot\left(C_{2} H_{5}\right)_{2} N H>C_{2} H_{5} N H_{2}>C_{6} H_{5} N H C H_{3}> \)
\( C_{6} H_{5} N H_{2} \)
B. \( \left(C_{2} H_{5}\right)_{2} N H>C_{6} H_{5} N H C H_{3}>C_{6} H_{5} N H_{2}> \)
\( C_{2} H_{5} N H_{2} \)
c. \( C_{6} H_{5} N H_{2}>C_{6} H_{5} N H C H_{3}>C_{2} H_{5} N H_{2}> \)
\( \left(C_{2} H_{5}\right)_{2} N H \)
D. \( C_{2} H_{5} N H_{2}>\left(C_{2} H_{5}\right)_{2} N H>C_{6} H_{5} N H C H_{3}> \)
\( C_{6} H_{5} N H_{2} \)
Subject: Maths
Given \( \boldsymbol{f}(\boldsymbol{x})= \)
\( \left\{\begin{array}{l}\frac{[\{|\boldsymbol{x}|\}] \boldsymbol{e}^{\boldsymbol{x}^{2}}\{[\boldsymbol{x}+\{\boldsymbol{x}\}]\}}_{\left(\frac{1}{\boldsymbol{e}^{x^{2}}-1}\right)} \boldsymbol{s} \boldsymbol{g n}(\sin \boldsymbol{x}) \\ \boldsymbol{0} \quad \text { for } \quad \boldsymbol{x}=\mathbf{0}\end{array}\right. \)
Where \( \{x\} \) is the fractional part
function; \( [x] \) is the step up function and
\( \operatorname{sgn}(x) \) is the signum function of \( x \) then,
\( \boldsymbol{f}(\boldsymbol{x}) \)
A. Is continuous at \( x=0 \)
B. Is discontinuous at \( x=0 \)
C. Has a removable discontinuity at \( x=0 \)
D. Has in irremovable disconitnuity at \( x=0 \)
Subject: Maths
If the sum and sum of squares of 10
observations are 12 and 18 resp., then, The \( S . D \) of observations is :
A \( \cdot \frac{1}{5} \)
B. \( \frac{2}{5} \)
\( c \cdot \frac{3}{5} \)
D. \( \frac{4}{5} \)
Subject: Chemistry
A solution containing 4 g of a nonvolatile organic solute per \( 100 \mathrm{mL} \) was found to have an osmotic pressure
equal to \( 500 \mathrm{cm} \) of mercury at \( 27^{\circ} \mathrm{C.The} \) molecular weight of solute is:
A . 14.97
B. 149.7
c. 1697
D. 1.497
Subject: Physics
A plane electromagnetic wave of frequency \( 25 ~ M H z \) travels in free space along \( x \) -direction. At a particular
point in space and time, electric field
\( \boldsymbol{E}=\mathbf{6 . 3} \boldsymbol{V} \boldsymbol{m}^{-1}, \) the magnitude of
magnetic field B at this point is:
A . \( 1.2 \times 10^{-6} T \)
В . \( 1.2 \times 10^{-8} T \)
c. \( 2.1 \times 10^{-6} T \)
D. \( 2.1 \times 10^{-8} T \)
Subject: Chemistry
In the crystal field of the complex
\( \left[\boldsymbol{F} e(\boldsymbol{C l})(\boldsymbol{C} \boldsymbol{N})_{4}(\boldsymbol{O})_{2}\right)^{4-}, \) the electronic
configuration of metal is found to be \( t_{2 g}^{6} \) \( e_{g}^{0}, \) then which of the following is/are true about this complex ion? This question has multiple correct options
A. It is paramagnetic complex
B. 0 - 0 bond length will be more than found in \( O_{2} \) molecule
c. Its IUPAC name will be chlorotetracyanosuperoxidoferrate (II) ion
D. It will show geometrical as well as optical isomerism
Subject: Chemistry
Which of the following represents
calcium chlorate?
A \( \cdot C a C l O_{2} \)
в. \( \operatorname{Ca}\left(C l O_{4}\right)_{2} \)
c. \( C a\left(C l O_{3}\right)_{2} \)
D. \( C a\left(C l O_{2}\right)_{2} \)
Subject: Maths
Find mode for the following data:
\( \begin{array}{llll}\text { Size } & \boldsymbol{2}- & \boldsymbol{5}- & \boldsymbol{8}- & \boldsymbol{1} \mathbf{1}- \\ & \boldsymbol{5} & \boldsymbol{8} & \boldsymbol{1} \mathbf{1} & \boldsymbol{1} \mathbf{4}\end{array} \) \( \mathbf{1 4} \) Number
of
shoes \( \quad 1 \quad 4 \quad 8 \quad 7 \)
\( \mathbf{A} \cdot 10.4 \)
B. 11.4
c. 12.4
D. 13.4
Subject: Chemistry
What is the velocity of electron present in first Bohr orbit of hydrogen atom?
A \( \cdot 2.18 \times 10^{5} m / s \)
B \( \cdot 2.18 \times 10^{6} m / s \)
C \( .2 .18 \times 10^{-18} \mathrm{m} / \mathrm{s} \)
D. \( 2.18 \times 10^{-9} \mathrm{m} / \mathrm{s} \)
Subject: Chemistry
What is the equilibrium constant expression for the reaction,
\( \boldsymbol{P}_{4}(s)+\mathbf{5} O_{2}(\boldsymbol{g}) \rightleftharpoons \boldsymbol{P}_{4} \boldsymbol{O}_{10}(s) \)
\( ^{\mathbf{A}} \cdot_{K_{c}}=\frac{\left[P_{4} O_{10}\right]}{\left[P_{4}\right]\left[O_{2}\right]^{5}} \)
в. \( _{K_{c}}=\frac{\left[P_{4} O_{10}\right]}{5\left[P_{4}\right]\left[O_{2}\right]} \)
\( \mathbf{c} \cdot_{K_{c}=\left[O_{2}\right]^{5}} \)
\( ^{\mathrm{D}} K_{c}=\frac{1}{\left[O_{2}\right]^{5}} \)
Subject: Maths
A cube of edge \( 3 \mathrm{cm} \) of iron weighs \( 12 \mathrm{g} \) What is the weight of a similar cube of
iron whose edge is \( 12 \mathrm{cm} \)
A. 768 g
в. 678 g
c. \( 964 \mathrm{g} \)
D. \( 864 \mathrm{g} \)
Subject: Physics
3 mole of gas "X" and 2 moles of gas "Y" enters from end "P" and "Q" of the cylinder respectively. The cylinder has the area of cross section, shown as
under
The length of the cylinder is \( 150 \mathrm{cm} \). The gas "X" intermixes with gas "Y" at the point. If the molecular weight of the
gases \( X \) and \( Y \) is 20 and 80 respectively, then what will be the distance of point \( \mathbf{A} \)
from Q?
A. \( 75 \mathrm{cm} \)
B. \( 50 \mathrm{cm} \)
c. 37.5
D. \( 90 \mathrm{cm} \)
Subject: Physics
Consider points \( A, B, C, D \) on a horizontal cardboard equidistant from center \( \boldsymbol{O} \) as shown in the figure. \( \mathbf{A} \) copper wire perpendicular to the
cardboard passes through the center \( O \) and carries an electric current
flowing upwards. Deflection of magnetic needle will be maximum when it is kept
at the point
A . \( A \)
в. \( B \)
\( c . c \)
\( D \)