The Sum Of 1 Plus 2 By 5 Plus 3 By 52 Plus 4 By 53 Upto N Terms Is Eq (1) (25/16) - (4n+5)/(16.5n-1) (2) (3/4) - (2n+5)/(16.5n-1) (3) (3/7) - (3n+5)/(16.5n-1) (4) (1/2) - (5n+1)/(3.5n+2) Solution: Let... View Article
The Nth Term Of The Series 2 Plus 4 Plus 7 Plus 11 Will Be (1) (n2 + n + 1)/2 (2) n2 + n + 2 (3) (n2 + n + 2)/2 (4) (n2 + 2n + 2)/2 Solution: Let S = 2+4+7+11+...n terms Sn-1 =... View Article
If Every Term Of A Gp With Positive Terms Is The Sum Of Its Two Previous Terms Then Common Ratio Of The Series Is 1) 1 2) 2/√5 3) (√5-1)/2 4) (√5+1)/2 Solution: Let a, ar, ar2 be the terms of the GP. Given a+ar = ar2 r2-r-1 = 0 Solving using... View Article
2 Plus 4 Plus 7 Plus 11 Plus 16 N Terms Eq (1) (â…™)(n2+3n+8) (2) (n/6)(n2+3n+8) (3) (â…™)(n2-3n+8) (4) (n/6)(n2-3n+8) Solution: Let S = 2+4+7+11+16+...n terms Sn-1 =... View Article
1 Plus 3 Plus 7 Plus 15 Plus 31 N Terms (1) 2n+1 - n (2) 2n+1- n - 2 (3) 2n- n - 2 (4) none of these Solution: Let Sn = 1 + 3 + 7 + 15 + 31+... tn …(i) Sn = 1 + 3 + 7 +... View Article
The Sum Of The Infinite Terms Of The Following Series 1 Pl 4 By 5 Pl 7 By 5 Sq Plus Will Be (1) 3/16 (2) 35/8 (3) 35/4 (4) 35/16 Solution: Let S = 1+ 4/5 + 7/52 + 10/53 +...upto ∞ …(i) Divide by 5 S/5 = 1/5 + 4/52 + 7/53... View Article
1 Plus 3 By 2 Plus 5 By 2 2 Plus 7 By 2 3 Plus Infinity Is Equal To (1) 3 (2) 6 (3) 9 (4) 12 Solution: Let S = 1+ 3/2 + 5/22 + 7/23 +...∞ ..(i) S/2 = 1/2 + 3/22+ 5/23 + 7/24+....∞ ..(ii) (i) -... View Article
If H Be The Harmonic Mean Between A And B Then The Value Of 1 By H A Plus 1 By H B Is (a) a + b (b) ab (c) 1/a + 1/b (d) 1/a - 1/b Solution: Since H is the HM between a and b, H = 2ab/(a+b) H-a = 2ab/(a+b) - a... View Article
Hm Between The Roots Of The Equation X2 10x 11 Eq 0 Is (1) 1/5 (2) 5/21 (3) 21/20 (4) 11/5 Solution: Let p and q be the roots of the equation x2-10x+11 = 0. Sum of roots, p+q = -b/a... View Article
The Harmonic Mean Of A By 1 Ab And A By 1 Plus Ab Is (a) a/√(1 - a2b2) (b) a/(1 - a2b2 ) (c) a (d) 1/(1 - ab) Solution: HM of x and y = 2xy/(x+y) Let x = a/(1-ab) y = a/(1+ab)... View Article
In An Hp Pth Term Is Q And Qth Term Is P Then Pq Th Term Is (1) 0 (2) 1 (3) pq (4) pq(p+q) Solution: Let the first term is a and d is the common difference of AP. tp = q 1/(a+(p-1)d) = q... View Article
If A B C Be In Hp Then (1) (a-b)/(b-c) = a/c (2) (b-c)/(c-a) = b/a (3) (c-a)/(a-b) = c/b (4) (a-b)/(b-c) = c/a Solution: Given a, b, c be in H.P, 1/a,... View Article
If A B C D Are In Hp Then Ab Bc Cd Is Equal To (1) 3ad (2) (a+b)(c+d) (3) 3ac (4) none of these Solution: Given a, b, c, d are in HP. b = 2ac/(a+c) Also c = 2bd/(b+d)... View Article
If A B C Are Three Distinct Positive Real Number Which Are In Hp Then 3a 2b By 2a B Plus 3c Plus 2b By 2c B Is (1) greater than or equal to 10 (2) less than or equal to 10 (3) only equal to 10 (4) None of these Solution: Given a, b, c are... View Article
If X Y Z Are In Hp Then The Value Of The Expression Log X Plus Z Plus Log X 2y Plus Z Will Be (1) log (x-z) (2) 2 log (x-z) (3) 3 log (x-z) (4) 4 log (x-z) Solution: Given x, y, z are in HP. So y = 2xz/(x+z) log (x+z)+ log... View Article
If Log10 X3 Y3 Log10 X2 Y2 Xy 2 The Maximum Value Of Xy For All X 0 Y 0 Is (1) 2500 (2) 3000 (3) 1200 (4) 3500 Solution: Given log10 (x3+y3) - log10(x2+y2-xy) ≤ 2 log10 [(x3+y3)/(x2+y2-xy)] ≤ 2 log... View Article
If A1 A2 A3 Are In Gp Then The Value Of The Determinant (1) -2 (2) 1 (3) 2 (4) 0 Solution: a1, a2, a3, ... are in GP. So r = a2/a1 = a3/a2 = …= an/an-1 C3 → C3-C2 C2 → C2-C1... View Article
Let An Denote The Number Of All N Digit Positive Integers Formed By The Digits 0 1 Of Both Such That No Consecutive Digits In Them Are 0 (1) 7 (2) 8 (3) 9 (4) 11 Solution: Find all 6 digit numbers which ends with 1 so that no consecutive digits are 0. There can be 3... View Article
Statement 1 The Sum Of The Series 1 1 2 4 4 Is 8000 Statement 2 (1) Statement I is false, Statement II is true (2) Statement I is true, Statement II is true; Statement II is a correct explanation of... View Article
Statement 1 For Every Natural Number N Greater Than 2 Statement 2 For Every Natural Number N Statement-1 : For every natural number n ≥ 2, 1/√1 + 1/√2 +... 1/√n >√n. Statement-2 : For every natural number n ≥ 2, √(n(n + 1)) < n+1.... View Article