AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Physics
A capillary tube when immersed vertically in a liquid rises to \( 3 \mathrm{cm} \). If the tube is held immersed in the liquid at
an angle of \( 60^{\circ} \) with the vertical,the length of the liquid column along the tube will be:
A. \( 2 \mathrm{cm} \)
B. 4.5 \( \mathrm{cm} \)
\( \mathrm{c} \cdot 6 \mathrm{cm} \)
D. 7.5 \( \mathrm{cm} \)
Subject: Chemistry
These ions differ in their number of
electrons by eight :
A. \( M g^{+} \) and \( F^{+} \)
B. \( L i^{+} \) and \( N e \)
\( c \cdot O^{2-} \) and \( O^{-} \)
D. \( N \) and \( P^{3-} \)
E \( \cdot C a^{2+} \) and \( C l \)
Subject: Physics
A pith ball of mass \( 9 \times 10^{-5} k g \) carries a
charge of \( 5 \mu C \). What must be charge on
another pith ball placed directly \( 2 \mathrm{cm} \) above the pith ball such that they are held in equilibrium?
A . \( 3.2 \times 10^{-11} C \)
B . \( 7.84 \times 10^{-12} C \)
c. \( 1.2 \times 10^{-13} C \)
D. \( 1.6 \times 10^{-19} C \)
Subject: Physics
A particle moves along with x-axis. The position \( x \) of article with respect to time \( \mathrm{t} \) from origin given by \( \boldsymbol{x}=\boldsymbol{b}^{0}+\boldsymbol{b}_{1} \boldsymbol{t}+ \)
\( b_{2} t^{2} . \) The acceleration of particle is:
\( A \cdot b_{0} \)
в. \( b_{1} \)
\( c \cdot b_{2} \)
D. \( 2 b_{2} \)
Subject: Chemistry
The thermo-chemical equation for solid and liquid rocket fuel are given below:
\( \mathbf{2} A l(s)+\mathbf{1} \frac{1}{2} O_{2}(g) \longrightarrow \)
\( \boldsymbol{A l}_{2} \boldsymbol{O}_{3}(\boldsymbol{s}), \boldsymbol{\Delta} \boldsymbol{H}=-\mathbf{1 6 6 7} . \boldsymbol{8 k} \boldsymbol{J} \)
\( \boldsymbol{H}_{2}(\boldsymbol{g})+\frac{1}{2} \boldsymbol{O}_{2}(\boldsymbol{g}) \longrightarrow \boldsymbol{H}_{2} \boldsymbol{O}(\boldsymbol{l}), \boldsymbol{\Delta} \boldsymbol{H}= \)
\( -285.9 k J \)
Then, \( \Delta H \) for the reaction:
\( A l_{2} O_{3}(s) \longrightarrow 2 A l(s)+1 \frac{1}{2} O_{2}(g) \) is :
A. \( 1667.8 \mathrm{kJmol}^{-1} \)
B. \( 1222.3 \mathrm{kJmol}^{-1} \)
c. \( 1458.2 \mathrm{kJmol}^{-1} \)
D. \( 1785.3 \mathrm{kJmol}^{-1} \)
Subject: Maths
If \( \left(a b^{-1}\right)^{2 x-1}=\left(b a^{-1}\right)^{x-2}, \) then what is
the value of \( x ? \)
\( \mathbf{A} \cdot \mathbf{1} \)
B . 2
\( c .3 \)
D.
