AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Maths
Construct a triangle \( A B C \) in which
\( \boldsymbol{B C}=\mathbf{8 c m}, \angle \boldsymbol{B}=\mathbf{4 5}^{\circ} \boldsymbol{a n d} \boldsymbol{A B}-\boldsymbol{A C}= \)
\( \mathbf{3 . 5 c m} \)
Subject: Maths
Write the degree of the following polynomials.
(i) \( \boldsymbol{p}+\boldsymbol{p}^{\mathbf{3}}+\boldsymbol{p}^{\boldsymbol{7}} \)
(ii) \( a+a^{3}-a^{0} \)
(iii) \( \boldsymbol{m}+\boldsymbol{a}^{4} \boldsymbol{m}+\boldsymbol{a}^{5} \boldsymbol{m}^{3}-\boldsymbol{m}^{2}-\boldsymbol{a}^{4} \boldsymbol{m}^{\boldsymbol{7}} \)
Subject: Maths
The minimum and maximum values of \( \mathbf{f}(\mathbf{x})=\sin (\cos \mathbf{x})+\cos (\sin \mathbf{x}) \forall-\frac{\boldsymbol{\pi}}{\mathbf{2}} \leq \)
\( x \leq \frac{\pi}{2} \) are respectively
A . \( \cos 1 \) and \( 1+\sin 1 \)
B. \( \sin 1 \) and \( 1+\cos 1 \)
c. \( \cos 1 \) and \( \cos \left(\frac{1}{\sqrt{2}}\right)+\sin \left(\frac{1}{\sqrt{2}}\right) \)
D. \( \frac{1}{\sqrt{2}} \)
Subject: Chemistry
The correct order of increasing acidic
strength is:
A. Phenol \( < \) Ethanol \( < \) Chloroacetic acid \( < \) Acetic acid
B. Ethanol \( < \) Phenol \( < \) Chloroacetic acid \( < \) Acetic acid
C. Ethanol \( < \) Phenol \( < \) Acetic acid \( < \) Chloroacetic acid
D. Chloroacetic acid \( < \) Acetic acid \( < \) Phenol \( < \) Ethanol
Subject: Maths
Which one of the following quantities is negative?
A \( \cdot \cos \left(\tan ^{-1}(\tan 4)\right) \)
B. \( \sin \left(\cot ^{-1}(\cot 4)\right) \)
c. \( \tan \left(\cos ^{-1}(\cos 5)\right) \)
D・cot \( \left(\sin ^{-1}(\sin 4)\right) \)
Subject: Chemistry
Henry's law constant for the molality of
methane in benzene at \( 298 \mathrm{K} \) is \( 4.27 \times \)
\( 10^{5} \mathrm{mm} H g \). Calculate the solubility of
methane in benzene at \( 298 \mathrm{K} \) under 760
\( \operatorname{mm} \boldsymbol{H} \boldsymbol{g} \)
A . \( 1.78 \times 10^{-4} \)
В. \( 1.78 \times 10^{-3} \)
c. \( 1.78 \times 10^{4} \)
D. \( 1.78 \times 10^{-6} \)
Subject: Physics
A speedy rabbit is hopping to the right with a velocity of \( 4.0 \frac{m}{s} \) when it sees a carrot in the distance. The rabbit speeds up its maximum velocity of \( 13 \frac{\mathrm{m}}{\mathrm{s}} \) with a constant acceleration of \( 2.0 \frac{m}{s^{2}} \) rightward. How many seconds does it take the rabbit to speed up from \( 4.0 \frac{m}{s} \) to \( 13 \frac{m}{s} ? \)
Subject: Chemistry
A mixture of toluene, benzoic acid, aniline and phenol was dissolved in diethyl ether and extracted with
\( 5 \% N a H C O_{3} \) solution. This extract
was acidified until a white crystalline compound appeared. What is the identity of this compound?
A. Toluene
B. Benzoic acid
c. Aniline
D. Phenol
Subject: Chemistry
Which of the following species is/are
isostructural with \( \boldsymbol{X} \boldsymbol{e} \boldsymbol{F}_{\mathbf{4}} \) ?
