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1 Rotational Motion

A hoop of radius r and mass m rotating with an angular velocity ω0 is placed on a rough horizontal surface. The initial velocity of the centre of the hoop is zero. What will be the velocity of the centre of the hoop when it ceases to slip ?

1) (rω₀)/4 2) (rω₀)/3 3) (rω₀)/2 4) rω₀

Option 1

Option 2

Option 3 Solution:

SOLUTION :
From law of conservation of momentum
Li = Lf
Iω₀ = I_ω + mvr
And v = ωr
m r² ω₀ = mr²ω + mvr = 2mvr
v=(rω₀)/2

Option 4

2 Chemistry in Everyday Life

AThe artificial sweetener, which is a derivative of sucrose, is:

1) stevia

2) saccharin

3) aspartame

4) sucralose

Option 1

Option 2

Option 3

Option 4 Solution:

Solution

sucralose is derived from sucrose.

3 Basic Principles of Organic Chemistry

Which of the following isomerism is shown by ethyl acetoacetate?

1) Diastereoisomerism

2) Geometry isomerism

3) Keto-enol isomerism

4) Enantisomerism

Option 1

Option 2

Option 3 Solution:

Option 4

4 General Principles & Process of Isolation of Metals

Which one of the following reactions is an example for calcination process?

1) $$2Ag+2HCl+\left( O \right) \rightarrow 2AgCl+{ H }_{ 2 }O$$
2) $$2Zn+{ O }_{ 2 }\rightarrow 2ZnO$$
3) $$2ZnS+3{ O }_{ 2 }\rightarrow 2ZnO+2S{ O }_{ 2 }$$
4) $$MgC{ O }_{ 3 }\rightarrow MgO+C{ O }_{ 2 }$$

Option 1

Option 2

Option 3

Option 4 Solution:

Solution

The concentrated ore is heated in absence of air to remove water or moisture from a hydrated oxide and $$CO_2$$ from a carbonate ore at a temperature below their melting point. This process is called calcination and it is generally carried out in a reverberatory furnace.

$$MgCO_3 \rightarrow MgO + CO_2$$

5 Limits Continuity and Differentiability

For the function which of the following is incorrect?

1) Continuous at x=1
2) Continuous at x=3
3) Derivable at x =1
4) Derivable at x =3

Option 1

Option 2

Option 3

Option 4 Solution:

SOLUTION

6 Classification of Elements and Periodicity

The ions O²⁻, F⁻, Na⁺, Mg²⁺ and Al³⁺ are isoelecronic. Their ionic radii show:

1) a significant increase from O²⁻ to Al³⁺
2) a significant decrease from O²⁻ to Al³⁺
3) an increase from O²⁻ to F⁻ and then decrease from Na⁺ to Al³⁺
4) an decrease from O²⁻ to F⁻ and then increase from Na⁺ to Al³⁺

Option 1

Option 2 Solution:

SOLUTION

As all the given species are iso electronic, the ionic radii decreases with increasing atomic number as effective nuclear charge increases. Hence from O²⁻ to Al³⁺, the size decreases significantly

Option 3

Option 4

7 Haloalkanes and Haloarenes

The reaction of 1-hexene with HBr in presence of peroxide yields 1-bromo cyclohexane. The mechanism of the reaction involves :

1 attack on alkene by a Br+ ion
2) attack on alkene by a bromide ion
3) attack on alkene by a bromine free radical
4) None of these

Option 1

Option 2

Option 3 Solution:

SOLUTION

The reaction of 1-Hexene with HBr in presence of peroxide yields 1-bromo cyclohexane.

The mechanism of the reaction involves an attack on alkene by a bromine atom. The reaction proceeds through a free radical mechanism.

In the presence of peroxide, bromine free radical is generated. This bromine free radical then attacks alkene.

Option 4

8 Probability

A pair of fair dice is thrown independently three times. The probability of getting a score of exactly 9 twice is

1) 8/729
2) 8/243
3) 1/729
4) 8/9

Option 1

Option 2 Solution:

Solution

P(a) = 4/36 = 1/9

Required probability = 3C2 × (1/9)² x 8/9 = 8 /243

Option 3

Option 4

9 Basic Concepts of Chemistry

A gaseous mixture contains CH4 and C2H6 in equimolar proportion. The weight of 2.24 litres of this mixture at NTP is ..
1) 4.6g
2) 1.6g
3) 2.3g
4) 23g

Option 1

Option 2

Option 3 Solution:

Solution

equimolar will occupy same volume i.e. 1.12 L each
22.4 L=1 mole
1.12 L=0.05 mole
Molecular weight of CH4=16g, ∴0.05 mole=0.8 g
Molecular weight of C2H6=30g, ∴ 0.05mole=1.5g
Total weight=0.8 +1.5=2.33g

Option 4

10 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)$$\displaystyle \frac {7}{30}$$

Option 1 Solution:

Solution

A room has $$3$$ electric lamps.

Out of $$10$$ bulbs present, $$6$$ bulbs are good.
$$\Rightarrow$$ $$4$$ bulbs are defective.
The probability that selected $$3$$ bulbs are good $$=1-$$ (Probability that selected $$3$$ bulbs are defective)
$$=1-\displaystyle\dfrac{{}^{4}C_{3}}{{}^{10}C_{3}}$$
$$=1-\displaystyle\dfrac{(4\times 3\times 2)}{(10\times 9\times 8)}=1-\dfrac{1}{30}$$
$$=\displaystyle\frac{29}{30}$$

Option 2

Option 3

Option 4

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