Subject: Physics
Mars has about \( \left(\frac{1}{10}\right)^{t h} \) as much mass as the Earth and half as a diameter of
earth. The acceleration of failing body on Mars is nearly:
\( \mathbf{A} \cdot 9.8 m s^{-2} \)
B . \( 1.96 \mathrm{ms}^{-2} \)
D. \( 4.9 \mathrm{ms}^{-2} \)
Subject: Maths
If both \( \alpha, \beta \) and \( 6 x^{2}+11 x+3=0 \) are
real roots of the equation then
A. both \( \cos ^{-1} \alpha \) and \( \cos ^{-1} \beta \) are real
B. both \( \operatorname{cosec}^{-1} \alpha \) and \( \cos ^{-1} \beta \) are real
C. both \( \cot ^{-1} \alpha \) and \( \cot ^{-1} \beta \) are real
D. none of these
Subject: Maths
Mean of marks obtained by 10 students
is 30
Marks obtained are
\( \mathbf{2 5}, \mathbf{3 0}, \mathbf{2 1}, \mathbf{5 5}, \mathbf{4 7}, \mathbf{1 0}, \mathbf{1 5}, \boldsymbol{x}, \mathbf{4 5}, \mathbf{3 5} \)
Find the value of \( x \)
A . 25
B. 37
c. 69
D. 17
Subject: Biology
toppr
-०६ा॥
Q Type your question
energy in a rooa cnaın. Eacn trophic level in the food chain is
represented by a bar in the pyramid,
with primary producers forming the
foundation of the pyramid. The size of
each block represents the productivity at each trophic level per unit of time.
In the above example, approximately
how much energy available in each
trophic level is converted into new
biomass in the trophic level above it?
\( \mathbf{A} \cdot 1 \% \)
B . \( 5 \% \)
c. \( 10 \% \)
D. \( 50 \% \)
E . \( 100 \% \)
Subject: Maths
Find the distances between the
following pair of parallel lines:
\( \mathbf{3} \boldsymbol{x}+\mathbf{4} \boldsymbol{y}+\mathbf{9}=\mathbf{0}, \mathbf{6} \boldsymbol{x}+\mathbf{8} \boldsymbol{y}+\mathbf{1 5}=\mathbf{0} \)
A \( \cdot \frac{3}{10} \)
B. \( \frac{3}{5} \)
c. \( \frac{33}{10} \)
D. \( \frac{24}{5} \)
Subject: Chemistry
The standard reduction potential of normal calomel electrode and reduction
potential of saturated calomel
electrodes are 0.27 and 0.33 volt
respectively. What is the concentration
of \( C l^{-} \) in saturated solution of \( K C l ? \)
A . \( 0.1 M \)
в. \( 0.01 M \)
c. \( 0.001 M \)
D. None
Subject: Physics
For a capacitor, distance between the plates \( =d, \) p.d between the plates \( = \)
\( \boldsymbol{V}, \boldsymbol{k}=\mathbf{1}, \) area of each plate \( =\boldsymbol{A} \) and
electric field between the plates \( =E \)
For another capacitor distance between
plates \( =\boldsymbol{d}, \) p.d between plates \( = \)
\( V, k=2, \) area of each plate \( =2 A \) and
electric field between the plates \( =\boldsymbol{E}^{1} \)
Relation between \( E \) and \( E^{1} \) is:
\( \mathbf{A} \cdot E^{1}=E / 4 \)
B . \( E^{1}=E / 2 \)
c. \( E^{1}=E \)
D. \( E^{1}=4 E \)
Subject: Maths
If \( 0 \leq x, y \leq 180^{\circ} \) and \( \sin (x-y)= \)
\( \cos (x+y)=\frac{1}{2}, \) then the values of \( x \)
and \( y \) are given by This question has multiple correct options
A. \( x=45^{\circ}, y=15^{\circ} \)
В. \( x=45^{\circ}, y=135^{\circ} \)
c. \( x=165^{\circ}, y=15^{\circ} \)
D. \( x=165^{\circ}, y=135^{\circ} \)
Subject: Physics
A person standing on a road has to hold
his umbrella at \( 60^{\circ} \) with the vertical to
keep the rain away. He throws the
umbrella and starts running at \( 20 m s^{-1} \)
He find that rain drops are hitting his head vertically. Find the speed of the rain drops with respect to (a) the road
and
(b) the moving person.
