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Time Allowed: 1 hour and 20 minutes, , 1,, , SND PUBLIC SCHOOL, , BINOMIAL, JEE main - Mathematics, , The sum of coefficients of integral powers of x in the binomial expansion (1 - 2,/)°" is, a) + (35 +1) b) 4 (350-1), c) 4 (359) d), 35, , The number of rational terms in the expansion of (2? + 3m) is, , a, 2, , $ (250+ 1), , a)6 b)s, 8 d)7, If (2x2 - x - 1)5 = ag + ayx + ax? +... + aqgx?9, then ap + ag + ag + ag + ag =, a) 15 b) 16, c) 30 d) 17, The coefficient of the middle term in the binomial expansion, in powers of x, of (1 + ax)* and, of (1 - ccx)® is same, if a equals, s ., a-a bh) — =, 10 3, os a =, , t 1\ 10, The sum of the rational terms in the binomial expansion of (23 + 37) is:, , a) 32 b) 41, 09 d) 25, , 5, The value of the expression “* Cy + S$ °C; is equal to:, i, , a) S2c, b) 49¢4, , 0) 47¢, a) 52¢,, If the sum of the coefficients in the expansion of (2 — 152 + 152°) 21 7x. 17x5 + 3)2915 is, n, then the number of dissimilar terms in the expansion of (1 + x)" is:, , a)3 b)1, , 4 dj2, , If C, stands for "C,, then the sum of the series, , 2(2)( 2), 2(3)G)t [Gj — 20} + 307 —...+ (—1)"(n+ 1)C2], where nis an even positive, , nl, , Maximum Marks: 100, , [4], , (4), , [4], , [4], , (4), , [4], , [4], , (4)
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10., , 11., , 12., 13., , 14,, , 15., , 16., , 17,, , 18., , 19,, , integer, is, a) (-1)"/(n + 2) D) (-1)%(n +1), c) None of these 4) (-1)"(n + 1), , t n, If the fifth term in the expansion of (« a+ 1) does nat depend on x, then n is equal to, , as bh) 20, e)12 d) 16, reed, Let (1 + x2)? (1 +x)" = S7 a, + a®, fay, ag, ag are in A.P, the n is equal to, mo, a) 2,3,4 b6, os a7, , Let X = (191)? + 2(1C2)* + (Cg)? + .... + 10(1C yo), where C,, r € {1, 2,...,10} denote, binomial coefficients. Then, the value of sor is, , The coefficient of x? in the expansion of (1 + x) (1 + x*) (1+ a4)... (1 + x!) is, , If some three consecutive coefficients in the binomial expansion of (x+1)" in powers of x are, , in the ratio 2:15:70, then the average of these three coefficients is, The sum of n terms of the series 4 + : + “ + = +, , , , , , , , , , , , , , 5 1 sn—1 3—20n, a+$ (1-4) - 2h b) 6+ 3, , 5 1 inl 25 1 Sn—L, Se-t(1-gh)- 95° 3(t-s)- ae, , Let (a4, a2, 43, ..., An) and (by, bg, bg, ..., by) be numbers such that aj + bj = 1 for all i= 1, 2, 3,...,, n. Ifa = A.M. of (a3, a2, .... @n), and b = A.M. of (by, bg, ..., bp), then ayby + agb2 + ... * andy + (ay , a)? + (ay - a)* +... +(ay- a)? =, a) nab b) n(a + b), © n(a* +b) @) nab?, , Ina certain A.P,, 5 times the 5" term is equal to 8 times the 8" term, then the 13" term is:, a) -13 bo, , e)-1 d) -12, Ifa, b and c be three distinct real numbers in GP and a + b + c = xb, then x cannot be, , a)-2 hb) -3, ey2 dj4, , Tor any three positive real numbers a, b and c, if 9(25a” + b*) + 25 (c? - 3ac) = 15b (3a + c), then, a) b, c and a are in AP b) b,c and a are in GP, , c) a,b and c are in GP d) a, band c are in AP, If the sides of a right-angled triangle are in A.P., then the sines of the acute angles are:, , [4], , [4], , [4], , [4], [4], , (4), , [4], , [4], , [4], , [4], , [4], , 2/3
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20,, , 21., , 22., , 23., , 24,, , 25., , , , a) v3.5 » fea fen, v VF, , Va, © {ve | fin a 2,4, Vor ye brs, Let a4, 82,...... a19 be in AP and hj, hg, equal to....., hag be in HP, If ay = hy = 2 and ayo = hig = 3,, then aghy is, a)3 b)2, os a6, , Ifa, b, c are in G.P. and log a - log 2b, log 2b - log 3c and log 3c - log a are in A.P., then a, b, c are, the lengths of the sides of a triangle which is:, , a) acute angled b) right angled, c) equilateral d) obtuse angled, Ifthe n' term of A.P. y'512, V/450, v/392, ... is V2, then n is:, a) 13 b) 15, ©) 16 d)14, Ifa, b, c are in G.P., then:, aaa st aa areinG.P. b) None of these, ©) a2, b?, c? are in G.P. ) a%(b + c), (a +b), b%a +c) are in, , GP., , 30 15, Let ay, @9,.....439 be an AP, S= Sa; and T= S$ ay;_1. fas = 27 and S - 2T = 75, then ayg is equal, i-1 1, , to ,, , Let X be the set consisting of the first 2018 terms of the arithmetic progression 1, 6, 11, ..., and, Y be the set consisting of the first 2018 terms of the arithmetic progression 9, 16, 23, .... Then,, the number of elements in the set X L Yis, , , , [4], , [4], , (4), , [4], , ), , (4), , 3/3
