AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Biology
Assertion
Suspended particulate matter (SPM) is an important pollutant released by diesel vehicles.
Reason
Catalytic converters greatly reduce pollution caused by automobiles.
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
Two crossroads,each \( 2 \mathrm{m} \) wide,run at
right angles through the center of a rectangular park of length \( 64 \mathrm{m} \) and
breadth \( 38 \mathrm{m} \),such that each is parallel to one of the sides of the rectangle. Find the area of the roads.also, find the area
of the remaining part of the park
Subject: Maths
If \( \boldsymbol{A}=\left\{\boldsymbol{x} \epsilon \boldsymbol{R} / \frac{\pi}{4} \leq \boldsymbol{x} \leq \frac{\pi}{3}\right\} \quad \) and
\( \boldsymbol{f}(\boldsymbol{x})=\sin \boldsymbol{x}-\boldsymbol{x} \quad, \) then \( \boldsymbol{f}(\boldsymbol{A})= \)
A \( \cdot\left[\frac{\sqrt{3}}{2}-\frac{\pi}{3}, \frac{1}{\sqrt{2}}-\frac{\pi}{4}\right] \)
B. \( \left[-\frac{1}{\sqrt{2}}-\frac{\pi}{4}, \frac{\sqrt{3}}{2}-\frac{\pi}{3}\right] \)
\( \mathbf{c} \cdot\left[-\frac{\pi}{3}, \frac{-\pi}{4}\right] \)
D. \( \left[\begin{array}{c}\pi \\ \hline 4\end{array}, \frac{\pi}{3}\right. \)
Subject: Physics
An ant is at a corner of a cubical room of
side a. The ant can move with a
constant speed u. The minimum time
taken to reach the farthest corner of the
cube is?
A \( \cdot \frac{3 a}{u} \)
B. \( \frac{\sqrt{3} a}{u} \)
c. \( \frac{\sqrt{5} a}{u} \)
D. \( \frac{(\sqrt{2}+1) a}{u} \)
Subject: Physics
Two cells, having the same e.m.f are connected in series through an external resistance R. Cells have internal
resistance \( r_{1} \) and \( r_{2}\left(r_{1}>r_{2}\right) \)
respectively. When the circuit is closed, the potential difference across the first cell is zero. the value of \( \mathrm{R} \) is
A \( \cdot \frac{r_{1}+r_{2}}{2} \)
B. \( \frac{r_{1}-r_{2}}{2} \)
\( \mathbf{c} \cdot r_{1}+r_{2} \)
D. \( r_{1}-r_{2} \)
Subject: Chemistry
The correct relation between elevation
of boiling point and molar mass of
solute is:
A \( \ldots_{M_{2}}=\frac{K_{b} \times W_{2}}{\Delta T_{b} \times W_{1}} \)
В. \( M_{2}=\frac{K_{b} \times W_{1}}{\Delta T_{b} \times W_{2}} \)
\( ^{\mathrm{C}} \cdot_{M_{2}}=\frac{\Delta T_{b} \times K_{b}}{W_{1} \times W_{2}} \)
D. \( M_{2}=\frac{\Delta T_{b} \times W_{1}}{K_{b} \times W_{2}} \)
Subject: Maths
Assertion
If \( a, b, c \) are three positive numbers in
G.P., then \( \left(\frac{a+b+c}{3}\right) \cdot\left(\frac{c+b}{a b+b c+c a}\right)= \)
\( (\sqrt[3]{a b c})^{2} \)
Reason
(A.M.) (H.M.) \( =(G . M .)^{2} \) is true for any
set of positive numbers.
