AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Chemistry
Assertion
Graphite is used as anode but not
diamond.
Reason
Graphite is good conductor of current
due to sp \( ^{2} \) hybridisation having mobile
\( \pi \) electrons. Diamond has \( s p^{3} \)
hybridisation and is insulater.
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
In a Vander waals interaction: \( \boldsymbol{U}= \)
\( \boldsymbol{U}_{0}\left[\left(\frac{\boldsymbol{R}_{0}}{\boldsymbol{r}}\right)^{12}-\boldsymbol{2}\left(\frac{\boldsymbol{R}_{0}}{\boldsymbol{r}}\right)^{6}\right] \)
A small displacement x is given from
equilibrium position \( r=R_{0} . \) Find the
approximate PE function.
A \( \cdot \frac{36 U_{0}}{R_{0}^{2}} x^{2}-U_{0} \)
в. \( \frac{24 U_{0}}{R_{0}} x-U_{0} \)
c. \( \frac{96 U_{0}}{R_{0}^{2}}-U_{0} \)
D. none of these
Subject: Maths
ABCD is a trapezium in which \( \boldsymbol{A B} \| \) \( \boldsymbol{D} \boldsymbol{C}, \boldsymbol{A B}=\mathbf{5 0} \mathrm{cm}, \boldsymbol{D} \boldsymbol{C}=\mathbf{3 0} \mathrm{cm} . \) If \( \boldsymbol{X} \)
and \( Y \) are respectively the mid-points
of \( A D \) and \( B C, \) prove that
\( \boldsymbol{a} \boldsymbol{r}(\operatorname{trap} \cdot \boldsymbol{D} \boldsymbol{C} \boldsymbol{Y} \boldsymbol{X})= \)
\( \frac{\mathbf{7}}{\mathbf{9}} \boldsymbol{a} \boldsymbol{r}(\operatorname{trap} . \boldsymbol{X} \boldsymbol{Y} \boldsymbol{B} \boldsymbol{A}) \)
Subject: Chemistry
Assertion
In the process of drying dishes with a towel, the wetting agent is the dish and the drying agent is the towel
Reason
The wetting agent gets wet during the
process.
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
Assertion
The relation \( \frac{x}{m}=k \cdot p^{1 / n} \) is known as Freundlich adsorption isotherm, where
\( x \) is the mass of gas adsorbed by \( m \)
grams of adsorbate, \( \boldsymbol{p} \) is the
equilibrium pressure, \( k \) and \( n \) are
constants for given system and
temperature
Reason
When several substances have the
same value of \( \frac{1}{n}, \) the lines by which their adsorption isotherms can be
represented will meet at a point.
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
Solve the following system of inequalities graphically:
\( \mathbf{3} \boldsymbol{x}+\mathbf{4} \boldsymbol{y} \leq \mathbf{6 0}, \quad \boldsymbol{x}+\mathbf{3} \boldsymbol{y} \leq \mathbf{3 0}, \quad \boldsymbol{x} \geq \)
\( 0 . y \geq 0 \)
Subject: Physics
The potential energy function for
a particle executing linear simple harmonic motion is given by
\( V(x)=k x^{2} / 2, \) where \( k \) is the force
constant of the oscillator.
