AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Chemistry
Which product will be obtained in the following reaction? \( \boldsymbol{P}_{4}(s)+\mathbf{3} N \boldsymbol{a} \boldsymbol{O} \boldsymbol{H}(\boldsymbol{a} \boldsymbol{g})+\boldsymbol{3} \boldsymbol{H}_{2} \boldsymbol{O}(l) \rightarrow \)
A \( \cdot P H_{3}(g)+3 N a H_{2} P 0_{2}(a q) \)
B . \( P H_{3}(g)+3 N a_{2} H P O_{2}(a q) \)
c. \( 2 P H_{3}(g) 3 N a_{2} H P O_{2}(a q) \)
D \( \cdot 2 P H_{3}(g)+3 N a H_{2} P O_{2}(a q) \)
Subject: Physics
Two waves represented by \( y_{1}=a \sin \omega t \) and \( y_{2}=a \sin (\omega t+\phi) \) and \( \phi=\frac{\pi}{2} \) are
superposed at any point at a particular instant. The resultant amplitude is
\( A \)
B. \( 4 a \)
\( c \cdot \sqrt{2} a \)
D. zero
Subject: Chemistry
Statement 1: The reaction of hydrogen
with oxygen to form water is an
exothermic reaction
Statement 2: Water molecules have
polar covalent bonds.
A. Both Statement 1 and Statement 2 are correct and
Statement 2 is the correct explanation of Statement 1
B. Both Statement 1 and Statement 2 are correct and Statement 2 is not the correct explanation of Statement 1.
c. Statement 1 is correct but Statement 2 is not correct.
D. Statement 1 is not correct but Statement 2 is correct.
E. Both the Statement 1 and Statement 2 are not correct.
Subject: Chemistry
Assertion
HCl doesn't used to acidify a \( K M n O_{4} \) solutions in volumetric estimations of
\( \boldsymbol{F} \boldsymbol{e}^{2+} \) or \( \boldsymbol{C}_{2} \boldsymbol{O}_{4}^{2-} \)
Reason
\( K M n O_{4} \) oxidizes HCl to \( C l_{2} \)
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 block of wood weights \( 12 \mathrm{kg} \) and has a relative density \( 0.6 . \) It is to be of its volume immersed. What weight of a metal is needed if the metal is on the
top of wood? [Relative density of metal =
14].
\( A \cdot 2 \mathrm{kg} \)
B. \( 4 \mathrm{kg} \)
\( c \cdot 6 \mathrm{kg} \)
\( D \cdot 8 \mathrm{kg} \)
Subject: Chemistry
Fora reaction, \( \boldsymbol{A} \rightarrow \boldsymbol{B}+\boldsymbol{C}, \) it was found
that at the end of 10 minutes from the
start, the total optical rotation of the
system was \( 50^{\circ} \) and when the reaction
is complete, it was \( 100^{\circ} \mathrm{C} \) Assuming
that only \( B \) and \( C \) are optically active and dextro rotatory, the rate constant of this first order reaction would be?
A \( \cdot 0.069 \min ^{-1} \)
B. 0.69 min \( ^{-1} \)
c. 6.9 min \( ^{-1} \)
D. \( 6.9 \times 10^{-2} \) min \( ^{-1} \)
Subject: Maths
Calculate the volume of a cylinder
where the area of a base is \( 40 \mathrm{mm}^{2} \) and
height is \( 4.5 \mathrm{mm} \)
A \( \cdot 180 \mathrm{cm}^{3} \)
В. \( 181 \mathrm{mm}^{3} \)
\( \mathbf{c} \cdot 180 m m^{3} \)
D. \( 180.4 \mathrm{mm}^{3} \)
Subject: Chemistry
Which of the following is not true?