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: Maths
A coin is tossed \( 2 n \) times. The chance
that the number of times one gets head is not equal to the number of times one
gets tail is
A \( \cdot \frac{(2 n) !}{(n ! !)^{2}} \cdot\left(\frac{1}{2}\right)^{2} n \)
B. \( _{1-} \frac{(2 n) !}{(n !)^{2}} \)
c. \( _{1-} \frac{(2 n) !}{(n !)^{2}} \cdot \frac{1}{4^{n}} \)
D. none of these
Subject: Maths
\( f\left|\begin{array}{lll}\boldsymbol{x} & \boldsymbol{2} & \boldsymbol{8} \\ \boldsymbol{2} & \boldsymbol{8} & \boldsymbol{x} \\ \boldsymbol{8} & \boldsymbol{x} & \boldsymbol{2}\end{array}\right|=\left|\begin{array}{lll}\boldsymbol{3} & \boldsymbol{x} & \boldsymbol{7} \\ \boldsymbol{x} & \boldsymbol{7} & \boldsymbol{3} \\ \boldsymbol{7} & \boldsymbol{3} & \boldsymbol{x}\end{array}\right|= \)
\( \left|\begin{array}{ccc}\mathbf{5} & \mathbf{5} & \boldsymbol{x} \\ \mathbf{5} & \boldsymbol{x} & \mathbf{5} \\ \boldsymbol{x} & \mathbf{5} & \mathbf{5}\end{array}\right|=\mathbf{0} \) then \( \boldsymbol{x} \) is equal to
\( \mathbf{A} \cdot \mathbf{0} \)
B. -10
\( c .3 \)
D. None of these
Subject: Physics
In a large commercial complex there are four ways to reach the main road. One of the path has loose soil, the second is laid with polished marble, the third is laid with bricks and the fourth
has gravel surface. It is raining heavily and Paheli wishes to reach the main
road. The path on which she is least likely to slip is:
A. loose soil
B. polished marble
c. bricks
D. gravel surface
Subject: Chemistry
When \( M n O_{2} \) is fused with \( \mathrm{KOH} \) and
\( K C l O_{3}, \) a coloured compound is formed, the product and its colour is:
A \( \cdot K_{2} M n O_{4}, \) green
B . \( K M n O_{4} \), purple
c. \( M n_{2} O_{3} \), brown
D. \( M n_{3} O_{4} \), black
Subject: Maths
In triangle \( A B C, D \) and \( E \) are mid-points of sides \( A B \) and \( B C \) respectively. Also, \( F \)
is a point in side \( A C \) so that DF is parallel to BC. Prove that DBEF is a parallelogram. Answer: DBEF is a parallelogram, If true then enter 1 else if False enter 0
Subject: Physics
Assertion
The maximum refractive index of liquid for total internal reflection of the ray
passing through the prism should be \( \sqrt{2} \)
Reason
Here critical angle is \( 45^{\circ} \)
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 parallel plate capacitor is connected to a battery. The quantities charge, voltage, electric field and energy associated with this capacitor are given
by \( Q_{0}, V_{0}, E_{0}, \) and \( U_{0} \) respectively. \( A \) dielectric slab is now introduced to fill
the space between the plates with the battery still in connection. The corresponding quantities now given by \( Q, V, E \) and \( U \) are related to the
previous ones are :
A \( \cdot Q>Q_{0} \)
в. \( V>V_{0} \)
c. \( E>E_{0} \)
D. \( U<U_{0} \)
Subject: Physics
A uniform rod \( A B \) of mass \( 2 k g \) is
hinged at one end \( A \). The rod is kept in
the horizontal position by a massless
string tied to point \( B \). Find the reaction
of the hinge \( (\text { in } N) \) on end \( A \) of the rod at the instant when string is cut.
\( \left(g=10 m / s^{2}\right) \)
\( A \cdot 6 \)
в. 40
\( c \cdot 15 \)
D.
Subject: Maths
\( \operatorname{Let} A=\left[\begin{array}{ccc}1 & -1 & -1 \\ 2 & 1 & -3 \\ 1 & 1 & 1\end{array}\right] \) and \( 10 B= \)
\( \left[\begin{array}{ccc}\mathbf{4} & \mathbf{2} & \mathbf{2} \\ -\mathbf{5} & \mathbf{0} & \boldsymbol{\alpha} \\ \mathbf{1} & \mathbf{- 2} & \mathbf{3}\end{array}\right], \) if \( \boldsymbol{B} \) is the inverse of
matrix \( A \), then \( \alpha \) is
\( A \)
B.
