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MATHEMATICS, , Daily Practice Problems, Class:XI, Q.1, , Q.2, , Discussion Date: 16-17/09/2015, , [SINGLE CORRECT CHOICE TYPE], [5 × 3 = 15], Let x1 and x2 be the real solutions to x2 + ax + 1 = 0 for some real number a. If x1 + 1, and x2 + 1 are solutions of the equation x2 – a2x + a2 = 0, then the sum of squares of all possible values, of a is, (A) 1, (B) 4, (C) 5, (D) 7, For x > 0, the sum of the series, (A), , Q.3, , Time: 30 Min., , 1, 4, , (B), , 1, (1  x ), (1  x ) 2, , ,  ....... is equal to, 1 x, (1  x ) 2, (1  x )3, , 1, 2, , For 0 < x < , the solution to the equation, , number. The value of (A + B) is, (A) 9, (B) 7, Q.4, , (C), , 3, 4, , (D) 1, , 2, (2  cos x )1, A, is x =, , where B is a prime, =, 2, ,  19, B, 3 , , 2  cos x , , , (C) 5, , (D) 4, , The sum of a certain infinite geometric series is 20. When all the terms in the series are squared, the sum, of the resulting series is 80. If the first term of the original series is expressed in lowest terms as, p, , (p, q  N) then the value of (p + q) is, q, (A) 21, (B) 22, , Q.5, , Target JEE, M.M.: 30, Dpp. No.-65, , (C) 23, , p6, , then p satisfies, 8p, (B) 6 < p < 8, (C) 7 < p < 8, , (D) 24, , If  is an acute angle and sin  , (A) 6 < p < 7, , (D) 4 < p < 7, , [COMPREHENSION TYPE], Paragraph for question nos. 6 & 7, Let f (x) = cos x + sin x – 1 and g(x) = sin 2x – 2., Q.6, , Q.7, , Q.8, , [2 × 3 = 6], , 7 , , is equal to, Number of solutions of the equation f(x) = g(x) in x   ,, 2 , , (A) 4, (B) 5, (C) 6, (D) 8, , If the equation f(x) = k has atleast one real solution then the number of possible integral values of k is, equal to, (A) 1, (B) 2, (C) 3, (D) 4, [MATRIX TYPE], [3+3+3=9], 5, In triangle ABC, if a = 10, b = 24 and sin A = ., 13, Column-I, Column-II, (A), Perimeter of triangleABC is, (P), 4, (B), Inradius of triangleABC is, (Q), 13, (C), Circumradius of triangleABC is, (R), 25, (S), 60, [Note :All symbols used have usual meaning in triangleABC.], PAGE # 1

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MATHEMATICS, , Daily Practice Problems, , Class:XI, , Target JEE, Discussion Date: 18-19/09/2015, M.M.: 24, Dpp. No.-66, , Time: 24 Min., , [SINGLE CORRECT CHOICE TYPE], Q.1, , Sum of the reciprocals of all the 100 harmonic means if these are inserted between 1 and, (A) 100, , Q.2, , [6 × 3 = 18], , (B) 5050, , (C), , 1, 100, , Let A, B where 0°  A, B  180° and sin A + sin B =, (A + B) is equal to, (A) 30°, , (B) 60°, , (D), , 1, 5050, , 3, , cos A + cos B =, 2, , (C) 90°, , 1, is, 100, , 1, , then the value of, 2, , (D) 120°, , Q.3, , Let an be a sequence such that a1 = 2 and an+1 – an = 2n for all n  N, then a100 equals, (A) 1010, (B) 5050, (C) 9902, (D) 10100, , Q.4, , Which one of the following formulas describes all solutions to the equation, log 2 + log (sin ) + log (cos ) = 0, where  is in radians?, , , (B)  = k +, 4, 4, [Note: Where k  I ], , (A)  = 2k +, , (C)  = k +, , , 2, , (D)  = 2k ±, , Q.5, , The sum of the series (2)2 + 2 (4)2 + 3 (6)2 + ………… upto 10 terms is equal to, (A) 11300, (B) 12100, (C) 12300, (D) 11200, , Q.6, , In the interval [0, 2], the equation logcos (sin 2) = 2 has, (A) no solution, (B) unique solution, (C) two solutions, , (D) infinitelymanysolutions, , [COMPREHENSION TYPE], Paragraph for question nos. 7 & 8, Let a, b, c be distinct non-zero real numbers such that, Q.7, Q.8, , , 4, , [2 × 3 = 6], ,   a 3 1  b 3 1  c3, , , , then, a, b, c, , The value of (a + b + c) is equal to, (A) 0, (B) 1, , (C) 2, , (D) 3, , The value of (a3 + b3 + c3) is equal to, (A) –1, (B) 2, , (C) 3, , (D) 4, , PAGE # 2

