Category: Class 11 Mathematics Objective Questions

250+ TOP MCQs on Functions & Answers | Class 11 Maths

Mathematics Multiple Choice Questions on “Functions”.

1. In a function from set A to set B, every element of set A has___________ image in set B.
a) one and only one
b) different
c) same
d) many

Answer: a
Clarification: A relation from a set A to a set B is said to be a function if every element of set A has one and one image in set B.

2. In a function from set A to set B, image can have more than one preimage.
a) True
b) False

Answer: a
Clarification: A relation from a set A to a set B is said to be a function if every element of set A has one and one image in set B. A preimage must have one image, an image can have more than one preimage.

3. Let R be a relation defined on set of natural numbers {(x, y): y=2x}. Is this relation can be called a function?
a) True
b) False

Answer: a
Clarification: Since every natural number has one and only image so this relation can be called a function.

4. Which of the following is not a function?
a) {(1,2), (2,4), (3,6)}
b) {(-1,1), (-2,4), (2,4)}
c) {(1,2), (1,4), (2,5), (3,8)}
d) {(1,1), (2,2), (3,3)}

Answer: c
Clarification: A relation from a set A to a set B is said to be a function if every element of set A has one and one image in set B.
In {(1,2), (1,4), (2,5), (3,8)}, since element 1 has two images 2 and 4 which is not possible in a function so, it is not a function. Rest all have one and only one image so they can be called a function.

5. f(x) = {(frac{|x|}{x}) for x≠0 and 0 for x=0}. Which function is this?
a) Constant
b) Modulus
c) Identity
d) Signum function

Answer: d
Clarification: f(x) = {(frac{|x|}{x}) for x≠0 and 0 for x=0}. Function is {(-3, -1), (-2, -1), (-1,1), (0,0), (1,1), (2,1), (3,1), …….}. This is signum function.

6. Find domain of function |x|.
a) Set of real numbers
b) Set of positive real numbers
c) Set of integers
d) Set of natural numbers

Answer: a

7. Find range of function |x|.
a) Set of real numbers
b) Set of positive real numbers
c) Set of integers
d) Set of natural numbers

Answer: b

8. f(x) = (sqrt{9-x^2}). Find the domain of the function.
a) (0,3)
b) [0,3]
c) [-3,3]
d) (-3,3)

Answer: c
Clarification: We know radical cannot be negative. So, 9-x,2 ≥ 0
(3-x) (3+x) ≥ 0 => (x-3) (x+3) ≤ 0 => x∈[-3,3].

9. f(x) = (sqrt{9-x^2}). Find the range of the function.
a) R
b) R+
c) [-3,3]
d) [0,3]

Answer: d
Clarification: We know, square root is always non-negative. So, (sqrt{9-x^2}) ≥ 0. So, range of the function is set of positive real numbers.

250+ TOP MCQs on Algebraic Solutions of Linear Inequalities in One Variable and their Graphical Representation & Answers | Class 11 Maths

Mathematics Questions & Answers for Exams on “Algebraic Solutions of Linear Inequalities in One Variable and their Graphical Representation”.

1. If x>7 then x+2>9 is true?
a) True
b) False
Answer: a
Clarification: We can add equal number on both sides of inequality so
if x>7 then x+2>7+2 => x+2>9

2. If x>7 then which is impossible?
a) x>4
b) x<6
c) x>9
d) x<14
Answer: b
Clarification: x>7 and 7>4 => x>7>4 => x>4.
If x>7 then x cannot be less than 6.
If x=11 then x>7 and x>9.
If x=11 then x>7 and x<14.

3. If x>5 then 2x>10 is true or not?
a) True
b) False
Answer: a
Clarification: We can multiply a positive number on both sides of inequality without any change in inequality sign. So, if x>5 multiplying 2 on both sides 2x>10.