This question has multiple correct options
\( \mathbf{A} \cdot I C l_{6}^{-} \)
в. \( I_{5}^{-} \)
c. \( B r F_{4}^{-} \)
D. \( X e O_{4} \)
Subject: Biology
The blood vascular system of mammals is known as double vascular system because
A. A group of arteries carries oxygenated and other groups of veins conducts deoxygenated blood
B. Oxygenated blood runs from heart to different organs by one set of arteries while deoxygenated blood runs from heart to lung by pulmonary artery
c. The two different systems never meet
D. All of the above
Subject: Physics
An electron of charge e and mass \( \mathrm{m} \) is moving in circular path of radius r with a uniform angular speed. Then which of the following statements are correct? This question has multiple correct options
A. The equivalent current flowing in the circular path is proportional to \( r^{2} \)
B. The magnetic moment due to circular current loop is independent of
C. The magnetic moment due to circular current loop is equal to \( 2 \mathrm{e} / \mathrm{m} \) time the angular momentum of the electron
D. The angular momentum of the particle is proportional to the areal velocoty of electron.
Subject: Physics
Three samples of the same gas \( A, B \) and
\( \boldsymbol{C}(\gamma=\mathbf{3} / \mathbf{2}) \) have initially equal
volume. Now the volume of each sample is doubled. The process is adiabatic for A, isobaric for \( \mathrm{B} \) and isothermal for \( \mathrm{C} \). If
the final pressures are equal for all the three samples, the ratio of their initial
pressures is:
A \( \cdot 2 \sqrt{2}: 2: 1 \)
B \( \cdot 2 \sqrt{2}: 1: 2 \)
c. \( \sqrt{2}: 1: 2 \)
D. \( 2: 1: \sqrt{2} \)
Subject: Physics
A heater of power \( \boldsymbol{P} \boldsymbol{W} \) raises the temperature of \( \mathrm{m} \) kg of a liquid by \( \Delta T K \) in time \( t s . \) Express the specific heat capacity of liquid in terms of above data
A \( \cdot c=\frac{P \Delta T}{m t} \)
в. \( c=\frac{P}{m \Delta T} \)
c. \( _{c}=\frac{P t}{m \Delta T} \)
D. \( c=\frac{P t}{\Delta T} \)
Subject: Physics
When two magnetic poles one of which
is four times greater than the other in pole strength, are placed \( 5 \mathrm{cm} \) apart in air. They exert a mutual force of 144
mg.wt. on each other. The pole strengths of the poles are (in ampere metre)
\( \left(g=10 \mathrm{m} / \mathrm{s}^{2}\right) \)
A .6,3
B. 9,3
c. 12,3
D. 18,6
Subject: Maths
The ellipse cuts \( x \) axis at \( A \) and \( y \) axis at \( \mathrm{B} \) and the line joining the focus \( \mathrm{S} \) and B makes an angle \( \frac{3 \pi}{4} \) with \( x \) -axis, then the eccentricity of the ellipse is:
A \( \cdot \frac{1}{\sqrt{2}} \)
B. \( \frac{1}{2} \)
c. \( \frac{\sqrt{3}}{2} \)
D. \( \frac{1}{3} \)
Subject: Physics
If Kinetic energy is expressed as \( m v^{2} / 2 \) for a particle undergoing uniform velocity motion, How is the kinetic energy expressed in case of the same particle, if it was rotating:
A \( \cdot m \omega^{2} / 2 \)
B. \( I \omega^{2} / 2 \)
c. \( m V^{2} / 2 \)
D. \( I V^{2} / 2 \)
Subject: Maths
In a construction job, following are some probabilities given:
Probability that there will be strike is \( 0.65, \) probability that the job will be completed on time if there is no strike is \( 0.80, \) probability that the job will be completed on time if there is strike is
