AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Physics
The dimensional formula for a physical
quantity \( x \) is \( \left[M^{-1} L^{3} T^{-2}\right] . \) The errors in measuring the quantities \( \mathrm{M}, \mathrm{L} \) and \( \mathrm{T} \) respectively are \( 2 \%, 3 \% \) and4\%. The maximum percentage of error that occurs in measuring the quantity x is
A . 9
B. 10
c. 14
D. 19
Subject: Physics
Focal length of a spherical mirror is \( 200 \mathrm{cm} . \) What will be its radius of
curvature?
A . \( 100 \mathrm{cm} \)
B. \( 25 \mathrm{cm} \)
\( c .50 c m \)
D. \( 400 \mathrm{cm} \)
Subject: Physics
One end of a rod of length \( L \) is fixed to a
point on the circumference of a wheel of radius R. The other end is sliding freely
along a straight channel passing
through the centre 0 of the wheel as
shown in the figure. The wheel is
rotating with a constant angular velocity \( \omega \) about \( 0 . \) Taking \( T=\frac{2 \pi}{P \omega} \) the
motion of the rod is?
A. Simple harmonic with a period of \( T \)
B. Simple harmonic with a period of \( T / 2 \)
c. Not simple harmonic but periodic with a period of \( T \)
D. Not simple harmonic but periodic with a period of \( T / 2 \)
Subject: Chemistry
Four students \( A, B, C, \) and \( D \) noted the
initial colour of the solution in beakers
I, II, Ill and IV. After inserting zinc rods in
each solution and leaving it
undisturbed for two hours, noted the
colour of each solution again. The recorded observations in the form of
the table given below:
Which student noted the colour change
in all the four beakers correctly.
\( A \cdot(A) \)
B. (B)
\( c \cdot(c) \)
\( D, \quad O \)
Subject: Chemistry
The IUPAC name for the coordination
compound \( \mathbf{B a}\left[\mathbf{B r} \mathbf{F}_{4}\right] \) is
A. Barium tetrafluorobromate (v)
B. Barium tetrafluorobromate (III)
c. Barium bis (tetrafluorobromate) (III)
D. Nne of these
Subject: Maths
The point lying on angle bisector of the
planes \( \boldsymbol{x}+\mathbf{2} \boldsymbol{y}+\mathbf{2} \boldsymbol{z}-\mathbf{6}=\mathbf{0} \) and \( \mathbf{2} \boldsymbol{x}- \)
\( \boldsymbol{y}+\boldsymbol{4}=\mathbf{0} \) is
A. (2,4,0)
B. (-1,3,2)
D. (-2,4,0)
Subject: Chemistry
Calculate standard enthalpy of
formation for benzene from the
following data. \( \boldsymbol{C}_{\boldsymbol{6}} \boldsymbol{H}_{\boldsymbol{6}(\ell)}+\frac{\mathbf{1 5}}{\mathbf{2}} \boldsymbol{O}_{\mathbf{2}(\boldsymbol{g})} \longrightarrow \boldsymbol{6} \boldsymbol{C} \boldsymbol{O}_{\boldsymbol{2}(\boldsymbol{g})}+ \)
\( \mathbf{3} \boldsymbol{H}_{2} \boldsymbol{O}_{(\ell)} \quad \boldsymbol{\Delta} \boldsymbol{H}^{o}=-\mathbf{3 2 6 7} \boldsymbol{K} \boldsymbol{J} \)
\( \Delta_{f} H^{o}\left(C O_{2}\right)=-393.5 K J m o l^{-1} \)
\( \Delta_{f} H^{o}\left(C_{2} O\right)=-285.8 K J m o l^{-1} \)
Subject: Chemistry
Amongs the following which are
correctly matched:

This question has multiple correct options
A. Meta boric acid : \( H B O_{2} \)
B. Mangnaic acid : \( H M n O_{4} \)
C . Xenic acid : \( H_{2} X e O_{4} \)
D. Dithionic acid : \( H_{2} S_{2} O_{6} \)
Subject: Physics
The component of a vector \( \vec{r} \) along \( x \) axis will have a maximum value if:
A. \( \vec{r} \) along +ve \( x \) -axis
B. \( \vec{r} \) along +ve \( y \) -axis
c. \( \vec{r} \) along -ve \( y \) -axis
D. \( \vec{r} \) makes an angle of \( 45^{\circ} \) with the \( x \) -axis
Subject: Physics
A train moves in straight line with a uniform acceleration. If \( x \) and \( y \) be the velocities with which the front and rear end of the train respectively cross a fixed pole then the velocity with which the middle of the train crosses the pole is:
\( ^{\text {A } \cdot} \frac{x^{2}+y^{2}}{2} \)
в. \( \frac{2 x y}{x+y} \)
c. \( \sqrt{\frac{1}{2}\left(x^{2}+y^{2}\right)} \)
D. \( \sqrt{\frac{1}{2}\left(y^{2}-x^{2}\right)} \)
Subject: Physics
Two bars \( A \) and \( B \) of circular section
and of the same volume and made of
the same material are subjected to tension. If the diameter of \( A \) is half that
of \( B \) and if the force supplied to both the rods is the same and is within the
elastic limit, the ratio of the extension
of \( A \) to that of \( B \) will be
A . 16
B. 8
\( c \cdot 4 \)
\( D \)
Subject: Maths
Let \( f(x) \) be a function in [0,5] such that
\( \boldsymbol{f}^{2}(\boldsymbol{x})=\mathbf{1} \forall \boldsymbol{x} \in[\mathbf{0}, \mathbf{5}] \) and \( \boldsymbol{f}(\boldsymbol{x}) \) is
discontinuous at all integers in \( [\mathbf{0}, \mathbf{5}] \) Find total number of fuctions.
Subject: Physics
A parallel narrow beam of light travelling through water in a container incident on an air bubble of radius 8
mm. What be the distance of image obtained due to refraction of beam on
first face of air bubble from the centre of bubble? \( \quad\left(\text { take } \mu_{w a t e r}=\frac{4}{3}\right) \)
\( \mathbf{A} \cdot 17.2 \mathrm{mm} \)
B. 32 mm
c. \( 41.5 \mathrm{mm} \)
D. 25.75 mm
Subject: Maths
A number \( a \) is called a perfect cube if
there exists a natural number \( b \) such
that
A. \( a=b \times b \times b \)
\( b \)
В. \( b=a \times a \times a \)
\( c, a=a \times b \times a \)
\( a \)
D. \( a=a \times b \times b \)
Subject: Maths
A function \( f \) is defined by \( f(x)=2 x^{3}- \)
\( \mathbf{3} \boldsymbol{x}, \boldsymbol{x} \boldsymbol{\epsilon} \boldsymbol{R} \). What is the value of \( \boldsymbol{f}(\boldsymbol{4}) ? \)
Subject: Maths
Q Type your question
shooting competition. Use a graph
sheet and draw an ogive for the distribution.
\( \begin{array}{ll}\text { Scores } & \text { No. of shooters } \\ 0-10 & 9 \\ 10-20 & 13 \\ 20-30 & 20 \\ 30-40 & 26 \\ 40-50 & 30 \\ 50-60 & 22 \\ 60-70 & 15 \\ 70-80 & 10 \\ 80-90 & 8 \\ 90-100 & 7\end{array} \) Use your graph to estimate the median.
