### Assertion & Reason Questions For Math Class 10 | Arithmetic Progression

Top of Form ASSERTION & REASON QUESTIONS CLASS 10  CHAPTER 1  REAL NUMBERS Competency based questions on ARITHMETIC PROGRESSION chapter 5 , Assertion and Reason based questions for class 10 ARITHMETIC PROGRESSION chapter 5

# Mathematics

Case study questions on Number System, Polynomials, Co-ordinate Geometry, Linear Equations in two Variables, Lines & Angles, Triangles, Quadrilaterals and Circles etc.

## CASE STUDY-1 CHAPTER -1 NUMBER SYSTEM

In a school one day the maths teacher told the students of class IX about the number systems. She drew a number line and told them that the number line represents various types of numbers on it.

Rational numbers can be represented on the number line. A number is called a rational number if it can be written in the form of p / q , where p and q are integers and q ≠ 0.

Based on the above information, answer the following questions.

Q1) A rational number between 2 and 3 is

a) 1                    b) 5/2                    c) 0                    d) ½

Q2) An irrational number between   and   is

a) 2                    b) 1                    c)                     d)

Q3) A rational number between    and  is

a)                 b)                  c) 1.5                d) 1

Q4) The product of (2 + )(2-) is

a) 4                 b) 1                    c) -1                d) 0

Q5) The    form of    is

a)                 b)                     c)                 d)

 Question Answer 1 b 2 d 3 c 4 b 5 c

## CASE STUDY-1 CHAPTER -2 POLYNOMIALS

An algebraic expression in which the exponent (Power) of the variable is a whole number (0, 1, 2, 3, ....... ) is called polynomials. Highest exponent of the variable in a polynomial is called its degree.

On the basis of above information, answer the following questions.

Q1) The degree of zero polynomial is

a) 1                b) 0                c) -1                d) not defined

Q2) The degree of a  non-zero constant polynomial is

a) 1                b) 0                c) -1                d) not defined

Q3) The coefficient of x2 in the polynomial  x3 – x2 + 2x + 1  is

a) -1                b) 1                    c) 0                        d) 2

Q4) A binomial of degree 10 is

a) x10                b) x10 + x9 + 3                c) x10 + 4                    d) x + 10

Q5) The value of the polynomial  x2 - 3x + 2 at x = -1 is

a) 0                    b) 6                    c) 5                        d) 2

 Question Answer 1 d 2 b 3 a 4 c 5 b

## LINEAR EQUATIONS IN TWO VARIABLES

Prime Minister's National Relief Fund (also called PMNRF in short) is the fund raised to provide support for people affected by natural and man-made disasters. Natural disasters that are covered under this include flood, cyclone, earthquake etc. Man-made disasters that are included are major accidents, acid attacks, riots, etc. Two friends Sita and Gita, together contributed Rs. 200 towards Prime Minister's Relief Fund. Answer the following

Q1) Which out of the following is not the linear equation in two variables ?

(a) 2x = 3

(b) x2 + x = 1

(c) 4 = 5x – 4y

(d) x – √2y = 3

Q2) How to represent the above situation in linear equations in two variables ?

(a) 2x + y = 200

(b) 200x = y

(c) x + y = 200

(d) 200 + x = y

Q3) If Sita contributed Rs. 76, then how much was contributed by Gita ?

a) Rs. 120                   b) Rs. 124                       c) Rs. 123                       d) Rs. 125

Q4) If both contributed equally, then how much is contributed by each?

(a) Rs. 50, Rs. 150

(b) Rs. 50, Rs. 50

(c) Rs. 100, Rs. 100

(d) Rs. 120, Rs. 120

Q5) Which is the standard form of linear equations x = – 5 ?