A. Ordinary water is electrolysed more rapidly than \( D_{2} O \)
B. Reaction between \( H_{2} \) and \( C l_{2} \) is much faster than
\( D_{2} \) and \( C l_{2} \)
\( \mathrm{C} \cdot D_{2} \mathrm{O} \) freezes at lower temperture than \( \mathrm{H}_{2} \mathrm{O} \)
D. Bond dissociation energy for \( D_{2} \) is greater than \( H_{2} 1 \)
Subject: Chemistry
During the electrolysis of \( 0.1 \mathrm{M} \) Cu SO solution using copper electrodes, a depletion of \( \left[C u^{2+}\right] \) occurs near the cathode with a corresponding excess near the anode, owing to inefficient stirring of the solution. If the concentrations of \( \left[C u^{2+}\right] \) near the
anode \( \& \) cathode are respectively 0.12 M
\& 0.08 M, calculate the back e.m.f.
developed. Temperature \( =298 \mathrm{K} \)
A . 22 \( \mathrm{mv} \)
B. 5.2 mv
c. \( 29 \mathrm{mv} \)
D. 59 mv
Subject: Physics
A cylinder of mass \( 10 k g \) and radius
\( 15 \mathrm{cm} \) is rolling perfectly on a plane of
inclinato of \( 30^{\circ} . \) The coefficient of
static friction \( \mu_{k}=0.25 . \) If the
inclination \( \theta \) of the plane is increased,
at what value of \( \theta \) does the cylinder begin to skid, and not roll perfectly?
A \( .37^{\circ} \)
В. \( 53^{\text {? }} \)
\( c \cdot 90^{\circ} \)
D. \( 0^{\circ} \)
Subject: Physics
The work done in carrying a charge \( q \) once round a circle of radius a with a
charge \( Q \) at its centre is:
A \( \cdot \frac{q Q}{4 \pi \varepsilon_{0} a} \)
в. \( \frac{q Q}{4 \pi \varepsilon_{0} a^{2}} \)
c. \( \frac{q}{4 \pi \varepsilon_{0} a} \)
D. zero
Subject: Maths
A part of the monthly expenses of a family is constant and the remaining varies with the price of wheat. When the price of wheat is Rs. 250 per quintal, the total monthly expenses are Rs. 1000 and when it is Rs. 240 per quintal, the total monthly expenses are Rs. 980 per quintal. The total monthly expenses of the family when the cost of wheat is Rs.
350 per quintal, will be:
A . Rs. 500
B. Rs. 1200
c. Rs. -1200
D. Rs. - 500
Subject: Physics
Consider two solid uniform spherical
objects of the same density \( \rho . \) One has
radius \( R \) and the other has radius \( 2 R \)
They are in outer space where the
gravitational fields from other objects are negligible. If they are arranged with their surface touching, what is the contact force between the objects due to their traditional attraction?
\( \mathbf{A} \cdot G \pi^{2} R^{4} \)
B. \( \frac{128}{81} G \pi^{2} R^{4} \rho^{2} \)
\( ^{\mathbf{C}} \cdot \frac{128}{81} G \pi^{2} \)
\( \stackrel{128}{87} G \pi^{2} R^{2} \)
Subject: Maths
The length of tangent drawn from an
external point \( P \) to a circle with centre
0, is \( 8 \mathrm{cm} \). If the radius of the circle is 6
\( \mathrm{cm}, \) then the length of OP (in cm) is :
A \( 2 \sqrt{7} \)
7
B. \( 4 \sqrt{7} \)
\( c \cdot 10 \)
D. 10.5
Subject: Maths
If \( \theta \) be the angle between the lines
whose direction cosines's are given by \( \mathbf{3} l+\boldsymbol{m}+\mathbf{5} \boldsymbol{n}=\mathbf{0}, \boldsymbol{6} \boldsymbol{m} \boldsymbol{n}-\boldsymbol{2} \boldsymbol{n} l+\mathbf{5} \boldsymbol{l} \boldsymbol{m}= \)
0. Find value of \( 6 \cos \theta \)
Subject: Chemistry
The \( K_{s p} \) of salt \( A g C l \) at \( 25^{\circ} C \) is \( 2.56 \times \)
\( 10^{-10} . \) The how much volume of \( H_{2} O \) is
required to dissolve 0.01 mole of salt.
\( \mathbf{A} \cdot 800 L \)
B. \( 400 L \)
c. \( 625 L \)
D. \( 50 L \)
Subject: Chemistry
\( C O_{2} \) and \( C H_{4} \) have critical
temperatures of \( 304 \mathrm{K} \) and \( 190 \mathrm{K} \)
respectively. \( P_{C} \) for \( C O_{2}=72 \) atm and
\( P_{C} \) for \( C H_{4}=45 \) atm. The ratio \( b_{C O_{2}}: \)
\( b_{C H_{4}} \) is?
