AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Physics
initial speed of \( 25 \mathrm{m} / \mathrm{s} \) at an angle \( \boldsymbol{\theta} \)
with the horizontal as shown in figure. Write down the equation of the
projectile of the football when the ball is
7 m (along x-axis) away from the
footballer.
A \( \cdot y=7 \tan \theta-\frac{49 g}{1350 \cos ^{2} \theta} \)
B. \( y=\tan \theta-\frac{9 g}{1350 \cos \theta} \)
c. \( y=7 \cot \theta-\frac{49 g}{1350 \cos ^{2} \theta} \)
D. \( y=7 \tan \theta-\frac{41 g}{1350 \cos 2 \theta} \)
Subject: Physics
If \( z=\frac{\lambda D}{4 d} \)
A \( \cdot[3-2 \sqrt{2}]^{2} \)
B \( \cdot[3+\sqrt{2}]^{2} \)
c. \( [3-\sqrt{2}]^{2} \)
D \( \cdot[3+2 \sqrt{2}]^{2} \)
Subject: Chemistry
A solution of \( 50 \% \) of \( A \) and \( 50 \% \) of \( B \) on
distillation results into
A. Seperation of an azeotropic mixture and pure \( A \)
B. Seperation of an azeotropic mixture and pure B.
C. Seperation of both pure \( A \) and pure \( B \)
D. None.
Subject: Physics
(A): the linear coefficients of expansion
of a crystal along three perpendicular
\( \operatorname{axes} \operatorname{are} \alpha, \frac{-\alpha}{2}, \frac{\alpha}{5} . \) its volume
coefficient is \( \frac{7 \alpha}{10} \)
(B): For an-isotropic solids
\( \boldsymbol{r}=\boldsymbol{\alpha}_{\boldsymbol{x}}+\boldsymbol{\alpha}_{\boldsymbol{y}}+\boldsymbol{\alpha}_{\boldsymbol{z}} \)
\( A \cdot A \) and \( B \) are correct and \( B \) is correct explanation for \( A \)
B. A and B are correct and B is not correct explanation for \( A \)
C. A is true and B is false
D. A and B both are wrong
Subject: Physics
Turpentine oil is flowing through a tube of length I and radius r. The pressure difference between the two ends of the
tube is p. The viscosity of oil is given \( \boldsymbol{\eta}=\frac{\boldsymbol{p}\left(\boldsymbol{r}^{2}-\boldsymbol{x}^{2}\right)}{\boldsymbol{4} \boldsymbol{v} \boldsymbol{l}}, \) where \( \mathbf{v} \) is velocity of oil
at a distance \( x \) from the axis of the tube.
The dimensional formula of viscosity is
\( \mathbf{A} \cdot\left[M^{0} L^{0} T^{0}\right] \)
B . \( \left[M^{1} L^{-1} T^{-1}\right] \)
\( \mathbf{c} \cdot\left[M L^{2} T^{-1}\right] \)
D \cdot \( \left[M^{-1} L^{-1} T^{1}\right] \)
Subject: Maths
The values of \( x \) in \( \left(0, \frac{\pi}{2}\right) \) satisfying the equation \( \sin x \cos x=\frac{1}{4} \) are
A \( \cdot \frac{\pi}{6}, \frac{\pi}{12} \)
в. \( \frac{\pi}{12}, \frac{5 \pi}{12} \)
c. \( \frac{\pi}{8}, \frac{3 \pi}{8} \)
D. \( \frac{\pi}{8}, \frac{\pi}{4} \)
Subject: Physics
If the resultant of two forces \( P \) and \( Q \) be
equal in magnitude to one of the
components \( \boldsymbol{P} \) and perpendicular to it
in direction, then the value of \( Q \) is
A. \( P \)
в. \( \frac{1}{\sqrt{2}} P \)
\( c \cdot \sqrt{2} P \)
D. \( \sqrt{3} P \)
Subject: Chemistry
What is true for acidic aqueous
solution?