0.32. Determine probability that the construction job will get complete on
time
A .0 .438
в. 0.538
\( c \cdot 0.488 \)
D. None of these
Subject: Chemistry
\( D- \) glucose \( \stackrel{H O^{-}}{\rightleftharpoons} A+B \)
\( A \) and \( B \) are:
\( A \cdot D- \) mannose and \( D \) - mannitol
B. D - mannose and D - Fructose
C. D - allose and D- Altrose
D. D - Glucose and D- - Idose
Subject: Maths
cosine of the angle of intersection of curves \( y=3^{x-1} \ln x \) and \( y=x^{x}-1 \) is
\( \mathbf{A} \cdot \mathbf{1} \)
B. \( 1 / 2 \)
\( c \cdot 0 \)
D. \( 1 / 3 \)
Subject: Maths
The quotient and remainder when
\( 3 x^{4}+6 x^{3}-6 x^{2}+2 x-7 \) is divided by
\( x-3 \) are
A. Quotient: \( 3 x^{3}+15 x^{2}+39 x+119 \) and Remainder: 350
B. Quotient: \( 3 x^{3}+10 x^{2}+39 x+119 \) and Remainder: 35
C . Quotient: \( 3 x^{3}+15 x^{2}+39 x+119 \) and Remainder: 50
D. Quotient: \( 3 x^{3}+15 x^{2}+119 \) and Remainder: 350
Subject: Chemistry
The freezing point of one molal \( N a C l \)
solution assuming \( N a C l \) to be \( 100 \% \) dissociated in water is:
[Molal depression constant is \( 1.86] \)
A \( .-2.72^{2} C \)
В. \( -3.72^{2} C \)
c. \( 2.72^{2} C \)
D. \( 3.72^{2} C \)
Subject: Physics
The charge through a conductor of
resistance \( R \) varies with time as \( \boldsymbol{q}= \)
\( a t-b t^{2} \) where a and \( b \) are constant.
Total heat produced in \( R \) is
A \( \cdot R a^{3} / 3 b \)
в. \( R a / 6 b \)
c. \( R a^{2} / 9 b \)
D. \( R a^{3} / 6 b \)
Subject: Physics
The pressure of a gas in a container is
\( 10^{-11} \) pascal at \( 27^{\circ} \mathrm{C} . \) The number of molecules per unit volume of vessel will
be
A \( \cdot 6 \times 10^{23} \mathrm{cm}^{-3} \)
В. \( 2.68 \times 10^{19} \mathrm{cm}^{-3} \)
c. \( 2.5 \times 10^{6} \mathrm{cm}^{-3} \)
D. \( 2400 \mathrm{cm}^{-3} \)
Subject: Physics
\( 4_{1} H^{1} \rightarrow_{2} H e^{4}+2_{+1} e^{0}+ \)energy
Energy released in this process is [lt is
\( \operatorname{given} 4_{1} H^{1}=4.031300 \mathrm{amu},_{2} H e^{4}= \)
\( \left.4.0026603 \text { amu, } 2_{1} e^{0}=0.01098 \text { amu }\right] \)
A . 14 Mev
B. 16.45 Mev
c. 37.2 Mev
D. \( 32.7 \mathrm{Mev} \)
Subject: Maths
The angle between the lines \( x \cos 30^{\circ}+ \)
\( y \sin 30^{\circ}=3 \)
\( x \cos 60^{\circ}+y \sin 60^{\circ}=5 \) is
A \( \cdot 90^{\circ} \)
B. \( 30^{\circ} \)
\( c \cdot 60^{\circ} \)
D. None of these
Subject: Biology
Ine aata glven In the table snows species richness of mosses, shrubs and trees calculated for one hectare
\( \left(10,000 m^{2}\right) \) of land every 50 years for
200 years based on a long running
ecological study. According to the data natural disaster
occurred during which time period?
\( \begin{array}{llll}\text { Year } & \text { Mosses } & \text { Shrubs } & \text { Trees } \\ 1800 & 16 & 2 & 0 \\ 1850 & 21 & 7 & 4 \\ 1900 & 10 & 5 & 3 \\ 1950 & 13 & 12 & 6 \\ 2000 & 17 & 28 & 14\end{array} \)
A . \( 1750-1800 \)
B. 1800-1850
c. \( 1850-1900 \)
D. 1900-1950
E \( 1950-2000 \)
Subject: Chemistry
Large quantity of \( K M n O_{4}, \) on
treatment with cold conc. \( \boldsymbol{H}_{2} \boldsymbol{S} \boldsymbol{O}_{4} \) forms
a compound \( (X) \) which decomposed
explosively, on heating forming \( (Y) \). The
\( (X) \) and \( (Y) \) are
respectively.