For \( \boldsymbol{k}=\mathbf{0 . 5} \boldsymbol{N} \boldsymbol{m}^{-1}, \) the \( \operatorname{graph} \) of \( \mathbf{V}(\mathbf{x}) \)
versus \( x \) is shown in Fig. Show that \( a \)
particle of total energy 1 J moving under this potential must turn back when
it reaches \( \boldsymbol{x}=\pm \mathbf{2 m} \)
Subject: Physics
A prism of \( \boldsymbol{R} . \boldsymbol{I} .=1.5 \) is immersed in
water of \( \boldsymbol{R} . \boldsymbol{I} .=\mathbf{4} / \mathbf{3} \) as shown in the
figure. For the total internal reflection
the correct choice is:
A \( \cdot \sin \theta<\frac{8}{9} \)
B. \( \sin \theta>\frac{8}{9} \)
\( \mathrm{c} \cdot \sin \theta=\frac{8}{9} \)
D. \( \sin \theta \leq \frac{8}{9} \)
Subject: Maths
Solve the following pair of linear (simultaneous) equations by the method of elimination:
\( \boldsymbol{x}+\mathbf{8} \boldsymbol{y}=\mathbf{1 9}, \mathbf{2} \boldsymbol{x}+\mathbf{1 1} \boldsymbol{y}=\mathbf{2 8} \)
A. \( x=3 \) and \( y=2 \)
B. \( x=12 \) and \( y=5 \)
c. \( x=1 \) and \( y=6 \)
D. \( x=9 \) and \( y=-6 \)
Subject: Maths
If \( f(x) \) is a polynomial function of the second degree such that \( \boldsymbol{f}(-\mathbf{3})= \) \( \mathbf{6}, \boldsymbol{f}(\mathbf{0})=\mathbf{6} \) and \( \boldsymbol{f}(\mathbf{2})=\mathbf{1 1}, \) then the
graph of the function \( f(x) \) cuts the
ordinate \( x=1 \) at the point:
B. (1,4)
c. (1,-2)
D. None of these
Subject: Maths
If \( \vec{A}=2 i+3 j \) and \( \vec{B}=2 \hat{j}+3 \hat{k} \) the
component of \( \bar{B} \) along \( \bar{A} \) is
A. 6
B. 1/6
\( c \cdot 6 / 13 \)
D. \( \frac{6}{\sqrt{13}} \)
Subject: Physics
A point object \( \boldsymbol{O} \) is placed at a distance
of \( 0.3 m \) from a convex lens (focal
length \( 0.2 m \) ) cut into two halves each
of which is displaced by \( 0.0005 m \) as
shown in the figure.
f this arrangement will generate more
than one image, then what will be the
total number of images?
4
B.
\( c \)
D
Subject: Maths
Solve:
\( \int \frac{x^{3}+x+1}{x^{2}-1} d x \)
A \( \cdot \frac{x^{2}}{2}+\log \left(x^{2}-1\right)+\frac{1}{2} \log \frac{x-1}{x+1}+c \)
B \( \cdot \frac{x^{2}}{2}+\log \left(x^{2}-1\right)-\frac{1}{2} \log \frac{x-1}{x+1}+c \)
\( ^{\mathbf{C}} \cdot \frac{x^{2}}{2}-\log \left(x^{2}-1\right)+\frac{1}{2} \log \frac{x+1}{x-1}+c \)
D \( \cdot \frac{x^{2}}{2}-\log \left(2 x^{2}-1\right)-\frac{1}{2} \log \frac{x-1}{x+1}+c \)
Subject: Physics
An aeroplane is moving towards north horizontally with a speed of \( 200 \mathrm{m} / \mathrm{s} \) at a
place where the vertical component of earths magnetic field is \( 0.5 \times 10^{-4} \) tesla.
Then the induced e.m.f. set up between the tips of the wings of the plane if they are \( 10 m \) apart is:
A. 0.1 volt
B. 0.01 volt
c. 10 volt
D. 1 volt
Subject: Chemistry
Consider the following isotopes of chlorine:
\( \mathbf{1 7} \boldsymbol{C l}^{\mathbf{3 5}}, \mathbf{1 7} \boldsymbol{C l}^{\mathbf{3 7}} \)
Atomic masses of these isotopes are different, while their chemical
properties are same. In the Mendeleev's periodic table isotopes of chlorine
was placed:
A. in the different groups
B. in the same group
c. in different periods
D. both (A) and (C) are correct
Subject: Maths
The distance between the straight lines
\( \mathbf{y}=\mathbf{m} \mathbf{x}+\mathbf{c}_{1}, \mathbf{y}=\mathbf{m} \mathbf{x}+\mathbf{c}_{2} \) is \( \left|\mathbf{c}_{1}-\mathbf{c}_{2}\right| \)
then \( \mathbf{m}= \)
\( \mathbf{A} \cdot \mathbf{0} \)
B.