4. If x>7 then -x>-7 is ___________
a) possible
b) certainly false
c) certainly true
d) depend on x
Answer: b
Clarification: If we multiply by negative number on both sides of inequality then sign of inequality will change i.e. if x>7 then (-1) x < (-1)7 => -x<-7.

5. If x is a positive integer and 20x<100 then find solution set of x.
a) {0,1,2,3,4,5}
b) {1,2,3,4,5}
c) {1,2,3,4}
d) {0,1,2,3,4}
Answer: c
Clarification: 20x<100
Dividing by 20 on both sides, x< (100/20) => x<5
Since x is a positive integer so x = 1,2,3,4.

6. If x is a natural number and 20x≤100 then find solution set of x.
a) {0,1,2,3,4,5}
b) {1,2,3,4,5}
c) {1,2,3,4}
d) {0,1,2,3,4}
Answer: b
Clarification: 20x≤100
Dividing by 20 on both sides, x ≤ (100/20) => x≤5
Since x is a natural number so x = 1,2,3,4,5.

7. If x is a whole number and 10x≤50 then find solution set of x.
a) {0,1,2,3,4,5}
b) {1,2,3,4,5}
c) {1,2,3,4}
d) {0,1,2,3,4}
Answer: a
Clarification: 10x≤50
Dividing by 10 on both sides, x ≤ (50/10) => x≤5
Since x is a whole number so x = 0,1,2,3,4,5.

8. If 2x+1 > 5 then which is true?
a) x>4
b) x<4
c) x>2
d) x<2
Answer: c
Clarification: 2x+1>5
=>2x>5-1
=>2x>4 => x>2.

9. If x-1>-x+7 then which is true?
a) x>4
b) x<4
c) x>2
d) x<2
Answer: a
Clarification: x-1>-x+7
=>2x>8 => x>4.

10. Rahul obtained 20 and 25 marks in first two tests. Find the minimum marks he should get in the third test to have an average of at least 30 marks.
a) 60
b) 35
c) 180
d) 45
Answer: d
Clarification: Average is at least 30 marks.
Let x be the marks in 3rd test.
Average = (20+25+x)/3 ≥30
=>45+x≥90 => x≥90-45 => x≥45.
Minimum marks in 3rd test should be 45.

11. Find all pairs of consecutive odd positive integers both of which are smaller than 8 such that their sum is more than 10.
a) (5,7)
b) (3,5), (5,7)
c) (3,5), (5,7), (7,9)
d) (5,7), (7,9)
Answer: a
Clarification: Let two numbers be x and x+2.
x + x+2 >10 => 2x>8 => x>4
and x<8
and x+2<8 => x<6.
4 x can be 5.
For x =5, x+2=7
So, Pairs of odd consecutive positive integers are (5,7).

12. The longest side of a triangle is 2 times the shortest side and the third side is 4 cm shorter than the longest side. If the perimeter of the triangle is at least 61 cm, find the minimum length of the shortest side.
a) 7
b) 9
c) 11
d) 13
Answer: d
Clarification: Let shortest side be x. Then longest side = 2x.
Third side = 2x-4.
Given, perimeter of triangle is at least 61 cm
=>x+2x+2x-4 ≥ 61 => 5x≥65 = x≥13.
Minimum length of the shortest side is 13 cm.

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250+ TOP MCQs on Various Forms of the Equation of a Line & Answers | Class 11 Maths

