### 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

# Case Study Based Questions Class 11 Mathematics

Case study questions on set theory, relations and functions, complex numbers, linear inequalities, permutations and combinations, sequence and series, and probability.

## CASE STUDY-1 CHAPTER -1 SET THEORY

In a group of 50 students, the number of students studying French, English and Sanskrit were found to be as follows:
French = 17, English = 13, Sanskrit = 15
French and English = 09, English and Sanskrit = 4
French and Sanskrit = 5, English, French and Sanskrit = 3.
Find the number of students who study :

Q 1) French only

a) 2
b) 6
c) 20
d) None of these

Q 2) English only

a) 9
b) 6
c) 1
d) 3

Q 3) Sanskrit only
a) 6
b) 12
c) 9
d) 3

Q 4) English and Sanskrit but not French
a) 2
b) 1
c) 3
d) 6

Q 5) French and Sanskrit but not English
a) 2
b) 6
c) 8
d) 10

Q 6) French and English but not Sanskrit
a) 2
b) 4
c) 6
d) 12

Q 7) At least one of the three languages
a) 2
b) 20
c) 36
d) 30
Q 8) None of the three languages
a) 30
b) 18
c) 20
d) None of these

 Question Answer 1 b 2 d 3 c 4 b 5 a 6 c 7 d 8 c

## CASE STUDY-2 CHAPTER -1 SET THEORY

Two non-empty sets A and B are given by
A = {x : x is a letter in I LOVE MATHEMATICS
B = { x : x is a letter in I LOVE STATISTICS
Based on the above information, answer the following questions.

Q 1) Which of the following is true
a) A = B
b) A ⊂ B
c) B ⊂ A
d) None of these
Q 2) A áˆ€ B is equal to
a) A
b) B
c) A ⋂ B
d) Ñ„

Q 3) A ⋂ B is equal to
a) A
b) B
c) A áˆ€ B
d) Ñ„

Q 4) B – A is equal to
a) A
b) B
c) A – B
d) Ñ„

Q 5) Number of proper subsets of set B is
a) 512
b) 511
c) 1024
d) 1023
 Question Answer 1 c 2 a 3 b 4 d 5 b

## CASE STUDY-1 CHAPTER -2 RELATIONS & FUNCTIONS

Given two non-empty set A = {x : x < 5, x ∈ N} and B = {x : x ≤ 2, x ∈ W }
Based on the above information, answer the following questions

i)  A X B as a set of ordered pair

a) {(1, 0), (1, 1), (1, 2), (2, 0), (2, 1), (2, 2), (3, 0), (3, 1), (3, 2), (4, 0), (4, 1), (4, 2)

b) {(1, 1), (1, 2), (2, 1), (2, 2), (3, 1), (3, 2),  (4, 1), (4, 2), (5, 1), (5, 2)}

c) {(1, 1), (1, 2), (2, 1), (2, 2), (3, 1), (3, 2), (4, 1), (4, 2)

d) {(1, 0), (1, 1), (1, 2), (2, 0), (2, 1), (2, 2), (3, 0), (3, 1), (3, 2), (4, 0), (4, 1), (4, 2), (5, 0), (5, 1),(5, 2)

ii)  (A áˆ€ B) X (A  B) as a set of ordered pair is

a) {(1, 0), (1, 1), (1, 2), (2, 0), (2, 1), (2, 2), (3, 0), (3, 1), (3, 2), (4, 0), (4, 1), (4, 2)

b) {(0, 1), (0, 2),  (1, 1), (1, 2), (2, 1), (2, 2), (3, 1), (3, 2), (4, 1), (4, 2)

c) {(1, 0), (1, 1), (1, 2), (2, 0), (2, 1), (2, 2), (3, 0), (3, 1), (3, 2), (4, 0), (4, 1), (4, 2), (5, 0), (5, 1), (5, 2)

d) {(1, 1),  (1, 2), (2, 1), (2, 2), (3, 1), (3, 2), (4, 1), (4, 2)

iii)  A relation R from A to B defined by

R = {(x, y): x + y = 4, x ∈ A, y ∈ B} as a set of ordered pair is

a) R = {(1, 3), (3, 1), (0, 4), (4, 0)

b)R = {(2, 2), (3, 1), (1, 3)

c) R = {(2, 2), (3, 1), (4, 0)}

d) R = {(2, 2), (1, 3), (0, 4)}

iv)  Domain of R is

a) {0, 1, 3, 4}

b) {1, 2, 3}

c) 2, 3, 4}

d) {0, 1, 2}

v)  Range of R is

a) {0, 1, 2}

b) {2, 3, 4}

c) {1, 2, 3}

d) {0, 1, 3, 4}

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

## CASE STUDY-2 CHAPTER -2 RELATIONS & FUNCTIONS

Let f and g be two real functions defined by f(x) = $\sqrt{x-1}$  and g(x) = 3-2x.
Based on the above information answer the following questions.
Q1) Domain of f is
a) (1, ∞)
b) [1, ∞)
c) (-∞, 1)
d) (-∞, 1]

Q2) Domain of  $\frac{1}{g}$  is
a) $R-\left\{\frac{3}{2} \right\}$
b) R
c)  $R-\left\{\frac{2}{3} \right\}$

d)  $R-\left\{-\frac{3}{2} \right\}$
Q3) Domain of f + g is
a) R
b) R-(1,∞)
c) [1,∞)
d)  $R-\left\{\frac{2}{3} \right\}$
Q4) Domain of   $\frac{g}{f}$
a)  (1, ∞)
b) [1, ∞)
c)   $R-\left\{\frac{3}{2} \right\}$
d) R

Q5) Domain of   $\frac{f}{g}$  is
a) $R-\left\{\frac{3}{2} \right\}$
b) R
c) $R-\left\{\frac{2}{3} \right\}$
d) $[1,\infty )-\left\{\frac{3}{2} \right\}$
 Question Answer 1 b 2 a 3 c 4 a 5 d

## CASE STUDY-1 CHAPTER -6 LINEAR INEQUALITIES

Marks obtained by Radhika in quarterly and half yearly examinations of Mathematics are 60 and 70 respectively.