\( c \cdot 2 \)
\( D \)
Subject: Chemistry
\( N a C l_{(a q)} \) gives a white precipitate with \( A g N O_{3} \) solution but \( C C l_{4} \) or \( C H C l_{3} \)
does not, because:
A. \( N a C I \) is a covalent compound and forms \( A g C l \) as white ppt
B. \( N a C l \) is an ionic compound and forms \( A g C l \) as white \( p p t \)
c. \( C C l_{4} \) and \( C H C l_{3} \) are ionic compound
D. none of these
Subject: Physics
Three resistors of each \( 1 \Omega \) are joined in the form of a triangle.The value of resistance between an the corners:
A \( \cdot \frac{2}{3} \Omega \)
B . \( \frac{3}{2} \Omega \)
\( c \cdot \frac{3}{4} \Omega \)
D. 3\Omega
Subject: Chemistry
For the cell Pt \( \mid \mathbf{H}_{2}(0.4 \text { at } m) \mid \mathbf{H}^{+}(p H=1) \) \( \left.\|(p H=2) \mid H_{2} 90.1 \text { atm }\right) \mid P t . \) The
measured potential at \( 25^{\circ} \mathrm{C} \) is:
A . \( -0.1 V \)
B. \( -0.5 V \)
c. \( -0.041 V \)
D. \( -0.030 V \)
Subject: Maths
If \( A \) and \( B \) are square matrices such
that \( B=-A^{-1} B A, \) then \( (A+B)^{2} \) is
equal to
\( \mathbf{A} \cdot \mathbf{0} \)
B. \( A^{2}+B^{2} \)
c. \( A^{2}+2 A B+B^{2} \)
D. \( A+B \)
Subject: Physics
Q Type your question
conducting rod of length I. Another point
particle of the same mass is attached to the other end of the rod. The two
particles carry charges \( +q \) and \( -q \) respectively. This arrangement is held
in a region of a uniform electric field \( \mathrm{E} \)
such that the rod makes a small angle \( \theta \)
(say of about 5 degrees) with the field direction. Find an expression for the minimum time needed for the rod to
become parallel to the field after it is set free.
A \( \cdot \frac{\pi}{2}, \sqrt{\frac{M L}{2 q E}} \)
В \( \cdot \frac{\pi}{2}, \sqrt{\frac{M L}{q E}} \)
c. \( \pi, \sqrt{\frac{M L}{q E}} \)
D. None of these
Subject: Physics
In scattering experiment, find the distance of closest approach, if a \( 6 \mathrm{MeV} \) \( \alpha \) -particle is used
A . \( 3.2 \times 10^{-16} \mathrm{m} \)
В. \( 2 \times 10^{-14} \mathrm{m} \)
c. \( 4.6 \times 10^{-15} \mathrm{m} \)
D. \( 3.2 \times 10^{-15} \mathrm{m} \)
Subject: Maths
Find \( A \triangle B \) and draw Venn diagram when:
\( \boldsymbol{A}=\{\boldsymbol{a}, \boldsymbol{b}, \boldsymbol{c}, \boldsymbol{d}\} \) and \( \boldsymbol{B}=\{\boldsymbol{d}, \boldsymbol{e}, \boldsymbol{f}\} \)
Subject: Maths
Let \( \boldsymbol{f}: \mathbb{N} \rightarrow \mathbb{N} \) be defined by \( \boldsymbol{f}(\boldsymbol{n})= \)
\( \left\{\begin{array}{ll}\frac{n+1}{2}, & \text { if } n \text { is odd } \\ \frac{n}{2}, & \text { if } n \text { is even }\end{array} n \in \mathbb{N}\right. \)
State whether the function \( f \) is
bijective. Justify your answer.
Subject: Physics
What would be the radius of second
orbit of \( \boldsymbol{H} \boldsymbol{e}^{+} \) ion?
A . \( 1.058 \AA \)
в. \( 3.023 \AA \)
c. \( 2.068 \hat{h} \)
D. \( 4.458 \dot{h} \)
Subject: Physics
A sound wave is a pressure wave; regions of high (compressions) and low pressure (rarefactions) are established
as the result of the vibrations of the
sound source. These compressions and
rarefactions result because sound:
A. is more dense than air and thus has more inertia causing the bunching up of sound
B. waves have a speed which is dependent only upon the properties of the medium.
C. is like all waves; it is able to bend into the regions of space behind obstacles
D. is able to reflect off fixed ends and interfere with incident wavesvibrates longitudinally; the longitudinal movement of air produces pressure fluctuations.