Subject: Chemistry
Calculate \( \Delta H_{f}^{o} \) for chloride ion from the following data:
\[
\begin{array}{l}
\frac{1}{2} H_{2}(g)+\frac{1}{2} C l_{2}(g \longrightarrow H C l(g) ; \Delta H= \\
-92.4 k J \quad m o l^{-1} \\
H C l(g)+n H_{2} O \longrightarrow H^{+}(a q .)+ \\
C l^{-}(a q .) ; \Delta H=-74.8 k J \quad m o l^{-1} \\
\quad \Delta H_{f\left(H^{+}(a q .)\right.}^{o}=0.0 k J \quad m o l^{-1}
\end{array}
\]
A \( .-167 k J \mathrm{mol}^{-} \)
в. 267 k \( J \) mol \( ^{-1} \)
\( \mathbf{c} \cdot 167 k J \operatorname{mol}^{-1} \)
D. \( -267 k J \mathrm{mol}^{-1} \)
Subject: Maths
if \( x_{1}, x_{2}, x_{3} \dots x_{n} \) denote the values of \( x \)
where \( f(x) \) vanishes such that \( x_{1}> \)
\( x_{2}>x_{3} \ldots x_{n}, \) then \( \lim _{n \rightarrow \infty} \sum_{r=1}^{n} \frac{r}{x_{r}} \) is equal to
A . -8
B. -4
\( c .-2 \)
D. -
Subject: Physics
In the given circuit, the value of resistance effect of the coil Lis exactly
equal to the resistance R. Bulbs B1 and B2 are exactly identical. Answer the following question.
a) Which one of the two bulbs lights up earlier, when key k is closed and why?
b) What will be the comparative brightness of the two bulbs after sometime if the key \( \mathrm{K} \) is kept closed
and why?
Subject: Maths
Let \( A B C D E F \) be a convex hexagon in which the diagonals \( A D, B E, C F \) are
concurrent at \( O . \) Suppose the area of
triangle \( O A F \) is the geometric mean of
those of \( O A B \) and \( O E F ; \) and the area
of triangle \( O B C \) is the geometric mean
of those of \( \boldsymbol{O} \boldsymbol{A} \boldsymbol{B} \) and \( \boldsymbol{O} \boldsymbol{C} \boldsymbol{D} \). Prove that
the area of triangle \( O E D \) is the
geometric mean of those of \( O C D \) and
OEF.
Subject: Physics
The nature of the image of a candle flame located \( 40 \mathrm{cm} \) from a concave
mirror is real, inverted and magnitude
four times. Then the radius of curvature
of the mirror is:
\( \mathbf{A} \cdot 32 c m \)
B. \( 64 \mathrm{cm} \)
\( \mathbf{c} \cdot 48 c m \)
D. \( 80 \mathrm{cm} \)
Subject: Biology
Assume that blue flowered plant is dominant character over the white.
When a blue flowered plant is crossed
with its white flowered plant, the
progeny showed \( 50 \% \) of plants with blue flowers is with white flowers. The
genotypes of blue and white parents respectively are
\( A \cdot b b, b b \)
B. ВВ, Вь
\( c \cdot B B, b b \)
D. Bb, bb
Subject: Chemistry
Identify electron-donating groups in resonance among the following:(A)
\( -\boldsymbol{C O N H}_{2}(\mathrm{B})-\boldsymbol{N O}_{2} \)
\( (\mathrm{C})-\mathrm{O} \mathrm{COCH}_{3} \)
(D) \( -\boldsymbol{C O C H}_{3} \)
\( -\boldsymbol{C H O}(\mathrm{F})-\boldsymbol{N} \boldsymbol{H} \boldsymbol{C O C H}_{3} \)
Subject: Physics
A cord is used to lower vertically a block
of mass \( M \) by a distance \( d \) with
constant downward acceleration \( \boldsymbol{g} / \mathbf{4} \) Work done by the cord on the block is:
A \( \cdot_{M g} \frac{d}{4} \)
в. \( 3 M g \frac{d}{4} \)
c. \( _{-3 M g_{\overline{4}}^{d}} \)
D. \( M g d \)