Mathematics Problems for Class 11 on “Various Forms of the Equation of a Line”.
1. If slope of a line is positive then its inclination is ___________
a) right angle
b) acute angle
c) obtuse angle
d) zero
View Answer
Answer: b
Clarification: If inclination is α slope is given by tan α. Given that slope of line is positive which means tan α is positive. We know, tan α is positive in 1st quadrant i.e. α should be acute angle.
2. If slope of a line is negative then its inclination is ___________
a) right angle
b) acute angle
c) obtuse angle
d) zero
View Answer
Answer: c
Clarification: If inclination is α slope is given by tan α. Given that slope of line is negative which means tan α is negative. We know, tan α is negative in 2nd quadrant i.e. α should be obtuse angle.
3. Find slope of line joining (1, 2) and (4, 11).
a) 1/3
b) 3
c) 9
d) 1/9
View Answer
Answer: b
Clarification: We know, slope of line joining two points (x1, y1) and (x2, y2) is given by (frac{y_2-y_1}{x_2-x_1}).
So, slope of line joining (1, 2) and (4, 11) is (frac{11-2}{4-1} = frac{9}{3}) = 3.
4. If two lines are parallel their inclination angle may be different.
a) True
b) False
View Answer
Answer: b
Clarification: If two lines are parallel then they form same angle with positive direction of x-axis in anticlockwise direction i.e. their inclinations are equal.
5. If two lines are parallel then their slopes must be equal.
a) True
b) False
View Answer
Answer: a
Clarification: Let the inclination of the two lines be α and β. Since they are parallel so, α = β.
=>tan α = tan β. Hence their slopes are equal.
6. If the two lines are perpendicular then difference of their inclination angle is ________
a) 45°
b) 60°
c) 90°
d) 180°
View Answer

Answer: c
7. If the two lines with slope m1 and m2 are perpendicular then their slopes has relation ______
a) m1 + m2 = 1
b) m1 * m2 = 1
c) m1 * m2 = -1
d) m1 + m2 = -1
View Answer
Answer: c
Clarification: If the two lines are perpendicular then if one line form angle α with positive x-axis then the other line form angle 90° + α.
If m1 = tan α then m2 will be tan (90°+ α) = – cot α = -1/tan α
=> m1 * m2 = – 1.
8. If angle between the two lines is 45° and slope of one line is 1/4 then which of the following is possible value of the slope of other line.
a) 5/3
b) 3/5
c) -5/3
d) 4/5
View Answer
Answer: a
Clarification: If angle between two lines with slopes m1 and m2 is α then tan α = |(m1-m2)/(1+m1*m2)|
tan 450 = (|frac{m-1/4}{1+m/4}| = frac{4m-1}{m+4})
=>1 = (frac{4m-1}{m+4}) => m+4 = 4m-1 => 3m = 5
=>m = 5/3.
9. If angle between the two lines is 45° and slope of one line is 1/4 then which of the following is possible value of the slope of other line.
a) 3/5
b) -3/5
c) -5/3
d) 4/5
View Answer
Answer: b
Clarification: If angle between two lines with slopes m1 and m2 is α then tan α = |(m1-m2)/(1+m1*m2)|
tan 45° = (|frac{m-1/4}{1+m/4}|)
=> (frac{4m-1}{m+4}) = -1
=>- m-4 = 4m-1 => 5m = -3
=> m = -3/5.
10. If slope of a line is 2/3 then find the slope of line perpendicular to it.
a) -3/2
b) 3/2
c) 2/3
d) -2/3
View Answer
Answer: a
Clarification: If lines with slopes m1 and m2 are perpendicular then m1 * m2 = – 1.
If m1 = 2/3 then m2 = -1 / (2/3) = -3/2.
11. If slope of one line is 1/4 and other is 5/3 then find the angle between two lines.
a) 30°
b) 45°
c) 90°
d) 180°
View Answer
Answer: b
Clarification: If angle between two lines with slopes m1 and m2 is α then tan α = |(m1-m2)/(1+m1*m2)|
tan α = (|frac{5/3-1/4}{1+5/3*1/4}| = |frac{20-3}{12+5}|) = 17/17 =1 => α = 45°
12. Find slope of line passing through origin and (3, 6).
a) 2
b) 3
c) 1/3
d) 1/2
View Answer
Answer: a
Clarification: We know, slope of line joining two points (x1, y1) and (x2, y2) is given by (y2-y1)/(x2-x1).
So, slope of line joining (0, 0) and (3, 6) is (6-0)/(3-0) = 6/3 = 2.
13. If line joining (1, 2) and (5, 7) is parallel to line joining (3, 4) and (11, x).
a) 10
b) 11
c) 12
d) 14
View Answer
Answer: d
Clarification: We know, slope of line joining two points (x1, y1) and (x2, y2) is given by(y2-y1)/(x2-x1).
Lines are parallel means slope is equal.
=>(x-4)/(11-3) = (7-2)/(5-1) => x-4 = 5*8/4 = 10 => x=14.
14. If line joining (1, 2) and (7, 6) is perpendicular to line joining (3, 4) and (11, x).
a) 12
b) 16
c) -16
d) -12
View Answer
Answer: c
Clarification: We know, slope of line joining two points (x1, y1) and (x2, y2) is given by(y2-y1)/(x2-x1).
Lines are perpendicular means m1*m2 = -1
=> ((frac{x-4}{11-3})(frac{6-2}{7-1})) = -1
=> (x-4)(4) = (-1)(8)(6)
=> x-4 = -12 => x= -16.
15. The points A (1, 2), B (3, 5), C (7, 8) are collinear.
a) True
b) False
View Answer
Answer: b
Clarification: We know, slope of line joining two points (x1, y1) and (x2, y2) is given by(y2-y1)/(x2-x1).
Slope of line AB = (5-2)/(3-1) = 3/2
Slope of line BC = (8-5)/(7-3) = 3/4
Since slope of AB is not equal to BC so, points are not collinear.
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250+ TOP MCQs on Mathematical Reasoning – Statements & Answers | Class 11 Maths

