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LAST UPDATED : 31/01/2022 | 06:30AM

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Q1. Which of the following are sets? Justify our answer.

(i) The collection of all months of a year beginning with the letter J.
(ii) The collection of ten most talented writers of India.
(iii) A team of eleven best-cricket batsmen of the world.
(iv) The collection of all boys in your class.
(v) The collection of all natural numbers less than 100.
(vi) A collection of novels written by the writer Munshi Prem Chand.
(vii) The collection of all even integers.
(viii) The collection of questions in this Chapter.
(ix) A collection of most dangerous animals of the world.
​
Q2.  If the set A has 3 elements and the set B = {3, 4, 5}, then find the number of elements in (A × B)?

Q3. Find the radian measures corresponding to the following degree measures:
(i) 25° (ii) – 47° 30′ (iii) 240° (iv) 520°.

Q4. Prove the following by using the principle of mathematical induction for all n ∈ N:

Q5. Express of the complex number given in the form a + ib.
(5i) (-3/5i)

Q6. Solve 24x < 100, when

(i) x is a natural number.
(ii) x is an integer.

Q7. How many 3-digit numbers can be formed from the digits 1, 2, 3, 4 and 5 assuming that

(i) Repetition of the digits is allowed?
(ii) Repetition of the digits is not allowed?

Q8. Expand the expressions.
(1 – 2x)5

Q9. Write the first five terms of the sequences, whose nth terms are:
an = n (n + 2) .

Q10. Draw a quadrilateral in the Cartesian plane, whose vertices are (– 4, 5), (0, 7), (5, – 5) and (– 4, –2). Also, find its area.

Q1. What is the concentration of sugar (C12H22O11) in mol L–1 if its 20 g are dissolved in enough water to make a final volume up to 2L?
​
Q2. If the density of methanol is 0.793 kg L–1, what is its volume needed for making 2.5 L of its 0.25 M solution?

Q3. (i) Calculate the number of electrons which will together weigh one gram.
(ii) Calculate the mass and charge of one mole of electrons.

Q4. What is the basic theme of organization in the periodic table?

Q5. Explain the formation of a chemical bond

Q6. Write Lewis dot symbols for atoms of the following elements :
a) Mg
b) Na
c) B
d) O
e) N
f) Br

Q7. What will be the minimum pressure required to compress 500 dm3 of air at 1 bar to 200 dm3 at 30°C?

Q8. Choose the correct answer. A thermodynamic state function is a quantity
(i) used to determine heat changes
(ii) whose value is independent of path
(iii) used to determine pressure volume work
(iv) whose value depends on temperature only

Q9. A liquid is in equilibrium with its vapour in a sealed container at a fixed temperature. The volume of the container is suddenly increased.

a) What is the initial effect of the change on vapour pressure?
b) How do rates of evaporation and condensation change initially? 
c) What happens when equilibrium is restored finally and what will be the final vapour pressure?

Q10. What is Kc for the following equilibrium when the equilibrium concentration of each substance is: [SO2]= 0.60M, [O2] = 0.82M and [SO3] = 1.90M ?
 

Q1. Some of the most profound statements on the nature of science have come from Albert Einstein, one of the greatest scientists of all time. What do you think did Einstein mean when he said: “The most incomprehensible thing about the world is that it is comprehensible”?

Q2. The length, breadth and thickness of a rectangular sheet of metal are 4.234 m, 1.005 m, and 2.01 cm respectively. Give the area and volume of the sheet to correct significant figures.

Q3. In which of the following examples of motion, can the body be considered
approximately a point object:
(a) a railway carriage moving without jerks between two stations.
(b) a monkey sitting on top of a man cycling smoothly on a circular track.
(c) a spinning cricket ball that turns sharply on hitting the ground.
(d) a tumbling beaker that has slipped off the edge of a table.

Q4. State whether the following physical quantities are scalar or vector.                  
(i) Mass
(ii) Volume
(iii) Speed
(iv) Acceleration
(v) Density
(vi) Number of moles
(vii) Velocity
(viii) Angular frequency
(ix) Displacement
(x) Angular velocity

Q5. Give the magnitude and direction of the net force acting on

(a) a drop of rain falling down with a constant speed
(b) a cork of mass 10 g floating on water
(c) a kite skillfully held stationary in the sky
(d) a car moving with a constant velocity of 30 km/h on a rough road
(e) a high-speed electron in space far from all material objects, and free of electric and magnetic fields.

Q6.The sign of work done by a force on a body is important to understand. State carefully if the following quantities are positive or negative:

(a) work done by a man in lifting a bucket out of a well by means of a rope tied to the bucket.
(b) work done by the gravitational force in the above case,
(c) work done by friction on a body sliding down an inclined plane,
(d) work done by an applied force on a body moving on a rough horizontal plane with uniform velocity,
(e) work done by the resistive force of air on a vibrating pendulum in bringing it to rest

Q7. Give the location of the centre of mass of a (i) sphere, (ii) cylinder, (iii) ring, and (iv) cube, each of uniform mass density. Does the centre of mass of a body necessarily lie inside the body?

