AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Physics
A current of \( 5 A \) is flowing at \( 220 V \) in the primary coil of a transformer. If the voltage produced in the secondary coil
is \( 2200 V \) and \( 50 \% \) of power is lost, then
the current in the secondary will be
A . \( 2.5 A \)
в. \( 0.5 A \)
c. \( 0.25 A \)
D. \( 5 A \)
Subject: Maths
The ratio of the length of the parallel
sides of a trapezium is 5: 3 and the
distance between then is 16 cm. If the
area of the trapezium is \( 960 \mathrm{cm}^{2} \), find the length of the parallel sides.
\( \mathbf{A} \cdot 45 \mathrm{cm} \) and \( 65 \mathrm{cm} \)
B. \( 35 \mathrm{cm} \) and \( 75 \mathrm{cm} \)
c. \( 45 \mathrm{cm} \) and \( 75 \mathrm{cm} \)
D. \( 55 \mathrm{cm} \) and \( 75 \mathrm{cm} \)
Subject: Maths
Let \( \boldsymbol{f}:\left(-\frac{\boldsymbol{\pi}}{\mathbf{2}}, \frac{\boldsymbol{\pi}}{\mathbf{2}}\right) \rightarrow \boldsymbol{A} \) be defined by
\( \boldsymbol{f}(\boldsymbol{x})=\sin \boldsymbol{x} . \) If \( \boldsymbol{f} \) is a bijection, write set
\( \boldsymbol{A} \)
Subject: Chemistry
Assertion
\( \boldsymbol{S} \boldsymbol{O}_{2} \) gas is easily liquefied while \( \boldsymbol{H}_{2} \)
gas is not
Reason
\( \boldsymbol{S} \boldsymbol{O}_{2} \) has low critical temperature while
\( \boldsymbol{H}_{2} \) has high critical temperature.
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
A coffee cup calorimeter initially contains 125 g of water at a
temperature of \( 24.2^{\circ} \) C. After adding of
\( 10.5 \mathrm{g} \) of \( K B r, \) the temperature
becomes \( 21.1^{\circ} \mathrm{C} \). The heat of solution
is:
A . \( 40 \mathrm{J} / \mathrm{g} \)
в. 117 J / \( g \)
c. \( 167.7 \mathrm{J} / \mathrm{g} \)
D. \( 420.05 \mathrm{J} / \mathrm{g} \)
Subject: Maths
If \( a, b \) and \( c \) are unit vectors then
\( |a-b|^{2}+|b-c|^{2}+|c-a|^{2} \) does not
exceed
\( \mathbf{A} \cdot \mathbf{4} \)
B. 9
\( c \cdot 8 \)
D. 6
Subject: Physics
Figures (a) and (b) show the refraction
of a ray in air incident at \( 60^{\circ} \) with the
normal to a glass-air and water-air interface, respectively. Predict the angle of refraction in a glass when the angle
of incidence in water is \( 45^{\circ} \) with the
normal to a water-glass interface [Fig.
\( (c)] \)
Subject: Maths
In a triangle \( A B C, \) medians \( A D \) and \( B E \)
are drawn. If \( \mathrm{AD}=4, \angle D A B=\frac{\pi}{6} \) and
\( \angle A B E=\frac{\pi}{3}, \) then the area of \( \Delta A B C \) is
A \( \cdot \frac{8}{3} \)
в. \( \frac{16}{3} \)
c. \( \frac{32}{3 \sqrt{3}} \)
D. \( \frac{64}{3} \)
Subject: Chemistry
Fractional distillation is used to
separate liquids which differ in their boiling points by?