Mathematics MCQs for IIT JEE Exam on “Mathematical Reasoning – Statements”.

1. A sentence is called statement if it is __________________
a) always true
b) always false
c) either true or false but not both
d) both true and false
Answer: c
Clarification: A sentence is called mathematically acceptable statement if it is either true or false but not both.

2. Which of the following is a statement?
a) Women are more intelligent than men
b) Two plus two is three
c) Open the door
d) Shut your mouth
Answer: b
Clarification: A sentence is called mathematically acceptable statement if it is either true or false but not both.
“Two plus two is three” is false so it is a statement. Rest we cannot decide whether they are true or false.

3. Which of the following is not a statement?
a) Two and two makes four
b) A prime number is always odd
c) Sum of a and b is 5
d) Elephant is heavier than ant
Answer: c
Clarification: “Two and two makes four” and “Elephant is heavier than ant” are true so they are statements. “A prime number is always odd” is false as prime number may be even so it is a statement. “Sum of and b is 5” is not a statement as it can be true or false based on the values of a and b taken.

4. Which of the following is a statement?
a) Today is Monday
b) Tomorrow will be holiday
c) If today is Tuesday then tomorrow will be Sunday
d) There will be full moon tonight
Answer: c
Clarification: “Today is Monday”, “Tomorrow will be holiday”, “There will be full moon tonight” are not the statements because we are not sure which day or night we are talking about.
“If today is Tuesday then tomorrow will be Sunday” is a statement because we are sure that it is false.
Wednesday come after Tuesday so if today is Tuesday then tomorrow will be Wednesday.

5. Which of the following is a statement?
a) There are 27 days in this month
b) February has 28 days
c) February has 29 days
d) There are 32 days in this month
Answer: d
Clarification: When we talk about this, that, here, there, we are not sure about what we are talking about so “There are 27 days in this month” is not a statement.
“February has 28 days” and “February has 29 days” both are not statements because February may have 28 days or 29 das based on the year. “There are 32 days in this month” is a statement as it is false. We cannot have 32 days in a month.

6. Is “How far is Delhi from here” a statement?
a) True
b) False
Answer: b
Clarification: “How far is Delhi from here” is not a statement as we cannot decide what is “here” and from where we are going to measure the distance to Delhi.