Subject: Maths
Find the area of the triangle formed by
the lines
\( \boldsymbol{a} \boldsymbol{x}^{2}+\boldsymbol{2 h} \boldsymbol{x} \boldsymbol{y}+\boldsymbol{b} \boldsymbol{y}^{2} \) and \( \boldsymbol{l} \boldsymbol{x}+\boldsymbol{m} \boldsymbol{y}+\boldsymbol{n}= \)
0
Subject: Physics
A capillary tube is immersed vertically
in water and the height of the water
column is \( x \). When this arrangement is
taken into a mine of depth \( d \), the height
of the water column is \( y . \) If \( R \) is the radius of the earth, the ratio \( \frac{x}{y} \) is :
A \( \cdot\left(1-\frac{d}{R}\right) \)
B \( \cdot\left(1-\frac{2 d}{R}\right) \)
c. \( \left(\frac{R-d}{R+d}\right) \)
D. \( \left(\frac{R+d}{R-d}\right) \)
Subject: Maths
If \( P(x, y, z) \) is a point on the line segment joining \( A(2,2,4) \) and \( B(3,5,6) \) such that projection of \( \overline{O P} \) on axes are \( \frac{13}{5}, \frac{19}{5}, \frac{26}{5} \) respectively, then \( P \) divide \( A B \) in the ratio
A .3: 2
B. 2: 3
c. 1: 2
D. 1: 3
Subject: Maths
The function \( \boldsymbol{f}(\boldsymbol{x})=\boldsymbol{a} \boldsymbol{x}+\boldsymbol{b} \) is strictly
increasing for all real \( \boldsymbol{x} \), if
\( \mathbf{A} \cdot a>0 \)
B. \( a<0 \)
\( \mathbf{c} \cdot a=0 \)
D. \( a \leq 0 \)
Subject: Physics
A horizontal circular platform of radius
\( 0.5 m \) and mass \( 0.45 k g \) is free to rotate
about its axis. Two massless spring toyguns, each carrying a steel ball of mass \( 0.05 k g \) are attached to the platform at a distance \( 0.25 m \) from the centre on its
either sides along its diameter (see figure). Each gun simultaneously fires the ball horizontally and perpendicular to the diameter in opposite directions. After leaving the platform, the ball have horizontal speed of \( 9 m s^{-1} \) with respect to the ground. The rotational speed of
the platform in \( r a d s^{-1} \) after the balls
leave the platform is :
Subject: Maths
Two complex numbers are represented by ordered pairs \( z_{1}:(2,4) \& z_{2}:(-4,5) \)
which of the following is real part for
\( \boldsymbol{z}_{1} \times \boldsymbol{z}_{2}=? \)
A . -6
B. -28
\( c \cdot 6 \)
D. None of these
Subject: Physics
Find the maximum possible percentage
error in the measurement of force on an
object(on mass \( \mathrm{m} \) ) travelling at velocity vin a circle of radius \( r, \) if \( m=(4.0 \) plus minus 0.1 ) \( \mathrm{kg}, \mathrm{v}=(10 \text { plus minus } 0.1) \mathrm{m} / \mathrm{s} \) and \( r=(8.0 \text { plus minus } 0.2) m \)
A. \( (50 \pm 1) \mathrm{N} \)
B. ( 50 ±2.5 ) N
c. \( (50 \pm 1.5) \mathrm{N} \)
D. \( (50 \pm 3.5) \) N
Subject: Maths
\( \mathbf{I f A}=\left\{\begin{array}{ccc}\mathbf{2} & \boldsymbol{x}-\mathbf{3} & \boldsymbol{x}-\mathbf{2} \\ \mathbf{3} & \mathbf{- 2} & \mathbf{- 1} \\ \mathbf{4} & \mathbf{- 1} & \mathbf{- 5}\end{array}\right\} \) is a
symmetric matrix then
\( A \cdot 0 \)
B. 3
\( c .6 \)
\( D \)
Subject: Maths
If \( f(x)=\left\{\begin{array}{ll}x^{2} & \text { for } 0 \leq x \leq 1 \\ \sqrt{x} & \text { for } 1 \leq x \leq 2\end{array} \) then \right.