A .2: 3
B. 1: 1
\( c \cdot 2: 1 \)
D. 3: 2
Subject: Chemistry
\( H_{3} P O_{4} \) is a tribasic acid with
\( \boldsymbol{p} \boldsymbol{K}_{a_{1}}, \boldsymbol{p} \boldsymbol{K}_{a_{2}} \) and \( \boldsymbol{p} \boldsymbol{K}_{a_{3}} \boldsymbol{2} .12, \boldsymbol{7} .21 \) and
\( 12.32, \) respectively. It is used in fertiliser productions and its various salts are used in food, detergent, toothpaste, and in metal treatment.
Small quantities of \( \boldsymbol{H}_{3} \boldsymbol{P} \boldsymbol{O}_{4} \) are used in imparting the sour or tart taste to soft drinkes, such as Coca Cola, and beers
in which \( H_{3} P O_{4} \) is present \( 0.05 \% \) by weight (density \( \left.=1.0 g m L^{-1}\right) \) \( \mathbf{1 0}^{-3} \boldsymbol{M} \boldsymbol{H}_{3} \boldsymbol{P} \boldsymbol{O}_{4}(\boldsymbol{p} \boldsymbol{H}=\mathbf{7}) \) is used in
fertilisers as an aqueous soil digesting. Plants can absorb zinc in water soluble
form only. Zinc phosphate is the source of zinc and \( P O_{2}^{3-} \) ions in the soil. \( K_{s p} \) of zonic phosphate \( =9.1 \times 10^{-33}\left[Z n^{2+}\right] \) ion in the soil is:
A \( .2 .9 \times 10^{-11} \mathrm{M} \)
В. \( 4.0 \times 10^{-10} M \)
c. \( 3.0 \times 10^{-6} M \)
D. \( 9.1 \times 10^{-5} M \)
Subject: Chemistry
\( (\triangle \boldsymbol{H}-\triangle \boldsymbol{E}) \) is maximum at a given
temperature in case of:
\( \mathbf{A} \cdot P C l_{5}(g) \rightarrow P C l_{3}(g)+C l_{2}(g) \)
B. \( C a C O_{3}(s) \rightarrow C a O_{3}(s)+C O_{2}(g) \)
\( \mathbf{c} \cdot N H_{4} H S(s) \rightarrow N H_{3}(g)+H_{2} S(g) \)
D. \( N_{2}(g)+O_{2}(g) \rightarrow 2 N O(g) \)
Subject: Chemistry
Which of the above represents the formula for the most common
compound of \( \boldsymbol{X} \) and \( \boldsymbol{Y} \) ? Where \( \boldsymbol{X} \) is
\( M g \) and \( Y \) is \( S \)
A. \( X_{2} Y \)
\( Y \)
в. \( X Y \)
c. \( X Y_{2} \)
D. \( X Y_{3} \)
E. \( X Y_{4} \)
Subject: Physics
Assertion
Each of the plates of a parallel-plate
capacitor is given equal positive charge
Q. The charges on the facing surfaces
will be same.
Reason
A negative charge \( (-Q) \) will be induced
on each of the facing 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. Assertion is incorrect but Reason is correct
Subject: Physics
When a current is passed in a
conductor, \( 3^{\circ} C \) rise in temperature is
observed. If the strength of current is made thrice, then rise in temperature will approximately be:
A \( \cdot 36^{\circ} \mathrm{C} \)
В. \( 27^{\circ} \mathrm{C} \)
\( \mathbf{c} \cdot 18^{\circ} C \)
D. \( 9^{\circ} C \)
Subject: Chemistry
A buffer solution is used in:
A. preparation of potash alum
B. the removal of \( P O_{4}^{3-} \) ions
C. increasing the pH value of a solution
D. precipitation of \( C r(O H)_{3} \) from \( \$ \$ \) Cr \( \{C \mid\}_{-}\{3\} \$ p \)
Subject: Chemistry
Assertion
The reaction \( \boldsymbol{X} \boldsymbol{e} \boldsymbol{O}_{3}+\boldsymbol{6} \boldsymbol{H}^{+}+\boldsymbol{6} \boldsymbol{e}^{-} \rightleftharpoons \)
\( X e+3 H_{2} O, E^{\circ}=2.1 V \) is not feasible
thermodynamically to oxidise \( H_{2} O \)
Reason
There is a high activation energy barrier between oxidation state +6 and 0 of \( X e \)
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 true but Reason is false
D. Assertion is false but Reason is true
Subject: Maths
\( A B \) is a straight line and \( O \) is a pont
lying on \( A B . A \) line \( O C \) is drawn from \( O \)
such that \( \angle C O A=36^{\circ} . O D \) is a line
within \( \angle C O A \) such that \( \angle D O A=\frac{1}{3} \) \( \angle C O A \). If \( O E \) is a line within the \( \angle B O C \)
\( \angle B O E=\frac{1}{4} \angle B O C, \) then \( \angle D O E \) must
be:
A \( \cdot 60^{\circ} \)
В \( \cdot 132^{\circ} \)
\( c \cdot 144^{\circ} \)
D. \( 108^{\circ} \)
Subject: Chemistry
Statement
As ice absorbs heat and begins to melt,
its temperature remains constant Because
Statement II
Changes of state bring about changes in a substances potential energy, not in its kinetic energy