7. Is “History is a boring subject” a statement?
a) True
b) False
Answer: b
Clarification: “History is a boring subject” is a not a statement as it all depends on reader whether he like History or not.

8. Which of the following is not a statement?
a) Product of 1 and 2 is -4
b) Squares are always positive
c) Give me a cup of tea
d) Sum of 2 and 3 is 9
Answer: c
Clarification: “Product of 1 and 2 is -4” is a statement as it is false. We know, product of 1 and 2 is 2.
“Squares are always positive” is a statement as it is true. “Sum of 2 and 3 is 9” is a statement as it is false. But “Give me a cup of tea” is not a statement as it is an order so it is imperative sentence.

9. Which of the following is true?
a) Statements generally not use word like today and tomorrow
b) Statements generally not use word like here and there
c) Statements generally not use word like sum and product
d) Statements generally not use word like this and that
Answer: c
Clarification: Statements generally not use ambiguous words like here, there, this, that, today, tonight, tomorrow.

10. Which of the following is a statement?
a) Close the door
b) 11 comes after 12
c) India is a beautiful country
d) This is useless
Answer: b
Clarification: “Close the door” is not a statement as it is an imperative sentence. “11 comes after 12”
is a statement as it is true. “India is a beautiful country” is not a statement as opinion of beautifulness vary from person to person. “This is useless” is not a statement as it involves this which doesn’t give any idea about what we are talking.

Mathematics MCQs for IIT JEE Exam,

250+ TOP MCQs on Trigonometric Functions – Angles & Answers | Class 11 Maths

Mathematics Multiple Choice Questions on “Trigonometric Functions – Angles”.

1. If the initial side is overlapping on the terminal side, then angle is ________
a) 0°
b) 180°
c) 90°
d) 270°
Answer: a
Clarification: The angle is formed if we start to rotate from initial side till terminal side comes. If they both overlap then angle is said to be 0°.

2. If we start to rotate and after completing one revolution again initial side overlap with terminal side, then the angle formed is _________
a) 0°
b) 180°
c) 90°
d) 360°
Answer: d
Clarification: The angle is formed if we start to rotate from initial side till terminal side comes. If we start to rotate and after completing one revolution again initial side overlap with terminal side, then the angle formed is 360°.

3. 1 radian is _______________
a) 54°48’
b) 57°16’
c) 180°
d) 17°46’
Answer: b
Clarification: We know, π radian = 180 degree
1 radian = 180/π degree = 57.27° = 57° (0.27*60)’ = 57°16’.

4. 1 degree is _________ radian.
a) π
b) 0.046
c) 0.1746
d) 0.01746
Answer: d
Clarification: 180 degree = π radian
1 degree = π/180 radian = 0.01746 radian.

5. 4 radians = _____________
a) 720°
b) 240°51’53”
c) 229°10’59”
d) 233°11’48”
Answer: c
Clarification: We know, π radians = 180 degrees
1 radian = 180/π degrees
4 radians = 720/π degrees = 229.183° = 229° (0.183*60)’ = 229 (10.98)’ = 229°10’59”.

6. If angle of arc is 60° and the length of arc is 20 cm. Find the radius of the circle from which arc is intercepted.
a) 18.08 cm
b) 17.07 cm
c) 19.09 cm
d) 18 cm
Answer: c
Clarification: 180 degree = π radian
1 degree = π/180 radians
60 degrees = 60* π/180 radians = π/3 radians
Angle=Arc length/Radius
π/3 = 20/Radius => Radius = 60/π = 19.09 cm.

7. If length of arc is 40 cm and radius of circle of arc is 10 cm then find the angle made by the arc.
a) 720°
b) 240°51’53”
c) 229°10’59”
d) 233°11’48”
Answer: c
Clarification: We know, Angle=Arc length/Radius
Angle = 40/10 = 4 radians
π radians = 180 degrees
1 radian = 180/π degrees
4 radians = 720/π degrees = 229.183° = 229° (0.183*60)’ = 229°(10.98)’= 229°10’59”.