\( \int_{0}^{2} f(x) d x= \)
A \( \cdot(1 / 3)(4 \sqrt{2}+1) \)
B. \( (1 / 3)(4 \sqrt{2}-1) \)
c. \( (1 / 3)(2 \sqrt{2}-1) \)
(年) \( (1 / 3)(2 \sqrt{2}-1)(\sqrt{2}-1) \)
D. \( (1 / 2)(3 \sqrt{2}-1) \)
Subject: Physics
A spherical ball of diameter \( 1 \mathrm{cm} \) and
density \( 5 \times 10^{3} \mathrm{kg} m^{-3} \) is dropped
gently in a large tank containing viscous liquid of density \( 3 \times 10^{3} \mathrm{kg} m^{-3} \)
and coefficient of viscosity \( 0.1 \mathrm{Ns} m^{-2} \)
The distance, the ball moves in 1 s after
attaining terminal velocity is \( (\boldsymbol{g}= \) \( \left.10 m s^{-2}\right) \)
A \( \cdot \frac{10}{9} \mathrm{m} \)
в. \( \frac{2}{3} \) m
c. \( \frac{4}{9} \mathrm{m} \)
D. \( \frac{4}{5} \mathrm{m} \)
E \( \cdot \frac{9}{10} \mathrm{m} \)
Subject: Physics
A small planet is revolving around a very massive star in a circular orbit of
radius R with a period of revolution T. If the gravitational force between the planet and the star were proportional to \( R^{-5 / 2}, \) then \( T \) would be proportional to
A \( \cdot R^{3 / 2} \)
B. \( R^{3 / 5} \)
c. \( R^{7 / 2} \)
D. \( R^{7 / 4} \)
Subject: Physics
In the relation, \( \boldsymbol{P}=\frac{\boldsymbol{\alpha}}{\boldsymbol{\beta}} \boldsymbol{e}^{\boldsymbol{\alpha} \boldsymbol{z} / k \boldsymbol{\theta}} \boldsymbol{P} \) is
pressure, \( Z \) is distance, \( K \) is Boltzmann
constant and \( \theta \) is the temperature. The
dimensions of \( \beta \) will be
A \( \cdot\left[M^{\circ} L^{2} T^{0}\right] \)
в. \( \left[M L^{2} T\right] \)
\( \mathbf{c} \cdot\left[M L^{\circ} T^{1}\right] \)
D. \( \left[M^{\circ} L^{2} T^{-1}\right] \)
Subject: Maths
The value of
\( \left(10^{11}-10^{9}-2 \times 11 \times 10^{8}-3 \times 11^{2} \times\right. \)
is equal to
\( \mathbf{A} \cdot \mathbf{0} \)
B. \( 11^{10} \)
\( c \cdot 11^{11} \)
D. \( 10^{11} \)
Subject: Biology
Which one represents pulmonary
circulation?
A. Left auricle (oxygenated blood) \( \rightarrow \) lungs (deoxygenated blood) \( \rightarrow \) Right auricle
B. Left auricle (deoxygenated blood) \( \rightarrow \) lungs (oxygenated blood) \( \rightarrow \) Right auricle
C. Left auricle (oxygenated blood) \( \rightarrow \) lungs (deoxygenated blood) \( \rightarrow \) Left auricle
D. Right auricle (deoxygenated blood) \( \rightarrow \) lungs (oxygenated blood) \( \rightarrow \) Left auricle
Subject: Physics
For a current carrying inductor, emf associated in \( 20 m V . \) Now, current
through it changes from \( 6 A \) to \( 2 A \) in \( 2 s \) The coefficient of mutual inductance is
\( \mathbf{A} \cdot 20 m H \)
в. \( 10 m H \)
\( \mathbf{c} \cdot 1 m H \)
D. \( 2 m H \)
Subject: Maths
A bag contains four tickets numbered
\( 00,01,10,11 . \) Four tickets are chosen at
random with replacement, the probability that the sum of the numbers on the tickets is \( 23, \) is
A \( .3 / 32 \)
в. \( 1 / 64 \)
c. \( 5 / 256 \)
D. \( 7 / 256 \)
Subject: Physics
The resistance of \( 10 \mathrm{m} \) long
potentiometer wire is \( 20 \Omega \). It is connected in series with a 3 V battery
and \( 10 \Omega \) resistor. The potential
difference between two points
separated by distance \( 30 \mathrm{cm} \) is equal to
A . \( 0.02 \mathrm{V} \)
B. \( 0.06 \mathrm{V} \)
c. \( 0.1 \mathrm{v} \)
D. 1.2v
Subject: Maths
Find the \( n^{t h} \) term and the \( 7^{t h} \) term of
\( \mathbf{3},-\mathbf{6},+\mathbf{1 2},-\mathbf{2 4}, \ldots \)
A . 191
в. 193
\( c \cdot 192 \)
D. 194
Subject: Biology
From which of the following crosses, \( \boldsymbol{F}_{1} \)
progeny showing maximum hybrid vigour can be obtained?