A. Statement 1 and Statement 2 are correct and Statement 2 is the correct explanation of Statement 1
B. Both the Statement 1 and Statement 2 are correct and Statement 2 is not the correct explanation of Statement 1.
c. Statement 1 is correct but Statement 2 is not correct.
D. Statement 1 is not correct but Statement 2 is correct.
E. Both the Statement 1 and Statement 2 are not correct
Subject: Physics
Assume that each diode as shown in
the figure has a forward bias resistance
of \( 50 \Omega \) and an infinite reverse bias
resistance. The current through the
resistance \( 150 \Omega \) is:
A \( .0 .66 A \)
B. \( 0.05 A \)
c. zero
D. \( 0.04 A \)
Subject: Maths
If \( \boldsymbol{A}=\{\mathbf{1}, \mathbf{4}, \mathbf{9}, \mathbf{1 6}, \mathbf{2 5}, \dots\} \) and \( \boldsymbol{B}= \)
\( \left\{\boldsymbol{x} \mid \boldsymbol{x}=\boldsymbol{n}^{2}, \boldsymbol{n} \in \boldsymbol{N}\right\}, \) then
A \( . A=B \)
в. \( A \neq B \)
c. \( A \subset B \)
D. \( B \subset A \)
Subject: Chemistry
The constituents of the electrolyte for the extraction of aluminium is
A. 40 parts cryolite +40 parts fluorspar +20 parts pure \( A l_{2} O_{3} \)
B. 60 parts cryolite +30 parts fluorspar +10 parts pure \( A l_{2} O_{3} \)
C. 30 parts cryolite +30 parts fluorspar +40 parts pure \( A l_{2} O_{3} \)
D. 60 parts cryolite +20 parts fluorspar +20 parts pure \( A l_{2} O_{3} \)
Subject: Physics
A mass of material exists in its solid
form at its melting temperature \( 10^{\circ} \mathrm{C} \) The following processes then occur to
the material:

Process 1: An amount of thermal energy
\( Q \) is added to the material and \( \frac{3}{4} \) of the material melts.
Process 2: An identical additional
amount of thermal energy \( Q \) is added to
the material and the material is now a
liquid at \( 50^{\circ} \mathrm{C} \)

What is the ratio of the latent heat of
fusion to the specific heat of the liquid
for this material?
A . 80
B. 60
c. 40
D. 20
Subject: Maths
State whether following statements are
true or false
Statement-1: The only circle having
radius \( \sqrt{10} \) and a diameter along line
\( 2 x+y=5 \) is \( x^{2}+y^{2}-6 x+2 y=0 \)
Statement-2: The line \( 2 x+y=5 \) is a
normal to the circle \( x^{2}+y^{2}-6 x+ \)
\( 2 y=0 \)
A. Statement- 1 is false, statement- 2 is true.
B. Statement-1 is true,statement-2 is true and statement 2 is NOT the correct explanation for statement-1.
c. Statement-1 is true, statement-2 is false.
D. Statement-1 is true, statement-2 is true and statement-2 is correct explanation for statement-
Subject: Chemistry
A certain dye absorbs light of \( \lambda=4500 \)
\( A^{\circ} \) and then fluoresces light of \( \lambda= \)
\( 5000 A^{\circ} . \) Assuming that under given conditions, \( 45 \% \) of the absorbed energy is re-emitted out as fluorescence,
calculate the ratio of qunts emitted out to the number of quanta absorbed.