Subject: Maths
For a matrix \( \boldsymbol{A}\left(\begin{array}{ccc}\mathbf{1} & \mathbf{0} & \mathbf{0} \\ \mathbf{2} & \mathbf{1} & \mathbf{0} \\ \mathbf{3} & \mathbf{2} & \mathbf{1}\end{array}\right), \) if \( \boldsymbol{U}_{1}, \boldsymbol{U}_{2} \)
and \( U_{3} \) are \( 3 \times 1 \) column matrices
satisfying \( \boldsymbol{A} \boldsymbol{U}_{\mathbf{1}}= \)
\( \left(\begin{array}{l}1 \\ 0 \\ 0\end{array}\right), A U_{2}\left(\begin{array}{l}2 \\ 3 \\ 0\end{array}\right), A U_{3}=\left(\begin{array}{l}2 \\ 3 \\ 1\end{array}\right) \) and \( U \) is
\( 3 \times 3 \) matrix whose columns are \( U_{1}, U_{2} \)
and \( U_{3} \)
Then sum of the elements of \( U^{-1} \) is
A . 6
B. \( 0(z e r o) \)
\( c . \)
D. \( 2 / 3 \)
Subject: Maths
Vector \( \vec{A} \) is \( 2 c m \) long and is \( 60^{\circ} \) above
the \( x \) -axis in the first quadrant. Vector
\( \vec{B} \) is \( 2 c m \) long and is \( 60^{\circ} \) below the \( x \) axis in the fourth quadrant. The sum \( \vec{A}+\vec{B} \) is a vector of magnitude
A. \( 2 c m \) along positive y-axis
B. 2cm along positive x-axis
c. \( 2 c m \) along negative y-axis
D. \( 2 c m \) along negative x-axis
Subject: Biology
If tree \( =A, \) large Birds \( =B, \) Insects \( =C \) and small birds = D, then in a single tree ecosystem, the pyramid of number stays correct in all of the following
except
\( A \cdot C>D>A \)
B. \( D>A>B \)
\( c \cdot c>B>A \)
D. \( D>B>C \)
Subject: Chemistry
Observe the following reaction \( : 2 A+ \)
\( B \rightarrow C . \) The rate of formation of \( C \) is
\( 2.2 \times 10^{-3} \) mol \( l^{-1} \) min \( ^{-1} . \) The is the
value of \( \frac{-\boldsymbol{d}[\boldsymbol{A}]}{\boldsymbol{d} \boldsymbol{t}}\left(\text { in } \boldsymbol{m o l} \boldsymbol{l}^{-1} \boldsymbol{m} \boldsymbol{i} \boldsymbol{n}^{-1}\right) \)
A \( .2 .2 \times 10^{-3} \)
В. \( 1.1 \times 10^{-3} \)
c. \( 4.4 \times 10^{-3} \)
D. \( 5.5 \times 10^{-3} \)
Subject: Biology
Consider the following two equations \( A \) and B.
Equation A Glucose \( \rightarrow \) Pyruvate \( \rightarrow C O_{2}+H_{2} O+ \)
Energy Equation B
Glucose \( \rightarrow \) Pyruvate \( \rightarrow C_{2} H_{5} O H+ \)
\( \boldsymbol{C O}_{2}+ \) Energy
Which one of the following is correct with respect to both the equations \( A \)
and B?