(1) \( A A b b \times a a B B \)
(II) \( A A b b \times a a b b \)
\( (\| I) \) aaBB \( \times \) aabb
\( (I V) A A B B \times \)
aabb
A \( . \) (II), (III)
B. (III), (IV)
\( c \cdot(1),(1 v) \)
D. (I), (II)
Subject: Physics
In winter season, a mild spark is often
seen when a man touches somebody
else's skin.Why?
A. Due to lack of humidity and rubbing with clothes, charge accumulate on human body which is discharged via sparking
B. Due to cold, electrostatic charge on body finds a lower resistance path to the skin of other's body
C. The static charge on sweaters worn by the two persons is different, hence discharge through sparking occurs
D. Similar to the lightning, extremely high potential exists on both the bodies and hence they discharge through sparking
Subject: Physics
A current of one ampere is passed
through a straight wire of length 2 metre. The magnetic field at a point in
air at a distance of \( 3 \mathrm{m} \) from one end of
the wire but lying on the axis of the wire will be:
A \( \cdot \mu_{0} / 2 \pi \)
B . \( \mu_{0} / 4 \pi \)
c. \( \mu_{0} / 8 \pi \)
D. zero
Subject: Chemistry
Which of the following complex ion has least stability?
A \( \cdot\left[\operatorname{Co}\left(N H_{2}\right)_{6}\right]^{2+} \)
в. \( \left[\operatorname{Co}(C N)_{6}\right]^{3-} \)
c. \( \left[\operatorname{Co}\left(N H_{3}\right)_{6}\right]^{3} \)
D \( \cdot\left[C o(C O)_{6}\right]^{3+} \)
Subject: Maths
The median of the observations
arranged in increasing order is \( 26 . \) Find
the value of \( x \)
\( \mathbf{1 0}, \mathbf{1 7}, \mathbf{2 2}, \boldsymbol{x}+\mathbf{2}, \boldsymbol{x}+\mathbf{4}, \mathbf{3 0}, \mathbf{3 6}, \mathbf{4 0} \)
Subject: Chemistry
The above laboratory setup can be used to prepare which of the following?
I. \( C O_{2}(g) \)
Il. \( \boldsymbol{H}_{2}(\boldsymbol{g}) \)
III. \( O_{2}(g) \)
A . I only
B. III only
c. I and III only
D. II and III only
E . I, II, and III
Subject: Chemistry
Which of the following reactions is not
correctly matched?
A \( \cdot 2 C_{2} H_{5} B r+2 N a \stackrel{\text {dry ether}}{\longrightarrow} C_{4} H_{1} 0+2 N a B r \)
Wurtz reaction
B . \( C H_{3} B r+A g F \stackrel{C}{\longrightarrow} H_{3} F+A g B r \)
Etards reaction
\( \mathbf{c} \cdot C_{5} H_{6} B r+2 N a+B r C_{2} H_{5} \stackrel{\text {dry ether}}{\longrightarrow} C_{6} H_{5} C_{2} H_{5}+ \)
\( N a B r \)
Wurtz fitting reaction
D \( \cdot 2 C_{6} H_{5} B r+2 N a \stackrel{\text {dryether}}{\longrightarrow} C_{6} H_{5} C_{6} H_{5}+2 N a B r \)
Fitting reaction
Subject: Chemistry
When a Dobereiner's triad is
considered, the sum of atomic weights of the terminal elements \( X \) and \( Z \) is
162.5. The atomic weight of \( Z \) is 50 units
less than 5 times that of \( X \). Identify the
periods of \( X, Y \) and \( Z \) respectively in the present periodic table.