\( \mathbf{A} \cdot M n_{2} O_{7}, M n O_{2} \)
в. \( M n_{2} O_{7}, M n_{2} O_{3} \)
c. \( M n S O_{4}, M n_{2} O_{3} \)
D. \( M n_{2} O_{3}, M n O_{2} \)
Subject: Maths
If \( a=107, b=13 \) using Euclid's
division algorithm find the values of \( q \)
and \( r \) such that \( a=b q+r \)
A \( \cdot q=8, r=8 \)
В . \( q=8, r=3 \)
c. \( q=0, r=3 \)
D. None of these
Subject: Chemistry
\( 0.61 \mathrm{g} \) of an organic substance was heated in carius tube and the sulphuric acid formed was precipitated as
\( B a S O_{4} \) with \( B a C l_{2} . \) The weight of the
\( \operatorname{dry} B a S O_{4} \) was 0.53 g. Find the percentage of Sulphur.
A . \( 11.90 \% \)
B . 43\%
c. \( 23.04 \% \)
D. 51.2\%
Subject: Maths
Let \( \boldsymbol{f}(\boldsymbol{x})=\boldsymbol{x}^{4}+\boldsymbol{3} \boldsymbol{x}+1,[-\boldsymbol{2},-1] \) then
\( A \cdot f \) has exactly two zeros in [-2,-1]
B. f has exactly one zero in [-2,-1
C \( \cdot \) f has at least one zero in [-2,-1]
D. f has no zero in [-2,-1]
Subject: Physics
Two identical particles of mass \( 1 \mathrm{kg} \) experience a gravitational force of 10N between them . The distance between
them is r. If the same setup is put in water (refractive index \( =1.5 \) ), how will
their gravitational force change
A. The gravitational force will reduce to 1 N
B. The gravitational force remains constant
c. The gravitational force becomes \( 20 / 3 \mathrm{N} \)
D. The gravitational force becomes 15 N
Subject: Chemistry
How many coulomb are required for the
oxidation of 1 mole of \( H_{2} O_{2} \) to \( O_{2} ? \)
A \( \cdot 9.65 \times 10^{4} C \)
B. \( 93000 C \)
c. \( 1.93 \times 10^{5} C \)
D. \( 19.3 \times 10^{2} C \)
Subject: Physics
The amount of heat energy required to raise the temperature of 1 g of Helium at \( \mathrm{NTP}, \) from \( \boldsymbol{T}_{1} \boldsymbol{K} \) to \( \boldsymbol{T}_{2} \boldsymbol{K} \) is
A \( \cdot \frac{3}{8} N_{a} k_{B}\left(T_{2}-T_{1}\right) \)
B \( \cdot \frac{3}{2} N_{a} k_{B}\left(T_{2}-T_{1}\right) \)
c. \( \frac{3}{4} N_{a} k_{B}\left(T_{2}-T_{1}\right) \)
D. \( \frac{3}{4} N_{a} k_{B}\left(\frac{T_{2}}{T_{1}}\right) \)
Subject: Maths
\( \frac{\boldsymbol{d}}{\boldsymbol{d} \boldsymbol{x}}\left\{\tan ^{-1} \frac{\boldsymbol{x}}{\mathbf{1}+\boldsymbol{x}^{2}}+\tan ^{-1} \frac{\mathbf{1}+\boldsymbol{x}^{2}}{\boldsymbol{x}}\right\}= \)
A . 0
B.