\( c \cdot 2 \)
D. 3
Subject: Physics
The relation between the acceleration
and time for an object is given below. Calculate the velocity with which the object is moving at \( \boldsymbol{t}=\mathbf{1}(\mathbf{A t} \boldsymbol{t}=\mathbf{0}, \boldsymbol{v}= \)
\( \mathbf{0} \)
\( \boldsymbol{a}=\boldsymbol{3} \boldsymbol{t}-\boldsymbol{4} \boldsymbol{t}^{2} \)
Subject: Chemistry
The correct order of increasing basicity
of the given conjugate bases \( \left(R=C H_{3}\right. \)
is:
A \( \cdot \mathrm{RCOO}^{-}<\mathrm{HC}=\mathrm{C}^{-}<\mathrm{R}^{-}<\mathrm{NH}_{2}^{-} \)
B . \( \mathrm{R}^{-}<\mathrm{HC} \equiv \mathrm{C}^{-}<\mathrm{RCOO}^{-}<\mathrm{NH}_{2}^{-} \)
C. \( \mathrm{RCOO}^{-}<\mathrm{NH}_{2}^{-}<\mathrm{HC} \equiv \mathrm{C}^{-}<\mathrm{R} \)
D. \( \mathrm{RCOO}^{-}<\mathrm{HC} \equiv \mathrm{C}^{-}<\mathrm{NH}_{2}^{-}<\mathrm{R} \)
Subject: Physics
Two particles \( A \) and \( B \), initially at rest, moves towards each other under a
mutual force of attraction. At the
instant when the speed of \( A \) is \( v \) and the
speed \( B \) is \( 2 v, \) the speed of centre of
mass is :
A . zero
в.
c. \( 1.5 v \)
D. \( 3 v \)
Subject: Maths
The p. \( m \). \( f \). \( X \) -number of major defects randomly selected appliance of a certain type is :
\[
x-x
\]
\( \begin{array}{lllll}\text { P(a) } & \text { 0.08 } & \text { 0.15 } & \text { 0.45 } & \text { 0.27 }\end{array} \)
Find the expected value and standard deviation of \( X \)
Subject: Maths
The sum of the first 9 terms of an \( A . P \) is
81 and the sum of it's first 20 terms is
400. Find the first term, the common
difference and the sum upto 15 th term
A \( \cdot a=1, d=2, S_{15}=235 \)
В . \( a=3, d=4, S_{15}=215 \)
c. \( a=5, d=3, S_{15}=205 \)
D. None of these
Subject: Maths
ff \( f(x) \) a polynomial of degree 2 in \( x \) such that \( \boldsymbol{f}(\mathbf{0})=\boldsymbol{f}(\mathbf{1})=\mathbf{3} \boldsymbol{f}(\mathbf{2})=-\mathbf{3} \)
then \( \int \frac{\boldsymbol{f}(\boldsymbol{x})}{\boldsymbol{x}^{3}-\mathbf{1}} \boldsymbol{d} \boldsymbol{x}= \)
A \( \cdot \log \left|x^{2}+x+1\right|+\log |x+1|+c \)
B \( \cdot \log |x-1|+\frac{2}{\sqrt{3}} \tan ^{-1}\left(\frac{2 x+1}{\sqrt{3}}\right)+c \)
\( ^{\mathbf{c}} \cdot \log \left|x^{2}+x+1\right|+\frac{2}{\sqrt{3}} \tan ^{-1}\left(\frac{2 x+1}{\sqrt{3}}\right)+c \)
D \( \cdot \log \left|x^{2}+x+1\right|-\log |x-1|+\frac{2}{\sqrt{3}} \tan ^{-1}\left(\frac{2 x+1}{\sqrt{3}}\right)+c \)
Subject: Maths
Find the sum of the following APs:
(i) \( 2,7,12, \dots, \) to 10 terms.