A. 3,4,5
в. 4,5,6
c. 2,3,4
D. 3,5,4
Subject: Chemistry
Assertion
A mixture of o- nitrophenol and \( p \) nitrophenol can be separated by steam distillation.
Reason
p-nitrophenol is steam volatile whereas o-nitrophenol is not steam volatile.
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
The threshold frequency of a metal corresponds to the wavelength of \( x n m \) In two separate experiments \( A \) and \( B \), incident radiations of wavelengths \( 1 / 2 x \) nm and \( 1 / 4 \times \) nm respectively are used. The ratio of kinetic energy of the released electrons in experiment B to that in experiment \( A \) is:
\( A \cdot 1 / 3 \)
B. 2
\( c \cdot 4 \)
\( D .3 \)
E. \( 1 / 2 \)
Subject: Physics
Assertion
In SHM let \( x \) be the maximum speed, \( y \)
the frequency of oscillation and \( z \) the maximum acceleration then \( \frac{x y}{z} \) is a
constant quantity.
Reason
This is because \( \frac{x y}{z} \) becomes a
dimensionless quantity
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
ABCD is a rectangle in which \( A B=10 \) \( \mathrm{cms}, \mathrm{BC}=8 \mathrm{cms} . \) A point \( \mathrm{P} \) is taken on
AB such that \( P A=x \). Then the minimum
value of \( P C^{2}+P D^{2} \) is obtained when \( x \)
\( = \)
A . 10
B. 5
\( c \cdot 8 \)
D. 4
Subject: Maths
If \( P(E) \) denotes the probability of an event \( \mathrm{E} \), then
A. \( P(E)<0 \)
В. \( P(E)>1 \)
c. \( 0 \leq P(E) \leq 1 \)
D. \( -1 \leq P(E) \leq 1 \)
Subject: Maths
Length of the latusrectum of the
hyperbola \( \boldsymbol{x} \boldsymbol{y}=\boldsymbol{c}, \) is equal to
A \( .2 c \)
B. \( \sqrt{2} c \)
c. \( 2 \sqrt{2} c \)
D. \( 4 c \)
Subject: Maths
In triangle \( A B C \), the medians intersect
at point \( G . \) Suppose \( \angle A B C=90^{\circ} \) and
\( \angle B A C+\angle B G C=180^{\circ} . \) Find the value
of \( \cos \angle A C B \)
A \( \cdot \frac{\sqrt{2}}{\sqrt{3}} \)
B. \( \frac{\sqrt{2}}{\sqrt{5}} \)
c. \( \frac{2}{\sqrt{5}} \)
D. None of these
Subject: Physics
Q Type your question
shown in figure are connected at one
end to a charged capacitor through a
switch \( S, \) which initially open. At the
other end, they are connected by a loose
wire. The capacitor has charge \( Q \) and
mass per unit length of the rod is \( \lambda \). The
effective resistance of the circuit after
closing the switch is \( R \). If the velocity of
each rod when the capacitor is discharged after closing the switch is \( \boldsymbol{v}=\frac{\boldsymbol{\mu}_{0} \boldsymbol{Q}^{2}}{\boldsymbol{x} \pi \boldsymbol{d} \boldsymbol{R} \boldsymbol{\lambda} \boldsymbol{l}} . \) Find \( \boldsymbol{x} \)
(Assume that the displacement of rods during the discharging time is
negligible)
Subject: Chemistry
The composition in brown ring test is :
\( \mathbf{A} \cdot\left[F e\left(H_{2} O\right)_{6} N O\right] S O_{4} \)
