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CBSE Class 10 Exam 2023 : Mathematics : Quadratic Equations

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MATHEMATICS TEST QUADRATIC EQUATIONS TEST - 2 CLASS X Time: 1 HOUR Date: August 2, 2023 Total marks: 30 SECTION - A Answer ALL the questions. Choose the correct answer. 3 1=3 V 1. If the sum of the squares of the zeroes of a quadratic polynomial P (x) = x2 8x + k is 40, then the value if k is (A) 9 (B) 12 (C) 11 (D) 14 M 2. If x = 1 is a common root of the equations ax2 + ax + 3 = 0 and x2 + x + b = 0, then ab = (A) 3 (B) 3.5 (C) 6 (D) -3 S 3. If and are the zeroes of the quadratic polynomial Q(x) = x2 +px+q, then a polynomial with 1 and 1 as its zeros are (A) x2 +qx+p (B) x2 px+q (C) qx2 +px+1 (D) px2 +qx+1 SECTION - B Answer ALL of the following questions. 4. Find the zeroes of the polynomial 4 5x2 17x + 3 5 = 0. 3 2=6 Or Solve for x: 6x + 7 (2x 7) = 0. 5. A girl is twice as old as her sister. Four years hence, the product of their age (in yaers) will be 160. Find their present ages. 1 6. Using quadratic formula, solve the following quadratic equation in x: p2 x2 + (p2 q 2 )x q 2 = 0. SECTION - C Answer ALL of the following questions. 3 3=9 7. Find the value of m for which the quadratic equation (m 1)x2 +2(m 1)x + 1 = 0 has two real equal roots. Or V 8. One fourth of a group of people claim they are creative, twice the square root of the group claim to be caring and the remaining 15 claim they are optimistic. Find the total number of people in the group. M The perimeter of a right traingle is 60 cm. Its hypotenuse is 25 cm. Find the area of the triangle. S 9. If p,q,r and s are real numbers such that pr = 2(q + s), then show that at least one of the equations x2 + px + q = 0 and x2 + rx + s = 0 has real roots. SECTION - D Answer ALL of the following questions. 3 4=12 10. Two pipes can fill a watertank in 35 minutes. If the pipe with larger diameter alone can fill the same tank in 24 minutes less than the time taken by the pipe with smaller diameter. Find the time taken by each pipe working alone to fill the tank. 11. Solve for x: 2 x+2 2x 3 9 2x 3 x+2 = 3; given that x 6= 2, x 6= 3/2. 2 12. A train travelling at a uniform speed for 360 km, would have taken 48 minutes less to travel the same distance if its speed were 5 km/hour more. Find the original speed of the train. Or V At present Asha s age (in years) is 2 more than the square of her daughter Nisha s age. When Nisha grows to her mother s present age, Asha s age would be one year less than 10 times the present age of Nisha. Find the present ages of both Asha and Nisha. S M - - - - - - ALL THE BEST - - - - - - 3

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