Subject: Maths
In parallelogram \( A B C D \) the length \( A B \)
and \( C D \) are both 4 , the length of
diagonal \( A C=4 \) and the length of
diagonal \( B D=6 . \) The length \( A D \) equal
to
A. \( \sqrt{10} \)
B. \( \sqrt{12} \)
\( c \cdot \sqrt{15} \)
D. \( \sqrt{20} \)
Subject: Physics
Two coils have a mutual inductance
\( 0.55 H . \) The current changes in the first
coil according to equation \( \boldsymbol{I}=\boldsymbol{I}_{0} \sin \omega \boldsymbol{t} \)
where, \( I_{0}=10 A \) and \( \omega=100 \pi r a d / s \)
The maximum value of emf in the
second coil is
A . \( 2 \pi \)
в. \( 5 \pi \)
c. \( \pi \)
D. \( 4 \pi \)
Subject: Chemistry
\( \boldsymbol{H}_{2} \boldsymbol{O}_{2} \rightarrow \boldsymbol{2} \boldsymbol{H}^{+}+\boldsymbol{O}_{2}+\boldsymbol{2} \boldsymbol{e}^{-} \)
The above equation represent which of
the following behaviour of \( \boldsymbol{H}_{2} \boldsymbol{O}_{2} ? \)
A. Reducing
B. Oxidising
c. Basic
D. Catalytic
Subject: Maths
Area of region bounded by \( \boldsymbol{x}=\mathbf{0}, \boldsymbol{y}=\mathbf{0} \)
\( \boldsymbol{x}=\mathbf{2}, \boldsymbol{y}=\mathbf{2}, \boldsymbol{y} \leq \boldsymbol{e}^{x} ; \boldsymbol{y} \geq \ln \boldsymbol{x} \) is
A \( .6-4 \ln 2 \)
B. \( 4 \ln 2-2 \)
c. \( 2 \ln 2-4 \)
D. \( 6-2 \ln 2 \)
Subject: Physics
A spring of force constant \( k \) is cut into
two pieces such that one piece is twice as long as the other. Then the longer piece will have a force constant of:
\( \mathbf{A} \cdot 3 k \)
в. \( \frac{2 k}{3} \)
\( c \cdot \frac{3 k}{2} \)
D. \( 6 k \)
Subject: Chemistry
Find the number of molecule(s)/ion
having Lewis basic property from the following
\( \boldsymbol{H}_{2} \boldsymbol{O}, \boldsymbol{N} \boldsymbol{H}_{3}, \boldsymbol{C} \boldsymbol{H}_{3} \boldsymbol{N} \boldsymbol{H}_{2}, \boldsymbol{R} \boldsymbol{O} \boldsymbol{H}, \boldsymbol{F} \boldsymbol{e} \boldsymbol{C l}_{3} \)
Subject: Maths
Given, \( \boldsymbol{f}(\boldsymbol{x})=-\frac{\boldsymbol{x}^{3}}{\mathbf{3}}+\boldsymbol{x}^{2} \sin \mathbf{1 . 5} \boldsymbol{a}- \)
\( x \sin a \cdot \sin 2 a-5 a r c \sin \left(a^{2}-8 a+17\right) \)
then
A. \( f(x) \) is not defined at \( x=\sin 8 \)
B. \( f^{\prime}(\sin 8)>0 \)
c. \( f^{\prime}(x) \) is not defined at \( x=\sin 8 \)
D. \( f^{\prime}(\sin 8)<0 \)
Subject: Chemistry
Assertion
Aluminium containers can be used for
\( \operatorname{storing} \boldsymbol{H} \boldsymbol{N} \boldsymbol{O}_{3} \)
Reason
Nitric acid cannot oxidize aluminium at
all.