8. The second hand of the watch is 2 cm long. How far the tip will move in 40 seconds?
a) 6.28 cm
b) 12.56 cm
c) 3.14 cm
d) 1.57 cm
Answer: b
Clarification: Radius of circle=2 cm
In 60 seconds, angle covered by second hand is 360°
In 40 seconds, angle covered by second hand is 360°*4/6 = 240°
240°=240*
Angle=Arc length/Radius
240*π/180 = Arc length/2
Arc length=8 π/3 = 12.56 cm.

9. If in two circles, arcs of the same length subtend angles 45° and 60° at Centre, find the ratio of their radii.
a) 2:3
b) 2:5
c) 3:4
d) 4:3
Answer: d
Clarification: Given θ1=45° and θ2=60°, L1=L2
We know, θ = l/r
r1 θ1 = r2 θ2
r1/r2=60/45=4/3.
So, radii are in ratio 4:3.

10. If minute hand covers 24 cm length in 30 minutes, then how much length minute hand have?
a) 19.1 cm
b) 38.2 cm
c) 57.3 cm
d) 45 cm
Answer: b
Clarification: In 60 minutes, angle covered by minute hand is 360°.
In 30 minutes, angle covered by minute hand is 180°.
L=24 cm, θ=180°=π
θ=L/r => π=24/r => r=24/π = 38.2 cm.

250+ TOP MCQs on Graphical Solution of Linear Variable in Two Variables & Answers | Class 11 Maths

Mathematics Question Paper on “Graphical Solution of Linear Variable in Two Variables”.
1. The region containing all the solutions of an inequality is called solution region.
a) True
b) False
View Answer
Answer: a
Clarification: When the inequalities are plotted on graph, the region containing all the solutions of an inequality is called the solution region.
2. 2x+y>5. Which of the following will satisfy the given equation?
a) (1,1)
b) (1,2)
c) (2,1)
d) (2,2)
View Answer
Answer: d
Clarification: 2x+y>5
(1,1) x=1 and y=1 gives 2(1)+1>5 =>3>5 which is false.
(1,2) x=1 and y=2 gives 2(1)+2>5 =>4>5 which is false.
(2,1) x=2 and y=1 gives 2(2)+1>5 =>5>5 which is false.
(2,2) x=2 and y=2 gives 2(2)+2>5 =>6>5 which is true.
3. IQ of a person is given by the formula
IQ =(MA/CA) × 100, where MA is mental age and CA is chronological age. If 40 ≤ IQ ≤ 120 for a group of 10 years old children, find the range of their mental age.
a) (9,16)
b) [9,16]
c) (4,12)
d) [4,12]
View Answer
Answer: d
Clarification: IQ =(MA/CA) × 100
=>MA = IQ * CA /100. Given, CA=10 years
40≤ IQ ≤120
=> 40*CA ≤ IQ*CA ≤ 120*CA
=> 40*10 ≤ IQ*CA ≤ 120*10
=> (frac{40*10}{100}≤frac{IQ*CA}{100}≤frac{120*10}{100})
=> 4 ≤ MA ≤ 12.
4. A solution is to be kept between 77° F and 86° F. What is the range in temperature in degree Celsius (C) if the Celsius / Fahrenheit (F) conversion formula is given by F = 9/5 C + 32°?
a) [15°, 20°]
b) [20°, 25°]
c) [25°, 30°]
d) [30°, 35°]
View Answer
Answer: c
Clarification: F = 9/5 C + 32°
C=(F-32°)*5/9
77° ≤ F ≤ 86°
=> 77°-32° ≤ F-32° ≤ 86° -32°
=> 45° ≤ F-32° ≤ 54°
=>45o*5/9 ≤ (F-32°) *5/9 ≤ 54°*5/9
=>25° ≤ C ≤ 30°.