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  1. ONE MILE ACADEMY CLASS TEST-OI (Quadratic Equation) Batch Name• Date MM:120 TIME: 1:30 hr 1. 2. 3. 4. 5. 6. 7. 8. 9. If p and q are roots of the equation 2cos x + 3sin x = 1, then the value of tan(p + q) is (c) 13 /9 (c) 12 /5 (d) none of these If sino and seco (0 < 0 < /2) are the roots of the equation 2x2 + kx + I = 0, then the value of k is equal to 7vfi (a) 5 7vG (d) 5 The value of p for which the sum of the squares of the roots of 2x2 — 2 (p - 2) x — p — 1 = 0 is least is If the product of the roots of the equation (u +1)x2 + (20 + 3) x +(3u + 4) = 0 be 2, then the sum of roots is If the ratio of the roots of ux2 + 2bx + c = 0 is same as the ratio of the px2 + 2qx + r = 0, then 2b cc c pr (c) ac pr b q ac pr (d) none of these If the roots of the equation 12x2 — mx + 5 = 0 are in the ratio 2 : 3, then m is equal to 21p2 = 0, where p e R. then the minimum value of 014 + [34 is If u and [3 be the roots of the equation x2 — PX - 2 If p(q - r) x2 + q(r - q) x + r(p - q) = 0 has equal roots, then — = q Let u, be the roots of the equation x2 — PX + r = 0 and -E, 2ß be the roots of the equation x2 — qx + r 0. Then the value of r is (a) (p - q) (2q - p) (b) (q — 2p) (2q - p) (c) (q - p) (2P - q) (d) (2P - q) (2q - p) 10. The equation formed by decreasing each roots of ux2 + bx + c by 1 is 2x2 8x + 2 = 0, then -a -c 11. If a and ß are the roots of the equation x2 - ax +b = 0 and An = an + [311; then which of the following is true (a) An +1 = a An + b An 1 (b) An +1 = ÜuAn - bAn—1 (C) An +1 = bAn + (XAn—1 (d) An +1 = bAn - (XAn—1 12. If the roots of the equation x2 — bx + c = 0 be two consecutive integers, then b2 — 4c equals 13. If the roots of the quadratic equation x2 + PX + q = 0 are tan 300 and tan 150, respectively, then the value of 2 + q —p is 14. If u and ß (u < ß) are the roots of the equations x2 + bx + c = 0, where c < 0 < b, then (d) u < 0 < lul < ß 15. Let f (x) = 3ux2 — 4bx + c (u, b, c e R, u #0), where u, b, c are in AP. Then the equation f (x) = 0 has (a) No real solution (b) Two unequal real roots (c) sum of roots always negative (d) products of roots always positive 16. If the roots of the quadratic equation x2 + 6x +b = 0 are real and distinct and they differ by at most 4, then the range of values of b is
  2. ONE MILE ACADEMY (b) [6, 10] 17. Let u, b, c e R and u be such that (u +c)2 < b2, then the quadratic equation ux2 + bx + c = 0 has (a) Imaginary roots (b) Real roots (c) two real roots lying between (-1, 1) (d) none of these 18. If the equation x2 4x + logl/2 u = 0 does not have two distinct real roots, then the maximum value of u is 1 (a) 16 (d) none of these 19. Let u, b, c be three sides of a triangle. Suppose u and b are the root of the equation x2 (c + 4) + 4 (c + 2) = 0 and the largest angle of the triangle is 0 degrees. Then 0 = (a) 1200 (b) 1350 (c) 1500 (d) 900 20. If the roots of the equation ux2 + x + b = 0 be real and distinct, then the roots of the equation x2 4 v/äb x +1 = 0 will be (a) Rational (b) Real (c) Irrational (d) Imaginary 21. The greatest value of a non-negative real number for which both the equations 2x2 + (X - l)x + 8= 0 and x2 — 8x + + 4 = 0 have real root is (b) 15 (c) 12 (d) 16 22. If a

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