Q8. Answer the following :
(a) You can shield a charge from electrical forces by putting it inside a hollow conductor. Can you shield a body from the gravitational influence of nearby matter by putting it inside a hollow sphere or by some other means?
(b) An astronaut inside a small space ship orbiting around the earth cannot detect gravity. If the space station orbiting around the earth has a large size, can he hope to detect gravity?
(c) If you compare the gravitational force on the earth due to the sun to that due to the moon, you would find that the Sun’s pull is greater than the moon’s pull. (you can check this yourself using the data available in the succeeding exercises). However, the tidal effect of the moon’s pull is greater than the tidal effect of the sun. Why?

Q9. A steel wire of length 4.7 m and cross-sectional area 3.0 × 10-5 m2 stretches by the same amount as a copper wire of length 3.5 m and cross-sectional area of 4.0 × 10–5 m2 under a given load. What is the ratio of Young’s modulus of steel to that of copper?

Q10. Explain why
(a) The blood pressure in humans is greater at the feet than at the brain
(b) Atmospheric pressure at a height of about 6 km decreases to nearly half of its value at the sea level, though the height of the atmosphere is more than 100 km
(c) Hydrostatic pressure is a scalar quantity even though the pressure is force divided by area
 

LAST UPDATED : 31/12/2021 | 06:30AM

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LAST UPDATED : 28/11/2021 | 06:30AM

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Twelve types of tenses in English Grammar are:

1. Present Simple
2. Present Past
3. Present Perfect
4. Present Perfect cont.
5. Past Simple
6. Past Past
7. Past Perfect
8. Past Perfect cont.
9. Future Simple
10. Future Past
11. Future Perfect
12. Future Perfect cont.

PRESENT TENSES IN ENGLISH

Present Tense Simple

Structure:

• Affirmative:  —— Subject. + V1(s/es) + Object.
• Negative: ——– Subject. + Do not/Does not + V1 + Object.
• Interrogative: ——— Do/Does + Subject. + V1 + Object. + ?

Table:

Present Continuous Tense

Structure:

• Affirmative: —— Subject. + is/are/am + V(ing) + Object..
• Negative: ——– Subject. + (Is, are, am) Not + V(ing) + Object.
• (?)——— is/are/am + Subject. + V(ing) + Object.. + ?

Table:

Present Perfect Tense

Structure:

• Affirmative: —— Subject. + Has/Have + V3 + Object..
• Negative: ——– Subject. + (Has/Have) not + V3 + Object.
• (?)——— Has/Have + Subject. + V3 + Object.. + ?

Table:

Present Perfect Continuous Tense

Structure:

• Affirmative: —— Subject. + (Has/Have) been + V(ing) + Object..
• Negative: ——– Subject. + (Has been/Have been) not + V(ing) + Object.
• Interrogative: ——— Has/Have + Subject. + been + V(ing) + Object.. + ?

Table:

PAST TENSES IN ENGLISH

Simple Past Tense

Structure:

• Affirmative: —— Subject. + V2 + Object..
• Negative: ——– Subject. + Did not + V1 + Object.
• Interrogative: ——— Did + Subject. + V1 + Object.. + ?

Table:

Past Continuous Tense

Structure:

• Affirmative: —— Subject. + was/were + V(ing) + Object..
• Negative: ——– Subject. + (was/were) Not + V(ing) + Object.
• Interrogative: ——— was/were + Subject. + V(ing) + Object.. + ?

Table:

Past Perfect Tense

Structure:

• Affirmative: —— Subject. + had + V3 + Object..
• Negative: ——– Subject. + had not + V3 + Object.
• Interrogative: ——— had + Subject. + V3 + Object.. + ?

Table:

Must Learn: Parts of Speech in English

 Past Perfect Continuous Tense

Structure:

• Affirmative: —— Subject. + had been + Verb(ing) + Object..
• Negative: ——– Subject. + had not + Verb(ing) + Object.
• Interrogative: ——— had + Subject. + been + Verb(ing) + Object.. + ?

Table:

FUTURE TENSES IN ENGLISH

Future Simple Tense

Structure:

• Affirmative: —— Subject. + will/shall + V1+ Object..
• Negative: ——– Subject. + (will/shall) not + V1 + Object.
• Interrogative: ——— will/shall + Subject. + V1 + Object.. + ?

Table:

Future Continuous Tense

Structure:

• Affirmative: —— Subject. + (will/shall) be + V(ing)+ Object..
• Negative: ——– Subject. + (will/shall) not + be + V(ing) + Object.
• Interrogative: ——— will/shall + Subject. + be + V(ing) + Object.. + ?

Table:

Future Perfect Tense

Structure:

• Affirmative: —— Subject. + (will/shall) have + V(3) + Object..
• Negative: ——– Subject. + (will/shall) + not + have + V(3) + Object.
• Interrogative: ——— will/shall + Subject. + have + V(3) + Object.. + ?

Table:

Future Perfect Continuous Tense

Structure:

• Affirmative: —— Subject. + (will/shall) have been + V(ing) + Object..
• Negative: ——– Subject. + (will/shall) + not + have been + V(ing) + Object.
• Interrogative: ——— will/shall + Subject. + have been + V(ing) + Object.. + ?

Table: