AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Physics
The frequency \( f \) of vibration of mass \( m \)
suspended from a spring of spring
contact \( k \) is given by \( \boldsymbol{f}=\boldsymbol{c} \boldsymbol{m}^{\boldsymbol{x}} \boldsymbol{k}^{\boldsymbol{y}} \)
Where \( c= \) dimensionless constant
then find the values of \( x \) and \( y \)
Subject: Maths
The equation \( 16 x^{2}-3 y^{2}-32 x+ \)
\( 12 y-44=0 \) represents a hyperbola.
A. The length of whose transverse axis is \( 4 \sqrt{3} \)
B. The length of whose conjugate axis is 4
c. whose centre is (-1,2)
D. whose eccentricity is \( \sqrt{\frac{19}{3}} \)
Subject: Maths
Assertion
If \( \lim _{x \rightarrow 0}\left\{f(x)+\frac{\sin x}{x}\right\} \) does not exist
then \( \lim _{x \rightarrow 0} f(x) \) does not exist.
Reason
\( \lim _{x \rightarrow 0} \frac{\sin x}{x} \) exists and has value 1
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
Which of the following is a secondary amine?
A. \( H_{2} N-N H_{2} \)
в. \( C H_{3}-N H_{2} \)
c. \( \left(C H_{3}\right)_{2} N C_{6} H_{5} \)
D. \( C_{6} H_{5}-N H-C H_{3} \)
Subject: Physics
In the figure shown below, the
maximum and the minimum possible
unknown resistance \( (X), \) that \( \operatorname{can} b e \)
measured by the post office box are \( X_{\max } \) is given by \( R \times 10^{5} \Omega, \) then R is :
(In this experiment, we take out only
one plug in arm \( A B \) and only one plug in
\( \operatorname{arm} \mathrm{BC}, \) but in arm \( \mathrm{AD} \) we can take out
many plugs):
Subject: Chemistry
The compound in which \( \underline{C} \) uses its \( s \boldsymbol{p}^{3} \) hybrid orbitals in bonding is:
A. \( H \subseteq O O H \)
B. \( \left(H_{2} N\right)_{2} \underline{C O} \)
c. \( \left(C H_{3}\right)_{3} \subseteq O H \)
D. \( C H_{3} \underline{C H O} \)
Subject: Physics
A wire of uniform cross-section is
suspended vertically from fixed point with a load attached to the other end.
What will be the ratio of change in
frequency to the altered new frequency
due to arise of temperature \( t^{\circ} \) C? The
coefficient of linear expansion of wire
is \( \alpha \) and the rise of temperature t is
small.
A \( \cdot \frac{\alpha t}{4} \)
в. \( \frac{\alpha t}{2} \)
\( c \cdot \frac{3 a t}{4} \)
D. \( \alpha \)
Subject: Physics
One mole of radium has an activity of \( 1 / 3.7 \) killo curie. Its decay constant will be
A \( \cdot \frac{1}{6} \times-10 s^{-1} \)
В. \( 10^{-10} s^{-1} \)
\( \mathbf{c} \cdot 10^{-11} s^{-1} \)
D. \( 10^{-8} s^{-1} \)
Subject: Chemistry
Two acids \( H_{2} S O_{4} \) and \( H_{3} P O_{4} \) are
neutralized separately by the same
amount of an alkali when sulphate and
dihydrogen phosphates are formed respectively.Find the ratio of the
masses of \( \boldsymbol{H}_{2} \boldsymbol{S} \boldsymbol{O}_{4} \) and \( \boldsymbol{H}_{3} \boldsymbol{P} \boldsymbol{O}_{4} \)
Subject: Chemistry
Assertion
Oxygen is more electronegative than
sulphur,yet \( \boldsymbol{H}_{2} \boldsymbol{S} \) is acidic, while \( \boldsymbol{H}_{2} \boldsymbol{O} \) is neutral
Reason
H- - -S bond is weaker than 0 - - -H bond
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
A point \( A \) is \( 26 c m \) away from the centre
of a circle and the length of tangent
drawn from \( A \) to the circle is 24 cm. Find
the radius of the circle.