A \( \cdot 0-10^{\circ} \mathrm{C} \)
B . \( 10-20^{\circ} \mathrm{C} \)
c. \( 20-40^{\circ} \mathrm{C} \)
D. \( 40-80^{\circ} \mathrm{C} \)
Subject: Maths
If the diagonals of a parallelogram are \( \bar{i}+5 \bar{j}-2 \bar{k} \) and \( -2 \bar{i}+\bar{j}+3 \bar{k}, \) then the
lengths of its sides are
A \( \cdot \frac{\sqrt{38}}{2}, \frac{\sqrt{50}}{2} \)
B. \( \frac{\sqrt{35}}{2}, \frac{\sqrt{45}}{2} \)
c. \( \sqrt{38}, \sqrt{50} \)
D. \( \sqrt{35}, \sqrt{45} \)
Subject: Physics
A small source of sound moves on a
circle as shown in fig. and an observer is
sitting at \( O . \) Let at \( v_{1}, v_{2}, v_{3} \) be the
frequencies heard when the source is at \( A, B \) and \( C \) respectively.
A \( \cdot v_{1}>v_{2}>v_{3} \)
в. \( v_{1}=v_{2}>v_{3} \)
с. \( v_{2}>v_{3}>v_{1} \)
D. \( v_{1}>v_{3}>v_{2} \)
Subject: Physics
Let \( N_{\beta} \) be the number of \( \beta \) particles emitted by 1 gram of \( ^{24} N a \) radioactive
nuclei (half life \( =15 h r s \) ) in 7.5 hours,
\( N_{\beta} \) is close to (Avogadro number \( = \)
\( \left.6.023 \times 10^{23} / g \text { mole }\right) \)
A . \( 1.75 \times 10^{22} \)
B. \( 6.2 \times 10^{21} \)
C \( .7 .5 \times 10^{21} \)
D. \( 1.25 \times 10^{22} \)
Subject: Maths
The given figure shows a parallelogram
\( A B C D \) with area \( 324 \mathrm{cm}^{2} . P \) is a point
in \( A B \) such that \( A P: P B=1: 2 \)
Find the area of \( \triangle \boldsymbol{A} \boldsymbol{P} \boldsymbol{D} \)
\( \mathbf{A} \cdot 34 \mathrm{cm}^{2} \)
B. \( 44 \mathrm{cm}^{2} \)
c. \( 24 \mathrm{cm}^{2} \)
D. \( 54 \mathrm{cm}^{2} \)
Subject: Physics
An electron is moving in an orbit of a hydrogen atom from which there can be
a maximum of six transitions. An
electron is moving in an orbit of another
hydrogen atom from which there can be
a maximum of three transitions. The
ratio of the velocity of the electron in
these two orbits is
\( \mathbf{A} \cdot \underline{5} \)
B. \( \frac{3}{4} \)
\( c \cdot \frac{1}{2} \)
D.
Subject: Maths
||\( \vec{a}|=3,| \vec{b}|=4,| \vec{c} \mid=5, \vec{a} \perp(\vec{b}+ \)
\( \vec{c}), \vec{b} \perp(\vec{c}+\vec{a}) \) and \( \vec{c} \perp(\vec{a}+\vec{b}) \) then
\( \sqrt{2}|\vec{a}+\vec{b}+\vec{c}| \) is equal to
Subject: Maths
If \( \boldsymbol{f}(\boldsymbol{x})= \)
\( \left\{\begin{array}{ccc}\sqrt{1+k x}-\sqrt{1-k x} & \text { for } & -1 \leq x<0 \\ x & \text { for } 0 \leq x<1\end{array}\right. \)
is continuous at \( \boldsymbol{x}=\mathbf{0} \) then \( \boldsymbol{k}= \)
Subject: Chemistry
Which of the following is not an
intermolecular redox reaction?
\( \mathbf{A} \cdot M g C O_{3} \longrightarrow M g O+C O_{2} \)
B. \( O_{2}+2 H_{2} \longrightarrow 2 H_{2} O \)
\( \mathbf{c} \cdot K+H_{2} O \longrightarrow K O H+(1 / 2) H_{2} \)
D. \( M n B r_{3} \longrightarrow M n B r_{2}+(1 / 2) B r_{2} \)
Subject: Maths
If \( x_{1}, x_{2}, \dots, x_{n} \) are an observation such that \( \sum_{i=1}^{n} x_{i}^{2}=400 \) and \( \sum_{i=1}^{n} x_{i}=80 \),then the least value of \( n \) is
A . 18
B. 12
\( c \cdot 15 \)
D. 16
Subject: Maths
\( \operatorname{Let} \boldsymbol{S}(\boldsymbol{k})=\mathbf{1}+\boldsymbol{3}+\mathbf{5}+\ldots+(\mathbf{2} \boldsymbol{k}- \)
1) \( =3+k^{2} . \) Then which of the following
is true?
A. Principle of mathematical induction can be used to prove the formula
в. \( S(k) \Rightarrow S(k+1) \)
c. \( S(k) \neq S(k+1) \)
D. \( S(1) \) is correct
Subject: Chemistry
Assertion
Tin exhibits +2 and +4 oxidation
states only and not +3 oxidation state.
Reason
Inert pair effect of electrons in the sorbital is responsible.
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 the pair of alkanes which can exhibit chain isomerism and has a neo
isomer respectively? This question has multiple correct options
A. \( C_{3} H_{8}, C_{4} H_{10} \)
B. \( C_{4} H_{10}, C_{5} H_{12} \)
c. \( C_{5} H_{12}, C_{6} H_{14} \)
D. \( C_{6} H_{14}, C_{7} H_{16} \)
Subject: Physics
\( P \) and \( Q \) are two objects with masses
5kg and 30kg respectively. Then
A. \( P \) has more inertia than \( Q \)
B. \( Q \) has more inertia than \( P \)
c. \( P \) and \( Q \) have the same inertia
D. Neither \( P \) nor \( Q \) has any inertia
Subject: Chemistry
Assertion
HClO\( _{4} \) is stronger acid than \( \boldsymbol{H} \boldsymbol{C l O}_{3} \)
Reason
Oxidation state of Cl in \( \boldsymbol{H} \boldsymbol{C l O}_{\mathbf{4}} \) is \( +\mathbf{V} \| \)
and in \( \boldsymbol{H} \boldsymbol{C l O}_{3} ; \) it is \( +\mathbf{V} \)
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 rectangular frame of wire abcd has
dimensions \( 32 \mathrm{cm} \times 8.0 \mathrm{cm} \) and a total
resistance of \( 2.0 \Omega . \) It is pulled out of a
magnetic field \( B=0.020 T \) by applying
a force of \( 3.2 \times 10^{-5} N \) (figure). It is
found that the frame moves with
constant speed. Find the emf induced in
the loop.
Subject: Chemistry
Compare the properties of metals and
non-metals with respect to electronic
configuration.
A. Metals have 1,2 valence electrons while non metals have 3,5,6 or 7 valence electrons
B. Metals have 1 or 3 valence electrons while non metals have 2,5 valence electrons
C. Metals have 2 or 3 valence electrons while non metals have 1,5,6 or 7 valence electrons
D. Metals have 1,2 or 3 valence electrons while non
metals have 4,5,6 or 7 valence electrons
Subject: Maths
\( \left|\begin{array}{ccc}a^{2} & b^{2} & c^{2} \\ (a+1)^{2} & (b+1)^{2} & (c+1)^{2} \\ (a-1)^{2} & (b-1)^{2} & (c-1)^{2}\end{array}\right|= \)
\( k(a-b)(b-c)(c-a), \) then find the
value of \( -\boldsymbol{k} \)
Subject: Physics
A sample of an ideal gas is contained in
a cylinder. The volume of the gas is suddenly decreased. A student makes the following statements to explain the change in pressure of the gas.