(a) x + 5 = 0

(b) 1.x – 5 = 0

(c) 1.x + 0.y + 5 = 0

(d) 1.x + 0.y = 5

 Question Answer 1 b 2 c 3 b 4 c 5 c

## LINEAR EQUATIONS IN TWO VARIABLES

Two friends Pankaj and Rohit went to a market. Pankaj bought 3 notebooks and 2 pens for Rs. 80. Rohit also bought the same types of notebooks and pens as Pankaj. He paid 110 for 4 notebooks and 3 pens.

From the above information answer the following questions

Q1) Form the pair of linear equations in two variables from this situation by taking

cost of one notebook as Rs. x and cost of one pen as Rs. y.

(a) 3x + 2y = 80 and 4x + 3y = 110

(b) 2x + 3y = 80 and 3x + 4y = 110

(c) x + y = 80 and x + y = 110

(d) 3x + 2y = 110 and 4x + 3y = 80

Solution

Here, the cost of one notebook be Rs. x and that of pen be Rs. y.

According to the statement, we have

3x + 2y = 80 and

4x + 3y = 110

Q2) Which is the solution satisfying both the equations formed in (i)?

(a) x = 10, y = 20

(b) x = 20, y = 10

(c) x = 15, y = 15

(d) none of these

Solution

3x + 2y = 3(20) + 2(10) = 60 + 20 = 80

4x + 3y = 4(20) + 3(10) = 80 + 30 = 110

Ans: (b) x = 20, y = 10

Q3) Find the cost of one pen?

(a) Rs. 20            (b) Rs. 10            (c) Rs. 5                (d) Rs. 15

Ans: (b) Rs. 10

Q4) Which is the solution satisfying both the equations formed in (i)?

(a) x = 10, y = 20

(b) x = 20, y = 10

(c) x = 15, y = 15

(d) none of these

Solution

3x + 2y = 3(20) + 2(10) = 60 + 20 = 80

4x + 3y = 4(20) + 3(10) = 80 + 30 = 110

Ans: (b) x = 20, y = 10

Q5) Find the total cost if they will purchase the same type of 15 notebooks and 12 pens.

(a) Rs. 400            (b) Rs. 350                (c) Rs. 450            (d) Rs. 420

Solution

Total cost = Rs. 15 x 20 + Rs. 12 x 10

= 300 + 120 = Rs. 420

## CASE STUDY-1 CHAPTER - 12 HERON'S FORMULA

Mohan has a piece of land in the shape of a given figure. He divides the land into two parts to produce different crops.

On the basis of the above information, answer the following questions:

Q1) The length of AC is

a) 40m                b) 50m                c) 30m                 d) 80 m

Q2) The area of △ABC is

a) 400 m2                b) 500 m2              c) 600 m2                  d) 800 m2

Q3) The area of ACD  is

a) 1000  m2            b) 500  m2                c) 1500  m2            d) 1000 m2

Q4) The cost of ploughing the land at the rate of  ₹ 20 / m2 is (Take  = 1.732)

a) ₹ 12000                b) ₹ 34640                c) ₹ 46640            d) None of these

Q5) The cost of fencing all around the land with barbed wire @ of ₹ 30 / is

a)  ₹ 6000                    b) ₹ 5000            c) ₹ 6500                d) ₹ 6600

 Question Answer 1 b 2 c 3 a 4 c 5 d

## SURFACE AREA AND VOLUME

Case Study Based Questions - 1
Mathematics teacher of a school took her 9th standard students to show Gol Gumbaz. It was a part of their educational trip. The teacher had interest in history as well. She narrated the facts of Gol Gumbaz to students. Gol Gumbaz is the tomb of king Muhammad Adil Shah, Adil Shah Dynasty. Construction of the tomb, located in Vijayapura, Karnataka, India, was started in 1626 and completed in 1656. It reaches up to 51 meters in height while the giant dome has an external diameter of 44 meters, making it one of the largest domes ever built. At each of the four corners of the cube is a dome shaped octagonal tower seven stories high with a staircase inside.