Subject: Chemistry
A solution contains \( 15 \% \) glucose
\( \left[\boldsymbol{C}_{6} \boldsymbol{H}_{12} \boldsymbol{O}_{6}\right] \) in water and has density \( \mathbf{1 . 5} \)
\( \mathrm{g} / \mathrm{ml} . \) Find the molarity and molality of this solution \( [\boldsymbol{C}=\mathbf{1 2}, \boldsymbol{H}=\mathbf{1}, \boldsymbol{O}=\mathbf{1 6}] \)
Subject: Chemistry
Calculate the pH of the following mixture given \( \boldsymbol{K}_{a}=\mathbf{1 . 8} \times \mathbf{1 0}^{-\mathbf{5}} \) and \( \boldsymbol{K}_{\boldsymbol{b}}=\mathbf{1 . 8} \times \)
\( \mathbf{1 0}^{-\mathbf{5}}\left(\boldsymbol{p} \boldsymbol{K}_{\boldsymbol{a}}=\boldsymbol{p} \boldsymbol{K}_{\boldsymbol{a}}=\mathbf{4 . 7 4 4 7}\right) \)
\( 50 m L 0.05 M N a O H+50 m L \) of
\( \mathbf{0 . 1} \boldsymbol{M} \boldsymbol{C H}_{3} \boldsymbol{C O O H} \)
Subject: Maths
If \( a \sin ^{2} \theta+b \cos ^{2} \theta=c, \) then \( \tan ^{2} \theta= \)
A \( \cdot \frac{b-c}{a-c} \)
в \( \cdot \frac{c-b}{a-c} \)
c. \( \frac{a-c}{b-c} \)
D. \( \frac{a-c}{c-b} \)
Subject: Maths
Examine the following curve for continuity and differentiability: \( \boldsymbol{y}=\boldsymbol{x}^{2} \)
for \( \boldsymbol{x} \leq \mathbf{0} ; \boldsymbol{y}=\mathbf{1} \) for \( \mathbf{0} \boldsymbol{x} \leq \mathbf{1} \) and \( \boldsymbol{y}=\mathbf{1} / \boldsymbol{x} \)
for \( x>1 . \) Also draw the graph of the
function.
Subject: Physics
What average speed, most nearly, is required to run a mile \( (1.6 \mathrm{km}) \) in 4 minutes?
A. \( 4.0 \mathrm{m} / \mathrm{s} \)
в. \( 7.0 \mathrm{m} / \mathrm{s} \)
c. \( 40.0 \mathrm{m} / \mathrm{s} \)
D. \( 400.0 \mathrm{m} / \mathrm{s} \)
Subject: Maths
Evaluate \( \left(\frac{a}{2 b}+\frac{2 b}{a}\right)^{2} \)
\( \left(\frac{a}{2 b}-\frac{2 b}{a}\right)^{2}-4 \)
\( A \cdot 2 \)
B. \( a b \)
\( c \)
\( D \)
Subject: Physics
A cricket ball of mass 120 g is moving with a velocity of \( 12 \mathrm{m} s^{-1} . \) It turns back
and moves with a velocity of \( 20 \mathrm{m} s^{-1} \)
when hit by a bat. Find the impulse if the force acts on the ball for 0.02 s.
A \( \cdot 4 \) N
B. 8 N s
c. 32 N \( s \)
D. 192 N s
Subject: Maths
The diameter of a metallic sphere is 6 cm. The sphere is melted and drawn into a wire of uniform circular cross-
section. If the length of the wire is \( 36 \mathrm{m} \) find the radius of its cross-section.
A \( .0 .8 \mathrm{cm} \)
B. \( 0.5 \mathrm{cm} \)
\( c .0 .3 \mathrm{cm} \)
D. \( 0.1 \mathrm{cm} \)
Subject: Chemistry
Reaction involved in
saponification process is \( \boldsymbol{C H}_{3} \boldsymbol{C O O C}_{2} \boldsymbol{H}_{5} \stackrel{N a O \boldsymbol{H}}{\longrightarrow} \)
\( \boldsymbol{C H}_{3} \boldsymbol{C O O N} \boldsymbol{a}+\boldsymbol{C}_{2} \boldsymbol{H}_{5} \boldsymbol{O H} \)
A. True
B. False
Subject: Chemistry
Wand X are \( _{\text {- - }} \), respectively.
\( A \cdot O_{3} \) and \( P_{4} O_{6} \)
B. \( O_{2} \) and \( P_{4} O_{6} \)
\( \mathrm{c} \cdot \mathrm{O}_{2} \) and \( P_{4} \mathrm{O}_{1} \)
D. \( O_{3} \) and \( P_{4} O_{1} \)
Subject: Chemistry
\( N_{2} O_{5} \) decomposes according to equation:
\[
\mathbf{2} N_{2} \boldsymbol{O}_{\mathbf{5}} \rightarrow \mathbf{4} \boldsymbol{N} \boldsymbol{O}_{\mathbf{2}}+\boldsymbol{O}_{\mathbf{2}}
\]
What does \( \frac{\boldsymbol{d}\left[\boldsymbol{O}_{2}\right]}{\boldsymbol{d} \boldsymbol{t}} \) denote?
Subject: Physics
Which of the following relations is not
correct?
A \( \cdot \frac{Y}{\eta}=2(1+\sigma) \)
в. \( \frac{Y}{3 K}=1-2 \sigma \)
c. \( _{Y}=\frac{9 K \eta}{3 K+\eta} \)
D. \( \frac{Y}{\eta}+\frac{Y}{3 K}=3 \)
Subject: Maths
\( \frac{1}{3}+\frac{1}{3}\left(\frac{1}{3}\right)^{3}+\frac{1}{5}\left(\frac{1}{3}\right)^{5}+\dots= \)
A \( \cdot \frac{1}{2} \log _{e} 2 \)
B \( \cdot 2 \log _{e} 2 \)
\( \mathbf{c} \cdot \log _{e} 2 \)
D. \( \log _{e} 3 \)
Subject: Maths
Mother, father and son line up at
random for a family photo. If \( A \) and \( B \) are two events given by \( A= \) Son on one
end, \( B= \) Father in the middle, find
\( \boldsymbol{P}(\boldsymbol{A} / \boldsymbol{B}) \) and \( \boldsymbol{P}(\boldsymbol{B} / \boldsymbol{A}) \)
Subject: Physics
For a medium with permitivity \( \epsilon \) and permeability \( \mu, \) the velocity of light is
given by:
\( \mathbf{A} \cdot \sqrt{\mu / \epsilon} \)
B . \( \sqrt{\mu \epsilon} \)
c. \( 1 / \sqrt{\mu \epsilon} \)
D. \( \sqrt{\epsilon / \mu} \)
Subject: Maths
If \( \boldsymbol{A}=\mathbf{3} \boldsymbol{i}-\mathbf{4} \boldsymbol{j} \) and \( \boldsymbol{B}=-\boldsymbol{i}-\boldsymbol{4} \boldsymbol{j} \)
calculate the direction of \( \boldsymbol{A}-\boldsymbol{B} \)
A. Along positive x axis
B. Along negative x axis
c. Along positive y axis
D. Along negative y axis
Subject: Physics
\( 200 g \) ball is tied to one end of a string of length \( 20 \mathrm{cm} . \) It is revolved in a
horizantal circle at an angular frequency of 6 rpm. Then, angular velocity \& linear velocities of the ball respectively are
rads \( ^{-1} \) and \( m s^{-1}: \)
A. 0.7284,0.1257
7
в. 0.6284,0.1257
c. 0.6284,0.1457
D. 0.7284,0.1457
Subject: Maths
The coordinates of a point which is equidistant from the point \( (0,0,0),(a, 0,0),(0, b, 0) \) and \( (0,0, c) \)
are given by
\( ^{\mathbf{A}} \cdot\left(\frac{a}{2}, \frac{b}{2}, \frac{c}{2}\right) \)
в. \( \left(\frac{-a}{2}, \frac{-b}{2}, \frac{c}{2}\right) \)
\( ^{\mathrm{c}}\left(\frac{a}{2}, \frac{-b}{2}, \frac{-c}{2}\right) \)
D \( \cdot\left(\frac{-a}{2}, \frac{b}{2}, \frac{-c}{2}\right) \)
Subject: Maths
\( \lim _{\boldsymbol{y} \rightarrow 0} \frac{\sqrt{1+\sqrt{1+\boldsymbol{y}^{4}}}-\sqrt{\mathbf{2}}}{\boldsymbol{y}^{4}} \)
A \( \cdot \) Exists and equals \( \frac{1}{4 \sqrt{2}} \)
B. Does not exist
C - Exist and equals \( \frac{1}{2 \sqrt{2}} \)
D. Exists and equals \( \frac{1}{2 \sqrt{2}(\sqrt{2}+1)} \)
Subject: Physics
Assertion
The relation among \( u, v \) and \( f \) for the spherical mirror is valid only for mirrors
whose sizes are very small compared to
their radii of curvature.
Reason
The laws of reflection are strictly valid
for plane surfaces but not for large spherical surfaces.
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
Calcium lactate is a salt of weal organic acid and strong base represented as \( \boldsymbol{C} \boldsymbol{a}(\boldsymbol{L} \boldsymbol{a} \boldsymbol{C})_{2} \cdot \boldsymbol{A} \) saturated solution of
\( \boldsymbol{C} \boldsymbol{a}(\boldsymbol{L} \boldsymbol{a} \boldsymbol{C})_{2} \) contains \( \boldsymbol{0} . \boldsymbol{6} \) mole in \( \boldsymbol{2} \) litre
solution. \( p O H \) of solution is \( 5.60 . \) If \( 90 \% \) dissociation of the salt takes place then
what is \( p K_{a} \) of lactic acid?
A. \( 2.8-\log (0.54) \)
B. \( 2.8+\log (0.54) \)
c. \( 2.8+\log (0.27) \)
D. None of these
Subject: Maths
\( A B C \) is an isosceles triangle inscribed in a circle of radius \( r . \) If \( A B=A C \) and \( h \)
is the altitude from \( A \) to BC. If the
triangle \( A B C \) has perimeter \( P \) and area
\( \Delta \) then \( \lim _{h \rightarrow 0} 512 r \frac{\Delta}{P^{3}} \) is equal to
Subject: Maths
Assertion
The area of the triangle formed by the
points \( \boldsymbol{A}(\mathbf{2 0 0 7}, \mathbf{2 0 0 9}), \boldsymbol{B}(\mathbf{2 0 0 8}, \mathbf{2 0 1 1}) \)
\( C(2009,2010) \) will be same as the
area formed by the points \( \boldsymbol{P}(\mathbf{0}, \mathbf{0}) \)
\( Q(1,2), R(2,1) \)
Reason
The area of the triangle remains same
w.r.t to transition of co-ordinate axes.
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 system of inequalities graphically \( \mathbf{3} \boldsymbol{x}+\mathbf{2} \boldsymbol{y} \leq \mathbf{1 5 0}, \boldsymbol{x}+\mathbf{4} \boldsymbol{y} \leq \mathbf{8 0}, \boldsymbol{x} \leq \mathbf{1 5}, \boldsymbol{y} \)
Subject: Maths
If first, second and last terms of an A.P.
are \( a, b \) and \( c \)
respectively. Then the number of terms =
A \( \cdot \frac{a+b-2 c}{a-c} \)
в. \( \frac{c+a-2 b}{c-b} \)
c. \( \frac{b+c-2 a}{b-a} \)
D. \( \frac{a+b+2 c}{2(b-c)} \)
Subject: Maths
\( \frac{1+\tan ^{2} x}{1-\tan ^{2} x} d x \) is equal to
A \( \cdot \log \frac{1-\tan x}{1+\tan x}+c \)
B. \( \log \frac{1+\tan x}{1-\tan x}+c \)
c. \( \frac{1}{2} \log \frac{1-\tan x}{1+\tan x}+c \)
D. \( \frac{1}{2} \log \frac{1+\tan x}{1-\tan x}+c \)
Subject: Physics
An RLC circuit has \( f_{1} \) and \( f_{2} \) as the half
power frequency and \( f_{0} \) as the resonant frequency. The Q factor of the circuit is given by:
A \( \cdot \frac{f_{1}+f_{2}}{2 f_{0}} \)
в. \( \frac{f_{1}-f_{0}}{f_{2}-f_{0}} \)
c. \( \frac{f_{0}}{f_{1}-f_{2}} \)
D. \( \frac{f_{1}-f_{2}}{f_{0}} \)
Subject: Maths
Find the value of \( s: \)
\( s(3 s-7)-3 s(s-8)=9 \)
A \( \cdot \frac{17}{9} \)
в. \( \frac{9}{17} \)
\( c \cdot \frac{-9}{17} \)
D. \( \frac{-17}{9} \)
Subject: Physics
Two satellites \( A \) and \( B \) revolve around a
planet in two coplanar circular orbits in
the same sense with radii \( 10^{4} \mathrm{km} \) and
\( 2 \times 104 \mathrm{km} \) respectively. Time period of
\( A \) is 28 hours. What is time period of
another
satellite?
Subject: Physics
A body dropped from the top of a tower
covers a distance \( 7 x \) in the last second
of its journey, where \( x \) is the distance
covered in the first second. How much
time does it take to reach the ground?
A . \( 3 s \)
B. \( 4 s \)
\( c .5 s \)
D. \( 6 s \)
Subject: Physics
A road is 10 mwide. Its radius of
curvature is \( 50 m \). The outer edge is above the lower edge by a distance of
1./5m. This road is most suited for the
velocity
A. \( 2.5 \mathrm{m} / \mathrm{sec} \)
B. \( 4.5 \mathrm{m} \) sec
c. \( 6.5 m \) sec
D. \( 8.5 m \) sec
Subject: Physics
Unpolarised light of intensity
\( 32 W m^{-2} \) passes through three polarizers such that transmission axis of first is crossed with third. If intensity
of emerging light is \( 2 W m^{-2} \), what is the angle of transmission axis between
the first two polarisers?
\( A \cdot 30 \)
B . 45
\( c \cdot 22.5 \)
D. \( 60^{\circ} \)
Subject: Physics
ass an in is
at the bottom of a fixed circular,
vertical task,which has a radius of R.
The contact surface between the mass
and loop is frictionless. A bullet of mass
\( m \) strikes the block horizontally with
initial speed \( v_{0} \) and remain embedded
in the block as the block and the bullet
circle the loop. Determine each of the
following in terms of \( \mathrm{m}, v_{0}, \mathrm{R} \) and \( \mathrm{g} \)
a)The speed of the masses immediately
after the impact.
b)The minimum initial speed of the
bullet if the block and bullet are to
successfully execute a complete ride on
the loop.
Subject: Maths
The solution of \( \sin ^{-1}\left(\frac{2 a}{1+a^{2}}\right)-\cos ^{-1}\left(\frac{1-b^{2}}{1+b^{2}}\right)= \)
\( 2 \tan ^{-1} x \)
A \( \frac{a-b}{1-a b} \)
B. \( \frac{1+a b}{a-b} \)
c. \( \frac{a b-1}{a+b} \)
D. \( \frac{a-b}{1+a b} \)
Subject: Maths
The equation normal to the curve \( \boldsymbol{x}^{2 / 3}+\boldsymbol{y}^{2 / 3}=\boldsymbol{a}^{2 / 3} \) at the point \( (\boldsymbol{a}, \boldsymbol{0}) \) is
\( \mathbf{A} \cdot x=a \)
B. \( x=-a \)
\( \mathbf{c} \cdot y=a \)
D. \( y=-a \)
Subject: Chemistry
How will you bring about the following conversions?
(i) Ethanol to but-1-yne
(ii) Ethane to bromoethene
(iii) Propene to1-nitropropane
(iv) Toluene to benzyl alcohol
(v) Propene to propyne Ethanol to ethyl fluoride
(vii) Bromomethane to propanone
(viii) But-1-ene to but-2-ene
(ix) 1 -Chlorobutane to n-octane
(x) Benzene to biphenyl.
Subject: Maths
In a group 14 males and 6 females, 8
and 3 of the males and females
respectively are aged above 40 years. The probability that a person selected at random from the group is aged above
40 years, given that the selected person is female, is
A \( \cdot \frac{2}{7} \)
B. \( \frac{1}{2} \)
\( c \cdot \frac{1}{4} \)
D.
Subject: Chemistry
An organic compound contains \( \boldsymbol{C}, \boldsymbol{H} \) and 0.0 .3 g of this compound on combustion yielded 0.44 g of \( C O_{2} \) and 0.18 g of \( H_{2} O . \) If the weight of 1 mole of compound is \( 60, \) then the molecular formula is :
A. \( C_{2} H_{4} O_{2} \)
в. \( C_{4} H_{6} O_{2} \)
c. \( C_{2} H_{6} \) 0
D. \( C_{2} H_{4} O \)
Subject: Maths
\( \overrightarrow{\boldsymbol{a}}=\hat{\boldsymbol{i}}+\hat{\boldsymbol{j}}+\hat{\boldsymbol{k}}, \overrightarrow{\boldsymbol{b}}=2 \hat{\boldsymbol{i}}-\boldsymbol{4} \hat{\boldsymbol{k}}, \overrightarrow{\boldsymbol{c}}=\hat{\boldsymbol{i}}+ \)
\( \lambda \hat{j}+3 \hat{k} \) are coplanar, then the value of
\( \lambda \) is
\( A \cdot \frac{5}{2} \)
B. \( \frac{3}{5} \)
\( c \cdot \frac{5}{3} \)
D. None of these
Subject: Maths
The maximum value of the function \( f(x)=\sin \left(x+\frac{\pi}{6}\right)+\cos \left(x+\frac{\pi}{6}\right) \) in
the interval \( \left(0, \frac{\pi}{2}\right) \) occurs at
A \( \cdot \frac{\pi}{12} \)
в.
\( c \cdot \frac{\pi}{4} \)
D. \( \frac{\pi}{3} \)
Subject: Chemistry
How many grams of potassium chloride \( (K C l) \) must be added to make \( 500 \mathrm{mL} \)
of \( 1.00 \mathrm{M} K C l \) solution?
A \( .1 .00 \mathrm{g} \)
B. 18.6 \( g \)
c. \( 37.3 \mathrm{g} \)
D. 74.5 g
E. \( 149 \mathrm{g} \)
Subject: Physics
The Sl unit of electron mobility is :
A \( . M^{2} S^{-1} V-1 \)
В. \( =m^{2} s^{-1} V^{-1} \)
\( \mathbf{c} \cdot m s^{-1} V \)
D. \( m^{2} s^{-2} V \)
Subject: Physics
Two identical metal plates are given
positive charge \( Q_{1} \) and \( Q_{2}\left(<Q_{1}\right) \)
respectively. If they are now brought close together to form a parallel plate
capacitor with capacitance \( C, \) the
potential difference between them is
\( \mathbf{A} \cdot\left(Q_{1}+Q_{2}\right) / 2 C \)
B \( \cdot\left(Q_{1}+Q_{2}\right) / C \)
c. \( \left(Q_{1}-Q_{2}\right) / C \)
D \( \cdot\left(Q_{1}-Q_{2}\right) /(2 C) \)
Subject: Chemistry
A saturated solution of iodine in water
contains \( 0.33 I_{2} / L . \) More than this can
dissolve in a \( K I \) solution because of the
following equilibrium : \( \boldsymbol{I}_{2}(\boldsymbol{a} \boldsymbol{q})+ \)
\( \left.\boldsymbol{I}^{-}(\boldsymbol{a} \boldsymbol{q})\right] \rightleftharpoons \boldsymbol{I}_{3}^{-}(\boldsymbol{a} \boldsymbol{q}) \cdot \mathbf{A} \mathbf{0} \cdot \mathbf{1} \mathbf{0} \boldsymbol{N} \boldsymbol{K} \boldsymbol{I} \)
solution \( \left(0.10 M I^{-}\right) \) actually dissolves \( 12.5 g \) of iodine \( / L, \) most of which is
converted to \( I_{3}^{-} . \) Assuming that the
concentration of \( \boldsymbol{I}_{2} \) in all saturated
solutions is the same, calculate the equilibrium constant for the above reaction. What is the effect of adding
water to a clear saturated of \( I_{2} \) in the
\( K I \) solution?
