Science-Class-11 Maths DPP Talent Search Examinations

Mathematics-XI MATHEMATICS 1. If the function f(x) = (x – a) (x – b) + k, a < b, k < 0 has real roots, then (a) both roots lie between a and b (b) only one of the roots lie between a and b (c) one root is smaller than a and other root is greater than b. (d) either both roots are smaller than a or both are greater than b. 2. The number of garlands that can be made out of 12 red identical flowers and 3 blue identical flowers is (a) 91 (b) 21 (c) 19 (d) 14 3. In a triangle, the minimum value of cot2A + cot2B + cot2C is (a) ½ (b) 1 (c) 2 (d) 3 4. In a triangle, the maximum value of sinA + sin B + sin C is (a) 1 (b) 3 (c) 3 3 2 (d) 33 5. In an acute angled triangle, the minimum value of tan A + tan B + tan C is (a) 3 (b) 33 (c) 9 (d) 27 6. The number of ways of distributing 5 Rasgullas, 4 Burfis and 1 Ladoo among 4 Beggars is (a) 3920 (b) 7840 (c) 15680 (d) 840 7. If the roots of the equation ax2 + bx + c = 0 are of form /(–1) and ( + 1)/, then the value of (a + b + c)2 is (a) 2b2 – ac (b) b2 – 2ac (c) b2 – 4ac (d) 4b2 – 2ac - : Rough Space : - [2] Mathematics-XI 8. If | z1 | = 1, | z2 | = 2, | z3 | = 3 and |z1 + z2 + z3 | = 1, then | 9z1z2 + 4z3z1 + z2z3 | is equal to (a) 6 (b) 36 (c) 216 (d) 1296 9. If a, b, c, p, q, r are six complex numbers such that p2  q2  c2 p  q  r  1 i and a b c a  b  c  0 , where i =  –1, p q r then value of a2 b2 r 2 is (a) 0 (b) – 1 (c) 2i (d) – 2i 10. If the ratio of the sums of m and n terms of an AP is m2 : n2, then the ratio of its mth and nth terms is (a) (m–1) : (n–1) (b) (2m + 1) : (2n +1) (c) (2m – 1) : (2n – 1) (d) none of the above 11. If a1, a2, a3, an are in HP, then a1 , a2  a3   an a2 a1  a3  ...an ,..., an a1  a2  an1 are in (a) AP (b) GP (c) HP (d) AGP 12. If (5 + 26)n = I + f; n, I  N; and 0  f < 1, then I equals (a) 1  f (b) 1  f  f (c) 1  f  f (d) 1  f  f m 10  20    p   13. The sum    ,  where,    0 if p  q  is maximum, when m is i 0  i  m  i    q   (a) 5 (b) 10 (c) 15 (d) 20 14. If 7 divides 323232 , the remainder is (a) 1 (b) 0 (c) 4 (d) 6 - : Rough Space : - [3] Mathematics-XI 15. In a game called “odd man out”, n(n>2) persons toss a coin to determine who will buy refreshments for the entire group. A person who gets an outcome different from that of the rest of the members of the group is called the odd man out. If the probability that there is a loser in any game is ½, then the value of n is (a) 4 (b) 7 (c) 8 (d) 11 16. The vertices of a triangle are A (x1, x1 tan ), B(x2, x2 tan ) and C(x3, x3 tan ). If the circumcentre of ABC coincides with the origin and H(a, b) be its orthocentre, then a b is equal to (a) cos  cos  cos  cos cos cos  (b) tan   tan  tan  sin   sin  sin  sin  sin sin  cos  cos  cos  (c) tan  tan tan  (d) sin  sin sin  17. Area of the parallelogram formed by the lines y = mx, y = mx + 1, y = nx and y = nx + 1 equals (a) | m  n | (m  n)2 (b) 2 | m  n | (c) 1 | m  n | (d) 1 | m  n | 18. Let AB be a chord of the circle x2 + y2 = r2 subtending a right angle at the centre, then the locus of the centroid of the triangle PAB as P moves on the circle is (a) a parabola (b) a circle (c) an ellipse (d) a pair of straight line 19. The number of rational point(s) (a point (a, b) is rational if a and b both are rational numbers) on the circumference of a circle having centre (, e) is (a) at most one (b) at least two (c) exactly two (d) infinite 20. PQ is any focal chord of the parabola y2 = 32x. The length of PQ can never be less than (a) 8 unit (b) 16 unit (c) 32 unit (d) 48 unit 🙤🙦🙥🙧 [4]