RD Sharma Test: Quadratic Equations - Class 10 MCQ

# RD Sharma Test: Quadratic Equations - Class 10 MCQ

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## 25 Questions MCQ Test Mathematics (Maths) Class 10 - RD Sharma Test: Quadratic Equations

RD Sharma Test: Quadratic Equations for Class 10 2024 is part of Mathematics (Maths) Class 10 preparation. The RD Sharma Test: Quadratic Equations questions and answers have been prepared according to the Class 10 exam syllabus.The RD Sharma Test: Quadratic Equations MCQs are made for Class 10 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for RD Sharma Test: Quadratic Equations below.
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RD Sharma Test: Quadratic Equations - Question 1

### A quadratic equation whose one root is 3 is

Detailed Solution for RD Sharma Test: Quadratic Equations - Question 1

x = 3 satisfies only the equation x2−5x+6 = 0
As (3)2−5×3+6 = 0
⇒ 9−15+6 = 0
⇒ 15−15 = 0
⇒ 0 = 0
⇒ L.H.S. = R.H.S.

RD Sharma Test: Quadratic Equations - Question 2

### The common root of 2x2+x−6 = 0 and x2−3x−10 = 0 is

Detailed Solution for RD Sharma Test: Quadratic Equations - Question 2

Given: p (x) = 2x2 + x - 6 = 0 and q (x) = x2 - 3x — 10 = 0
∴ p (-2) = 2(-2)2 + (-2) - 6 = 0 = 8 - 2 - 6 = 8 - 8 = 0
∴ q (-2) = (-2)2 - 3 (-2) - 10 = 0 = 4 + 6 - 10 = 10 - 10 = 0
Since p (-2) = 0 and q (-2) = 0 therefore, - 2 is the common root of 2x2 + x - 6 = 0 and x2 - 3x - 10 = 0

RD Sharma Test: Quadratic Equations - Question 3

### In a cricket matchKumble took three wickets less than twice the number of wickets taken by Srinath. The product of the number of wickets taken by these two is 20, then the number of wickets taken by Kumble is

Detailed Solution for RD Sharma Test: Quadratic Equations - Question 3

Let the number of wickets taken by Srinath be x then the number of wickets taken by Kumble will be 2x−3

According to question, x (2x−3) = 20

⇒ 2x2−3x−20 = 0

⇒ 2x2−8x+5x−20 = 0

⇒ 2x(x−4)+5(x−4) = 0

⇒ (x−4)(2x+5) = 0

⇒ x−4 = 0and 2x+5 = 0

Therefore, number of wickets taken by Srinath is 4.
Then number of wickets taken by Kumble = 2 x 4 - 3 = 5

RD Sharma Test: Quadratic Equations - Question 4

(x2+1)− x2 = 0 has

Detailed Solution for RD Sharma Test: Quadratic Equations - Question 4

Given: (x2+1)− x= 0
⇒ x+ 1  + 2x − x= 0
⇒ 2x + 1 = 0
⇒ x = −1/2
Therefore, (x2+1)− x2 = 0 has no real roots.

RD Sharma Test: Quadratic Equations - Question 5

If the sum and product of the roots of the equation kx2+6x+4k = 0 are equal, then k =

Detailed Solution for RD Sharma Test: Quadratic Equations - Question 5

RD Sharma Test: Quadratic Equations - Question 6

One of the roots of the quadratic equation a2x2−3abx+2b2 = 0 is

Detailed Solution for RD Sharma Test: Quadratic Equations - Question 6

Explanation here:a2x2−3abx+2b= 0
⇒ a2x2−2abx−abx+2b= 0
⇒ ax(ax−2b)−b(ax−2b) = 0
⇒ (ax−b)(ax−2b) = 0
⇒ x−b = 0and ax−2b = 0

RD Sharma Test: Quadratic Equations - Question 7

The product of two successive integral multiples of 5 is 1050. Then the numbers are

Detailed Solution for RD Sharma Test: Quadratic Equations - Question 7

Let one multiple of 5 be x then the next consecutive multiple of will be (x+5) According to question,

x = −35 is not possible therefore x = 30
Then the other multiple of 5 is x+5 = 30+5 = 35
Then the number are 30 and 35.

RD Sharma Test: Quadratic Equations - Question 8

The angry Arjun carried some arrows for fighting with Bheeshma. With half the arrows, he cut down the arrows thrown by Bheeshma on him and with six other arrows he killed the rath driver of Bheeshma. With one arrow each he knocked down respectively the rath, flag and bow of Bheeshma. Finally with one more than four times the square root of arrows he laid Bheeshma unconscious on an arrow bed. The total number of arrows that Arjun had is

Detailed Solution for RD Sharma Test: Quadratic Equations - Question 8

RD Sharma Test: Quadratic Equations - Question 9

Which of the following has no real root?