\( \mathbf{B} \cdot\left[F e\left(H_{2} O\right)_{5} N O\right] S O_{4} \)
\( \mathbf{c} \cdot\left[F e\left(H_{2} O\right)_{4}(N O)_{2}\right] S O_{4} \)
\( \mathbf{D} \cdot\left[F e\left(H_{2} O\right)_{3} N O\right] S O_{4} \)
Subject: Chemistry
In the following reaction, \( P \) gives two
products \( Q \) and \( R \), each in \( 40 \% \) yield
f the reaction is carried out with
\( 420 m g \) of \( P . \) the reaction yields
\( 108.8 m g \) of \( Q . \) The amount of \( R \)
produced in the reaction is closest to:
A. \( 97.6 \mathrm{mg} \)
B. \( 108.8 \mathrm{mg} \)
c. \( 84.8 \mathrm{mg} \)
D. \( 121.6 \mathrm{mg} \)
Subject: Maths
The remainder obtained when \( t^{6}+ \)
\( 3 t^{2}+10 \) is divided by \( t^{3}+1 \) is
A \( \cdot t^{2}-11 \)
B . \( 3 t^{2}+11 \)
\( \mathbf{c} \cdot t^{3}-1 \)
D. \( 1-t^{3} \)
Subject: Chemistry
Matte is a mixture of :
\( \mathbf{A} \cdot C u_{2} S+F e S(\mathrm{small} \text { amount }) \)
B \( \cdot F e S+C u_{2} S \) (small amount)
\( \mathrm{c} \cdot \mathrm{Cu}_{2} \mathrm{O}+\mathrm{FeO} \) (small amount)
D. \( F e O+C u_{2} O \) (small amount)
Subject: Chemistry
(a)Account for the following:
(i)Acidic character increase from \( \boldsymbol{H} \boldsymbol{F} \)
to \( H I \)
(ii)There is a large difference between the melting and boiling points of oxygen and sulphur.
(iii) Nitrogen does not form pentahalide.
(b) Draw the structures of the following:
(i) \( C l F_{3} \)
(ii) \( \boldsymbol{X} \boldsymbol{e} \boldsymbol{F}_{\boldsymbol{4}} \)
Subject: Maths
\( \bar{a} \) and \( \bar{b} \) are non-zero vectors such that
\( \bar{a} \times \bar{b}=\bar{b} \times \bar{a} \) then \( \bar{b}, \bar{a} \) are
A. this result is always true
B. this result is impossible
c. parallel to each other
D. perpendicular to each other
Subject: Maths
Place the elements of the following sets
in the proper location on the given Venn
diagram.
\( \boldsymbol{U}=\{\mathbf{5}, \mathbf{6}, \mathbf{7}, \mathbf{8}, \mathbf{9}, \mathbf{1 0}, \mathbf{1 1}, \mathbf{1 2}, \mathbf{1 3}\} \)
\( M=\{5,8,10,11\}, N=\{5,6,7,9,10\} \)
Subject: Maths
Give a non-empty set \( X . \) Consider \( P(X) \) which is the set of all subsets of \( \boldsymbol{X} \)
Define the relation \( R \) in \( P(X) \) as follows:
For subsets \( \boldsymbol{A} \) and \( \boldsymbol{B} \) in \( \boldsymbol{P}(\boldsymbol{X}), \boldsymbol{A} \boldsymbol{R} \boldsymbol{B} \) if
\( \boldsymbol{A} \subset \boldsymbol{B}, \) is \( \boldsymbol{R} \) an equivalence relation on
\( \boldsymbol{P}(\boldsymbol{X}) ? \)
Justify your answer.
Subject: Maths
The polynomial \( \boldsymbol{p}(\boldsymbol{x})=\boldsymbol{a} \boldsymbol{x}^{3}+\boldsymbol{4} \boldsymbol{x}^{2}+ \)
\( 3 x-4 \) and \( q(x)=x^{3}-4 x+a \) leave
same remainder when divided by
\( (x-3) . \) Find \( a \) and hence find the
remainder when \( p(x) \) is divided by
\( (x-2) \)