Based on the above information, answer the following questions

i) Minimum marks she should get in the annual exam to have an average of at least 70 marks is

a)  80

b) 85

c) 75

d)  90

ii) Maximum marks, she should get in the annual exam to have an average of at most 75 marks is

a)  85

b) 90

c) 95

d) 80

iii)  Range of marks in annual exam, so that the average marks is at least 60 and at most 70 is

a)  [60, 70]

b) [50, 80]

c) [50, 70]

d) [60, 80]

iv)  If the average of at least 60 marks is considered pass, then minimum marks she need to score in annual exam to pass is

a) 60
b) 65
c) 70
d) 50

v)  If she scored at least 20 and at most 80 marks in annual exam, then the range of average marks is

a) [50, 70]

b) [60, 70]

c) 50, 60]

d [50, 80]

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

## PERMUTATIONS & COMBINATIONS

In a certain city all telephone numbers have seven digits. City is divided into 6 zones. Each zone is allotted a specific non-zero digit which is to be used as first digit of all telephone numbers of that zone.
Based on the above information answer the following questions.

Q1) How many different telephone numbers are there in the city zone, if the digit on first place is not used again?

Q2) How many different telephone numbers are there in the city, if there is no restriction.

Q3) How many different telephone numbers are there in each zone with all digits distinct?

Q4) How many different telephone numbers are there  in each zone if repetition of digits is allowed.

Q5) How many different telephone numbers with no restriction are there in the city, if first two digits of different zones are 12, 23, 34, 45, 56, and 67?

 Question Answer 1 96 2 $6\times 10^{6}$ 3 10P6 4 106 5 $6\times 10^{5}$

## PERMUTATIONS & COMBINATIONS

The letters of the word  " COMPUTER" are arranged in all possible ways.
Based on the above information, answer the following questions.

Q1) Find the total number of words with or without meaning that can be formed from the letters of   COMPUTER

Q2) Find the number of words in which vowels occupy odd places?

Q3) Find the number of words in which all vowels occur together?

Q4)Find the number of words starting with C and end with R ?

Q5) If all the words are arranged as in dictionary order, then the rank of the word computer is

 Question Answer 1 $^{8}P_{8}$ 2 $^{4}P_{3}\times 5!$ 3 3! X 6! 4 6! 5 1607

## SEQUENCE & SERIES

Arithmetic Progression is a sequence in which the difference of any two consecutive terms remain same throughout the sequence. Above figures are made up of squares and the count of these squares are in AP. Carefully observe above figures.

Based on the above information answer the following questions

Q1) How many squares will be in 10th figure ?

a)  17                  b)  31                  c)  34                  d) 37

Q2)  Which figure will have 79 small squares ?

a)  23rd             b)  24th                 c)  25th                 d)  26th

Q3) If each square has a side of length 0.5 cm, what will be the area of the 12th  figure ?

a)  9.75 cm2                     b) 10 cm2                         c)  10.75 cm2                        d) 11 cm2

Q4) The number of squares in the figures shown are in A. P. Which of the following will not be a part of this sequence ?

a)  67                  b)  85                  c)  93                  d)  139

Q5)  ) If the side of each  small square is 0.5 cm, what is the sum of the areas of first 10 figures ?

a)  50 cm2                        b)  51.25 cm2                   c)52.5 cm2                       d)  55 cm2

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

## SEQUENCE & SERIES

The figure shows a big triangle in which multiple other triangles are seen. Observe the pattern.

Based on the above information, answer the following questions:

Q1) How many triangles will be there in the 15th row ?
a) 28                b)  29                c) 30                   d)  31

Q2)  In which row will the number of triangles be 47 ?
a)  22                b)  23                c) 24                  d)  25

Q3)  How many small triangles will be there in the figure in 10 rows ?
a)  90                b)  100                c) 110                d)  95

Q4) The number of dark triangles in each row are in AP. The total number of dark triangles in first 15 rows is
a) 90            b) 100            c)  110            d)  120

Q 5)  The number of light triangles in each row are in AP. The number of light triangles in 20th row is
a) 20            b)  19        c) 21        d) 18

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

## SEQUENCE & SERIES

The number of bacteria in a certain culture doubles every hour. Given that the number of bacterial present at the end of 4th hour was 160000.
Based on the above information, answer the following questions.

Q1) Find the original number of bacteria?

Q2) Find the number of bacteria present at the end of 7th hour?

Q3) Find the number bacteria present at the beginning of 3rd hour was

Q4) The sum of number of bacterial present originally to the end of 8th hour is

Q5) If the number of bacteria triples every hour, then find the number of bacteria present at the end of 4th hour.

 Question Answer 1 10000 2 1280000 3 40000 4 5110000 5 810000