\( \mathbf{A} \cdot 10 \mathrm{cm} \)
B. \( 20 \mathrm{cm} \)
\( \mathbf{c} \cdot 25 c m \)
D. \( 15 \mathrm{cm} \)
Subject: Maths
Applying the principal of mathematical
induction of prove that
\[
\frac{2 \sin \theta}{\cos \theta+3 \cos \theta}+\frac{2 \sin \theta}{\cos \theta+5 \cos \theta}+
\]
\( \frac{2 \sin \theta}{\cos \theta+\cos (2 n+1) \theta} \)
\[
=\tan (n+1) \theta-\tan \theta
\]
Subject: Chemistry
Which of the following options does not
show instantaneous rate of reaction at
\( 40^{t h} \) second?
A \( \frac{V_{5}-V_{2}}{50-30} \)
3. \( \frac{V_{4}-V_{2}}{50-30} \)
\( c \cdot \frac{V_{3}-V_{2}}{40-30} \)
D. \( \frac{V_{3}-V_{1}}{40-20} \)
Subject: Maths
If \( \boldsymbol{A}_{\mathbf{3} \times \mathbf{3}} \) and \( |\boldsymbol{A}| \neq \mathbf{0} \Rightarrow \boldsymbol{A} \boldsymbol{d} \boldsymbol{j}(\boldsymbol{A} \boldsymbol{d} \boldsymbol{j} \boldsymbol{A})= \)
\( \mathbf{A} \cdot|A|^{2} A \)
B \( \cdot|A| A \)
c. \( \frac{A}{|A|} \)
D. \( \frac{A}{|A|^{2}} \)
Subject: Chemistry
The \( \boldsymbol{K}_{s p} \) for \( \boldsymbol{C r}(\boldsymbol{O} \boldsymbol{H})_{3} \) is \( \mathbf{1 . 6} \times \mathbf{1 0}^{-\mathbf{3 0}} \)
The molar solubility of this compound in water is:
Subject: Maths
How many bricks, each measuring
\( 25 c m \times 12.5 c m \times 7.5 c m \) will be
needed to construct a wall \( 15 \mathrm{m} \) long,
1.8 \( m \) high and \( 37.5 \mathrm{cm} \) thick?
A. 4400
B. 4660
\( c .4320 \)
D. 4575
Subject: Chemistry
In the electrolysis of aqueous \( N a C l \) solution, side reactions taking place
are :
(I) \( 2 O H^{-}+C l_{2} \longrightarrow 2 O C l^{-}+H_{2} \)
(II) \( 2 N a+2 H_{2} O \longrightarrow 2 N a O H+H_{2} \)
(III) \( 4 O H^{-} \longrightarrow O_{2}+2 H_{2}+4 e^{-} \)
Select the correct alternate.
A . ।, ॥
B. ॥, ॥ I
c. ।, ॥ा
D. I, II and III
Subject: Maths
Assertion \( f(x)=\sin ^{2} x+\sin ^{2}\left(x+\frac{\pi}{3}\right)+ \)
\( \cos x \cos \left(x+\frac{\pi}{3}\right) \) then \( f^{\prime}(x)=0 \)
Reason Derivative of a constant function is
always zero
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
What will be the unit in which the
solubility product of \( C a_{3}\left(P O_{4}\right)_{2} \) is
expressed?
