# MCQ Questions for Class 10 Quadratic Equation

Please refer to the MCQ Questions for Class 10 Maths Quadratic Equation with Answers. The following Quadratic Equation Class 10 Maths MCQ Questions have been designed based on the current academic year syllabus and examination guidelines for Class 10. Our faculty has designed MCQ Questions for Class 10 Maths with Answers for all chapters as per your NCERT Class 10 Mathematics book.

Question. Roots of the quadratic equation 3x2 – 2√6x + 2 = 0

Ans.

1

Question. Find the roots of the quadratic equation √2x2 + 7x + 5√2 = 0

Ans.

2

Question. Find two numbers whose sum is 24 and product is 143
(1) 13, 11
(2) 12, 12
(3) 8, 16
(4) none of these

Ans.

1

Question. What value of K the equation 9x2 – kx + 81 = 0 has equal roots
(1) +24
(2) +32
(3) +54
(4) +46

Ans.

3

Question. Solve for x, x/x+1 + x+1/x = 34/15

Ans.

4

Question. If p and q are the roots of the equation x2 + px + q = 0, then find the value of p
(1) 1, 2
(2) 2, 3
(3) 4, 0
(4) 1, 0

Ans.

4

Question. Find the roots of the equation 1/x + 4 – 1/x – 7 = 11/30, x – 4, 7, x – 4, 7
(1) 1, 2,
(2) 2, 3
(3) 4, 7
(4) 1, 6

Ans.

1

Question. The hypotenuse of a right angled triangle is 6 cm more than twice the shortest side. If the third side is 2 cm less than the hypotenuse. Find the side of the triangle
(1) 10, 24, 26
(2) 4, 6, 8
(3) 3, 4, 5
(4) 5, 12, 13

Ans.

1

Question. Solve for x, 4/x – 3= 5/2x + 3, x 0,- 3/2
(1) 1, -2
(2) 1, 2
(3) 4, 3
(4) 4, 6

Ans.

1

Question. Find two consecutive odd positive integers, sum of whose squares is 290
(1) 13, 15
(2) 11, 13
(3) 7, 9
(4) 5, 7

Ans.

2

Question. A motor boat whose speed is 18 km/hr in still water takes 1 hr more to go 24 km upstream than to return down stream to the same spot. Find the speed of the stream
(1) 4 km/hr
(2) 5 km/hr
(3) 6 km/hr
(4) 8 km/hr

Ans.

3

Question. Solve for x

(1) -1/3
(2) 2/3
(3) 1, -1/3
(4) 1/3, -1

Ans.

1

Question. Find the discriminant of the quadratic equation 2x2 – 4x + 3 = 0
(1) -4
(2) -8
(3) 4
(4) 6

Ans.

2

Question. A rectangular park has perimeter 80 m and area 400 m2. Find its length and breadth
(1) 40, 10
(2) 20, 20
(3) 16, 25
(4) none of these

Ans.

2

Question. Find the numbers such that their sum is 15 and sum of their reciprocal 3/10
(1) 8, 7
(2) 6, 9
(3) 10, 5
(4) 4, 11

Ans.

3

Question. A train covers a distance of 300 km at a certain average speed. If its speed were decreased by 10 km/hr, the Journey would take 1 hour’ longer. What is average speed of the train.
(1) 40 km/hr
(2) 50 km/hr
(3) 45 km/hr
(4) 60 km/hr

Ans.

4

Question. Find two consecutive numbers whose squares have the sum 85
(1) 6, 7
(2) 6, 9
(3) 6, 8
(4) none of these

Ans.

1

Question. Solve for x, x2 + x/2-1=0

Ans.

3

Question. Solve for x √3x2 – 2√2x – √3 = 0
(1)√6,-√6/3
(1)√3, 2
(1)√7, √7/2
(1)√6, √3

Ans.

1

Question. There are three consecutive positive integers such that the sum of the square of the first and the product of the other two is 154. What are the integers
(1) 6, 7, 8
(2) 7, 8, 9
(3) 8, 9, 10
(4) 9, 10, 11

Ans.

3

Question. An aeroplane takes 1 hour less for a journey of 1200 km if its speed increased by 100 km/hr from its usual speed. Find its usual speed
(1) 280 km/hr
(2) 290 km/hr
(3) 270 km/hr
(4) 300 km/hr

Ans.

4

Question. The hypotenuse of a right triangle is 3√10cm. If the smaller side is tripled and the longer side doubled, new hypotenuse will be 9√5 cm. How long are the sides of the triangle
(1) 3cm, 6 cm,
(2) 3cm, 9cm
(3) 4cm, 6cm
(4) 6cm, 9cm

Ans.

2

Question. If the list price of a toy is reduced by Rs 2, a person can buy 2 toys more for Rs. 360. Find the original price of the toy
(1) Rs. 18
(2) Rs. 19
(3) Rs. 20
(4) Rs. 21

Ans.

3

Question. Solve for y2 + y1 2-3 = 0
(1) -2, 6
(2) -2, 3/2
(3) 2, 3/2
(4) 3, 4

Ans.