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 biconvex lens of focal length \( f \) forms a
circular image of sun of radius \( r \) in focal plane. Then,
A \( \cdot \pi r^{2} \propto f \)
В \( \cdot \pi r^{2} \propto f^{2} \)
c. if lower half part is covered by black sheet, then area of the image is equal to \( \pi r^{r} / 2 \)
D. if \( f \) is doubled intensity will increase
Subject: Physics
The dimensions of a rectangular
parallelepiped are \( 1 \mathrm{cm} \times 1 \mathrm{cm} \times \)
\( 100 \mathrm{cm} . \) If its specific resistance is \( 3 x \)
\( 10^{-7} \Omega m \) then the resistance between
its rectangular faces will be
A \( \cdot 3 \times 10^{-9} \Omega \)
В. \( 3 \times 10^{-7} \Omega \)
c. \( 3 \times 10^{-5} \Omega \)
D. \( 3 \times 10^{-3} \Omega \)
Subject: Chemistry
The hybridization of carbon atoms in
\( C-C \) single bond of \( H C \equiv C- \)
\( \boldsymbol{C H}=\boldsymbol{C H}_{2} \) is:
A \( \cdot s p^{3}-s p^{3} \)
В \( \cdot s p^{2}-s p^{3} \)
\( \mathbf{c} \cdot s p-s p 2 \)
D. \( s p^{3}-s p \)
Subject: Physics
Assertion
A spherical equipotential surface is not
possible for a point charge.
Reason
A spherical equipotential surface is possible inside a spherical capacitor.
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
During one dimensional collision or
head on collision:
a) The bodies move along the line
joining their centre of mass before and after collision.
b) The bodies should move in opposite direction.
c) The bodies change their direction after collision.
d) The bodies move along the line joining their centre of mass before and after collision either in same direction
or in opposite direction.
A. Only a is correct
B. Only a \& b are correct
\( c . \) a, b \( \& \mathrm{c} \) are correct
D. Only a and d are correct
Subject: Maths
If \( g(x)=x^{2}+x-2 \) and \( \frac{1}{2} g o f(x)= \)
\( 2 x^{2}-5 x+2, \) then which is \( f(x) \)
A \( .2 x-3 \)
B. \( -2 x-3 \)
c. \( x-3 \)
D. \( x+3 \)
Subject: Maths
If \( \sin \left[2 \cos ^{-1}\left\{\cot \left(2 \tan ^{-1} x\right)\right\}\right]=0, x> \)
\( 0, \) then
This question has multiple correct options
\( \mathbf{A} \cdot x=1 \)
В. \( x=\sqrt{2}+1 \)
c. \( x=\sqrt{2}-1 \)
D. \( x=3 \)
Subject: Physics
A car starts from rest and acceleration
\( \operatorname{at} 4 m / s^{2} \) for \( 5 s . \) After that it moves
with constant velocity for \( 25 s \) and then
retards at \( 2 m / s^{2} \) until it comes to rest. The total distance travelled by the car is
\( \mathbf{A} \cdot 650 m \)
B. \( 527 m \)
c. \( 675 m \)
D. 573 m
Subject: Maths
\( \boldsymbol{\alpha}=\sin ^{-1}\left(\cos \left(\sin ^{-1} x\right)\right) \) and \( \beta= \)
\( \cos ^{-1}\left(\sin \left(\cos ^{-1} x\right)\right) \) then:
\( A \cdot \tan \alpha=\cot \beta \)
B. \( \tan \alpha=-\cot \beta \)
\( \mathbf{c} \cdot \tan \alpha=\tan \beta \)
D. \( \tan \alpha=-\tan \beta \)
Subject: Maths
Let \( p \) be a nonsingular matrix, and \( I+ \)
\( \boldsymbol{p}+\boldsymbol{p}^{2}+\ldots . .+\boldsymbol{p}^{n}=\mathbf{0}, \) then find \( \boldsymbol{p}^{-1} \)
A . \( I \)
B . \( p^{n+1} \)
c. \( p^{n} \)
D \( \cdot\left(p^{n+1}-I\right)(p-I) \)
Subject: Physics
A body is executing \( \mathrm{SHM} \), At a displacement \( x, \) its potential energy is
\( E_{1} \) and at a displacement \( y, \) its
potential energy is \( E_{2} \). Find its potential energy \( \mathrm{E} \) at displacement \( (\mathrm{x}+\mathrm{y}) \)
B . \( \sqrt{E}=\sqrt{E}_{1}+\sqrt{E}_{2} \)
c. none of these
D. all of these
Subject: Physics
Two forces acting in opposite directions
have a resultant of \( 10 \mathrm{N} 10 \mathrm{N} \). What are the
magnitudes of the two forces?