A \( \cdot \operatorname{mol} d m^{-3} \)
B. \( m o l^{2} d m^{-6} \)
\( \mathbf{c} \cdot m o l^{3} d m^{-9} \)
D. \( m o l^{5} d m^{-15} \)
Subject: Maths
Find the sum of \( 2 n \) terms of the series
\( \mathbf{5}^{\mathbf{3}}+\mathbf{4 . 6}^{\mathbf{3}}+\mathbf{7}^{\mathbf{3}}+\mathbf{7}^{\mathbf{3}}+\mathbf{4 . 8}^{\mathbf{3}}+\mathbf{9}^{\mathbf{3}}+ \)
\( 4.10^{3}+\ldots \)
Subject: Maths
Range of the function \( \boldsymbol{f}(\boldsymbol{x})= \)
\( \sin ^{2}\left(x^{4}\right)+\cos ^{2}\left(x^{4}\right) \) is
\( A \cdot(-\infty, \infty) \)
B . \{1\}
c. (-1,1)
D. (0,1)
Subject: Maths
Show that the latus rectum of the
parabola \( \left(\boldsymbol{a}^{2}+\boldsymbol{b}^{2}\right)\left(\boldsymbol{x}^{2}+\boldsymbol{y}^{2}\right)=(\boldsymbol{b} \boldsymbol{x}+ \)
\( a y-a b)^{2} \) is \( 2 a b \div \sqrt{a^{2}+b^{2}} \)
Subject: Maths
\( \boldsymbol{M B} \)
\( \mathbf{A} \cdot \overrightarrow{M B}=\frac{1}{2}(\bar{a}-2 \bar{b}) \)
B \( \cdot \overrightarrow{M B}=\frac{1}{2}(2 \bar{a}-\bar{b}) \)
C \( \cdot \overrightarrow{M B}=\frac{1}{2}(\bar{a}+2 \bar{b}) \)
D \( \cdot \overrightarrow{M B}=\frac{1}{2}(2 \bar{a}+\bar{b}) \)
Subject: Chemistry
When equal volumes of the solutions
indicated are mixed, precipitation
should occur only for:
\( \left(\boldsymbol{K}_{s p} \) for \right.
\( \boldsymbol{M} \boldsymbol{g}(\boldsymbol{O} \boldsymbol{H})_{2}, \boldsymbol{B} \boldsymbol{a} \boldsymbol{F}_{2}, \boldsymbol{C} \boldsymbol{a}(\boldsymbol{O} \boldsymbol{H})_{2}, \boldsymbol{P} \boldsymbol{b} \boldsymbol{S} \boldsymbol{O}_{4} \)
\( \operatorname{are} 7.1 \times 10^{-12}, 1 \times 10^{-6}, 5.5 \times \)
\( 10^{-6}, 1.6 \times 10^{-8} \) respectively
A \( \cdot 2 \times 10^{-3} M M g^{2+}+2 \times 10^{-3} M O H^{-} \)
B . \( 2 \times 10^{-3} M B a^{2+}+2 \times 10^{-3} M F^{-} \)
C \( \cdot 2 \times 10^{-3} M C a^{2+}+2 \times 10^{-2} M O H^{-} \)
D . \( 2 \times 10^{-3} M C a^{2+}+2 \times 10^{-3} M O H^{-} \)
E \( \cdot 2 \times 10^{-4} M P b^{2+}+2 \times 10^{-5} M S O_{4}^{2-} \)
Subject: Physics
Assertion
An electric field is preferred in comparison to magnetic field for detecting the electron beam in a television picture tube
Reason
Electric field requires low voltage.
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
The length of potentiometer wire is \( 10 \mathrm{m} \) and is connected in series with an
accumulator. The e.m.f. of a cell balances against \( 250 \mathrm{cm} \) length of wire. If the length of potentiometer wire is increased by \( 1 \mathrm{m} \), calculate the new balancing length of wire.