I. The average kinetic energy of the gas atoms increases.
II. The atoms of the gas hit the walls of the cylinder more frequently.
III. Temperature of the gas remains unchanged. Which of these statements is true?
A. I and II only
B. I and III only
c. ॥ and III only
D. I, II and III
Subject: Physics
Assertion
Assertion: In physics, we attempt to derive the properties of a bigger, more complex system from the properties and interactions of its constituent
simpler parts.
Reason
Reason: This approach is called unification and is at the heart of
physics.
A. both assertion and reason are true and reason is the correct explanation of assertion
B. both assertion and reason are true and reason is not the correct explanation of assertion
c. assertion is true but reason is false
D. both assertion and reason are false.
Subject: Chemistry
In the reaction \( C(s)+C O_{2} \rightleftharpoons 2 C O(g) \)
the equilibrium pressure is 12 atm. If
\( 50 \% C O_{2} \) reacts, calculate
\( \boldsymbol{K}_{\boldsymbol{P}}: \)
A \( \cdot_{K_{P}}=0.25 \) atm
В \( \cdot_{K_{P}}=4 \quad \) atm
\( \mathbf{c} \cdot_{K_{P}=16} \) atm
D. \( _{K_{P}}=8 \) atm
Subject: Chemistry
A graph plotted between \( \log \left(\frac{x}{m}\right) \) vs \( \log P(P \) is pressure of gas in atm) shows a straight line with slope equal
to 1 and intercept equal to \( 0.4771 . \) The extent of adsorption \( \left(\frac{x}{m}\right) \) of gas at the
pressure 2 atm is :
Subject: Physics
The resistance \( \boldsymbol{R}_{1} \) and \( \boldsymbol{R}_{2} \) are joined in parallel and a current is passed so that the amount of heat liberated is \( \boldsymbol{H}_{1} \) and
\( H_{2} \) respectively. The ratio \( \frac{H_{1}}{H_{2}} \) has the
value
A \( \cdot \frac{R_{2}}{R_{1}} \)
в. \( \frac{R_{1}}{R_{2}} \)
c. \( \frac{R_{1}^{2}}{R_{2}^{2}} \)
D. \( \frac{R_{2}^{2}}{R_{1}^{2}} \)
Subject: Maths
The area of the triangle formed by the
\( \operatorname{lines} x+y=3, x-3 y+9=0 \) and
\( 3 x-2 y+1=0 \) is
A \( -\frac{16}{7} \) sq. units
B \( \cdot \frac{10}{7} \) sq. units
c. 4 sq. units
D. 9 sq. units
Subject: Maths
Which of the following is always true
A \( \cdot(p \Longrightarrow q) \equiv \sim q \Longrightarrow \sim p \)
в. \( (p \Longrightarrow q) \equiv p \wedge \sim q \)
\( \mathbf{c} . \sim(p \vee q) \equiv \vee p \vee \sim q \)
D. \( (p \vee q) \equiv \sim p \wedge \sim q \)
Subject: Maths
If \( \boldsymbol{A}=\left[\begin{array}{ll}\mathbf{1} & \mathbf{2} \\ \mathbf{1} & \mathbf{1}\end{array}\right] \) and \( \boldsymbol{B}=\left[\begin{array}{cc}\mathbf{0} & -\mathbf{1} \\ \mathbf{1} & \mathbf{2}\end{array}\right], \) then
what is \( B^{-1} A^{-1} \) equal to?
\begin{tabular}{ll} 
A. \( \left[\begin{array}{cc}1 & -3 \\
-3 & 2\end{array}\right] \) \\
\hline
\end{tabular}
B. \( \left[\begin{array}{cc}-1 & 3 \\ 1 & -2\end{array}\right] \)
\( \mathbf{c} \cdot\left[\begin{array}{cc}-1 & 3 \\ -1 & -2\end{array}\right] \)
D. \( \left[\begin{array}{cc}-1 & 1 \\ -3 & -2\end{array}\right] \)
Subject: Chemistry
Nitrogen and phosphorus are both in Group 15 of the Periodic Table.