A \( \cdot\left[H_{3} O^{+}\right]=10^{-7} \mathrm{M} \)
в. \( \left[H_{3} O^{+}\right]<10^{-7} \mathrm{M} \)
c. \( \left[H_{3} O^{+}\right]>10^{-7} \) М
D \( \cdot\left[H_{3} O^{+}\right]<\left[O H^{-}\right] \)
Subject: Maths
If \( 3 x+5 y=4, \) which of the following is
equivalent to the expression \( (6 x+ \)
\( (10 y)(100 x+100 y) ? \)
A. \( 100 x+100 y \)
в. \( 200 x+200 y \)
c. \( 400 x+400 y \)
D. \( 800 x+800 y \)
E . \( 1,600 x+1,600 y \)
Subject: Maths
The above diagram shows a number line.

The above number line represents the
solution for:
A. \( -3 \leq x \) and \( x>4 \)
B. \( -3<x<4 \)
c. \( -3 \leq x<4 \)
D. \( -3<x \) and \( x \leq 4 \)
Subject: Maths
The point (3,4) is the focus and \( 2 x- \)
\( 3 y+5=0 \) is the directrix of a
parabola. Lenghth of latus rectum is
A \( \cdot \frac{2}{\sqrt{13}} \)
в. \( \frac{4}{\sqrt{13}} \)
c. \( \frac{1}{\sqrt{13}} \)
D. \( \frac{3}{\sqrt{13}} \)
Subject: Maths
Consider \( A \) and \( B \) two square matrices
of same order. Select the correct
alternative.
\( \mathbf{A} \cdot|A B| \) must be greater than \( |A| \)
B. \( \left[\begin{array}{ll}1 & 1 \\ 1 & 1\end{array}\right] \) is not unit matrix
C \( \cdot|A+B| \) must be greater than \( |A| \)
D. If \( A B=0 \), either \( A \) or \( B \) must be zero matrix
Subject: Maths
In a test an examine either gusses or copies or knows the answer to a
multiple choice question with \( m \) choices out of which exactly one is correct. The probability that he makes a guess is \( 1 / 3 \) and the probability that he copies the answer is 1/6. The probability that his answer is correct given that the copied it, is \( 1 / 8 . \) If the probability that he knew the answer to the question given that he correctly answered it is \( 120 / 141 \)
find \( \boldsymbol{m} \)
Subject: Physics
thickness as shown in figure. One is made pf material \( \boldsymbol{A} \) of refractive index
1.5. The other is made of two materials
\( B \) and \( C \) with thickness in the ratio 1: 2
The refractive index of \( C \) is \( 1.6 . \) If a
monochromatic parallel beam passing
through the slabs has the same number of wavelengths inside both, the
refractive index of \( \boldsymbol{B} \) is
\( \mathbf{A} \cdot 1.1 \)
B. 1.2
c. 1.3
D . 1.4.