\( c \cdot \frac{1}{2} \)
\( D \)
Subject: Biology
Study the following flow chart and
select the correct option for \( P, Q, R \) and
\( \mathbf{S} \)
\( A \cdot P \) - Banana, Canna
\( \mathrm{Q} \) - Fan palm
\( \mathrm{R} \) - Mango, Peepal
\( \mathrm{S}- \) Smilax, Zizyphus
B. P- Banana, Canna Q- Smilax, Zizyphus
\( \mathrm{R} \) - Mango, Peepal
\( S \) - Fan palm
C. P - Mango, Peepal
\( \mathrm{Q}- \) Banana, Canna
\( \mathrm{R} \) - Fan palm
S - Smilax, Zizyphus
D. P - Mango, Peepal
\( \mathrm{Q}- \) Fan palm
R - Smilax, Zizyphus
S-Banana, Canna
Subject: Maths
If \( \boldsymbol{x}=-1, \) then find \( \frac{\boldsymbol{x}^{4}-\boldsymbol{x}^{3}+\boldsymbol{x}^{2}}{\boldsymbol{x}-\mathbf{1}} \)
A. \( -\frac{3}{2} \)
в. \( -\frac{1}{2} \)
c. 0
D. \( \frac{1}{2} \)
E \( \cdot \frac{3}{2} \)
Subject: Physics
In the relation \( y=r \sin (\omega t-k x), \) the
dimensions of \( \omega / k \) are
\( \mathbf{A} \cdot\left[M^{0} L^{0} T^{0}\right] \)
B . \( \left[M^{0} L^{1} T^{-1}\right] \)
\( \mathbf{c} \cdot\left[M^{0} L^{0} T^{1}\right] \)
\( \mathbf{D} \cdot\left[M^{0} L^{1} T^{0}\right] \)
Subject: Physics
An automobile engine propels a \( 1000 \mathrm{kg} \) car \( A \) along a leveled road at a speed of \( 36 k m h^{-1} . \) The frictional force is 100
N. Suppose after traveling a distance of \( 200 \mathrm{m}, \) this car collides with another
stationary car \( \mathrm{B} \) of the same mass and comes to rest. Let Its engine also stop at the same time. Now, car B starts
moving on the same level road without getting its engine started. Find the speed of the car B just after the collision.
A. \( 36 \mathrm{km} / \mathrm{h} \)
B. 72 km/h
\( \mathbf{c} \cdot 18 \mathrm{km} / \mathrm{h} \)
D. \( 100 \mathrm{km} / \mathrm{h} \)
Subject: Physics
A domain in ferromagnetic iron in the
form of cube is having \( 5 \times 10^{10} \) atoms.
If the side length of this domain is
1.5 \( \mu m \) and each atom has a dipole moment of \( 8 \times 10^{-24} \mathrm{A} m^{2}, \) then
magnetisation of domain is?
A. \( 11.8 \times 10^{5} \mathrm{A} \mathrm{m}^{-1} \)
B. \( 1.18 \times 10^{4} \mathrm{A} \mathrm{m}^{-1} \)
c. \( 11.8 \times 10^{4} \mathrm{A} \mathrm{m}^{-1} \)
D. \( 1.18 \times 10^{5} \mathrm{A} \mathrm{m}^{-1} \)
Subject: Maths
Find the greatest and the least values of the following functions. Fin the extrema of the function \( \boldsymbol{f}(\boldsymbol{x})= \) \( 2 x \sin 2 x+\cos 2 x-\sqrt{3} \) on the
interval \( [-\boldsymbol{\pi} / 2, \mathbf{3} \boldsymbol{\pi} / \mathbf{8}] \)
Subject: Maths
In the adjoining figure \( A O B \) is a
diameter \( M P Q \) is a tangent at \( P \) then
the value of \( \angle M P A \) is equal to
A \( \cdot 25 \)
B \( .26^{\circ} \)
\( c \cdot 27^{\circ} \)
\( D \cdot 30^{\circ} \)
Subject: Physics
toppr
Q Type your question
capacitor \( C \) as shown in the figure.
Magnetic field \( B \) is into the plane.
Consider the following statements:
(i) Current in loop \( \boldsymbol{A} \boldsymbol{E} \boldsymbol{F} \boldsymbol{B} \boldsymbol{A} \) is
anticlockwise.