A . 2.00
B . 2.25
c. 2.50
D. 2.75
Subject: Maths
Seven digits from the numbers 1,2,3,4 5,6,7,8,9 are written down nonrepeatedly in a random order to form a seven digit number. The probability that this seven digit number is divisible by 9
is
\( A \cdot \frac{2}{9} \)
B. \( \frac{7}{36} \)
\( c \cdot \frac{1}{9} \)
\( D \cdot \frac{7}{12} \)
Subject: Physics
Before using the clinical thermometer
mercury level should be below:
\( \mathbf{A} \cdot 45^{\circ} C \)
B . \( 35^{\circ} \mathrm{C} \)
\( \mathbf{c} \cdot 95^{\circ} C \)
D. \( 55^{\circ} \mathrm{C} \)
Subject: Maths
Day Number of coffee sold
3
21
4
35
5
\[
53
\]
6
\[
75
\]
7
101
The above data shows the number of
coffee sold by the famous coffee shop at
a particular venue. If the number is
shown by \( v \) and days as \( t, \) then they are
related by
\( \mathbf{A} \cdot v(t)=2 t^{2}+3 \)
\( B \)
\[
v(t)=\frac{t^{2}}{2}+3
\]
C \( \cdot v(t)=2 t^{2}+21 \)
D.
\[
v(t)=\frac{t^{2}}{2}+21
\]
Subject: Chemistry
Which of the following is false?
A. Bracket spectral series for which \( n_{1}=4 \) and \( n_{2}=5,6 \) 7,....lies in the infrared region of the electromagnetic radiation
B. The orbital 3d \( _{z}^{2} \) is symmetrical about z-axis
C. The orbital 3d \( _{x y} \) ha no probability of finding electron along \( x \) - and \( y \) -axis
D. The orbital 3d \( _{x^{2}-y^{2}} \) has no probability of finding electron along \( x \) -axis and \( y \) -axis
Subject: Physics
Match of the physical quantities given here under having same units and dimensions
Section-A
a)
e) \( \frac{1}{2} \rho\left(v_{2}^{2}-\frac{2}{1}\right) \)
Kinematic viscosity
b) Dynamic lift
\( \eta \)
c) Bernoullis theorer
g) a \( v= \) constant
d) Equation
h) \( p+\frac{1}{2} \rho v^{2}+\rho g h= \)
of continuity \( \quad \) constant
\( A \cdot a-f ; b-e ; c-h ; d-g \)
B. a-f; b-e; c-g; d-h
c. a-g; b-f; c-e; d-h
D. a-h; b-g; c-f; d-e
Subject: Chemistry
Identify (A) to (F) in the following:
\( F e S O_{4} \stackrel{\Delta}{\rightarrow} \underbrace{(A)}_{\text {solid }}+\underbrace{(B)+(C)}_{g a s} \)
\( (B) \stackrel{O_{2}}{\longrightarrow} \)
\( (C) \quad(A) \stackrel{H_{2} O}{\rightarrow} \)
\( (D) \) brown \( p p t \)
\( (D) \stackrel{\Delta}{\rightarrow}(A) \)
\( (A) \stackrel{H C l}{\rightarrow} \)
deep yellow solution \( (E) \)
\( (E)^{K_{4}\left[F e(C N)_{6}\right]} \)
blue ppt. \( (F) \)
Subject: Physics
The minimum and maximum values of
\( F \) to keep the cylinder in static
equilibrium just after the water starts
to spill through the hole, if the coefficient of static friction between
contact surfaces is 0.01 , are
A \( 0,40 N \)
N
B. \( 5.4 N, 52.2 N \)
\( c .0,70 N \)
D. \( 0,52.2 N \)
Subject: Chemistry