(ii) \( 37,33,29, \dots, \) to 12 terms.
(iii) \( 0.6,1.7,2.8, \dots, \) to 100 terms.
(iv) \( \frac{1}{15}, \frac{1}{12}, \frac{1}{10}, \dots, \) to 11 terms.
Subject: Physics
The number of electrons that must be
removed from an electrically neutral silver dollar to give it a charge of \( +2.4 C \)
is
A \( .2 .5 \times 10^{19} \)
B. \( 1.5 \times 10^{19} \)
c. \( 1.5 \times 10^{-19} \)
D. \( 2.5 \times 10^{-19} \)
Subject: Maths
Assertion
If \( \boldsymbol{B} \subset \boldsymbol{A}, \) then \( \boldsymbol{P}(\boldsymbol{A} \cap \overline{\boldsymbol{B}})=\boldsymbol{P}(\boldsymbol{A})- \)
\( \boldsymbol{P}(\boldsymbol{B}) \)
Reason
\( (\boldsymbol{A} \cap \overline{\boldsymbol{B}}) \cup \boldsymbol{B}=\boldsymbol{A} \)
A. Both Assertion \& Reason are individually true \& Reason is correct explanation of Assertion
B. Both Assertion \& Reason are individually true but Reason is not the , correct (proper) explanation of Assertion
c. Assertion is true but Reason is false
D. Assertion is false but Reason is true
Subject: Maths
Find the conjugates of the following complex numbers:
\( \frac{(3-2 i)(2+3 i)}{(1+2 i)(2-i)} \)
A \( \cdot \frac{63}{25}-\frac{16}{25} i \)
В \( \cdot \frac{62}{25}+\frac{16}{25} i \)
c. \( \frac{63}{25}+\frac{17}{25} i \)
D. \( \frac{63}{25}+\frac{16}{25} i \)
Subject: Chemistry
Which chromium compound in widely used in training of leather?
A. \( C r_{2} O_{3} \)
в. \( C r O_{2} C l_{2} \)
c. \( C r C l_{3} \)
D. \( K_{2} S O_{4} \cdot C r_{2}\left(S O_{4}\right)_{3} .24 H_{2} O \)
Subject: Chemistry
Consider the following statements and arrange in the order of true/false as given in the codes.
\( S_{1}: \) The rate of the reaction \( A \rightarrow B \) having the rate \( \operatorname{law}-\frac{\boldsymbol{d}[\boldsymbol{A}]}{\boldsymbol{d} \boldsymbol{t}}=\boldsymbol{k}[\boldsymbol{A}][\boldsymbol{B}] \)
when plotted against time will exhibit a
maximum at some time.
\( S_{2}: \) A catalyst in a chemical reaction
increases the forward \( \mathrm{E}_{a} \) and decreases
the backward \( \boldsymbol{E}_{\boldsymbol{a}} \)
\( S_{3}: \) A catalyst in a chemical reaction
decreases both forward and backward
\( \boldsymbol{E}_{\boldsymbol{a}} \)
\( S_{4}: \) For a first-order reaction, the time
required to reduce successively the concentration of reactant by a constant fraction is always same.
A. गाग
B. FFFF
c. FTFT
\( D \)
Subject: Maths
If \( x^{y}+y^{x}=a^{b} \) then find that \( \frac{d y}{d x} \)
A. \( -\frac{y x^{x-1}+y^{x} \log y}{x^{y} \log x+x y^{x-1}} \)
B. \( \frac{y x^{x-1}+y^{x} \log y}{x^{y} \log x+x y^{x-1} y^{x}} \)
\( ^{\mathrm{C}}-\frac{y x^{x-1}+y^{x} \log y}{x^{y} \log x+x y^{x}} \)
D. None of these
Subject: Maths
A manufacturer estimates that on
inspection \( 12 \% \) of the articles he has produced will be rejected. He accepts an
order to supply 4400 articles at Rs15 each. Calculate the least number of
articles he must manufacture) to
ensure the completion of the order
He estimates the profit on his outlay. including the manufacturing of rejected articles to be \( 20 \% \). Find the
\( \operatorname{cost} \) of manufacturing each article.
Subject: Physics
If pressure at the half depth of a lake is equal to \( \frac{3}{4} \) times the pressure at its
bottom, then find the depth of the lake.
[Take \( \left.g=10 m / s^{2}\right] \)
A. \( \frac{P_{0}}{\rho g} \)
в. \( \frac{2 P_{0}}{\rho g} \)
c. \( \frac{P_{0}}{2 \rho g g} \)
D. \( \frac{3 P_{0}}{\rho g} \)
Subject: Physics
An optician while testing the eyes finds the vision of a patient to be \( 6 / 12 . \) By this he means that:
A. The person can read the letters of 6 inches from a distance of 12 \( \mathrm{m} \)
B. The person can read the letters of 12 inches from 6 \( \mathrm{m} \).
C. The person can read the letters from 6 \( \mathrm{m} \) which the normal eye can read from 12 \( \mathrm{m} \)
D. The focal length of eye lens has become half that of the normal eye
Subject: Physics
A long straight wire along the Z-axis
carries a current \( ^{\prime} \boldsymbol{I}^{\prime} \) in the negative \( \mathbf{Z}^{-} \)
direction. The induced magnetic field \( B \)
at a point having coordinates \( (x, y) \) is:
\( ^{\mathrm{A}} \cdot_{\frac{\mu_{0} I}{2 \pi}} \frac{(x \hat{\imath}-y \hat{\jmath})}{\left(x^{2}+y^{2}\right)} \)
в. \( \frac{\mu_{0} I}{2 \pi} \frac{(x \hat{\jmath}-y \hat{\imath})}{\left(x^{2}+y^{2}\right)} \)
c. \( \frac{\mu_{0} I}{2 \pi} \frac{(x \hat{i}+y \hat{j})}{\left(x^{2}+y^{2}\right)} \)
D \( \frac{\mu_{0} I}{2 \pi} \frac{(y \hat{i}-x \hat{j})}{\left(x^{2}+y^{2}\right)} \)
Subject: Physics
When a metal surface is illuminated by
light of wavelengths \( 400 \mathrm{nm} \) and 250 \( \mathrm{nm}, \) the maximum velocities of the
photoelectrons ejected are v and 2v respectively. The work function of the metal is
A \( \cdot 3.972 \times 10^{-19} \mathrm{J} \)
В. \( 1.59 \times 10^{-19} \mathrm{J} \)
D. \( 0.5 \times 10^{-19} \mathrm{J} \)
Subject: Maths
\( f(x)=\frac{\left(e^{k x}-1\right)(\sin k x)}{4 x^{2}}, x \neq 0 \)
\( \boldsymbol{f}(\mathbf{0})=\mathbf{9}, \) is continuous at \( \boldsymbol{x}=\mathbf{0}, \) then \( \mathbf{k} \)
\( =? \)
\( \mathbf{A} \cdot \pm 2 \)
B. ±6
\( c .\pm 4 \)
D. None of the above
Subject: Maths
Let \( \boldsymbol{A}=\{\boldsymbol{x}, \boldsymbol{y}, \boldsymbol{z}\}, \boldsymbol{B}=\{\boldsymbol{u}, \boldsymbol{v}, \boldsymbol{w}\} \) and
\( \boldsymbol{f}: \boldsymbol{A} \rightarrow \boldsymbol{B} \) be defined by \( \boldsymbol{f}(\boldsymbol{x})= \)
\( \boldsymbol{u}, \boldsymbol{f}(\boldsymbol{y})=\boldsymbol{v}, \boldsymbol{f}(\boldsymbol{z})=\boldsymbol{w} . \) Then \( \boldsymbol{f} \) is
A. surjective but not injective
B. injective but not surjective
c. bijective
D. none of these
Subject: Physics
A small mass \( m \) is moved slowly from the surface of the earth to a height \( h \) above the surface. The work done (by an external agent) in doing this is
This question has multiple correct options
A. \( m g h, \) for all values of \( h \)
B. \( m g h, \) for \( h<<R \)
c. \( \frac{1}{2} \) mgR, for \( h=R \)
D. \( -\frac{1}{2} \) mgR, for \( h= \)
Subject: Physics
The frequency of the 1 st harmonic of a sonometer wire is \( 160 H z \). If the length
of the wire is increased by \( 50 \% \) and the tension in the wire is decreased by
\( 19 \%, \) the frequency of its first overtone
is :
(Assume linear mass density to be constant
A. \( 180 H z \)
в. \( 192 \mathrm{Hz} \)
c. \( 220 H z \)
D. 232 Нг
Subject: Maths
A pole \( 15 \mathrm{m} \) long rests against a vertical
wall at an angle of \( 30^{\circ} \) with the ground
How high up the wall does the pole reach?