(ii) Current in loop \( \boldsymbol{A} \boldsymbol{E} \boldsymbol{F} \boldsymbol{B} \boldsymbol{A} \) is
clockwise
(iii) Current through the capacitor is
zero.
(iv) Energy stored in the capacitor is
\( \frac{1}{2} C B^{2} L^{2} V^{2} \)
Which if the following options is
correct?
A. Statements (i) and (iii) are correct
B. Statements (ii) and (iv) are correct
c. Statements (i), (iii) and (iv) are correct
D. None of these
Subject: Physics
Position of a particle in a rectangular coordinate system is (3,2,5) . Then its position vector will be
A \( \cdot 3 \hat{i}+5 \hat{j}+\hat{k} \)
B \( \cdot 3 \hat{i}+2 \hat{j}+5 \hat{k} \)
c. \( 5 \hat{i}+3 j+2 \hat{k} \)
D. None of tese
Subject: Chemistry
Choose the incorrect relation on the
basis of Bohr's theory.
A \( \cdot \) velocity of electron \( \propto \frac{1}{n} \)
B. Frequency of revolution \( \propto \frac{1}{n^{3}} \)
c. Radius of orbit \( \propto n^{2} Z \)
D. Force on electron \( \propto \frac{1}{n^{4}} \)
Subject: Chemistry
Which of the following choices both show the correct order of elements by
increasing atomic radius AND by increasing ionization energy?
A. \( A l, S, C l \) and \( A l, S, C l \)
в. \( A l, S, C l \) and \( C l, S, A l \)
c. \( C l, S, A l \) and \( C l, S, A l \)
D. \( C l, S, A l \) and \( A l, S, C l \)
Subject: Maths
Let \( f(x)=x^{3} e^{-3 x}, x>0 . \) Then the
maximum value of \( f(x) \) is
A \( \cdot e^{-3} \)
B. \( 3 e^{-3} \)
\( \mathbf{c} \cdot 27 e^{-9} \)
D. \( \infty \)
Subject: Physics
A thin circular ring of mass \( M \) and
radius \( r \) is rotating about its axis with constant angular velocity \( \omega . \) Two objects each of mass \( m \) are attached gently to the opposite ends of a diameter of the ring. The ring now rotates with angular velocity given by:
A \( \cdot \frac{(M+2 m) \omega}{2 m} \)
в. \( \frac{2 M \omega}{M+2 m} \)
c. \( \frac{(M+2 m) \omega}{M} \)
D. \( \frac{M \omega}{M+2 m} \)
Subject: Maths
Let \( \boldsymbol{A}=\left[\begin{array}{cc}\mathbf{2} & \mathbf{3} \\ \mathbf{- 1} & \mathbf{5}\end{array}\right] \cdot \) If \( \boldsymbol{A}^{-\mathbf{1}}=\boldsymbol{x} \boldsymbol{A}+\boldsymbol{y} \boldsymbol{I} \)
find \( \boldsymbol{x}+\mathbf{2} \boldsymbol{y} \)
Subject: Physics
A rectangular loop of resistance \( \mathrm{R} \) and sides I and \( x \) is pulled out of a uniform magnetic field B with a steady velocity
v. The necessary force F required for maintaining uniform velocity of withdrawal is
A. \( B x l^{2} v / R \)
B \( \cdot B^{2} l^{2} v / R \)
c \( \cdot B^{2} l^{2} v^{2} / R \)
D. zero
Subject: Chemistry
The formation of \( C u S \) which is formed
by
A \( \cdot S O_{4}^{2-}+8 H^{+}+8 e^{-} \rightarrow S^{2-}+H_{2} O \)
B. \( S O_{2}+6 H^{+}+6 e^{-} \rightarrow H_{2} S+2 H_{2} O \)
c. Both (a) and (b)
D. None of the above
Subject: Biology
Match the list I with list II and choose
the correct option.