Consider the following solubility data
for various chromates at \( 25^{\circ} \mathrm{C} \)
\[
\begin{array}{cc}
\boldsymbol{K}_{\boldsymbol{s} \boldsymbol{p}} \\
\boldsymbol{A} \boldsymbol{g}_{\boldsymbol{2}} \boldsymbol{C r} \boldsymbol{O}_{\boldsymbol{4}} & \boldsymbol{9 . 0} \times \mathbf{1 0}^{-\mathbf{1 2}} \\
\boldsymbol{B a C r} \boldsymbol{O}_{\boldsymbol{4}} & \boldsymbol{2 . 0} \times \mathbf{1 0}^{-\mathbf{1 0}} \\
\boldsymbol{P b C r O}_{\boldsymbol{4}} & \boldsymbol{1 . 8} \times \mathbf{1 0}^{-\mathbf{1 4}}
\end{array}
\]
The chromate that is the most soluble
in water at \( 25^{\circ} \mathrm{C} \) on a molar basis is
\( \mathbf{A} \cdot A g_{2} C r O_{4} \)
B \( . \) BaCr \( \mathrm{O}_{4} \)
\( \mathbf{c} \cdot P b C r O_{4} \)
D. impossible to determine
E. none of these
Subject: Chemistry
Chlorine is prepared in the laboratory by the reaction between:
A. \( Z n \) and \( H C l \)
в. \( M n O_{2} \) and \( H C l \)
c. \( C a C O_{3} \) and \( H C l \)
D \( \cdot P b\left(N O_{3}\right)_{2} \) and \( H C l \)
Subject: Physics
The figure gives experimentally measured B vs. H variation in a
ferromagnetic material. The retentivity
co-ercivity and saturation, respectively, of the material are :
A. \( 1.5 T, 50 A / m \) and 1.07
B. \( 150 A / m, 1.0 T \) and \( 1.5 T \)
c. \( 1.5 T, 50 A / m \) and 1.07
D. \( 1.0 T, 50 A / m \) and 1.57
Subject: Physics
A particle is released on a vertical
smooth semicircular track from point
\( X \) so that \( O X \) makes an angle \( \theta \) from
the vertical (see figure). The normal reaction of the track on the particle
vanishes at point \( Y \) where \( O Y \) makes
and angle \( \phi \) with the horizontal. then:
\( A \cdot \sin \phi=\cos \theta \)
B. \( \sin \phi=\frac{1}{2} \cos \theta \)
c. \( \sin \phi=\frac{2}{3} \cos \theta \)
D. \( \sin \phi=\frac{3}{4} \cos \theta \)
Subject: Maths
Calculate mode of the following data.
\( \begin{array}{lllll}\text { Marks } & 0- & 20- & 40- & 60- \\ & 20 & 40 & 60 & 80\end{array} \)
Number
of
students \( \quad 8 \quad \begin{array}{ll}8 & 10 \\ \text { students }\end{array} \)
Subject: Maths
Solution of differential equation \( x^{2}= \) \( 1+\left(\frac{x}{y}\right)^{-1} \frac{d y}{d x}+\frac{\left(\frac{x}{y}\right)^{-2}\left(\frac{d y}{d x}\right)^{2}}{2 !}+ \)
\( \frac{\left(\frac{x}{y}\right)^{-3}\left(\frac{d y}{d x}\right)^{3}}{3 !}+\ldots \)
Subject: Chemistry
In the manufacture of acetic acid from
aerial oxidation of acetaldehyde, the catalyst used is :
A . acidified \( K_{2} C r_{2} O_{7} \)
в. \( \left(C H_{3} C O O\right)_{2} M n \)
\( \mathrm{c} \cdot \mathrm{HgSO}_{4} \)
D. \( N i \)
Subject: Maths