\( A \cdot 5 m \)
в. 7
c. \( 7.5 \mathrm{m} \)
\( D \cdot 8 m \)
Subject: Physics
A steel wire of diameter \( d=1.0 \) mm is
stretched horizontally between two clamps located at the distance \( l= \) \( 2.0 m \) from each other. A weight of mass
\( \boldsymbol{m}=\mathbf{0 . 2 5} \boldsymbol{k g} \) is suspended from the
midpoint \( O \) of the wire. What will the
resulting descent of the point \( O \) be in millimetres?E=2 \( \times 10^{11} N / m^{2} \)
Subject: Physics
In a plane transmission grating, the width of a ruling is \( 12000 A \) and the width of a slit is \( 8000 A \), the grating element is:
A. \( 20 \mu m \)
В. \( 2 \mu m \)
c. \( 200 \mu m \)
D. \( 10 \mu m \)
Subject: Physics
The frequency of a man's voice is 300 \( \mathrm{Hz} \) and its wavelength is 1 meter. If the wavelength of a child's voice is \( 1.5 \mathrm{m} \) then the frequency of the child's voice is
A. 200 \( \mathrm{Hz} \)
в. 150 нz
\( c \cdot 100 \) нz
D. 350 нz
Subject: Maths
In a study of diabetic patients in a village, the following observations were noted:
\( \begin{array}{llll}\text { Age in } & \mathbf{1 0}- & \mathbf{2 0}- & \mathbf{3 0}- \\ \text { years } & \mathbf{2 0} & \mathbf{3 0} & \mathbf{4 0}\end{array} \)
No. of \( ^{f}_{n t s}^{2} \) patien
Calculate the mean and standard
deviation. Also interpret the results
Subject: Maths
The common area between the curve
\( x^{2}+y^{2}=8 \) and \( y^{2}=2 x \) is
A \( \cdot \frac{4}{3}+2 \pi \)
B. \( (2 \sqrt{2}+\pi-1) \)
c. \( (\sqrt{2}+\pi-1) \)
D. None of these
Subject: Physics
There is an isolated planet having mass 2M and radius 2R, where M and R are
the mass and radius of the earth.
simple pendulum having mass \( \mathrm{m} \) and length \( \mathrm{R} \) is made to small oscillations on the planet. Find the time period of SHM of the pendulum in second. (Take \( \left.\pi=3.00, \mathrm{g}=10 \mathrm{m} / \mathrm{s}^{2}, \sqrt{2}=1.41\right) \)
A. 8000
B. 6768 s
c. 9000 s
D. 7968 s
Subject: Maths
The solution of \( \frac{\boldsymbol{d} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}}=\frac{\boldsymbol{x} \boldsymbol{y}}{\boldsymbol{x}^{2}+\boldsymbol{y}^{2}} \) is
A. \( \quad \frac{x^{2}}{y^{2}} \)
\[
x=c e^{\frac{1}{2}}
\]
в. \( \quad y=c e^{\frac{x^{2}}{y^{2}}} \)
c.
\[
y=c e^{\frac{x^{2}}{2 y^{2}}}
\]
D. \( \quad x=c e^{\frac{2 x^{2}}{y^{2}}} \)
Subject: Chemistry
In which of the following, all bond length are not equal?