Subject: Maths
The area of the triangle formed by plane \( 2 x+3 y+6 z+9=0 \) with \( y \) -axis, \( z^{-} \)
axis is?(in Sq. units)
A . 9
B. \( \frac{9}{2} \)
\( c \cdot \frac{9}{4} \)
D. None
Subject: Physics
A cell of emf \( E \) and internal resistance \( r \)
is connected in series with an external
resistance \( n r . \) Then, the ratio fo the
terminal potential difference to E.M.F is
\( \mathbf{A} \cdot 1 / n \)
в. \( \frac{1}{n+1} \)
c. \( \frac{n}{n+1} \)
D. \( \frac{n+1}{n} \)
Subject: Chemistry
Match the column-I with Column-II
and select the correct answer:
Column -II Column - I
Curie
\[
\text { A. } 10^{6} \text { dis } s e c^{-1}
\]
(I) urle
(II) I) Rutherford
\[
\text { В. } 3.7 \times 10^{10} \text { dis sec}^{-1}
\]
(III) Becquerel C. 1 dis \( s e c^{-1} \) C. 1 \( s s e c \)
A. I-B II-A III-C
B. I-B II-C III-A
c. I-A II-B III-C
D. I-C II-B III-A
Subject: Physics
A container is filled with water,
accelerating with acceleration \( 10 m / s^{2} \)
long \( +v e X \) -axis on a smooth horizontal
surface. The velocity of efflux of water at
a point \( \boldsymbol{P} \) at the bottom of the tank and
near its left most corner is
\( \mathbf{A} \cdot 4.43 m / s \)
B. \( 5.48 \mathrm{m} / \mathrm{s} \)
\( \mathbf{c} \cdot 4 m / s \)
D. \( 3 m / s \)
Subject: Maths
If \( y=\log (\sec x+\tan x), \) then \( \frac{d y}{d x}= \)
\( \mathbf{A} \cdot \sec x \)
в. \( \frac{1}{\sec x+\tan x} \)
C. \( \log \left(\cos x+\sec ^{2} x\right) \)
D. none of these
Subject: Chemistry
An aqueous solution freezes at \( 272.4 K \)
while pure water freezes at \( 273.0 K \)
while pure water freezes at \( 273.0 K \) Determine
(a) the molality of the solution
(ii) boiling point of the solution
(iii) lowering of vapour pressure of water at \( 298 K \)
(Given, \( \boldsymbol{K}_{\boldsymbol{f}}=\mathbf{1 . 8 6 K} \boldsymbol{k g} \boldsymbol{m o l}^{-1}, \boldsymbol{K}_{\boldsymbol{b}}= \)
\( 0.512 K k g \) mol\( ^{-1} \) and vapour pressure
of water at \( 298 K=22.756) \)
Subject: Maths
Find the sum of the series \( 1+(1+ \)
\( \boldsymbol{x})+\left(\mathbf{1}+\boldsymbol{x}+\boldsymbol{x}^{2}\right)+\ldots \) to \( n \) terms, \( \boldsymbol{x} \neq \mathbf{1} \)
Subject: Chemistry
Saccharin \( \left(\boldsymbol{K}_{\boldsymbol{a}}=\mathbf{2} \times \mathbf{1 0}^{-\mathbf{1 2}}\right) \) is a weak
acid represented by formula \( \boldsymbol{H} \boldsymbol{S} \boldsymbol{a} \boldsymbol{C} . \boldsymbol{A} \)
\( 4 \times 10^{-4} \) mole of saccharin is dissolved
is \( 200 \mathrm{mL} \) of water of \( P h=3 \), Assuming
no change in volume, calculate \( \left[\boldsymbol{S a C}^{\ominus}\right] \) in the solution at equilibrium.
A \( \cdot 4 \times 10^{-12} \mathrm{M} \)
В . \( 4 \times 10^{-8} M \)
c. \( 4 \times 10^{-10} M \)
D. \( 4 \times 10^{-6} M \)
Subject: Maths
\( \boldsymbol{U}=\{\boldsymbol{a}, \boldsymbol{b}, \boldsymbol{c}, \boldsymbol{d}, \boldsymbol{e}, \boldsymbol{f}, \boldsymbol{g}\},\left(\boldsymbol{A}^{\prime}\right)=\{\boldsymbol{b}, \boldsymbol{d}, \boldsymbol{f}\} \)
show that Venn diagram.
Subject: Physics
A Young's interference experiment is performed with monochromatic light. The separation between the slits is
\( 0.5 m m, \) and the interference pattern on a screen is \( 3.5 m \) away, shows the first
order maximum at \( 3.6 m m \) from the
centre of the pattern. The wavelength is
A \( .515 n m \)
B. \( 315 \mathrm{mm} \)
c. 215 cm
D. \( 15 m \)
Subject: Physics
Three rods of material \( X \) and three rods
of material \( Y \) are connected as shown
in figure. All the rods are identical in length and cross-sectional area. If the
end \( A \) is maintained at \( 60^{\circ} \mathrm{C} \) and the
junction \( E \) at \( 10^{\circ} \mathrm{C} \), calculate the
temperatures of the junctions \( B, C, D \)
The thermal conductivity of \( X \) is 0.92
\( C G S \) units and that of \( Y \) is \( 0.46 C G S \)
units.