Subject: Physics
A progressive wave is represented by \( y= \) \( 12 \sin (5 t-4 x) \mathrm{cm} . \) On this wave, how far
away are the two points having phase
difference of \( 90^{\circ} ? \)
A \( \cdot \frac{\pi}{2} c m \)
в. \( \frac{\pi}{4} c m \)
с. \( \frac{\pi}{8} \mathrm{cm} \)
D. \( \frac{\pi}{16} \mathrm{cm} \)
Subject: Chemistry
Assertion (A): The solubility of aldehydes and ketones in water
decreases with increase of size of the
alkyl group Reason
(R) Alkyl groups are electron releasing groups
A. Both A and R ae true and R is the correct
explanation of A
B. Both A and R are true and R is not the
correct explanation of A
c. A is true but R is false
D. A is false but R is true.
Subject: Physics
While measuring the length of a wooden box, the reading at one end is \( 1.5 \mathrm{cm} \) and the other end is \( 4.7 \mathrm{cm} . \) What is the
length of the wooden box?
A. \( 4.7 \mathrm{cm} \)
B. \( 1.5 \mathrm{cm} \)
c. 3.2 \( \mathrm{cm} \)
D. 6.2 cm
Subject: Physics
Student 1 is
grips wrench here
(wrench turns winch clockwise)
A. correct, because the torque that the wrench must exert to lift the block depend on the wrench's length
B. correct, because the torque that the wrench must exert to lift the block doesn't depend on the wrench's length
C. incorrect, because the torque that the wrench must exert to lift the block doesn't depend on the wrench's length
D. incorrect, because using a longer wrench decreases the torque it must exert on the winch.
Subject: Maths
Calculate Mean deviation from Median
for the given data.
Wages(Rs) \( \quad 20 \) 18 \( \mathbf{1 6} \) 14
Frequency \( \quad 2 \quad 4 \quad 9 \)
A .6 .84
в. 4.44
c. 2.24
D. 3.21
Subject: Maths
If \( \triangle A B C \) has differnence side length
\( a, b, c \) and \( a^{2}, b^{2}, c^{2} \) as side will again
form another \( \triangle P Q R, \) then \( \triangle A B C \) will
always be
A. Acute angle triangle only
B. Obtuse angle triangle only
c. Something Acute or something obtuse depending on value of \( a, b \) and \( c \)
D. None of these
Subject: Biology
Fermentation is represented by which of
the following equation?
\( \mathbf{A} \cdot \$ \$ \mathrm{C}_{-}\{6\} \mathrm{H}_{-}\{12\} \mathrm{O}_{-}\{6\} \backslash, \) ।rightarrow \( \backslash, 6 \mathrm{CO}_{-}\{2\} \backslash,+_{-} \backslash \)
\( 6 \mathrm{H}_{-}\{2\} 01,+\backslash, 673 \mathrm{K} \backslash, \mathrm{cal} \$ \$ \)
B. \( C_{6} H_{12} O_{6} \rightarrow 2 C_{2} H_{5} O H+2 C O_{2} \)
\( \mathbf{c} \cdot 6 C O_{2}+12 H_{2} O \rightarrow C_{6} H_{12} O_{6}+6 H_{2} O+6 O_{2} \)
\( \mathrm{D} \cdot 6 \mathrm{CO}_{2}+6 \mathrm{H}_{2} \mathrm{O} \frac{\text {light}}{\text {chlorophyll}} C_{6} \mathrm{H}_{12} \mathrm{O}_{6}+6 \mathrm{O}_{2} \)
Subject: Chemistry
The conc. of \( F e^{3+} \) ions in a sample of
water is found to be \( 50 \times 10^{-5} M \)
Calculate the \( p H \) (nearest integer) at
which \( 99 \% \) of \( F e^{3+} \) will be precipitated. \( \boldsymbol{K}_{s p_{F e(O H)_{3}}}=\mathbf{1 0}^{-\mathbf{3 6}} \)