\( \triangle P Q R \) is right angled at \( Q, Q X \perp \)
\( \boldsymbol{P R}, \boldsymbol{X} \boldsymbol{Y} \perp \boldsymbol{R} \boldsymbol{Q} \) and \( \boldsymbol{X} \boldsymbol{Z} \perp \boldsymbol{P Q} \) are
drawn. Prove that \( \boldsymbol{X} \boldsymbol{Z}^{2}=\boldsymbol{P} \boldsymbol{Z} \times \boldsymbol{Z} \boldsymbol{Q} \)
Subject: Physics
In \( Y D S E, d=2 m m, D=2 m \) and \( \lambda=500 \)
nm. If intensity of two slits are \( l_{0} \) and \( 9 l_{0} \)
then find intensity at \( \boldsymbol{y}=\frac{1}{6} \)
A. \( 7 l_{0} \)
B. \( 10 l_{0} \)
c. \( 16 l_{0} \)
D. \( 4 l_{0} \)
Subject: Physics
A block of mass \( 15 \mathrm{kg} \) is placed on a long trolley The coefficient of friction between the block and trolley is 0.18
The trolley accelerates rest with \( 0.5 \mathrm{m} / \)
\( s^{2} \) for 20 s then what is the friction force
A. 3.5 N
B. 133.3 N
\( c \cdot 7.5 \mathrm{N} \)
D. N.O.T
Subject: Chemistry
Major products formed in the reaction of t-butyl methyl ether with \( H I \) are
\( A \)
and
and \( \quad \mathbf{H}_{3} \mathbf{C}-\mathbf{O H} \)
\( c \)
\( \mathbf{H}_{3} \mathbf{C}-\mathbf{O H} \quad \) and
D
and \( \mathbf{H}_{3} \mathbf{C}-\mathbf{O} \mathbf{H} \)
Subject: Maths
The value of \( \cos ^{2} A+\cos ^{2} B- \)
\( \mathbf{2} \cos \boldsymbol{A} \cos \boldsymbol{B} \cos (\boldsymbol{A}+\boldsymbol{B})- \)
\( \sin ^{2}(\boldsymbol{A}+\boldsymbol{B}) \)
Subject: Chemistry
A gas \( x \) at 1 atm is bubbled through a solution containing a mixture of \( 1 \mathrm{M} \) \( Y^{\ominus} \) and \( 1 \mathrm{M} Z^{\ominus} \) at \( 25^{\circ} \mathrm{C} . \) If the reduction
potential is \( \mathbf{Z}>Y>\mathbf{X}, \) then :
This question has multiple correct options
A. Y will oxidize X only
B. Y will oxidize Z only
c. z will oxidize \( x \) and \( Y \)
D. zwill reduce both \( x \) and \( y \)
Subject: Chemistry
Consider the reaction:
\( \boldsymbol{N} \boldsymbol{O}_{2} \rightleftharpoons \frac{1}{2} \boldsymbol{N}_{2}+\boldsymbol{O}_{2}, \boldsymbol{K}_{1} \)
\( N_{2} O_{4} \rightleftharpoons 2 N O_{2}, K_{2} \)
Give the equilibrium constant for the
formation of \( N_{2} O_{4} \) from \( N_{2} \) and \( O_{2} \)
A \( \cdot \frac{1}{K_{1}^{2}} \frac{1}{K_{2}} \)
в. \( \frac{1}{K_{1} K_{2}} \)
c. \( \sqrt{\frac{1}{K_{1} K_{2}}} \)
D. \( \frac{K_{2}}{K_{1}} \)
Subject: Biology
I am located above the kidneys and
hence are called as supra renal glands. have two regions adrenal cortex and adrenal medulla. Adrenal cortex
secretes the hormones like cortisol,
aldosterone and androgens. Adrenal medulla secretes the hormones like
adrenaline and nor-adrenaline. I also
secrete hormone of fight or flight or the emergency hormone. Who am I?