2

Question. The distance between Delhi and Aligarh is 192 km. Travelling by Kalka mail, it takes 48 minutes less than other train. Calculate the speed of Kalka mail if the speed of the two trains differ
by 20 km/hr
(1) 60 km/hr
(2) 80 km/hr
(3) 90 km/hr
(4) 100 km/hr

Ans.

2

Question. A farmer wishes to grow a 100 m2 rectangular corn field. Since he has with him only 30 meter wire, he fences three sides of the rectangular garden letting compound wall of the house act as fourth side fence. Find the dimension of the garden.
(1) 5, 20
(2) 6, 10
(3) 16, 9
(4) 21, 4
Trick = xy = 100, x + 2y = 30

Ans.

1

Question. One side of a rectangle exceeds its other side by 2 cm. If its area is 195 cm2, determine the side of the rectangle
(1) 13, 15
(2) 14, 14
(3) 20, 8
(4) 12, 16

Ans.

1

Question. Solve for x 5x2 – 2x – 2 = 0

Ans.

1

Question. Solve for y, 1/y+1 + 2/y+2 = 4/y+4
(1) 2+√3
(2) 1+2√3
(3) 2+2√3
(4) 4+2√3

Ans.

3

Question. A man on attempting to arrange the boys in the form of a solid square found that 24 boys were left. When he increased the size of the square by one boy, he found that he was short of 25 boys. Find the number of boys.
(1) 580
(2) 590
(3) 600
(4) 610
Trick x2 + 24 = (x+1)2 – 25

Ans.

3

Question.. Solve for y 2(y-1/y+3) -7 (y+3/y+1) = 5 given that y≠_ 3, y≠1
(1) -1, – 23/5
(2) -2, – 23/7
(3) -3, – 21/5
(4) -4, – 20/7

Ans.

1

Question. 300 marbles are distributed equally among a certain number of students. Had there been 10 more students, each would have received one marble less. Find the number of students.
(1) 50
(2) 40
(3) 60
(4) 70
Trick 300/x – 300/x + 10 = 1

Ans.

1

Question. Solve for z 36z2 – 12 cz + (c2 – d2) = 0
(1) c-d/2, c+d/2
(2) c-d/6, c+d/6
(3) c-d/4, c+d/4
(4) c-d/3, c+d/3

Ans.

1

Question. Find the roots of the equation 5y2 – 6y – 2 = 0 by the method of completing square
(1) 3+ √19/2, 3- √19/2
(2) 6+ √19/3, 6- √19/3
(3) 3+ √19/4, 3- √19/5
(4) none of these

Ans.

3

Question. Find the value of a for which the quadratic equation 4y2 – 3ay + 1 = 0
(1) + 2/3
(2) + 4/7
(3) + 1/3
(4) + 4/3

Ans.

4

Question. Determine the value of k for which the quadratic equation 4z2 – 2 (k + 1) z + (k + 4) = 0 has equal roots
(1) -2 or 5
(2) -3 or 5
(3) -1 or 2
(4) 5 or -1

Ans.

2

Question. Determine the value of such that the quadratic equation ( – 12) y2 + 2 ( -12) y + 2 = 0 has equal roots
(1) 14
(2) 12
(3) 10
(4) 13

Ans.

1

Question. Determine the value of p such that 9z2 – pz + 81 = 0 has equal roots
(1) + 54
(2) + 52
(3) + 53
(4) + 51

Ans.

1

Question. if x = √1+√1+√1+………… then x is equal to
(1) 1+√5/3
(2) 1-√5/2
(3) 1+√5/2
(4) none of these

Ans.

1

Question. The value of

(1) 1-√2
(2) 1+√2
(3) 1+√2
(4) none of these

Ans.

2

Question. if √3x2-7x-30 + √2x2-7x-5 = x + 5 …………then x is equal to
(1) 2
(2) 3
(3) 6
(4) 5

Ans.

4

Question. the number of real root of 3, 2x2-7x+7 = 9 is
(1) zero
(2) 2
(3) 1
(4) 4

Ans.

2

Question. If x = √6+√6+√6+……….∝ then x is equal to
(1) 3, -2
(2) -2
(3) = 3
(4) none of these

Ans.

3

Question. Determine a such that the quadratic equation a (y – 2) y + 6 = 0 has equal roots
(1) 2
(2) 4
(3) 5
(4) 6

Ans.

4

Question. The sum of the ages of two boys is 20 years. Four years ago, the product of their ages in years was 48. Determine their present ages.
(1) 8, 12
(2) 4, 16
(3) 15, 5
(4) can not be determined

Ans.

4

Question. Sum of the areas of the two squares is 468 m2. If the difference of their perimeters is 24 m. Find the sides of the two squares.
(1) 18m, 12m
(2) 17m, 13m
(3) 16m, 14m
(4) 20m, 10m

Ans.