Subject: Chemistry
Fullerene is an allotrope of carbon which is similar to a football. It has 60
carbon atoms joined together and no other element in it. There are various
types of fullerenes. \( C_{60}, C_{70}, C_{74} \) and \( C_{75} \)
are the members of the fullerene family.
But \( C_{60} \) (pronounced as \( C \) sixty) is the most stable and most studied form
of fullerenes. What do you think is the
nature of the bond which is
joining these atoms together?
A. lonic
B. Covalent
c. Hydrogen
D. Polar covalent
Subject: Physics
A stone is moved in a horizontal circle of
radius \( 4 \mathrm{m} \) by means of a string at a height of \( 20 \mathrm{m} \) above the ground. The string breaks and the particle' flies off horizontally, striking the ground 10m away. The centripetal acceleration during circular motion is
A \( \cdot 6.25 m s^{-2} \)
B. \( 12.5 m s^{-2} \)
c. \( 18.75 \mathrm{ms}^{-2} \)
D. \( 25 m s^{-2} \)
Subject: Physics
An airplane in which the distance
between the tips of the wings is 50 meter is flying horizontally with a speed of 360 km/hour over a place where the vertical
component of earths magnetic field is \( 2.0 \times 10^{-4} \) Testa. The potential difference
between the tips of the wings would be:-
A . 0.1
B. 1.0
c. \( 0.2 v \)
D. \( 0.0 \mathrm{v} \)
Subject: Maths
If the position vectors of the points \( \boldsymbol{A}, \boldsymbol{B}, \boldsymbol{C}, \boldsymbol{D} \operatorname{are}(\boldsymbol{0}, \boldsymbol{2}, \boldsymbol{1}),(\boldsymbol{3}, \boldsymbol{1}, \boldsymbol{1}) \)
(-5,3,2),(2,4,1) respectively and if \( \boldsymbol{P A}+\boldsymbol{P B}+\boldsymbol{P C}+\boldsymbol{P D}=\mathbf{0} \) then the
position vector of \( \mathrm{P} \) is
A \( \cdot\left(0, \frac{5}{2}, \frac{5}{4}\right) \)
в. \( \left(\frac{5}{2}, \frac{5}{2}, \frac{5}{4}\right) \)
c. \( \left(\frac{5}{2}, 0, \frac{5}{4}\right) \)
D \( \left(\frac{5}{2}, \frac{5}{4}, 0\right) \)
Subject: Maths
Assertion
Let \( A, B \) and \( C \) be three events such
that \( \boldsymbol{P}(\boldsymbol{C})=\mathbf{0} \)
\( \boldsymbol{P}(\boldsymbol{A} \cap \boldsymbol{B} \cap \boldsymbol{C})=\mathbf{0} \)
Reason
\( \boldsymbol{P}(\boldsymbol{A} \cup \boldsymbol{B} \cup \boldsymbol{C})=\boldsymbol{P}(\boldsymbol{A} \cup \boldsymbol{B}) \)
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
Assertion
An astronaut in an orbiting space
station above the Earth experiences
weightlessness.
Reason
An object moving around the Earth
under the influence of Earths
gravitational force is in a state of free-
fall.
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 integers are selected at random
from the set \( 1,2, \ldots, 11 . \) Given that the sum of selected numbers is even, the
conditional probability that both the
numbers are even is:
A \( \cdot \frac{2}{5} \)
B. \( \frac{1}{2} \)
\( c \cdot \frac{3}{5} \)
D. \( \frac{7}{10} \)
Subject: Chemistry
The EMF of the cell
\( Z n\left|Z n^{2+}(0.01 M) \| F e^{2+}(0.001 M)\right| F e \) at
\( 298 K \) is 0.2905 then the value of
equilibrium constant for the cell reaction
is :
B. \( 10^{\frac{1.33}{35}} \)
\( \mathbf{c} \cdot 10 \frac{0.25}{15} \)
D. \( 10^{\frac{0.32}{0.539}} \)
Subject: Chemistry
The functional group present in acyl chlorides is:
A. \( -C l \)
в.