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MATHEMATICS, , Daily Practice Problems, Class:XI, Q.1, , Q.2, , Time: 24 Min., , [SINGLE CORRECT CHOICE TYPE], [6 × 3 = 18], Let a1, a2, a3, ...... , an be in geometric progression. If a1 + a3 + a5 = 455 and a2 + a4 + a6 = 1365,, then the ratio between each consecutive term is, (A) 2, (B) 3, (C) 4, (D) any other number, , Let f(x) =, , x 2  px  1, . If f(x) is defined for every x  R, then the number of integers in the range, x2  p, , of p, is, (A) 2, , Q.3, , (B) 3, , (C) 4, , (D) 5, , b, In triangle ABC, if a sin A sin B + b cos2A = 2 a, then the value of   is, a, , (A), Q.4, , Discussion Date: 21-22/09/2015, , Target JEE, M.M.: 26, Dpp. No.-67, , 1, 2, , (B) 2, , (C), , 2, , If 3 cos2x + 7 sin2x = 4, then (cosec2 x + cot2x) is equal to, (A) 4, (B) 5, (C) 6, , (D) 1, , (D) 7, , Q.5, , Number of values of x  [0, 360°] satisfying the equation cos 2x = 3 cos x – 2 is, (A) 6, (B) 4, (C) 3, (D) 2, , Q.6, , If e and e– are the roots of equation 3x2 – (a + b)x + 2a = 0, a, b,  R,  0 then least integral, value of b is, (A) 4, (B) 5, (C) 9, (D) 10, , Q.7, , Q.8, , [MULTIPLE CORRECT CHOICE TYPE], [2 × 4 = 8], th, If Sn denotes the sum of first n terms of an Arithmetic progression and an denotes the n term of the, same A.P. Given Sn = n2p; Sk = k2p; where k, p, n  N and k  n then, (A) a1 = p, (B) common difference = 2p, 3, (C) Sp = p, (D) ap = 2p2 – p, The general solution of the trigonometric equation sin x cos 2x + sin 2x cos 5x = sin 3x cos 5x, is, n, 3, (where n  I), , (A), , (B), , 2 n, 9, , (C) 2n, , (D), , n, 2 n, , 3, 9, , PAGE # 3

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MATHEMATICS, , Daily Practice Problems, Class:XI, , Time: 24 Min., , Discussion Date: 23-24/09/2015, , Target JEE, M.M.: 26, Dpp. No.-68, , [SINGLE CORRECT CHOICE TYPE], 2, , If x [0, 2], then the number of solution of equation 81sin, (A) 2, (B) 4, (C) 8, , Q.2, , The value of the expression (2 sin2 91º – 1) (2 sin2 92º – 1) ............... (2 sin2 180º – 1) is equal to, (A) 0, (B) 1, (C) 290, (D) 290 – 90, , Q.3, , Consider the quadratic function f(x) = ax2 + bx + c where a, b, c  R and a  0,, such that f(x) = f(2 – x) for all real number x. The sum of the roots of f (x) is, (A) 1, (B) 2, (C) 3, (D) 4, , Q.4, , A geometric sequence has four positive terms a1, a2, a3, a4. If, (B) 9, ,  81cos, , [4 × 3 = 12], , Q.1, , (A) 3, , x, , 2, , x, ,  30 , are equal to, (D) Infinite, , a3, 4, = 9 and a1 + a2 = , then a4 equals, a1, 3, , (C) 27, , (D) 3 3, , [COMPREHENSION TYPE], [2 × 3 = 6], Paragraph for question nos. 5& 6, Let  and  be the roots of the equation x2 – 3x + 5 = 0. p and q are two real numbers given as, p = 33 – 92 + 15 + 2 and q = 4 – 33 + 72 – 6 + 13., Q.5, Q.6, , Q.7, , The value of p + q is equal to, (A) 3, (B) 5, , (D) 9, , If the equation 2x2 – bx + c = 0 , (b, c  Q) has one of the roots is p + q , then the value of (b + c), is equal to, (A) – 6, (B) – 3, (C) 6, (D) 10, [MULTIPLE CORRECT CHOICE TYPE], With usual notation in a  ABC, b2 sin2C + c2 sin2B equals, (A), , Q.8, , (C) 7, , abc, R, , (B), , 2abc, R, , (C), , abc, 2R, , [2 × 4 = 8], , (D) 2 bc sinA, , If log10(sin x) + log10(tan y) + log10 2 = 0 and cot y = 2 3 cos x, then ordered pair (x, y) satisfying, the equations simultaneouslyis(are),  , (A)  , , 3 3, ,  , (B)  , , 3 6, ,   2 , , (C)  ,, 6 3 , ,   7 , , (D)  ,, 3 6 , , PAGE # 4