Q1) What is the total surface area of a cuboid?

a) lb + bh + hl

b) 2(lb + bh + hl)

c) 2(lb + bh)

d) 12 + b2 + h2

Q2) What is the curved surface area of hemispherical dome ?

a) 908π m2            b) 968π m2                c) 340π m2                    d) 780π m2

Q3) What is the height of the cuboidal part ?

a) 14 m                b) 7 m                c) 29 m                    d) 18 m

Q4) What is the circumference of the base of the dome ?

a) 34 π             b) 22 π             c) 44 π m                d) 55 π m

Q5) The total surface area of a hemispherical dome having radius 7 cm is

a)  462 cm2          b) 294 cm2         c) 588 cm2         d) 154 cm2

 Question Option Answer 1 b 2(lb + bh + hl) 2 b 968π m2 3 c 29 m 4 c 44 π m 5 a 462 cm2

## SURFACE AREA AND VOLUME

Mathematics teacher of a school took her 9th standard students to show Red fort. It was a part of their Educational trip. The teacher had interest in history as well. She narrated the facts of Red fort to students. Then the teacher said in this monument one can find combination of solid figures. There are 2 pillars which are cylindrical in shape. Also 2 domes at the corners which are hemispherical.7 smaller domes at the centre. Flag hoisting ceremony on Independence Day takes place near these domes.

i) How much cloth material will be required to cover 2 big domes each of radius 2.5 m Take π = 22/7

Ans: 78.57 m2

ii) Write the formula to find the volume of a cylindrical pillar.

Ans: πr2h

iii) Find the lateral surface area of two pillars if height of the pillar is 7m and radius of the base is 1.4m

Ans: 123.2 m2

iv) How much is the volume of a hemisphere if the radius of the base is 3.5m ?

Ans: 89.83 m3

v) What is the ratio of sum of volumes of two hemisphere of radius 1 cm each to the volume of a sphere of radius 2 cm ?

Ans: 1:8

## CASE STUDY-1 CHAPTER - 14 STATISTICS

Given below is the data found on a group of school going students.

 Height Intervals (in cms) No. of students 131-140 1 141-150 7 151-160 5 161-170 9 171-180 9 181-190 10 Total 41

Study the data and answer the questions that follow

Q1) Class size of third class interval is

a) 8                b) 9                    c) 9.5                    d) 10

Q2) Upper limit of 5th class interval is

a) 180                b)170.5                c) 180.5                d)179.5

Q3) Class mark of 6th  class interval is

a) 184.5            b)185                    c)185.5                    d)186

Q4) How many students have their height more than 160 cm

a) 19                b) 18                    c) 27                        d) 28

Q5) How many students have their height less than or equal to 180 cm ?

a) 31                b) 19                    c)29                        d) 22

 Question Answer 1 d 2 c 3 c 4 d 5 a

## CASE STUDY-1 CHAPTER - 15 PROBABILITY

Dice are small, throwable objects with marked sides that can rest in multiple positions. They are used for generating random numbers, commonly as part of tabletop games, including dice games, board games, role playing games and games of chance. A traditional die is a cube with each of its six faces marked with a different number of dots (pips) from one to six. When thrown or rolled, the die comes to rest showing a random integer from one to six on its upper surface, with each value being equally likely.

A die is rolled.

Q1) The probability of getting a prime number is

a)  4/6                b)  3/6                c) 2/6                d) None of these

Q2) The probability of getting a non-prime number is

a) 4/6                b) 3/6                    c) 2/6                d) 5/6

Q3) The probability of getting a composite number is

a) 4/6                b) 3/6                    c) 2/6                d) None of these

Q4) The probability of getting a divisor of 24 is

a) 3/6                b) 4/6                    c) 5/6                    d) 1

Q5) The probability of getting a number less than 8 is

a) 0                    b) 1/2                    c) 1/3                    d) 1

 Question Answer 1 b 2 b 3 c 4 c 5 d