\[
\begin{array}{c}
0 \\
-C-C l
\end{array}
\]
\( c \)
\[
\begin{array}{c}
0 \\
-C-O C l
\end{array}
\]
D. \( -C H_{2}- \) OCl
Subject: Physics
Mass equivalent to the energy \( 931 \mathrm{MeV} \) is:
\( \mathbf{A} \cdot 6.02 \times 10^{-27} k g \)
В. \( 1.662 \times 10^{-27} k g \)
c. \( 16.66 \times 10^{-27} k g \)
D. \( 16.02 \times 10^{-27} \mathrm{kg} \)
Subject: Maths
The following data gives the distribution of total monthly household
expenditure of 200 families of a village. Find the modal monthly expenditure of
the families. Also, find the mean
monthly expenditure:
Expenditure (in C) \( \quad \) Number of families 4 \( 1000-1500 \) 24 The line 1 1 \( 1500-2000 \) 40
33 \( 2000-2500 \) A 3 \( \begin{array}{lll}2500-3000 & 28 \\ 3000-3500 & 30 \\ 3500-4000 & 22 \\ 4000-4500 & 16 \\ 4500-5000 & 7\end{array} \)
Subject: Physics
A galvanometer having a coil resistance of \( 60 \Omega \) shows full scale deflection when a current of 1.0 amp passes through it. It can be converted into an ammeter to
read currents upto 5.0 amp by :
A. Putting in parallel a resistance of \( 15 \Omega \)
B. Putting in parallel a resistance of \( 240 \Omega \)
c. Putting in series a resistance of \( 15 \Omega \)
D. Putting in series a resistance of \( 240 \Omega \)
Subject: Maths
Find the perimeter of a rectangular hall, if its length exceeds its breadth by \( 7 \mathrm{m} \)
and the area of the hall is \( 228 m^{2} \)
A. 72 m
в. \( 70 \mathrm{m} \)
\( c .64 \mathrm{m} \)
D. \( 62 \mathrm{m} \)
Subject: Chemistry
Gas \( A \) (molar mass 16 ) and \( \operatorname{gas} B \)
(molar mass 4 ) are confirmed in a
vessel at partial pressure of 2 atm each at \( 27^{0} C . \) The gases are then allowed to
effuse out at \( 27^{0} C \) through a value till the pressure inside the vessel becomes 2 atm after which the value is closed
and the gases are heated to \( 127^{0} C \) and
allowed to react as \( \boldsymbol{A}+\boldsymbol{B} \rightleftharpoons \boldsymbol{C} ; \boldsymbol{K}_{\boldsymbol{p}}= \)
\( 0.1 a t m^{-1} . \) The partial pressure of \( C \) at
equilibrium assuming \( C \) is not formed till the effusing process is completed at \( 27^{0} C \) is \( X \) atm. \( X \) is:
A. 0.126
B. 0.177
c. 0.187
D. 0.113
Subject: Chemistry
The IUPAC name of the well known
terpene camphor having the structure
is:
A. 6 -oxo-1,2,2-trimethylbicyclo[2.2.1]heptane
B. 1,7,7-trimethyl bicyclo[2.2.1]heptane-2-one
C. 1,5,5 -trimethyl bicyclo[2.1.1]hexane-2-one
D. 1,7,7 -trimethyl bicyclo[2.1.2]heptane-2-one
Subject: Maths
Find the value of \( x \) and \( y \). (Use
Pythagoras theorem)
A \( . x=12 \) and \( y=3 \)
3. \( x=10 \) and \( y=5 \)
c. \( x=12 \) and \( y=5 \)
\( x=11 \) and \( y=5 \)
Subject: Chemistry
Number of electrons involved in the
electrodeposition of \( 63.5 g \) of \( C u \) from a
solution of \( C u S O_{4} \) is?
A \( \cdot 6.022 \times 10^{23} \)
3 \( 3.02 \times 10^{2}+0.62^{23} \)
B. \( 3.011 \times 10^{23} \)
c. \( 12.044 \times 10^{23} \)
D. \( 6.022 \times 10^{22} \)
Subject: Maths
\( \frac{5}{7}+\frac{4}{7}-\frac{3}{7} \) is equal to
A \( \cdot \frac{3}{7} \)
B. \( \frac{5}{7} \)
\( c \cdot \frac{6}{7} \)
D. \( \frac{12}{7} \)
Subject: Physics
An engine working on Carnot cycle rejects \( 40 \% \) of absorbed heat from the source, while the sink temperature is
maintained at \( 27^{0} C \), then what is
the source temperature \( \left(\text { in }^{0} C\right) ? \)
A . 477
B. 346
\( c \cdot 564 \)
D. none of the above
Subject: Maths
If \( m \) arithmetic means are inserted
between 1 and \( 31, \) so that the ratio of
the \( 7^{t h} \) and \( (m-1)^{t h} \) means is 5: 9
then the value of \( m \) is
\( \mathbf{A} \cdot \mathbf{9} \)
B. 11
c. 13
D. 14
Subject: Chemistry
The electronic configuration is given as:
\( 1 s^{2} 2 s^{2} 2 p^{6} 3 s^{2} 3 p^{6} 3 d^{10} 4 s^{2} 4 p^{6} 4 d^{10} 5 s^{2} \)
is for:
A. \( f \) -block element
B. \( d \) -block element
c. \( p \) -block element
D. \( s \) -block element
Subject: Chemistry
Identify the correct option(s) related
with the physical properties of the unknown compounds [X] and [Y] formed as major and minor product
respectively in the given reaction.
This question has multiple correct options
A. Water solubility of [Y] is greater than [X]
B. Boiling point of [Y] is greater than [X]
C. Melting point of [Y] is greater than [X]
D. \( [x] \) is more volatile than \( [Y] \)
Subject: Chemistry
Match the following:
\( \begin{array}{ll}\text { List - I } & \text { List - II } \\ \text { A. } P_{c} & \text { (i) } 3 b \\ \text { B. } V_{c} & \text { (ii) } 8 a / 27 b R \\ \text { C. } T_{c} & \text { (iii) } a / 27 b^{2}\end{array} \)
\( \mathbf{A} \cdot A-(i), B-(i i), C-(i i i) \)
B . \( A-(i i i), B-(i i), C-(i) \)
c. \( A-(i i), B-(i i i), C-(i) \)
D. \( A-(i i i), B-(i), C-(i i) \)
Subject: Maths
If a function such that \( \boldsymbol{f}(\mathbf{0})= \)
\( \mathbf{2} ; \boldsymbol{f}(\mathbf{1})=\mathbf{3} \) and \( \boldsymbol{f}(\boldsymbol{x}+\mathbf{2})=\mathbf{2} \boldsymbol{f}(\boldsymbol{x})- \)
\( \boldsymbol{f}(\boldsymbol{x}+\mathbf{1}) \forall \boldsymbol{x} \in \boldsymbol{R} \) then \( \mathrm{f}(5)= \)
\( A \cdot 7 \)
B. 13
\( c \)
D.
Subject: Maths
If the planes \( 2 x-y-3 z-7=0 \) and
\( 4 x-2 y+5 k z+9=0 \) are parallel
then \( 5 k^{2}+6= \)
A \( \frac{-6}{5} \)
в. \( \frac{-5}{6} \)
c. \( \frac{36}{5} \)
D. \( \frac{66}{5} \)
Subject: Maths
The angle made by the tangent line at (1
3) on the curve \( y=4 x-x^{2} \) with \( \overline{O X} \) is
\( A \cdot \tan ^{-1} 2 \)
B. \( \tan ^{-1}(1 / 2) \)
\( c \cdot \tan ^{-1}-2 \)
D. None of these
Subject: Physics
A dog weighting \( 5 k g \) is standing on a flat boat so that it is \( 10 \mathrm{m} \) from the
shore. The walks on the boat towards
the shore and then halts. The boat
weights \( 20 k g \) and one can assume that
then no friction between it and the
water. How far is the dog from the shore
at the end of this time?
\( \mathbf{A} \cdot 3.2 m \)
в. \( m \)
\( c .10 m \)
D. \( 6.8 m \)
Subject: Maths
Factorize:
\( (x-y)^{3}-8 x^{3} \)
\( \mathbf{A} \cdot-2(x+y)\left(7 x^{2}-4 x y+y^{2}\right) \)
B . \( -(x-y)\left(x^{2}-4 x y+6 y^{2}\right) \)
\( \mathbf{c} \cdot-(x+2 y)\left(x^{2}-4 x y+y^{2}\right) \)
\( \mathbf{D} \cdot-(x+y)\left(7 x^{2}-4 x y+y^{2}\right) \)
Subject: Chemistry
The ammonia \( \left(N H_{3}\right) \) released on
quantitative reaction of \( 0.6 g \) urea
\( \left(N H_{2} C O N H_{2}\right) \) with sodium hydroxide
\( (N a O H) \) can be neutralized by:
A . \( 200 \mathrm{ml} \) of \( 0.2 \mathrm{N} \) HCl
в. 200ml of 0.4N HCl
c. \( 100 m l \) of \( 0.1 N \) HCl
D. \( 100 m l \) of \( 0.2 N H C l \)
Subject: Physics
A man applying a force \( \boldsymbol{F} \) upon a stretched spring is stationary in a compartment moving with constant
speed \( v . \) If the compartment covers a
distance \( L \) in some time \( t, \) then
This question has multiple correct options
A. The man acting with force F on spring does the work \( (w)=F L \)
B. The total work performed by man on the compartment with respect to ground is zero
c. The work done by friction acting on man with respect to ground is, (w) \( =F L \)
D. The total work done by man with respect to ground is \( (w)=F L \)
Subject: Chemistry
Which of the following ores can be concentrated by froth floatation method and why?
\( \boldsymbol{F} \boldsymbol{e}_{2} \boldsymbol{O}_{3}, \boldsymbol{Z} \boldsymbol{n} \boldsymbol{S}, \boldsymbol{A} \boldsymbol{I}_{2} \boldsymbol{O}_{3} \)
Subject: Maths
A black and a red dice are rolled.
(a) Find the conditional probability of
obtaining a sum greater than \( 9, \) given that the black die resulted in a 5 .
(b) Find the conditional probability of
obtaining the sum 8 , given that the red die resulted in a number less than 4
A. 0.33,0.11
B. 0.51,0.76
c. 0.56,0.43
D. 0.11,0.65
Subject: Physics
Using mass(M), length (L), time(T), and electric current(A) as fundamental
quantities, the dimensions of permittivity will be
\( \mathbf{A} \cdot\left[M L T^{-1} A^{-1}\right] \)
в. \( \left[M L T^{-2} A^{-2}\right] \)
\( \mathbf{C} \cdot\left[M^{-1} L^{-3} T^{4} A^{2}\right] \)
D・ \( \left[M^{2} L^{-2} T^{-2} A\right. \)
Subject: Physics
When the current in the inductor has
half its maximum value, what is the charge on the capacitor?
A \( \cdot 1.33 \times 10^{6} C \)
B. \( 9.33 \times 10^{-6} C \)
\( \mathbf{c} \cdot 4.33 \times 10^{-6} C \)
D. \( 7.33 \times 10^{6} C \)
Subject: Physics
Which of the following relations is
correct?