\( \begin{array}{ccccc} & \text { List I } & & \text { List II } & \\ \mathrm{A} & \text { Oxytocin } & 1 & \begin{array}{l}\text { Milk ejection } \\ \text { hormone }\end{array} \\ \mathrm{B} & \text { Glucagon } & 2 & \begin{array}{l}\text { Increase in heart } \\ \text { rate }\end{array} \\ \mathrm{C} & \text { Adrenaline } & 3 & \begin{array}{l}\text { Increases blood } \\ \text { glucose }\end{array} \\ \mathrm{D} & \text { Thyroxine } & 4 & \text { Controls BMR }\end{array} \)
\( \mathbf{A} \)
B. A- 2, B-3, C-4,D-1
C. A-3, B- 4, C- 2, D-1
D. A- 4, B- 2, C-1, D-3
Subject: Maths
Examine the continuity of the function:
\( f(x)=\frac{\log 100+\log (0.01+x)}{3 x}, \) for
\( \boldsymbol{x} \neq \mathbf{0} \)
\( =\frac{\mathbf{1 0 0}}{\mathbf{3}} \quad \) for \( \boldsymbol{x}= \)
\( \mathbf{0} ; \boldsymbol{a} \boldsymbol{t} \boldsymbol{x}=\mathbf{0} \)
Subject: Physics
A block of mass \( m \) slides down an
inclined plane of inclination \( \theta \) with
uniform speed. The coefficient of friction between the block and the plane
is \( \mu . \) The contact force between the
block and the plane is
\( \mathbf{A} \cdot m g \sin \theta \sqrt{1+\mu^{2}} \)
B. \( \sqrt{(m g \sin \theta)^{2}+(\mu m g \cos \theta)^{2}} \)
\( \mathrm{c} \cdot m g \sin \theta \)
D. \( m g \)
Subject: Maths
If \( \frac{a^{3}+3 a b^{2}}{3 a^{2} b+b^{3}}=\frac{x^{3}+3 x y^{2}}{3 x^{2} y+y^{3}}, \) then
A \( \cdot b x=a y \)
в. \( b y=a x \)
\( \mathbf{c} \cdot b^{2} y=a^{2} x \)
D. \( b^{2} x=a^{2} y \)
Subject: Chemistry
What is the oxidation state of \( \boldsymbol{T} \boldsymbol{h} \) in
organometallic compound
\( \left[T h H O R\left(C_{5} M e_{5}\right)_{2}\right] ? \)
A \( .+1 \)
B. +2
\( c \cdot+4 \)
D. +3
Subject: Chemistry
For a reaction \( \boldsymbol{P}+\boldsymbol{Q} \rightarrow \mathbf{2} \boldsymbol{R}+\boldsymbol{S} . \) Which
of the following statements is incorrect?
A. Rate of disappearance of \( P= \) Rate of appearance of
B. Rate of disappearance of \( P=2 \times \) Rate of appearance of \( R \)
c. Rate of disappearance of \( P= \) Rate of disappearance of \( Q \)
D. Rate of disappearance of \( Q=\frac{1}{2} \times \) Rate of appearance
of \( R \)
Subject: Chemistry
Calculate the value of \( \log \boldsymbol{K}_{\boldsymbol{p}} \) (nearest integer) for the reaction, \( N_{2}(g)+ \)
\( \mathbf{3} \boldsymbol{H}_{\mathbf{2}}(\boldsymbol{g}) \rightleftharpoons \mathbf{2} \boldsymbol{N} \boldsymbol{H}_{\mathbf{3}}(\boldsymbol{g}) \) at \( \mathbf{2 5}^{\circ} \boldsymbol{C} . \) The
standard enthalpy of formation of
\( N H_{3}(g) \) is \( -46 \mathrm{kJ} \) and standard
entropies of \( N_{2}(g), H_{2}(g), N H_{3}(g) \) are
\( \mathbf{1 9 1}, \mathbf{1 3 0}, \mathbf{a n d} \mathbf{1 9 2} \mathbf{J K}^{-\mathbf{1}} \mathbf{m o l}^{-\mathbf{1}} \)
respectively. \( \left(\boldsymbol{R}=\mathbf{8 . 3} \boldsymbol{J} \boldsymbol{K}^{-1} \boldsymbol{m o l}^{-1}\right) \)
Subject: Maths
f \( \alpha, \beta, \gamma \) are the roots of the equation
\( x^{3}+p x+q=0 \) then the value of the
determinant \( \left|\begin{array}{lll}\boldsymbol{\alpha} & \boldsymbol{\beta} & \gamma \\ \boldsymbol{\beta} & \gamma & \boldsymbol{\alpha} \\ \boldsymbol{\gamma} & \boldsymbol{\alpha} & \boldsymbol{\beta}\end{array}\right| \) is
\( \mathbf{A} \cdot \mathbf{q} \)
B.
