1 Probability
A room has three electric lamps. From a collection of 10 electric bulbs of which 6 are good 3 are selected at random & put in the lamps. Find the probability that the room is lighted
1)$$\displaystyle \frac {29}{30}$$
2)$$\displaystyle \frac {1}{30}$$
3)$$\displaystyle \frac {23}{30}$$
4)$$\displaystyle \frac {7}{30}$$
2 Current Electricity
A standard cell is balanced at 150 cm. height of a potentiometer wire. If this cell is shunted by a resistance of 2 Ω, the balanced position is obtained at 100 cm. length. The internal resistance of the cell will be :
(1) 2 Ω
(2) 1 Ω
(3) 0.66 Ω
(4) 0.1Ω
SOLUTION
The internal resistance of cell is given by :-
(l1?: balance length without shunt
3 Chemical Bonding and Molecular Structure
The bond order in increasing order
1) O2 < O2−1 < O2+1 < O2−2 2) O2−1 < O2+1 < O2−2 < O2 3) O2+1 < O2−2 < O2−1 < O2 4) O2−2 < O2−1 < O2 < O2+1
4 Probability
While shuffling a pack of 52 playing cards, 2 are accidentally dropped. The probability that the missing cards to be of different colours is
1) $$\dfrac {29}{52}$$ 2) $$\dfrac {1}{2}$$ 3) $$\dfrac {26}{51}$$ 4) $$\dfrac {27}{51}$$
5 Probability
One card is drawn from a well-shuffled deck of $$52$$ cards. Find the probability that the card drawn is a spade or a face card:
1) $$\displaystyle \frac{9}{26}$$ 2) $$\displaystyle \frac{3}{26}$$ 3) $$\displaystyle \frac{11}{26}$$ 4) None of these
6 Capacitance
A capacitor of capacitance 1µF . is filled with two dielectrics of dielectric constants 4 and 6. What is the new capacitance?
1) 10 µF 2) 5 µF 3) 4 µF 4) 7 µF
7 States of Matter
Some moles of O2 diffuse through a small opening in 18 second. Same number of moles of an unknown gas diffuse through the same opening in 4545 second. Molecular mass of the unknown gas is: 1) $$32\times \dfrac {(45)^{2}}{(18)^{2}}$$ 2) $$32\times \dfrac {(18)^{2}}{(45)^{2}}$$ 3) $$(32)^{2}\times \dfrac {45}{18}$$ 4) $$(32)^{2}\times \dfrac {18}{45}$$
The rate of diffusion is the ratio of number of moles diffuesd to the time taken for diffusion The rate of diffusion is inversely proportional to the square root of its molar mass. $$\displaystyle \dfrac {r_{O2}}{r_X}= \dfrac {n_{O2}}{t_{O2}} \times \dfrac {t_{X}}{n_X} =\sqrt {\dfrac {M_X}{M_{O2}}}$$ $$\displaystyle n_{O2}=n_X$$ $$\displaystyle \dfrac {n_{X}}{ 18} \times \dfrac {45}{n_X} =\sqrt {\dfrac {M_X}{32}}$$ $$\displaystyle \dfrac {45}{ 18} =\sqrt {\dfrac {M_X}{32}}$$ $$\displaystyle \dfrac {(45)^2}{ (18)^2}= \dfrac {M_X}{32}$$ The molecular mass of gas X is $$\displaystyle M_X = 32\times \dfrac {(45)^{2}}{(18)^{2}}$$ g/mol.
8 Sets relations and functions
If f(x) = tan x - tan3 x + tan5 x - ... ∞ with 0 < x < π/4, then
1) 1 2) 0 3) 1/4 4) 1/2 5) - (1/4)
9 Kinematics
An ant goes from P to R on a circular path in 20 second Radius OP=10m. What is the average speed and average velocity of it ?
1) (π/6) m/s, 3 m/s 2) (π/3) m/s, √3/2 3) (π/3) m/s,√3 4) π √6
Length of arc=(2π/3) × (op) Speed=Length of arc/ time Displacement PR From figure angle POM=60° thus PM=OPsin60 PM=10 (√3 /2) Thus PR=2PM=10( √3) Velocity=PR/time=√3/2
10 Hydrocarbons
Which of the following compounds will not undergo Friedel -Craft's reaction easily?
1) Cumene 2) Xylene 3) Nitrobenzene 4) Toluene
Nitro group being electron withdrawing, deactivates the benzene nucleus to such an extent so that it becomes incapable to give Friedel -Crafts reaction. Nitrobenzene because of its unreactivity towards Friedel-Craft's reaction is used as a solvent for this reaction.
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