Unit Test: Quadratic Equations | Mathematics (Maths) Class 10 PDF Download

Time: 1 hour

M.M. 30

Attempt all questions.

• Question numbers 1 to 5 carry 1 mark each.
• Question numbers 6 to 8 carry 2 marks each.
• Question numbers 9 to 11 carry 3 marks each.
• Question number 12 & 13 carry 5 marks each.

Q1: Equation of (x+1)²-x²=0 has number of real roots equal to: (1 Mark)
(a) 1
(b) 2
(c) 3
(d) 4

Q2: The sum of two numbers is 27 and product is 182. The numbers are: (1 Mark)
(a) 12 and 13
(b) 13 and 14
(c) 12 and 15
(d) 13 and 24

Q3: A train travels 360 km at a uniform speed. If the speed had been 5 km/h more, it would have taken 1 hour less for the same journey. Find the speed of the train. (1 Mark)
(a) 30 km/hr
(b) 40 km/hr
(c) 50 km/hr
(d) 60 km/hr

Q4: A quadratic equation ax2 + bx + c = 0 has no real roots, if _______________________________. (1 Mark)

Q5: The maximum number of roots for a quadratic equation is equal to (1 Mark)
(a) 1
(b) 2
(c) 3
(d) 4

Q6: The sum of areas of two squares is 468m2. If the difference of their perimeters is 24cm, find the sides of the two squares. (2 Marks)

Q7: If x =1, is a solution of the quadratic equation 3x² + 2kx – 3 = 0, find the value of k. (2 Marks)

Q8: The diagonal of a rectangular field is 60 metres more than the shorter side. If the longer side is 30 metres more than the shorter side, find the sides of the field. (2 Marks)

Q9: Solve the quadratic equation 2×2 – 7x + 3 = 0 by using quadratic formula. (3 Marks)

Q10: Find two numbers whose sum is 30 and product is 200. (3 Marks)

Q11: Find the roots of the following quadratic equations by factorization: (3 Marks)
(i) x² + 7x + 10 = 0
(ii) 3x² − 5x − 2 = 0

Q.12: A cottage industry produces a certain number of pottery articles in a day. It was observed on a particular day that the cost of production of each article (in rupees) was 3 more than twice the number of articles produced on that day. If, the total cost of production on that day was Rs.90, find the number of articles produced and the cost of each article. (5 Marks)

Q13: The diagonal of a rectangular field is 60 meters more than the shorter side. If the longer side is 30 meters more than the shorter side, find the sides of the field. (5 Marks)