A. Adrenal gland
B. Thyroid gland
c. Pancreas
D. Pineal gland
Subject: Chemistry
\( \boldsymbol{H}_{3} \boldsymbol{C}-\boldsymbol{C H}_{2}-\stackrel{\boldsymbol{C}}{\boldsymbol{C}}=\boldsymbol{C} \boldsymbol{H}-\underset{\boldsymbol{C}_{2} \boldsymbol{H}_{5}}{\boldsymbol{C} \boldsymbol{H}} \)
\( C H_{3} \)
\( \boldsymbol{C H}-\boldsymbol{C H}_{2}-\boldsymbol{C H}_{2}-\boldsymbol{C H}_{3} \)
The correct IUPAC name of the
compound:
A. 5-Ethyl-3, 6-dimethylnon-3-ene
B. 5-ethyl-4,7-dimethyl non-3-ene
c. 4 -methyl-5, 7-diethyloct-2-ene
D. 2,4-ethyl-5-methyl oct-2-ene
Subject: Chemistry
2-Methyl propane on monochlorination under photochemical condition give:
A. 2 -chloro-2-methylpropane as major product
B. (1:1) mixture of 1-chloro-2-methylpropane and 2chloro-2-methylpropane
C. 1 -chloro-2-methylpropane as a major product
D. \( (1: 9) \) mixture of 1 -chloro- 2 -methylpropane
Subject: Chemistry
\( S F_{2}, S F_{4} \) and \( S F_{6} \) have the
hybridisation of sulphur atom
respectively as:
A \( \cdot s p^{2}, s p^{3}, s p^{3} d^{2} \)
B \( \cdot s p^{3}, s p^{3}, s p^{3} d^{2} \)
\( \mathbf{c} \cdot s p^{3}, s p^{3} d, s p^{3} d^{2} \)
D \( \cdot s p^{3}, s p^{3} d^{2}, d^{2} s p^{3} \)
Subject: Physics
A wire of length \( L \) and cross-sectional area \( A \) is constructed of a material
whose Young's modulus of elasticity is
Y. The energy density stored in the wire when stretched by \( x \) meter will be
A. \( Y \times x^{2} \)
в. \( \frac{Y \times x^{2}}{L} \)
c. \( \frac{Y \times x^{2}}{2 L^{2}} \)
D. \( \frac{Y \times x^{2}}{L^{2}} \)
Subject: Physics
A steady current \( I \) flows through a wire
of radius \( r, \) length \( L \) and resistivity \( \rho \)
The current produces heat in the wire. The rate of heat loss in a wire is
proportional to its surface area. The steady temperature of the wire is independent of
A. \( L \)
B. \( r \)
c. \( I \)
D.
Subject: Chemistry
Choose the incorrect statement.
A. Size of \( 4 d \) and \( 5 d \) series elements is almost same
B. Generally, negative value of standard reduction potential \( \left(M^{2+} / M\right) \) of \( 3 \mathrm{d} \) -series element decreases across the period
\( \mathrm{C} \cdot \mathrm{Cr}_{2} \mathrm{O}_{7}^{2-} \) has one type of \( \mathrm{Cr}-\mathrm{O} \) bond length
D. Generally, actinide and lanthanide shows +3 oxidation
state
Subject: Maths
The expression in the vector form for the
point \( \vec{r}_{1} \) of intersection of the plane \( \vec{r}_{1} \cdot \vec{n}=d \) and the perpendicular line
\( \vec{r}=\vec{r}_{0}+t \vec{n} \) where \( t \) is a parameter
given by
A \( \cdot \overrightarrow{r_{1}}=\overrightarrow{r_{0}}+\left(\frac{d-\overrightarrow{r_{0}} \cdot \vec{n}}{\vec{n}^{2}}\right) \vec{n} \)
B \( \cdot \overrightarrow{r_{1}}=\overrightarrow{r_{0}}+\left(\frac{\overrightarrow{r_{0}} \cdot \vec{n}}{\vec{n}^{2}}\right) \vec{n} \)
C・ \( _{\overrightarrow{r_{1}}}=\overrightarrow{r_{0}}+\left(\frac{\overrightarrow{r_{0}} \cdot \vec{n}-d}{|\vec{n}|}\right) \vec{n} \)
D \( \overrightarrow{r_{1}}=\overrightarrow{r_{0}}+\left(\frac{\overrightarrow{r_{0}} \cdot \vec{n}}{|\vec{n}|}\right) \vec{n} \)
Subject: Physics
