Which constant should be added and subtracted to solve the quadratic equation 4x2 − 3x − 5 0 by the method of completing the square?

Get here Important MCQs for Class 10 Maths Chapter 4 - Quadratic Equations to help in the preparation for the Board Exam 2021-2022.

CBSE Class 10 Maths Question Paper in Term I Board Exam will have Multiple Choice Type Questions. To score good marks in these questions students must revise all the fundamental concepts. To make exam preparations easy for students, we are providing the MCQs based on important concepts and topics involved in class 10 Maths. In this article, we are providing the MCQs on Maths Chapter 4 Quadratic Equations. All these questions are provided with answers and their detailed explanation. Check the MCQs provided below to get an idea of the type of questions to be asked in the CBSE Class 10 Maths Exam 2021-2022.

Check below the solved MCQs from Class 10 Maths Chapter 4 Quadratic Equations:

1. The roots of quadratic equation 5x2 – 4x + 5 = 0 are

(A) Real & Equal                                               

(B) Real & Unequal

(C) Not real                                                        

(D) Non-real and equal

Answer:  (C)

Explanation: To find the nature, let us calculate b2 – 4ac

b2 – 4ac = 42 – 4 x 5 x 5

= 16 – 100

= -84 < 0

2. Equation (x+1)2 – x2 = 0 has _____ real root(s).

(A) 1                                                     

(B) 2

(C) 3                                                      

(D) 4

Answer:  (A)

Explanation:

Since (x + 1)2 – x2 = 0

⟹ x2 + 1 + 2x – x2 = 0

⟹ 1 + 2x = 0

⟹ x= -1/2

This gives only 1 real value of x.

3. Which constant should be added and subtracted to solve the quadratic equation 4x2 − √3x + 5 = 0 by the method of completing the square?

(A) 9/16                                               

(B) 3/16               

(C) 3/4                                                 

(D) √3/4

Answer:  (B)

Explanation:

This can be written as

Hence the given equation can be solved by adding and subtracting 3/16.

4. If 1/2 is a root of the equation x2 + kx – (5/4) = 0 then the value of k is

(A) 2                                                                                                     

(B) – 2

(C) 3                                                                                                      

(D) –3

Answer:  (A)

Explanation:

As one root of the equation x2 + kx – (5/4) = 0 is 1/2

Also Check: CBSE Class 10 Science Important MCQs: All Chapters

5. A natural number, when increased by 12, equals 160 times its reciprocal. Find the number.

(A) 3                                     

(B) 8      

(C) 4                                      

 (D) 7

Answer:  (B)

Explanation:

Let the number be x

Then according question,

x + 12 = 160/x

x2 + 12x – 160 = 0

x2 + 20x – 8x – 160 = 0

(x + 20) (x – 8) = 0

x = -20, 8

Since the number is natural, so we consider only positive value.

6. The product of two successive integral multiples of 5 is 300. Then the numbers are:

(A) 25, 30                                                                            

(B) 10, 15

(C) 30, 35                                                                            

(D) 15, 20

Answer:  (D)

Explanation:

Let the consecutive integral multiple be 5n and 5(n + 1) where n is a positive integer.

According to the question:

5n × 5(n + 1) = 300

⇒ n2 + n – 12 = 0

⇒ (n – 3) (n + 4) = 0

⇒ n = 3 and n = – 4.

As n is a positive natural number so n = – 4 will be discarded.

Therefore the numbers are 15 and 20.

(A) 3.5

(B) 4

(C) 3                                                                      

(D) – 3

Answer: (C)

Explanation:

Since y cannot be negative as negative square root is not real so y = 3.

8. If p2x2 – q2 = 0, then x =?

(A) ± q/p                                             

(B) ±p/q

(C) p                                                     

(D) q

Answer:(A)

Explanation:

p2x2 – q2 = 0

⇒p2x2 = q2

⇒x = ±p/q

(A) 3                                                                     

(B)5       

(C) 4                                                                      

(D) 7

Answer:(B)

Explanation:

10. If x2 (a2 + b2) + 2x (ac + bd) + c2 +d2 = 0 has no real roots, then

(A) ad≠bc                                                                           

(B) ad<bc

(C) ad>bc                                                                            

(D) all of these

Answer: (D)

Explanation:

If equation has no real roots then discriminant of the equation must be less than zero.

11. If the one root of the equation 4x2 – 2x + p – 4 = 0 be the reciprocal of other. Then value of p is

(A) 8                                                                                     

(B) – 8

(C) – 4                                                                                  

(D) 4

Answer:A

Explanation:

If one root is reciprocal of other, then product of roots is:

12. Rohini had scored 10 more marks in her mathematics test out of 30 marks, 9 times these marks would have been the square of her actual marks. How many marks did she get in the test?

(A) 14                                                   

(B) 16

(C) 15                                                                   

(D) 18

Answer:  (C)

Explanation:

Let her actual marks be x

Therefore,

9 (x + 10) = x2

⇒x2 – 9x – 90 = 0

⇒x2 – 15x + 6x – 90 = 0

⇒x(x – 15) + 6 (x – 15) = 0

⇒(x + 6) (x – 15) = 0

Therefore  x = – 6 or x =15

Since x is the marks obtained, x ≠ – 6. Therefore, x = 15.

13. A train travels at a certain average speed for a distance of 63 km and then travels a distance of 72 km at an average speed of 6 km/h more than its original speed. If it takes 3 hours to complete the total journey, what is its original average speed?

(A) 42 km/hr                                                                                                      

(B) 44 km/hr

(C) 46 km/hr                                                                                                      

(D) 48 km/hr

Answer: (A)

Explanation:

Let the original speed be x,

Then according to question

This gives x = -3 and x = 42

Since speed cannot be negative, so we ignore –3,

Therefore original average speed is 42 km/hr.

14. Satvik observed that in a clock, the time needed by the minute hand of a clock to show 3 PM was found to be 3 min less than t2/4 minutes at t minutes past 2 PM. Then t is equal to

(a) 14                                                                    

(b) 15

(c) 16                                                                    

(d) None of these

Answer: (A)

Explanation: We know that the time between 2 PM to 3 PM = 1 hr = 60 min

Given that at t minutes past 2 PM, the time needed by the minute’s hand of a clock to show 3 PM was found to be 3 minutes less than t2/4minutes

Therefore,

15. A takes 6 days less than B to finish a piece of work. If both A and B together can finish the work in 4 days, find the time taken by B to finish the work.

(A)12 days                                                                                          

(B) 12 ½ Days

(C) 13 days                                                                                         

(D) 15days

Answer: (A)

Explanation: Let B alone finish the work in x days.

Therefore, A alone can finish the work in (x – 6) days

A’s one day work = 1/x-6

B’s one day work = 1/x

Given that (A + B) can finish the work in 4 days.

Therefore, A’s one day work + B’s one day work = (A + B)’s one day work

As, x ≠ 2 , because if x = 2 , then A alone can finish work in (2 – 6) = – 4 days which is not possible.

Therefore we consider x = 12.

This implies B alone can finish work in 12 days and A alone will finish the work in 12 – 6 = 6 days.

All the above questions can also be downloaded in PDF from the following link:

Important Articles for the Preparations of Class 10 Maths Exam 2021-2022:

We have prepared some articles which will help the class 10 students in preparations for their Maths exam by summarising all important resources in one place. Students can check the following links to explore the important articles to prepare in an effective manner and perform well in the exam:

CBSE Class 10 Maths Important Questions and Answers for Board Exams

CBSE Class 10 Maths Solved Previous Year Question Papers

CBSE Class 10th Maths Chapter-wise Important Formulas, Theorems & Properties