A. A is aerobic respiration consisting of glycolysis and Krebs cycle, B is anaerobic fermentation reaction
B. A is anaerobic respiration and B is aerobic fermentation reaction
c. A is aerobic respiration B is anaerobic lactic acid fermentation
D. In both A and B reactions, pyruvate undergoes complete oxidation.
Subject: Chemistry
For the reaction, \( \boldsymbol{P C l}_{5}(\boldsymbol{g}) \rightleftharpoons \boldsymbol{P} \boldsymbol{C l}_{3}(\boldsymbol{g})+ \)
\( C l_{2}(g), \) the position of equilibrium can
be shifted to the right by:
A. doubling the volume
B. increasing the temperature
c. addition of equimolar quantities of \( P C l_{3} \) and \( P C l_{5} \)
D. addition of \( C l_{2} \) at constant volume
Subject: Physics
If \( M_{E} \) is the mass of the earth and \( R_{E} \)
its radius, the ratio of the acceleration
due to gravity and the gravitational constant is:
\( ^{\text {A }} \cdot \frac{R_{E}^{2}}{M_{E}} \)
в. \( \frac{M_{E}}{R_{E}^{2}} \)
c. \( M_{E} R_{E}^{2} \)
D. \( \frac{M_{E}}{R_{E}} \)
Subject: Chemistry
Assertion
As temperature increases, heat of
reaction also increase for exothermic as
well as endothermic reactions.
Reason
\( \Delta H_{\text {reaction}} \) varies according to the
relation:
\( \frac{\Delta \boldsymbol{H}_{2}-\boldsymbol{\Delta} \boldsymbol{H}_{1}}{\boldsymbol{T}_{2}-\boldsymbol{T}_{1}}=\boldsymbol{\Delta} \boldsymbol{C}_{\boldsymbol{P}} \)
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
Which of the following wires of the same material will have higher resistance :-
A. radius is 1 \( \mathrm{mm} \) and the length is 40 \( \mathrm{m} \)
B. radius is 2 \( \mathrm{mm} \) and the length is 40 \( \mathrm{m} \).
c. radius is \( 1 \mathrm{mm} \) and the length is \( 80 \mathrm{m} \)
D. radius is 2 \( \mathrm{mm} \) and the length is 80 \( \mathrm{m} \).
Subject: Biology
Assertion
Ramenta are scales which cover
young rhizome and leaves of Dryopteris
Reason
Pteridium lacks ramenta
A. If both the assertion and the reason are true and the reason is a correct explanation of the assertion
B. If both the assertion and reason are true but the reason is not a correct explanation of the assertion
c. If the assertion is true but the reason is false
D. If both the assertion and reason are false
Subject: Physics
Three resistors of \( 10 \Omega, 15 \Omega \) and \( 20 \Omega \)
are connected in series in a circuit. If
the potential drop across the \( 15 \Omega \)
resistor is \( 3 V \), find the current in the
circuit, potential drop across \( 10 \Omega \) and the net emf of the source used in the
circuit. (Draw the circuit diagram)
Subject: Physics
A galvanometer of resistance \( 50 \Omega \) is
connected to a battery of \( 3 V \) along with a resistance of \( 2950 \Omega \) in series. A full-
scale deflection of 30 divisions is obtained in the galvanometer. In order to reduce this deflection to 20 divisions, the resistance in series should be equal
to
A . \( 5050 \Omega \)
B. \( 5550 \Omega \)
c. \( 6050 \Omega \)
D. \( 4450 \Omega \)
Subject: Maths
Which of the following is factorization of \( \left(-56 m n p^{2}+7 m n p\right) \)
A. \( 7 m n p(-8 p+1) \)
в. \( 7 m n p(8 p+1) \)
\( \mathrm{c} .7 m n p(8 p-1) \)
D. None of these
Subject: Chemistry
\( \boldsymbol{A} \rightarrow \boldsymbol{B} \)
\( \boldsymbol{K}_{\boldsymbol{A}}=\mathbf{1 0}^{\mathbf{1 5}} \boldsymbol{e}^{\mathbf{2 0 0 0} / \boldsymbol{T}} \)
\( \boldsymbol{C} \rightarrow \boldsymbol{D} \quad \boldsymbol{K}_{\boldsymbol{C}}=\mathbf{1 0}^{14} \boldsymbol{e}^{\mathbf{1 0 0 0} / \boldsymbol{T}} \)
Temperature \( \mathrm{T} \mathrm{K} \) at which \( \left(\boldsymbol{K}_{\boldsymbol{A}}=\boldsymbol{K}_{\boldsymbol{C}}\right) \)
is :
\( A \cdot 1000 K \)
B. 2000 K
D. (1000 / 2.303) K
Subject: Chemistry
In which of the following reactions, does a non-metal act as a reducing agent?