\( \boldsymbol{P C l}_{5}, \boldsymbol{S F}_{4}, \boldsymbol{C l F}_{3}, \boldsymbol{X} \boldsymbol{e F}_{2},\left[\boldsymbol{S F}_{5}\right]^{+},\left[\boldsymbol{C l} \boldsymbol{F}_{4}\right]^{+} \)
\( A \cdot 6 \)
B. 7
\( c \cdot 5 \)
D.
Subject: Maths
Given below are some points, with their
co-ordinates.
\( \boldsymbol{P}(\mathbf{4}, \boldsymbol{3}), \boldsymbol{Q}(-\boldsymbol{3}, \boldsymbol{2}), \boldsymbol{R}(\mathbf{5}, \mathbf{1}), \boldsymbol{S}(\mathbf{0},-\boldsymbol{4}) \)
What is the \( y- \) coordinate of point \( R ? \)
Subject: Chemistry
On electrolysing \( K_{2} S O_{4} \) solution using inert electrodes, \( 1.68 L(\mathrm{STP}) \) of gases was
obtained. How many moles of \( M n O_{4}^{-} \) could be reduced to \( M n^{2+} \) by the same
quantity of electricity?
A . 0.10
B. 0.20
c. 0.15
D. 0.02
Subject: Chemistry
Which of the following organic compounds polymerizes to form the polyester Dacron?
A. Propylene and para \( H O-\left(C_{6} H_{4}\right)-O H \)
B. Benzolic acid and ethanol
c. Terepthalic acid and ethylene glycol
D. Benzoic acid and para \( H O-\left(C_{6} H_{4}\right)-O H \)
Subject: Maths
If \( X \) is a point on the line \( A B . Y \) and \( Z \)
are points outside such that \( \angle A X Y= \)
\( 45^{\circ} \) and \( \angle Y X Z=150^{\circ}, \) then \( \angle A X Z \) is
equal to:
A \( \cdot 120^{\circ} \)
B. \( 135^{\circ} \)
\( c \cdot 150^{\circ} \)
D. \( 165^{\circ} \)
Subject: Biology
Assertion
During an ecological succession, the
number of species increases, the
community biomass increases and the community's ratio of respiration to photosynthesis also increases.
Reason
At climax community of an ecological
succession, the rate of photosynthesis of a community is almost equal to the rate of respiration.
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
If \( \boldsymbol{y}= \)
\( (1+x)\left(1+x^{2}\right)\left(1+x^{4}\right) \dots\left(1+x^{2^{n}}\right) \)
then \( \frac{d y}{d x} \) at \( x=0 \) is
\( \mathbf{A} \cdot \mathbf{1} \)
B. - -
c. 0
D. none of these
Subject: Chemistry
Lanthanoids are:
A. 14 elements in the seventh period left ( atomic no. \( =90 \) to \( 103 \text { right }) \) that are filling \( 5 f \) sublevel
B. 14 elements in the sixth period left ( atomic no. 58 to 71 right ) that are filling \( 4 f \) sublevel
C. 14 elements in the seventh period left ( atomic no. \( =58 \) to \( 71 \text { right }) \) that are filling \( 4 f \) sublevel
D. 14 elements in the sixth period left ( atomic no. 90 to \( 103 \text { right }) \) that are filling \( 4 f \) sublevel
Subject: Physics
In the adjoining diagram, a currentcarrying loop pqrs placed with its sides parallel to a long current-carrying wire.
The currents \( i_{1} \) and \( i_{2} \) in the wire and
loop are \( 20 \mathrm{A} \) and 16 A respectively. If \( a= \) \( 15 \mathrm{cm}, \mathrm{b}=6 \mathrm{cm}, \) and \( \mathrm{d}=4 \mathrm{cm}, \) what will
be the force on current \( i_{2} \) in the loop is
clockwise instead of anticlockwise?