Phosphorus forms a chloride with the
formula \( P C l_{5} \) but nitrogen does not
form \( \boldsymbol{N} \boldsymbol{C l}_{5} \)
Which statements help to explain this?
1. Nitrogen's outer shell cannot contain more than eight electrons.
2. Nitrogen cannot have an oxidation
state of +5
3. Nitrogen is less electronegative than phosphorus.
A .1,2 and 3 are correct
B. 1 and 2 only are correct
c. 2 and 3 only are correct
D. 1 only is correct
Subject: Chemistry
Assertion
Across the period effective nuclear charge decreases.
Reason
The third period contains only 8
elements and not 18 like 4 th period.
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 incorrect but Reason is correct
D. Both Assertion and Reason are incorrect
Subject: Maths
If angles of a triangle are in the ratio 2 :
\( 4: 9, \) then the difference of the two
smaller exterior angles of the triangle is:
A \( \cdot 24^{\circ} \)
B. \( 30^{\circ} \)
\( c \cdot 44^{0} \)
D. \( 60^{\circ} \)
Subject: Chemistry
Statement I: \( C H C l_{3} \) is stored in
transparent bottles.
Statement II: \( C H C l_{3} \) is oxidised in air.
A. Statement I \& Statement II are correct and statement is the correct explanation of statement
B. Statement I \& Statement II are correct and statement is not the correct explanation of statement!
c. statement lis correct and Statement II is wrong
D. Statement I is wrong and Statement II is correct
Subject: Chemistry
In the reaction
\[
\left(\boldsymbol{C H}_{3}\right)_{3} \boldsymbol{C}-\boldsymbol{O}-\boldsymbol{C H}_{2} \boldsymbol{C H}_{3}+
\]
\[
\begin{array}{c}
\boldsymbol{H I} \\
(\mathbf{1 m o l e})
\end{array}
\]
the product(s) formed is(are):
\( A \)
\[
\left(C H_{3}\right)_{3} C-O H \text { and } C H_{3} C H_{2} I
\]
в.
\[
\left(C H_{3}\right)_{3} C-I \text { and } C H_{3} C H_{2} O H
\]
c. \( \left(C H_{3}\right)_{3} C-I \) and \( C H_{3} C H_{2} I \)
D.
\[
\begin{array}{ccc}
C- & O^{+} & -C H_{2} C H_{3} I
\end{array}
\]
\[
\left(C H_{3}\right)_{3}
\]
Subject: Chemistry
Formation of \( C l F_{3} \) from \( C l_{2} \) and \( F_{2} \) is an
exothermic process. The equilibrium
system can be represented as:
\( \boldsymbol{C l}_{2(\boldsymbol{g})}+\boldsymbol{3} \boldsymbol{F}_{2} \rightleftharpoons \boldsymbol{2} \boldsymbol{C l} \boldsymbol{F}_{3} ; \boldsymbol{\Delta} \boldsymbol{H}=-\boldsymbol{3} \boldsymbol{2} \boldsymbol{9} \mathbf{k} \mathbf{J} \)
Which of the following will increase
quantity of \( C l F_{3} \) in the equilibrium
mixture?