A. \( \operatorname{SiO}_{2}+2 C \rightarrow S i+2 C O \)
в. \( A l N+3 H_{2} O \rightarrow A l(O H)_{3}+N H_{3} \)
\( \mathbf{c} \cdot 2 M g+N_{2} \rightarrow M g_{3} N_{2} \)
D. \( H g C l_{2}+2 K I \rightarrow H g I_{2}+2 K C l \)
Subject: Physics
An element \( \boldsymbol{X} \) decays first by positron emission and then \( 2 \alpha \)
particles are emitted in succession. If the product nucleus has mass number 229 and atomic number 89
then the mass number and atomic
number of element \( \boldsymbol{X} \) are
A .237,93
в. 237,94
c. 238,93
D. 237,92
Subject: Maths
An employer sends a letter to his employee but he does not receive the
reply (It is certain that employee would have replied if he did receive the letter).
It is known that one out of \( n \) letters does
not reach its destination. Find the
probability that employee does not receive the letter.
A \( \cdot \frac{1}{n-1} \)
B. \( \frac{n}{2 n-1} \)
c. \( \frac{n-1}{2 n-1} \)
D. \( \frac{n-2}{n-1} \)
Subject: Biology
If \( P_{a t m}=0 \mathrm{mm} \mathrm{Hg} \) and \( P_{a l v}=-2 \mathrm{mm} \mathrm{Hg} \)
then
A. it is the end of the normal inspiration and there is no airflow
B. it is the end of the normal expiration and there is no airflow
C. transpulmonary pressure \( \left(P_{t p}\right) \) is \( -2 \mathrm{mm} \) Hg
D. air is flowing into the lungs
Subject: Chemistry
In the formatioin of octahedral complex
ligands approach towards
and orbital of
central metal
\( \mathbf{A} \cdot d_{z^{2}}, d_{x^{2}-y^{2}} \)
B . \( d_{x^{2}-y^{2}}, d_{x y} \)
\( \mathbf{c} \cdot d_{x y}, d_{y z} \)
D. \( d_{z^{2}}, d_{x z} \)
Subject: Physics
A compass needle free to turn in a horizontal plane is placed at the centre of circular coil of 30 turns and radius 12
\( \mathrm{cm} . \) The coil is in a vertical plane
making an angle of \( 45^{\circ} \) with the magnetic meridian. When the current in the coil is 0.35 A, the needle points west
to east.
(a) Determine the horizontal component of the earth's magnetic field at the location.
(b) The current in the coil is reversed, and the coil is rotated about its vertical
axis by an angle of \( 90^{\circ} \) in the anticlockwise sense looking from above. Predict the direction of the
needle. Take the magnetic declination at the places to be zero.
Subject: Chemistry
For the reaction \( \boldsymbol{H}_{2}(\boldsymbol{g})+\boldsymbol{B} \boldsymbol{r}_{2}(\boldsymbol{g}) \rightarrow \)
\( 2 H B r(g), \) the experiment data
suggested that \( r=k\left[H_{2}\right]\left[B r_{2}\right]^{1 / 2} . \) The
molecularity and order of the reaction are respectively:
A. 2, 3/2
B. 3/2,3/2
c. Not defined, 3/2
D. \( 1,1 / 2 \)
Subject: Chemistry
If Atom 1 has 19 protons and 22 neutrons and Atom 2 has 20 protons
and 22 neutrons, are these isotopes of the same element?
A. There is not enough information to determine this.
B. No, because they have different numbers of protons.
c. No, because they have the same number of neutrons.
D. Yes, because they have different numbers of protons
E. Yes, because they have the same number of neutrons
Subject: Maths
Evaluate.
\( \mid \begin{array}{ccc}\frac{1}{z} & \frac{1}{z} & -\frac{(x+y)}{z^{2}} \\ -\frac{(y+z)}{x^{2}} & \frac{1}{x} & \frac{1}{x} \\ -\frac{y(y+z)}{x^{2} z} & \frac{x+2 y+z}{x z} & -\frac{y(x+y)}{x z^{2}}\end{array} \)
Subject: Maths
Let \( a, b, c \) be non-zero real numbers
such the :
\( \int_{0}^{1}\left(1+\cos ^{8} x\right)\left(a x^{2}+b x+c\right) d x= \)
\( \int_{0}^{2}\left(1+\cos ^{8} x\right)\left(a x^{2}+b x+c\right) d x, \) then
the quadratic equation \( a x^{2}+b x+c= \)
0 has
\( A \cdot \) no root in (0,2)
B. atleast one root in (0,2)
C \( . \) a double root in (0,2)
D. none
Subject: Maths
Mr. Ambani purchased a car of 3,00,000 and a bike for his son for
1, 00, 000. He sold the car at a profit of
\( 10 \% \) and bike at a loss of \( 20 \% . \) What is
the net gain or loss?