A. \( \quad \) Distance \( =\frac{\text { Speed }}{\text { Time }} \)
B. Distance\( =\frac{\text {Time}}{\text {Speed}} \)
c. Distance\( = \)Speed\( \times \)Time
Distance \( =\frac{1}{\text {Speed } \times \text { Time}} \)
Subject: Maths
If \( A \) and \( B \) are acute positive angles satisfying the equations \( 3 \sin ^{2} A+ \) \( 2 \sin ^{2} B=1 \) and \( 3 \sin 2 A-2 \sin 2 B= \)
\( 0, \) then \( A+2 B \) is equal to
A \( \cdot \frac{\pi}{4} \)
в.
\( \mathrm{c} \cdot_{3} \frac{\pi}{4} \)
D. \( \frac{2 \pi}{3} \)
Subject: Chemistry
Two zinc rods are placed in contact with
dilute \( \boldsymbol{H}_{2} \boldsymbol{S} \boldsymbol{O}_{4} \) and \( \operatorname{conc.} \boldsymbol{H}_{2} \boldsymbol{S} \boldsymbol{O}_{4} \) in two
separate containers \( A \) and \( B \). The
characteristic gases evolved in the containers are respectively:
A. the gas in container' \( ^{2} \) ' turns \( K_{2} C r_{2} O_{7} \) green and the gas in container' \( B \) ' turns lead acetate black
B. \( A \rightarrow \) Pungent smelling gas, \( B \rightarrow \) colourless, odourless gas
C \( . A \rightarrow \) Inflammable gas, \( B \rightarrow \) Turns \( K_{2} C r_{2} O_{7} \) green
D. \( A \rightarrow \) Can react with \( O_{2} \) explosively, \( B \rightarrow \) No reaction with \( O_{2} \) at all
Subject: Physics
A particle is moving in a plane with a velocity given by \( \vec{v}=\hat{i} u_{0}+\hat{j} a \omega \cos \omega t \) if
the particle is at origin at \( t=0 \) Distance of the particle from origin at
time \( 3 \pi / 2 \omega \) is
A \( \cdot \sqrt{a^{2}+\left(3 \pi u_{0} / 2 \omega\right)^{2}} \)
B . \( \sqrt{a^{2}+\left(2 \pi u_{0} / \omega\right)^{2}} \)
\( ^{\mathbf{c}} \cdot\left(\frac{\pi u_{0}}{\omega}\right)^{2}+a^{2} \)
Subject: Physics
A particle having a charge of \( 10 \mu C \) and
mass \( 1 \mu g \) moves in a horizontal circle of radius \( 10 \mathrm{cm} \) under the influence of a
magnetic field of 0.1 T. When the particle
is at a point \( P, \) a uniform electric field is
switched on so that the particle starts
moving along the tangent with uniform
velocity. The electric field is
A. \( 0.1 \mathrm{V} / \mathrm{m} \)
B. 1.0 \( \mathrm{V} / \mathrm{m} \)
c. \( 10.0 \mathrm{V} / \mathrm{m} \)
D. \( 100 \mathrm{V} / \mathrm{m} \)
Subject: Chemistry
The concentration of \( C a\left(H C O_{3}\right)_{2} \) in a
sample of hard water is 486 ppm. The density of water sample is \( 1.0 \mathrm{g} / \mathrm{ml} \). The molarity of the solution is :
A . \( 3.0 \times 10^{-3} M \)
в. \( 5.0 \times 10^{-3} M \)
c. \( 2.0 \times 10^{-3} M \)
D. \( 6.0 \times 10^{-3} M \)
Subject: Maths
\( \int e^{x}(\sin x+2 \cos x) \sin x d x \) is equal to
A \( \cdot e^{x} \cos x+C \)
B. \( e^{x} \sin x+C \)
\( \mathbf{c} \cdot e^{x} \sin ^{2} x+C \)
D. \( e^{x} \sin 2 x+C \)
E \( \cdot e^{x}(\cos x+\sin x)+C \)
Subject: Maths
For \( n \) being natural number, if \( ^{2 n} C_{r}= \) \( ^{2 n} C_{r+2}, \) find \( r \)
A \( . n \)
B. \( n-1 \)
\( \mathbf{c} \cdot n-2 \)
D. \( n-3 \)