A. Increase in temperature, decrease in pressure, addition of \( C l_{2} \)
B. Decrease in temperature and pressure, addition of \( C l F_{3} \)
C. Increase in temperature and pressure, removal of \( C l_{2} \)
D. Decrease in temperature, increase in pressure addition of \( F_{2} \)
Subject: Chemistry
The expression for de Broglie wavelength is :
A \( \cdot p=\frac{h}{\lambda} \)
в. \( p=\frac{h}{2 \lambda} \)
c. \( _{p}=\frac{2 \pi}{h \lambda} \)
D. \( p=\frac{2 \pi}{\lambda} \)
Subject: Physics
The \( p . d . V \) across and current \( I \) flowing
through an instrument in an \( a . c . \) circuit
are given by \( V=2 \cos \omega t V \) and \( I= \)
\( 2 \sin \omega t A . \) The power dissipated in the
instrument is:
\( \mathbf{A} \cdot 0 W \)
B . \( 2.5 W \)
c. \( 1.5 W \)
D. \( 9 ~ W \)
Subject: Chemistry
For which of the following change
\( \triangle \boldsymbol{H}=\triangle \boldsymbol{E} ? \)
A \( \cdot H_{2}(g)+I_{2(g)} \rightarrow 2 H I_{(g)} \)
B. \( H C l_{(a q)}+N a O H_{(a q)} \rightarrow N a C l_{(a q)}+H_{2} O \)
c. \( C_{(s)}+O_{2(g)} \rightarrow 2 C O_{(g)} \)
D. \( N_{2(g)}+3 H_{2(g)} \rightarrow 2 N H_{3(g)} \)
Subject: Physics
In the circuit shown in figure, the
current through
A. The \( 3 \Omega \) resistor is \( 1.00 A \)
B. The \( 3 \Omega \) resistor is 0.25 A
C. The \( 4 \Omega \) resistor is \( 0.50 A \)
D. The \( 4 \Omega \) resistor is \( 0.25 A \)
Subject: Physics
Which of the following is/are correct?
This question has multiple correct options
A. Random errors can not be estimated by repeating a measurement several (perhaps many) times.
B. Random errors can result due to unpredictable fluctuations in temperature or line voltage during experimental measurements.
C. Am impoperly "Zeroed" instrument (such as an ammeter) can result in systematic errors.
D. Large degree of precision implies accuracy.
Subject: Maths
The coordinates of the point where the line segment joining \( \boldsymbol{A}(\mathbf{5}, \mathbf{1}, \boldsymbol{6}) \) and \( B(3,4,1) \) crosses the yz plane are
A \( \cdot\left(0, \frac{17}{2}, \frac{13}{2}\right) \)
в. \( \left(0,-\frac{17}{2}, \frac{13}{2}\right) \)
c. \( \left(0, \frac{17}{2},-\frac{13}{2}\right) \)
D. \( \left(0,-\frac{17}{2},-\frac{13}{2}\right) \)
Subject: Maths
The sum of first \( n \) terms of the \( A . P . \) \( \sqrt{\mathbf{2}}+\sqrt{\mathbf{8}}+\sqrt{\mathbf{1 8}}+\sqrt{\mathbf{3 2}}+\ldots \ldots . . \) is
A \( \cdot \frac{n(n+1)}{2} \)
B. \( 2 n(n+1) \)
c. \( \frac{n(n+1)}{\sqrt{2}} \)
D.
Subject: Chemistry
Find Kinetic energy of an \( \alpha \) -particle?
\( \left.\boldsymbol{v}=\mathbf{3} \times \mathbf{1 0}^{7}\right) \)
\( \mathbf{A} \cdot 1.3 \times 10^{-5} \) erg
В \( \cdot 2.9 \times 10^{-5} \) erg
c. \( 8.0 \times 10^{18} \) erg
D. \( 8 \times 10^{-18} \) erg
Subject: Chemistry
Assertion
Statement \( -1: N F_{3} \) is a weaker ligand
\( \operatorname{than} N\left(C H_{3}\right)_{3} \)
Reason
Statement \( -2: N F_{3} \) ionizes to give \( F^{-} \)
ion in aqueous solution.
A. Statement -1 is true, Statement -2 is true and Statement - 2 is correct explanation for Statement -
1.
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 false, Statement -2 is true
Subject: Maths
If the tangent to the curve, \( y=x^{3}+ \)
\( a x-b \) at the point (1,-5) is
perpendicular to the line, \( -\boldsymbol{x}+\boldsymbol{y}+ \)
\( 4=0, \) then which one of the following
points lies on the curve?
