If Sum Of An Infinite Geometric Series Is 4 By 5 And Its First Term Is 3 By 4 Then Its Common Ratio Is Eq (1) 7/16 (2) 9/16 (3) 1/9 (4) none of these Solution: Given sum of infinite geometric series = 4/5 a = ¾ a/(1-r) = 4/5 3/4(1-r)... View Article
In A Gp T2 Plus T5 Eq 216 And T4 To T6 Eq 1 4 And All Terms Are Integers Then Its First Term Is (1) 16 (2) 14 (3) 12 (4) None of these Solution: For GP, tn = arn-1 t2 = ar t5 = ar4 Given t2 + t5 = 216 So ar + ar4 = 216... View Article
If The Sum Of The Series 1 Plus 2byx Plus 4 By X2 Plus 8 By X3 Infinity Is A Finite Number Then (1) x >2 (2) x>-2 (3) x >1/2 (4) none of these Solution: 1 + 2/x +4/x2 + 8/x3 +...∞ Here a = 1, r = 2/x S = a/1-r =... View Article
Consider An Infinite Gp With First Term A And Common Ratio R Its Sum Is 4 And The Second Term Is 3 By 4 Then (1) a = 4/7, r = 3/7 (2) a = 3/2, r = 1/2 (3) a = 2, r = 3/8 (4) a = 3, r = 1/4 Solution: Given first term = a Common ratio = r... View Article
If X Is Added To Each Of Number 3 9 21 So That The Resulting Numbers May Be In Gp Then The Value Of X Will Be (1) 3 (2) 1/2 (3) 2 (4) 1/3 Solution: 3+x, 9+x, 21+x are in GP. (9+x)2 = (3+x)(21+x) x2+18x+81 = x2+24x+63 6x = 18 So x = 18/6... View Article
If S Is The Sum To Infinite Of A Gp Whose First Term Is A Then The Sum Of The First N Terms Is (1) S(1-a/S)n (2) S(1-(1-a/S)n) (3) a(1-(1-a/S)n) (4) none of these Solution: Given first term = a Sum to infinity, S = a/(1-r)... View Article
X Eq 1 Plus Aplus A Sq Infinity Y Eq 1 Plus B Plus B Sq Infinity Then The Value Of 1 Plus Ab Plus A2b2 Infinity (1) xy/(x+y-1) (2) xy/(x+y+1) (3) xy/(x-y-1) (4) xy/(x-y+1) Solution: Given x = 1+a+a2+...∞ Here first term, a = 1, r = a Sum of... View Article
If Y Eq X X2 Plus X3 X4 Then The Value Of X Will Be (1) y + 1/y (2) y/(1+y) (3) y - 1/y (4) y/(1-y) Solution: Given y = x - x2 + x3-x4 +...∞ Here a = x Common ratio, r = -x Sum of... View Article
If 1 Plus Sin X Plus Sin Sq 2x Plus Upto Infinity Eq 4 2root3 Then X (1) π/3, 2π/3 (2) π/6, π/3 (3) π/3, 5π/6 (4) 2π/3, π/6 Solution: Given 1 + sin x + sin2x + ….upto ∞ = 4 + 2√3 This is an infinite... View Article
If A Eq 1 Plus R Z Plus R 2 Z Plus R 3z Infinity Then The Value Of R Will Be (1) A(1-A)z (2) ((A-1)/A)1/z (3) (1/A - 1)1/z (4) A(1-A)1/z Solution: Here a = 1 Common ratio, r = rz Sum of infinite terms of... View Article
If 3 Plus 3 Alpha Plus 3 Alpha Sq Infinity Eq 45 8 Then The Value Of Alpha Will Be (1) 15/23 (2) 7/15 (3) 7/8 (4) 15/7 Solution: Here a = 3 Common ratio, r = α Sum of infinite terms of GP = a/(1-r) 3 + 3α + 3α2... View Article
If The Product Of Three Consecutive Terms Of Gp Is 216 And The Sum Of Product Of Pair Wise Is 156 Then The Numbers Will Be (1) 1, 3, 9 (2) 2, 6, 18 (3) 3, 9, 27 (4) 2, 4, 8 Solution: Let a/r, a, ar be the 3 consecutive terms of GP. Product = 216... View Article
If S Is The Sum Of An Infinite Gp The First Term A Then The Common Ratio R Given By (1) (a-s)/s (2) (s-a)/s (3) a/(1-s) (4) (s-a)/a Solution: The sum of an infinite GP, s = a/(1-r) s(1-r) = a s-sr = a (s-a) = sr... View Article
The Sum To Infinity Of The Progression 9 3 1 1 By 3 Is (1) 9 (2) 9/2 (3) 27/4 (4) 15/2 Solution: Given series is a GP. Here a = 9 r = -1/3 Sum of infinite terms of GP, Sn = a/(1-r)... View Article
If A B C Are In Gp Then Which Is Correct (1) a2, b2, c2 are in G.P (2) a2(b + c), c2(a + b), b2(a + c) are in G.P (3) a/(b+c), b/(c+a), c/(a+b) are in G.P (4) None of the above... View Article
The Gm Of The Numbers 3 3 Sq 3 Cube 3n Is (1) 32/n (2) 3(n+1)/2 (3) 3n/2 (4) 3(n-1)/2 Solution: GM of 3, 32, 33….3n = (3 × 32 ×...3n)1/n = (31+2+3+...n)1/n =... View Article
If G Is The Geometric Mean Of X And Y Then 1 By G2 X2 Plus 1 By G2 Y2 Eq (1) G2 (2) 1/G2 (3) 2/G2 (4) 3G2 Solution: Since G is the geometric mean of x and y G2 = xy 1/(G2-x2) + 1/(G2-y2) = 1/(xy-x2) +... View Article
If N Geometric Means Be Inserted Between A And B Then The Nth Geometric Mean Will Be (1) a(b/a)n/(n-1) (2) a(b/a)(n-1)/n (3) a(b/a)n/(n+1) (4) a(b/a)1/n Solution: When n GMs inserted between a and b, then the series... View Article
The Product Of N Positive Numbers Is Unity Their Sum Is (1) A positive integer (2) Equal to n + 1/n (3) Divisible by n (4) Never less than n Solution: Let a1, a2, a3...an be the positive... View Article
The Solution Of The Equation 1 Plus A Plus A Sq Plus Ax Eq 1 A 1 A2 1 A4 Then X Is Equal To (1) 3 (2) 5 (3) 7 (4) None of these Solution: Given 1 + a + a2 + a3 + ...ax = (1+a)(1+a2)(1+a4) This is the sum of a GP with... View Article