1

Question. The height of a right triangle is 7 cm less than its base. If the hypotenuse is 13 cm, find the other two sides
(1) 5 cm, 12 cm
(2) 10 cm, 7 cm
(3) 13 cm, 4 cm
(4) 9 cm, 8 cm

Ans.

1

Question. Solve for y 1/a+b+y = 1/a + 1/b + 1/y
(1) a, b
(2) – a, – b
(3) a, – b,
(4) -a, – b

Ans.

2

Question. Determine the value of a for which the quadratic equation y2 + 7 (3 + 2a) – 2y (1 + 3a) = 0 has equal roots
(1) -2,10/9
(2) 2, 10/9
(3) 2, -10/9
(4) -2, -10/9

Ans.

3

Question. Determine the value of k for which the quadratic equation (k – 3) z2 + 4 (k – 3) z + 4 = 0 has equal roots
(1) 4
(2) 5
(3) 6
(4) 7

Ans.

1

Question. If a and P are the roots of the equation x2 + kx + 12 = 0 such that α – β= 1, what is the value of ‘k’?
(1) 0
(2) ± 5
(3) ±1
(4) ± 7

Ans.

D

Question. How are the roots of 3x2 +7x + 8 = 0 ?
(1) Real and unequal
(2) Real and equal
(3) Not real
(4) Cannot be determined.

Ans.

3

Question. The sum of squares of two consecutive positive even numbers is 340. Find them.
(1) 12, 14
(2) 12, 10
(3) 10, 8
(4) 14, 16

Ans.

1

Question. What is the nature of the roots of 3x2 + x = 6 = 0 ?
(1) Real and equal
(2) Real and distinct
(3) Not real
(4) Cannot be determined.

Ans.

3

Question. Find the value of ‘p’ so that x2 + 5px + 16 = 0 has no real root.
(1) Greater than 8/5
(2) Less than -8/5
(3) Lies between -8/5 and 8/5
(4) Less than 15/8

Ans.

3

Question. Find the sum of the roots of x2 + x – 210 = 0
(1) -2
(2) 29
(3) 20
(4) -1

Ans.

4

Question. If the equation ax – 5x + c = 0 has 10 as the sum of the roots and also as the product of the roots, which of the following is true?
(1) a – c = 5
(2) a = 2,c = 3
(3) a = 5, c =1
(4) a = 3, c = 2

Ans.

1

Question. A two digit number is 4 times the sum of its digits and also 16 more than the product of digits. Find the number.
(1) 48
(2) 36
(3) 44
(4) 32

Ans.

1

Question. Find ‘a’ if a – 3 = √10/a .
(1) 5,- 2
(2) -√7 , 7
(3) √7 , 7
(4) – 5,2

Ans.

1

Question. Find the common root of the equations x2 – 7x + 10 = 0 and x2 -10x +16 = 0.
(1) – 2
(2) 3
(3) 5
(4) 2

Ans.

4

Question. What is the value of ‘k’ for which the roots of the quadratic equation 3x2 + 2kx + 27 = 0 are real and equal?
(1) 9 only
(2) -9 only
(3) 9 or-9
(4) Neither 9 nor-9.

Ans.

3

Question. Find the product of the roots of the quadratic equation 9m2 + 24 m + 16 = 0 .
(1) 4/3
(2) 9/16
(3) 16/9
(4) 3/4

Ans.

C

Question. The length and breadth of a rectangle are (3k + 1) cm and (2k – 1) cm respectively. Find the perimeter of the rectangle if its area is 144cm2 .
(1) 50 cm
(2) 10 cm
(3) 32 cm
(4) 25 cm

Ans,

A

Question. Find ‘a’ if a – 3 = 10/a
(1) 5,-2
(2) -√7,7
(3) √7,7
(4) -5,2

Ans.

A

Question. The age of a man is the square of his son’s age. A year ago, the man’s age was eight times the age of his son. What is the present age of the man?
(1) 47 years
(2) 49 years
(3) 36 years
(4) 48 years

Ans,

B

Question. The ratio of the length and breadth of a rectangular photo frame is 3 : 2. Find its length if its area is 864 cm2.
(1) 34 cm
(2) 26 cm
(3) 24 cm
(4) 36 cm

Ans.

D

Question. Find two consecutive positive odd numbers, the sum of whose squares is 514.
(1) 11, 13
(2) 15, 17
(3) 11, 9
(4) 13, 15

Ans,

B

Question. Which of the following statements is correct?
(1) x = 1is a root of 2x2 + 3x +1 = 0 .
(2) x = 2 is not a root of 6x2 + 7x – 5 = 0 .
(3) x = -1is a root of 3x2 – x – 1 = 0 .
(4) x = – (2/5) is not a root of 5x2 – 8x – 4 = 0 .

Ans,

B

Question. How are the roots of 3x2 + 7x + 8 = 0 ?
(1) Real and unequal
(2) Real and equal
(3) Not real
(4) Cannot be determined.

Ans.

C

Question. Divide 63 into two parts such that their product is 962.
(1) 24, 3C
(2) 28, 35
(3) 26, 37
(4) 27, 36

Ans.

C