The acceleration due to gravity \( g \) and
density of the earth \( \rho \) are related by
which of the following relations.? (where \( G \) is the gravitational constant
and \( R_{E} \) is the radius of the earth)
\( ^{\mathbf{A}} \cdot_{\rho}=\frac{4 \pi G R_{E}}{3 g} \)
в. \( \rho=\frac{3 g}{4 \pi G R_{E}} \)
c. \( _{\rho}=\frac{3 G}{4 \pi g R_{E}} \)
D. \( \rho=\frac{4 \pi g R_{E}}{3 G} \)
Subject: Physics
Three points \( A, B \) and \( C \) on a steady flow of a non viscous and
incompressible fluid are observed. The
pressure, velocity and height of the points \( A, B \) and \( C \) are \( (2,3,1) .(1,2,2) \)
and (4,1,2) respectively. Density of the
fluid is \( 1 k g m^{-3} \) and all otner
parameters are given in Sl units. Then
which of the following is correct? \( (\boldsymbol{g}= \)
\( \left.10 m s^{-2}\right) \)
A. points \( A \) and \( B \) lie on the same stream line
B. point B and C lie on same stream line
c. point \( C \) and \( A \) lie on same stream line
D. None of the above
Subject: Maths
Evaluate \( \int \frac{d x}{1+\sqrt{x^{2}+2 x+2}} \)
\( \mathbf{A} \cdot I=\ln (x+1-\sqrt{x^{2}+2 x+2})+ \)
\( \frac{2}{(x+2)+\sqrt{x^{2}+2 x+2}}+C \)
B \( \cdot I=\ln (x-2-\sqrt{x^{2}-2 x-4})+ \)
\( \frac{2}{(x+2)+\sqrt{x^{2}+2 x+2}}+C \)
C \( . I=\ln (x+1+\sqrt{x^{2}+2 x+2})+ \)
\( \frac{2}{(x+2)+\sqrt{x^{2}+2 x+2}}+C \)
D. None of these
Subject: Physics
Two charges of equal magnitude ' \( q \) ' are
placed in air at a distance \( ^{\prime} 2 a^{\prime} \) apart
and third charge \( -2 q^{\prime} \) is placed at midpoint. The potential energy of the system is \( \left(\epsilon_{0}= \) permittivity of free \right. space) :
\( ^{\mathrm{A}} \cdot-\frac{q^{2}}{8 \pi \epsilon_{0} a} \)
в. \( -\frac{3 q^{2}}{8 \pi \epsilon_{6} a} \)
c. \( -\frac{5 q^{2}}{8 \pi \epsilon_{0} a} \)
D. \( -\frac{7 q^{2}}{8 \pi \epsilon_{6} a} \)
Subject: Biology
Choose the correct labeling
Glyceraldehyde-3-P
\( \mathbf{1}, \mathbf{3} \)
A. a. Ethanol
b. \( C O_{2} \)
c. Acetaldehyde
B. a. \( C O_{2} \)
b. Acetaldehyde
c. Ethanol
\( \mathrm{c} \cdot \) a. \( \mathrm{CO}_{2} \)
b. Ethanol
c. Acetaldehyde
D. a. Ethanol
b. Acetaldehyde
c. \( C O_{2} \)
E. a. Acetaldehyde
b. \( C O_{2} \)
c. Ethanol
Subject: Chemistry
Adsorption of a gas follows Freundlich
adsorption isotherm \( x \) is the mass of
the gas adsorbed on mass \( m \) of the adsorbent. The plot of \( \log \frac{x}{m} \) versus log \( p \) is shown in the given graph. \( \frac{x}{m} \) is
proportional to :
\( A \cdot p^{3 / 2} \)
В \( \cdot p^{3} \)
\( c \cdot p^{2 / 3} \)
D. \( p^{2} \)
Subject: Chemistry
The treatment of \( \left(\boldsymbol{C H}_{3}\right)_{2} \boldsymbol{C}=\boldsymbol{C H} \boldsymbol{C H}_{3} \)
with boiling \( K M n O_{4} \) produces :
A. \( C H_{3} C O C H_{3}+C H_{3} C O C H_{3} \)
в. \( C H_{3} C O C H_{3}+C H_{3} C H O \)
c. \( C H_{3} C H O+C O_{2} \)
D. \( C H_{3} C O C H_{3} \quad \) only
Subject: Physics
Assertion - On reflection from a rigid boundary there takes place a complete reversal of phase.
Reason - On reflection from a denser
medium, both the particle velocity and wave velocity are reversed in sign.
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