c. \( p \)
D. \( p^{2}-2 q \)
Subject: Maths
Solve for \( \boldsymbol{a}: \boldsymbol{4} \boldsymbol{a}-\boldsymbol{9}>\boldsymbol{9} \boldsymbol{a}-\boldsymbol{2} \boldsymbol{4} \)
\( \mathbf{A} \cdot a>3 \)
B. \( a<3 \)
c. \( a<-3 \)
D. \( a<9 \)
Subject: Chemistry
Titanium tetrachloride, \( \boldsymbol{T} \boldsymbol{i} \boldsymbol{C} \boldsymbol{l}_{4}, \) is a
liquid at room temperature and has a very high vapor pressure. Which statement best explains these
observations?
A. Titanium tetrachloride is an ionic compound, with \( T i^{4+} \) and \( C l^{-} \) ions arranged in a lattice
B. Titanium tetrachloride is a molecular substance, with
\( T i C l_{4} \) molecules held together by covalent bonds
c. The bonding in titanium tetrachloride is metallic, with a sea of electrons being shared equally between all the atoms in a sample.
D. Titanium tetrachloride is a network covalent substance, with an essentially infinite lattice of covalently-bonded \( T i \) and \( C l \) atoms
E. Titanium tetrachloride is simply a mixture of titanium atoms and chlorine atoms, which are not bonded to each other in any particular way
Subject: Maths
If the equation of family of curves be
\( \boldsymbol{y}=\boldsymbol{a} \cos (\boldsymbol{x}+\boldsymbol{b}), \) where \( a, \boldsymbol{b} \) are arbitrary
constants,and \( \boldsymbol{y}^{\prime}=\frac{\boldsymbol{d} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}}, \boldsymbol{y}^{\prime \prime}=\frac{\boldsymbol{d}^{2} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}^{2}^{\prime}} \) etc
then their differential equation is :
A \( \cdot y^{\prime \prime}=y \)
B \( \cdot y^{\prime \prime}=y y^{\prime} \)
C \( \cdot y^{\prime \prime}+y=0 \)
\( \mathbf{D} \cdot y^{\prime \prime}=y+y^{\prime} \)
Subject: Physics
A small block of superdene material
has mass \( 2 \times 10^{24} \) kg. It isn't at a
height \( h<<R \). It falls towards earth.
Find its speed when it is at a height \( h / 2 \)
A \( \cdot \sqrt{\frac{2 g h}{3}} \)
в. \( \sqrt{\frac{3 g h}{4}} \)
c. \( \sqrt{\frac{2 g h}{5}} \)
D. \( \sqrt{\frac{g h}{2}} \)
Subject: Chemistry
Assertion
Fr burns in air forming \( \boldsymbol{F} \boldsymbol{r} \boldsymbol{O}_{2} \)
Reason
The larger alkali metal ions stabilities
\( O_{2}(\text { superoxide }) \)
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: Chemistry
Identify \( X \) in the equation given below.
\( \boldsymbol{F} \boldsymbol{e} \boldsymbol{C l}_{3}+\boldsymbol{S O}_{2}+\boldsymbol{H}_{2} \boldsymbol{O} \rightarrow \boldsymbol{F} \boldsymbol{e} \boldsymbol{C l}_{2}+ \)
\( \boldsymbol{H} \boldsymbol{C l}+\boldsymbol{X} \)
A \( . H_{2} S \)
в. \( S O_{3} \)
c. \( H_{2} S O_{4} \)
D. \( H_{2} S O_{3} \)