A. (-2,2)
)
в. (2,-2)
c. (2,-1)
D. (-2,1)
Subject: Maths
Assertion
f \( \vec{a}=\hat{i}, \vec{b}=\hat{j} \) and \( \vec{c}=\hat{i}+\hat{j} \) then \( \vec{a} \) and
\( \vec{b} \) are linearly independent but \( \vec{a}, \vec{b} \) and \( \vec{c} \) are linearly dependent.
Reason
If \( \vec{a} \) and \( \vec{b} \) are linearly dependent and \( \vec{c} \) is any vector then \( \vec{a}, \vec{b} \) and \( \vec{c} \) are linearly dependent.
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
Assertion
The \( 4 f- \) and \( 5 f \) - inner transition series of
elements are placed separately at the bottom of the periodic table.
Reason
(i) This prevents the undue expansion of the periodic table i.e., maintains its
structure.
(ii) This preserves the principle of classification by keeping elements with similar properties in a single column.
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 teak wood log is cut first in the form of a cuboid of length \( 2.3 \mathrm{m}, \) width \( 0.75 \mathrm{m} \)
and of a certain thickness. Its volume is
\( 1.104 \mathrm{m}^{3} . \) How many rectangular planks of size \( 2.3 \mathrm{m} \times 0.75 \mathrm{m} \times 0.04 \mathrm{m} \) can be
cut from the cuboid?
Subject: Maths
Find square of the following expression \( \frac{3 a}{2 b}-\frac{2 b}{3 a} \)
A \( \cdot \frac{9 a^{2}}{4 b^{2}}-2+\frac{b^{2}}{a^{2}} \)
в. \( \frac{9 a^{2}}{4 b^{2}}+2+\frac{4 b^{2}}{9 a^{2}}^{2} \)
c. \( \frac{a^{2}}{4 b^{2}}-2+\frac{4 b^{2}}{9 a^{2}} \)
D. \( \frac{9 a^{2}}{4 b^{2}}-2+\frac{4 b^{2}}{9 a^{2}} \)
Subject: Maths
Let \( f(x)=\frac{2025^{x}}{45+2025^{x}}, \) then the value of \( f\left(\frac{1}{2025}\right)+f\left(\frac{2}{2025}\right)+ \)
\( f\left(\frac{3}{2025}\right)+\ldots+f\left(\frac{2024}{2025}\right) \) is equal to
A. 1011
в. 1012
\( c .1013 \)
D. 2024
Subject: Chemistry
For a first order reaction with rate
constant \( k \) and initial concentration a
the half-life period is given by:
This question has multiple correct options
A \( \cdot \frac{\ln 2}{k} \)
B. \( \frac{1}{k} \)
c. \( \frac{0.693}{k} \)
D. \( \frac{2.303}{k} \log 2 \)
Subject: Maths
If the projection of \( \vec{a} \) on \( \vec{b} \) and the projection of \( \vec{b} \) on \( \vec{a} \) are equal then the angle between \( \vec{a}+\vec{b} \) and \( \vec{a}-\vec{b} \) is
\( A \cdot \frac{\pi}{3} \)
B. \( \frac{\pi}{2} \)
\( c \cdot \frac{\pi}{4} \)
D. \( \frac{2 \pi}{3} \)
Subject: Chemistry
The basic character of the hydrides of
\( V^{t h} \) group elements decreases in the
order:
\( \mathbf{A} \cdot N H_{3}>P H_{3}>A s H_{3}>S b H_{3} \)
\( \mathbf{B} \cdot S b H_{3}>A s H_{3}>P H_{3}>N H_{3} \)
\( \mathbf{C} \cdot N H_{3}>S b H_{3}>P H_{3}>A s H_{3} \)
\( \mathbf{D} \cdot S b H_{3}>P H_{3}>A s H_{3}>N H_{3} \)
Subject: Maths