Detailed Solution for RD Sharma Test: Quadratic Equations - Question 9

Since b2 - 4ac < 0 therefore, x2 - 4x + 3√2 = 0 has no real roots

RD Sharma Test: Quadratic Equations - Question 10

If ‘sin α’ and ‘cos α’ are the roots of the equation ax2+bx+c = 0 a then b2 =

Detailed Solution for RD Sharma Test: Quadratic Equations - Question 10

RD Sharma Test: Quadratic Equations - Question 11

The quadratic equation whose roots are 7+√3 and 7−√3 is

Detailed Solution for RD Sharma Test: Quadratic Equations - Question 11

RD Sharma Test: Quadratic Equations - Question 12

The roots of the quadratic equation 9a2b2x2−16abcdx−25c2d2 = 0 are

Detailed Solution for RD Sharma Test: Quadratic Equations - Question 12

RD Sharma Test: Quadratic Equations - Question 13

The constant that must be added and subtracted to solve the quadratic equation   by the method of completing the square is

Detailed Solution for RD Sharma Test: Quadratic Equations - Question 13

RD Sharma Test: Quadratic Equations - Question 14

Which of the following has two distinct roots?

Detailed Solution for RD Sharma Test: Quadratic Equations - Question 14

In equation x2+x−5 = 0
a = 1,b = 1,c = −5
∴ b2−4ac = (1)2−4×1×(−5) = 1 + 20 = 21
Since b2−4ac > 0 therefore, x2+x−5 = 0 has two distict roots.

RD Sharma Test: Quadratic Equations - Question 15

If ‘a’ and ‘b’ are the roots of the equation x2+ax+b = 0, then a+b =

Detailed Solution for RD Sharma Test: Quadratic Equations - Question 15

Since sum of the roots = -b/a ∴ a+ b = -a/1 = -a

RD Sharma Test: Quadratic Equations - Question 16

If x = 2 is a root of the quadratic equation 3x2 – px – 2 = 0, then the value of ‘p’ is

Detailed Solution for RD Sharma Test: Quadratic Equations - Question 16

Given: p(x) = 3x2−px−2 = 0
∴ p(2) = 3(2)2−p(2)−2 = 0
⇒ 12−2p−2 = 0
⇒ −2p = −10
⇒ p = 5

RD Sharma Test: Quadratic Equations - Question 17

The sum of reciprocals of Sharma’s age 3 years ago and 5 years from now is 1/3, then his present age is

Detailed Solution for RD Sharma Test: Quadratic Equations - Question 17

Let Sharma’s present age be x years then his age 3 years ago is (x−3) years and 5 years from now is (x+5) years. According to question,

But x = 3 does not satisfy the given condition.
Therefore, Sharma's present age is 7 years.

RD Sharma Test: Quadratic Equations - Question 18

If ax2+bx+c = 0 has equal roots, then c is equal to

Detailed Solution for RD Sharma Test: Quadratic Equations - Question 18

If ax2+bx+c = 0 has equal roots, then
b2−4ac = 0
⇒ 4ac = b2
⇒ c =

RD Sharma Test: Quadratic Equations - Question 19

If the quadratic equation kx(x – 2) + 6 = 0 has equal roots, then the value of ‘k’ is

Detailed Solution for RD Sharma Test: Quadratic Equations - Question 19

If the quadratic equation 6x2 - 2kx + 6 = 0 has equal roots, then

RD Sharma Test: Quadratic Equations - Question 20

If one root of the equation ax2+bx+c = 0 is three times the other, then b2 : ac =

Detailed Solution for RD Sharma Test: Quadratic Equations - Question 20

Let one root be α then other root will be 3α.
∴ Sum of the roots

And Product of the roots

Equating the coefficients of α2 and subtracing e.q. (ii) from e.q. (i), we get

RD Sharma Test: Quadratic Equations - Question 21

5x2+8x+4 = 2x2+4x+6 is a

Detailed Solution for RD Sharma Test: Quadratic Equations - Question 21

Given: 5x2+8x+4 = 2x2+4x+6
⇒ 5x2−2x2+8x−4x+4−6 = 0
⇒ 3x2+4x−2 = 0
Here, the degree is 2, therefore it is a quadratic equation.

RD Sharma Test: Quadratic Equations - Question 22

A train travels 360km at a uniform speed. If the speed had been 5 km/hr more, it would have taken 1 hour less for the same journey, then the actual speed of the train is

Detailed Solution for RD Sharma Test: Quadratic Equations - Question 22

RD Sharma Test: Quadratic Equations - Question 23

Let b = a + c. Then the equation ax2+bx+c = 0 has equal roots if

Detailed Solution for RD Sharma Test: Quadratic Equations - Question 23

RD Sharma Test: Quadratic Equations - Question 24

The discriminant of the quadratic equation 3√3x2+10x+√3 = 0 is

Detailed Solution for RD Sharma Test: Quadratic Equations - Question 24

Given: 3√3x2+10x+√3 = 0 Discriminant = b2−4ac = (10)2−4×3√3×√3 = 100−36 = 64

RD Sharma Test: Quadratic Equations - Question 25

If one root of the equation 4x2−2x+(λ−4) = 0 be the reciprocal of the other, then the value of is

Detailed Solution for RD Sharma Test: Quadratic Equations - Question 25

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