Quadratic Equations Practice Problems: Level 02

Q1. The length of a rectangle is less than twice its breadth by 1 cm. The length of its diagonal is 17 cm. Find its length and breadth
A. 15 cm, 8 cm
B. 13 cm, 4 cm
C. 10 cm, 6 cm
D. 8 cm, 9 cm
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Q2. The sum of the squares of two consecutive natural numbers is 145. Find those numbers.
A. 6, 7
B. 10, 11
C. 8, 9
D. 10, 9
Q.3. The sum of the squares of two consecutive even natural numbers is 52. Find those numbers.
A. 2, 4
B. 4, 6
C. 8, 10
D. 7, 9
Q.4. The length of a rectangle is greater than twice its breadth by 2 cm. The length of its diagonal is 13 cm. Find the length and the breadth of the rectangle.
A. 12 cm, 5 cm
B. 5 cm, 3 cm
C. 6 cm, 15 cm
D. 9 cm, 7 cm
Q.5. In a right-angled triangle the length of one of the side containing the right angle is greater than twice the length of the other by 4 cm. The area of the triangle is 80 sq. cm. Find the length of the sides containing the right angle.
A. 3 cm, 4 cm
B. 7 cm, 8 cm
C. 20 cm, 8 cm
D. 13 cm, 15 cm
Q.6. In a rectangular mango-grove, the number of trees lengthways is 5 more than the number of trees breadthways. If the total number of trees is 1,400, find the number of trees lengthways and breadthways.
A. 35, 40
B. 45, 40
C. 30, 25
D. 40, 35
Q.7. If α and β are the roots of the equation x2 + ax + b = 0, where b ≠ 0, then the roots of the equation bx 2 + ax + 1 = 0 are:
A. 1/α, 1/β
B. α2β2
C. 1/α2, 1/β2
D. α/β, β/α
Q8. Sum of three numbers in GP is 70. If the two extreme terms are multiplied by 4, and the middle term by 5, the resultants are in AP. What is the highest of the three numbers given?
A. 20
B. 40
C. 10
D. 100
Q9. There are three terms ; a, b, c between 2 & 18 such that (i) their sum is 25, (ii) 2, a, b are consecutive terms of an A.P. and (iii) b, c, 18 are the consecutive terms of a G.P. Find the value of c.
A. 5
B. 8
C. 15
D. 12
Q10. The sum of three numbers in GP is 21/4 and their product is 1. What are the numbers?
A. 4, 1, 1/4
B. 2, 1, 1/2
C. 3, 1, 1/3
D. None of these
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