\( \mathbf{A} \cdot F_{1}=40 N, F_{2}=30 N \)
B. \( F_{1}=30 N, F_{2}=40 N \)
C . \( F_{1}=50 N, F_{2}=40 N \)
D. \( F_{1}=100 N, F_{2}=60 N \)
Subject: Maths
The range of the function \( f(x)=x^{2}+ \)
\( \frac{1}{x^{2}+1} \) is
\( A \cdot[1,+\infty) \)
B. \( [2,+\infty) \)
\( ^{\mathbf{C}} \cdot\left[\frac{3}{2},+\infty\right) \)
D. None of these
Subject: Physics
The wave equation is \( y= \) \( 0.30 \sin (314 t-1.57 x) \) where \( t, x \) and \( y \)
are in second, metre and centimetre
respectively. The speed of the wave is
A. \( 400 \mathrm{m} / \mathrm{s} \)
в. \( 100 \mathrm{m} / \mathrm{s} \)
c. \( 200 m / s \)
D. \( 50 \mathrm{m} / \mathrm{s} \)
Subject: Physics
An arrangement with a pair of quarter circular coils of radii \( r \) and \( R \) with a
common centre \( C \) and carrying a
current I is shown.
The permeability of free space is \( \mu_{0} . \) The
magnetic field at \( \mathrm{C} \) is :
A \( \cdot \mu_{0} I(1 / r-1 / R) / 8 \) into the page
B. \( \mu_{0} I(1 / r-1 / R) / 8 \) out the page
C. \( \mu_{0}(1 / r+1 / R) / 8 \) into the page
D・ \( \mu_{0}(1 / r+1 / R) / 8 \) out the page
Subject: Chemistry
Identify the correct statement(s)
This question has multiple correct options
A. Ozone is a powerful oxidizing agent as compared to \( O_{2} \)
B. Ozone reacts with KOH and gives an orange coloured solid \( K O_{3} \)
C. There is a decrease in volume when ozone
decomposed to form \( O_{2} \)
D. The decomposition of \( O_{3} \) to \( O_{2} \) is exothermic.
Subject: Physics
A police party is moving in a jeep at a
constant speed \( V . \) They saw a thief at a
distance \( x \) on a motorcycle which is at
rest. The moment the police saw the
thief, the thief started at constant
acceleration \( a . \) Which of the following
relations is true if the police is able to catch the thief?
A \( \cdot V^{2}<a x \)
B. \( V^{2}<2 a x \)
\( \mathbf{c} \cdot V^{2} \geq 2 a x \)
D. \( V^{2}=a x \)
Subject: Physics
If the system is not in free fall, which of
the following statements is true about
hydrostatic pressure?
This question has multiple correct options
A. In a liquid, point at different depth can never be at the
same pressure.
B. In a liquid, point at different depth may be at the same pressure.
C. In different liquids, points at different depths can be at the same pressure.
D. In different liquids, points at the same depths can never be at the same pressure.
Subject: Maths
toppr
Q Type your question
pressure in atmospheres. For example if
a substance at a particular temperature and pressure lies in gas area, the substance exists only as a
gas.

However, if the temperature-pressure
pairing is on the line segment between gas and liquid, the substance exists as
both a gas and a liquid.. If \( \boldsymbol{T}>\mathbf{0} \) and
\( P>0, \) which of the following systems of
inequalities would describe the
temperature and pressure ranges in which this substance exists only as a liquid?
\( ^{\text {A }} P<\frac{17}{2} T-1,860 ; P>\frac{5}{18} T-\frac{460}{9} \)
В \( \cdot P>\frac{17}{2} T-1,860 ; P<\frac{5}{18} T-\frac{460}{9} \)
c. \( \quad P<\frac{17}{2} T-1,860 ; P>\frac{11}{200} T-\frac{460}{9} \)
\( P \geq \frac{17}{2} T-1,860 ; P \leq \frac{11}{200} T-\frac{460}{9} \)
Subject: Maths
The slope of the line, \( l_{1} \) is \( \frac{-3}{5} \) and \( l_{1} \) and
\( l_{2} \) are parallel. Find the slope of \( l_{2} \)
A \( \cdot \frac{-5}{3} \)
в. \( \frac{-1}{5} \)
c. \( \frac{-3}{5} \)
D. \( \frac{3}{5} \)