A . 2\% gain
B. 1.5\% gain
c. \( 2.5 \% \) loss
D. 2.5\% gain
Subject: Physics
A particle is thrown up inside a stationary lift of sufficient height. The
time of flight is \( T . \) Now it is thrown
again with same initial speed \( v_{0} \) with
respect to lift. At the time of second
throw, lift is moving up with speed \( v_{0} \) and uniform acceleration \( g \) upward (the
acceleration due to gravity). The new
time of flight is :
A \( \cdot \frac{T}{4} \)
в. \( \frac{T}{2} \)
c. \( T \)
D. \( 2 T \)
Subject: Chemistry
Assertion
pH of 10 M H Cl aqueous solution is
less than 1.
Reason
pH is negative logarithm of \( \boldsymbol{H}^{+} \)
concentration.
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 calorie is a unit of heat energy and its
value is \( 4.18 \mathrm{J} \) where \( 1 J=1 k g m^{2} s^{-2} \)
Suppose we use a new system of units in which unit of mass equals \( \boldsymbol{\alpha} \) kg, the
unit of length equals \( \beta \mathrm{m} \) and the unit
of the time is \( \gamma \) sec. Then the value of a
calorie in the new system of units is
then
A \( \cdot \) 4.18 \( \frac{\gamma^{2}}{\alpha \beta^{2}} \)
B. \( 4.18 \frac{\alpha \beta^{2}}{\gamma^{2}} \)
c. \( 4.18 \frac{\gamma^{2}}{\alpha} \)
D. \( 4.18 \frac{\beta^{2}}{\alpha \gamma^{2}} \)
Subject: Maths
If one of the zeroes of the quadratic
polynomial \( (k-1) x^{2}+k x+1 \) is -3
then the value of \( k \) is.
A \( \cdot \frac{4}{3} \)
в. \( \frac{-4}{3} \)
\( c \cdot \frac{2}{3} \)
D. \( \frac{-2}{3} \)
Subject: Biology
Assertion
Secreting hypotonic urine is effective in reducing urinary loss of water.
Reason
Hypotonic urine is more concentrated and higher in osmotic pressure than the blood.
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
Let \( \boldsymbol{J}, \boldsymbol{g}:\lfloor-\mathbf{1}, \boldsymbol{2}\rfloor \rightarrow \boldsymbol{K} \) be continuous
functions which are twice differential
on the interval \( (-1,2) . \) Let the values of
\( f \) and \( g \) at the points -1,0 and 2 be as given in the following table:
\( f(x)=\left\{\begin{array}{l}3 ; x=-1 \\ 6 ; x=0 \quad \text { and } g(x)= \\ 0 ; x=2\end{array}\right. \)
\( \left\{\begin{array}{l}0 ; x=-1 \\ 1 ; x=0 \\ 0 ; x=-1\end{array}\right. \)
In each of the intervals (-1,0) and
\( (0,2), \) the function \( (f-3 g)^{\prime \prime} \) never
vanishes. Then the correct statement(s)
is (are)
This question has multiple correct options
A \( \cdot f^{\prime}(x)-3 g^{\prime}(x)=0 \) has exactly three solutions in (-1,0)\( \cup(0,2) \)
B. \( f^{\prime}(x)-3 g^{\prime}(x)=0 \) has exactly one solutions in (-1,0)
C \( \cdot f^{\prime}(x)-3 g^{\prime}(x)=0 \) has exactly one solutions in (0,2)
D. \( f^{\prime}(x)-3 g^{\prime}(x)=0 \) has exactly two solutions in (-1,0) and exactly two solutions in (0,2)