If S1 S2 S3 Are The Sum Of First N Natural Numbers Their Squares And Their Cubes Respectively Then S3 1 8 S1 By S2 Sq Is Equal To
(1) 1 (2) 3 (3) 9 (4) 10 Solution: S1 = sum of first n natural numbers = n(n+1)/2 S2... View Article
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If 1 5 Plus 2 52 Plus 3 53 Plus N 5n Eq 4n 1 5a Plus 1 Plus B By 16 Then
(1) a = n, b = 1 (2) a = n, b = 5 (3) a = 1, b =... View Article
If A1 A2 A3 A1 Greater Than 0 Are In Gp With Common Ratio R Then The Value Of R For Which The Inequality 9a1 Plus 5a3 Greater Than 14a2 Holds Cannot Lie In The Interval
If a1, a2, a3 (a1>0) are in GP with common ratio r, then the value of r, for which the... View Article
Let A B C Be The Positive Real Numbers Such That Bx2 Plus Root A Plus C2 Plus 4b2x Plus A Plus C Greater Than 0 For All X Belongs To R Then A B C Are In
(1) AP (2) GP (3) HP (4) None of these Solution: bx2+√((a+c)2+4b2)x+ a+c ≥ 0 bx2+((a+c)2+4b2)0.5x+ a+c ≥ 0 Discriminant... View Article
Let The Sum Of First N1 First N2 And First N3 Terms Of An Ap Be Denoted By S1 S2 And S3 Respectively Then The Value Of
Let the sum of first n1, first n2 and first n3 terms of an AP be denoted by S1, S2... View Article
The Sum Of The Products Taken Two At A Time Of The Numbers 1 2 2 2 2 N 2 2 N 1 Is
The sum of the products taken two at a time of the numbers 1, 2, 22,….2n-2, 2n-1 is (1) (1/3)22n... View Article
The Sum Of The Series 9 By 19 Plus 99 By 19 Square Plus 999 By 19 Cube Plus Infinity Is
(1) 19/18 (2) 18/19 (3) 7/18 (4) none of these Solution: Given 9/19 + 99/192 + 999/193 + 9999/194 +….∞... View Article
The Sum Of The N Terms Of The Series 12 By 1 3 Plus 22 By 3 5 Plus 32 By 5 7 Plus N2 By 2n 1 2n Plus 1 Is
(1) (2n2+1)/(2n+1) (2) n(n+1)/2(2n+1) (3) (2n2+1)/4(2n+1) (4) none of these Solution: Given series 12/1.3 + 22/3.5 + 32/5.7 +…..+n2/(2n-1)(2n+1) Here... View Article
The Sum Of The N Terms Of The Series 1 Sq By 1 Plus 1 Sq Plus 2 Sq 1 Plus 2 Plus 12 Is
The sum of the n terms of the series 12/1 + (12+22)/(1+2) + (12+22+32)/(1+2+3) + ….is (1) (n+1)(n+2)/3 (2) n(n+2)/3... View Article
If 5 Plus 9 Plus 13 Plus N Terms By 7 Plus 9 Plus 11 Plus N 1 Terms 17 By 16 Then N Is Equal To
(1) 7 (2) 6 (3) 9 (4) none of these Solution: Given (5+9+13+…n terms)/(7+9+11+…(n+1) terms) = 17/16 (5+9+13+…n terms) =>... View Article
Let F N Equal N Plus 50 By 100 Where N Denotes The Integral Part Of X Then
Let f(n) = [(n+50)/100] where [n] denotes the integral part of x . Then (1) ∑n = 1100 f(n) =... View Article
1 Plus 3 1 1 Plus 3 2 1 Plus 3 4 1 Plus 3 8 1 Plus 3 2n Is Equal To
(1+3-1)(1+3-2)(1+3-4)(1+3-8) …..(1+3-2n) is equal to (1) \(\begin{array}{l}\frac{3}{2}(1+3^{-2^{n}})\end{array} \) (2) \(\begin{array}{l}\frac{3}{2}(1-3^{-2^{n}})\end{array} \) (3) \(\begin{array}{l}\frac{3}{2}(1-3^{-2^{n+1}})\end{array} \) (4) none of these Solution: S... View Article
Let Ai Plus Bi Eq 1 I Eq 1 2 N And A Eq 1 By N A1 Plus A2 Plus An B Eq 1 By N B1 Plus B2 Plus Bn Then A1b1 Plus A2b2 Plus Anbn Is Equal To
Let ai + bi = 1 (i = 1,2,..n) and a = (1/n)(a1 + a2 +….+an) , b = (1/n)(b1... View Article
A B C Are Positive Real Numbers Which Are In Hp Then A Plus B By 2a B Plus C Plus B By 2c B Is
(1) ≥ 4 (2) 0 (3) ≤ 4 (4) none of these Solution: Given a, b, c are in HP.... View Article
If Xi Greater Than 0 I Equal 1 2 3 N Then X1 Plus X2 Plus Xn 1 By X1 Plus 1 By X2 Plus 1 By Xn Is Equal To
(1) n2 (2) ≥ n2 (3) ≤ n2 (4) none of these Solution: Arithmetic mean, A of x1, x2, …xn... View Article
If An Equal Sigma N By N Factorial Then The Sum Of The Series Sigma An Is
(1) e (2) e-1 (3) 3e/2 (4) e/2 Solution: an = Σn/n! = n(n+1)/2n! = (n+1)/2(n-1)! = (n-1+2)/2(n-1)! = (½)... View Article
The Sum Of The Series 12 By 2 Fact Plus 28 By 3 Fact Plus 50 By 4 Fact Plus 78 By 5 Fact Is
(1) e (2) 4e (3) 3e (4) 5e Solution: Let Sn = 12 + 28 + 50 + 78 +…tn... View Article
5 By 1 2 3 Plus 7 By 3 4 5 Plus 9 By 5 6 7 Plus Is Equal To
(1) log (8/e) (2) log 8e (3) log e/8 (4) none of these Solution: S = 5/1.2.3 + 7/3.4.5 +... View Article
1 Plus 3 By 2 Fact Plus 7 By 3 Fact Plus 15 By 4 Fact Plus Infinity Equals
(1) e(e+1) (2) e(1-e) (3) e(e-1) (4) 3e Solution: Let S = 1+ 3/2! + 7/3! + 15/4! +…∞ Tn... View Article
The Sum Of 1 Sq 2 By 1 Fact Plus 2 Square 3 By 2 Fact Plus Infinity
(1) 5e (2) 3e (3) 7e (4) 2e Solution: Given 12.2/1! +22.3/2! + 32.4/3! +….∞ Tn = n2(n+1)/n! = n(n+1)/(n-1)!... View Article