(i) Verify the Rolle's theorem for the function
\( \boldsymbol{f}(\boldsymbol{x})=\sin ^{2} \boldsymbol{x}, \mathbf{0} \leq \boldsymbol{x} \leq \boldsymbol{\pi} \)
(ii) Find the critical numbers of
\( \boldsymbol{x}^{3 / 5}(\boldsymbol{4}-\boldsymbol{x}) \)
Subject: Chemistry
If an electron is moving with a velocity of \( 1.1 \times 10^{6} \mathrm{ms}^{-1} \) de broglie wave
length approximately is:
A \( \cdot 4.1 \times 10^{-11} \mathrm{m} \)
В . \( 4.9 \times 10^{-9} \mathrm{m} \)
c. \( 7 \times 10^{-10} m \)
D. \( 3.306 \times 10^{-8} \mathrm{m} \)
Subject: Chemistry
Which compound is prepared by the following reaction? \( X e+F_{2}\left(2: 1 \text { volume ratio) } \frac{N i}{\rightarrow} \text { at } 673 \mathrm{K}\right. \)
\( \mathbf{A} \cdot X e F_{4} \)
B . \( X e F_{2} \)
с. \( X e F_{6} \)
D. None of these
Subject: Maths
The equation \( \frac{x^{2}}{2-a}+\frac{y^{2}}{a-5}+1=0 \)
represents an ellipse if \( \boldsymbol{a} \in \)
\( ^{\mathbf{A}} \cdot\left(2, \frac{3}{2}\right) \cup\left(\frac{3}{2}, 5\right) \)
в. \( \left(2, \frac{3}{2}\right) \)
c. \( \left(1, \frac{3}{2}\right) \)
D. \( \left(\frac{3}{2}, 5\right) \)
Subject: Chemistry
The vapour pressure in \( \mathrm{mm} \) of \( \boldsymbol{H} \boldsymbol{g} \), of an aqueous solution obtained by adding 18 g of glucose \( \left(C_{6} H_{12} O_{6}\right) \) to 180 gof water at \( \left(100^{\circ} \mathrm{C}\right) \) is:
A . 7.60
B. 76.0
c. 759
D. 752.4
Subject: Physics
Two concentric spheres of radius \( R \) and
\( 2 R \) have charges \( Q \) and \( 2 Q . \) The potential at a point \( \mathrm{P} \) situated at a point 3R/2 distance from common centre is
\( V, \) Now if outer sphere is earthed, the
potential at point \( P \) is :
A. \( V / 5 \)
в. \( V / 10 \)
c. \( V / 3 \)
D. \( V \)
Subject: Physics
A small source of light is \( 4 \mathrm{m} \) below the surface of a liquid of refractive index
\( 5 / 3 . \) In order to cut off all the light coming out of liquid surface, minimum diameter of the disc placed on the surface of liquid is
A. 3 m
B. \( 4 \mathrm{m} \)
\( c \cdot 6 m \)
\( D \cdot \infty \)
Subject: Chemistry
Which rule explains the electronic configuration of chromium is \( [\mathrm{Ar}] \) \( 3 d^{5} 4 s^{1} \) instead of \( [A r] 3 d^{4} 4 s^{2} ? \)
A. Pauli's exclusion principle
B. Aufbau Principle
c. Hund's rule
D. Heisenberg principle
Subject: Maths
Evaluate the integral \( \int_{0}^{1} \frac{\sin ^{-1} x}{x} d x \)
\( A \cdot \pi \log 2 \)
в. \( -\pi \log 2 \)
C \( \cdot-\frac{\pi}{2} \log 2 \)
D. \( \frac{\pi}{2} \log 2 \)
Subject: Chemistry
In which of the following solution, \( A g C l \)
has minimum solubility:
A. \( 0.05 M A g N O_{3} \)
в. \( 0.01 M \) Са \( C l_{2} \)
c. \( 0.01 M \) NaCl
D. \( 0.01 M N H_{4} O H \)