Subject: Physics
A particle of mass m is under the
influence of a force \( \mathrm{F} \) which varies with
the displacement \( x \) according to the
relation \( F=-k x+F_{0} \) in which \( k \) and \( F_{0} \)
are constants.The particle when
disturbed will oscillate
A. about \( x=0, \) with \( \omega \neq \sqrt{k / m} \)
B. about \( x=0, \) with \( \omega=\sqrt{k / m} \)
C . about \( x=F_{0} / k, \) with \( \omega=\sqrt{k / m} \)
D. about \( x=F_{0} / k, \) with \( \omega \neq \sqrt{k / m} \)
Subject: Maths
Area common to the curves \( y^{2}=a x \)
and \( x^{2}+y^{2}=4 a x \) is equal to
A \( \cdot(9 \sqrt{3}+4 \pi) \frac{a^{2}}{3} \)
B . \( (9 \sqrt{3}+4 \pi) a^{2} \)
c. \( (9 \sqrt{3}-4 \pi) \frac{a^{2}}{3} \)
D. None of these
Subject: Maths
Let \( S=x^{2}+y^{2}+2 g x+2 f y+c=0 \)
be a given circle. Then the locus of the foot of the perpendicular drawn from the origin upon any chords of \( S \) which
subtends right angle at the origin is:
A \( \cdot x^{2}+y^{2}+g x+f y+c / 2=0 \)
B . \( x^{2}+y^{2}=g \)
c. \( x^{2}+y^{2}=f \)
D. \( x^{2}+y^{2}+g=0 \)
Subject: Maths
\( \boldsymbol{A B}\|\boldsymbol{C D}\| \boldsymbol{E F} \) and \( \boldsymbol{G H} \| \boldsymbol{D I} \)
\( \angle D I H=95^{\circ} \) then the measure of
\( \angle G C D \) is equal to
\( A \cdot 95 \)
B. \( 105^{\circ} \)
\( c \cdot 90 \)
\( D .85 \)
Subject: Physics
Two block of mass \( m_{1} \) and \( m_{2} \) are kept
a part d from each other. What happen to
the magnitude of the force on \( m_{1} \) if the
mass of \( m_{2} \) is doubled?
A. It is quadrupled
B. It is doubleo
c. It remain the same
D. It is halved
E. It is quartered
Subject: Maths
Mark the correct alternative of the
following.
The angles of a triangle are in the ratio \( 2: 3: 7 . \) The measure of the largest angle is?
\( A \cdot 84^{\circ} \)
B. \( 91^{\circ} \)
\( c \cdot 105 \)
D. \( 98^{\circ} \)
Subject: Maths
n Figure, \( P Q \) is a chord of length \( 8 \mathrm{cm} \)
of a circle of radius \( 5 \mathrm{cm} . \) The tangents
at \( P \) and \( Q \) intersect at a point \( T . \) The
ength of \( T P \) is equal to \( \frac{w}{3}, \) then the
value of \( a \) is
Subject: Maths
The element in the first row and third
column of the inverse of the matrix
\( \left[\begin{array}{ccc}1 & 2 & -3 \\ 0 & 1 & 2 \\ 0 & 0 & 1\end{array}\right] \) is
A . -2
B.
\( c \cdot 1 \)
D. 7
Subject: Physics
A body dropped from a height reaches
the ground in \( 5 s . \) The velocity with which it reaches the ground is \( (g= \)
\( \left.9.8 m s^{-2}\right) \)
A \( .0 m s^{-1} \)
в. \( 49 \mathrm{ms}^{-1} \)
c. \( 4.9 \mathrm{ms}^{-1} \)
D. \( 9.8 \mathrm{ms}^{-1} \)
Subject: Maths
The area of the figure bounded by \( y^{2}= \)
\( 2 x+1 \) and \( x-y-1=0 \) is:
\( A \cdot 2 / 3 \)
B . \( 4 / 3 \)
\( c \cdot 8 / 3 \)
D. \( 11 / 3 \)