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If Abc Are Three Vectors Such That A3 B4 C5 And Abc Are Perpendicular To Bccaab

1) 5√2 2) 6√2 3) 3√2 4) 4√2 Answer: 5√2 Solution: Given, a,b,c are three vectors such that ∣a∣=3,∣b∣=4,∣c∣=5 a,b,c are perpendicular to... View Article

If Theta Be The Angle Between The Vectors A2i2jk And B6i3j2k Then

1) cos θ = 4/21 2) cos θ = 3/19 3) cos = 2/19 4) cos θ = 5/21 Answer: cos θ = 4/21 Solution: a = 2i+2j-k and b = 6i-3j+2k cos θ =... View Article

The Sum Of The Series 6 66 666 Upto N Terms Is

(1) (10n-1 - 9n + 10)/81 (2) 2(10n+1 - 9n - 10)/27 (3) 2(10n - 9n - 10)/27 (4) none of these Solution: S = 6 + 66 + 666 + ... upto... View Article

If The Sum Of Three Terms Of Gp Is 19 And Product Is 216 Then The Common Ratio Of The Series Is

1) -3/2 2) 3/2 3) 2 4) 3 Solution: Let a/r, a, ar be the three terms of GP. Product = 216 (a/r)a(ar) = 216 a3 = 216 a = 6 Sum... View Article

The Sum Of 100 Terms Of The Series 09 Plus 009 0009 Will Be Equal To

(1) 1- (1/10)100 (2) 1+ (1/10)106 (3) 1- (1/10)106 (4) 1+ (1/10)100 Solution: Here first term, a = 0.9 Common ratio, r = 0.09/0.9... View Article

If The Nth Term Of A Gp 5 5 By 2 5 By 4 Is 5 By 1024 Then The Value Of N Is

1) 11 2) 10 3) 9 4) 4 Solution: Let a be first term of GP with common ratio r. The nth term, an = arn-1 Given GP 5, -5/2, 5/4,... View Article

The 6th Term Of A Gp Is 32 And Its 8th Term Is 128 Then The Common Ratio Of The Gp Is

1) -1 2) 2 3) 4 4) -4 Solution: Let a be first term of GP with common ratio r. The nth term, an = arn-1 Given 6th term = 32... View Article

If The 10th Term Of A Geometric Progression Is 9 And 4th Term Is 4 Then Its 7th Term Is

(1) 6 (2) 36 (3) 4/9 (4) 9/4 Solution: Let a be the first term of GP with common ratio r. The nth term, an = arn-1 10th term,... View Article

If The Pth Qth And Rth Term Of A Gp Are A B C Respectively Then Aq Rbr P Cp Q Is Equal To

(1) 0 (2) 1 (3) abc (4) pqr Solution: Let A be first term of GP with common ratio R. The nth term, An = ARn-1 pth term= ARp-1... View Article

In A Geometric Progression Consisting Of Positive Terms Each Term Equals The Sum Of The Next Two Terms

(1) (1-√5)/2 (2) √5/2 (3) √5 (4) (√5-1)/2 Solution: Let a, ar, ar2 be three terms of GP. Given a = ar + ar2 r2 + r - 1 = 0... View Article

If P Q Th Term Of A Gp Be M And P Qth Term Be N Then The Pth Term Will Be

(1) m/n (2) mn (3) √(mn) (4) 0 Solution: Let a be first term of GP with common ratio r. The nth term, an = arn-1 Given (p+q)th... View Article

If The 4th 7th And 10th Terms Of A Gp Be A B C Respectively Then The Relation Between A B C Is

(1) b = (a+c)/2 (2) a2 = bc (3) b2= ac (4) c2 = ab Solution: Let A be first term of GP with common ratio r. The nth term, An =... View Article

Sum Of N Terms Of The Following Series 1 Cube 3 Cube 5 Cube Is

(1) n2(2n2 - 1) (2) n3(n - 1) (3) n3 + 8n + 4 (4) 2n4 + 3n2 Solution: Given series 13 + 33 + 53 + 73 + .. Here nth term, tr =... View Article

7th Term Of The Sequence Root 2 Root 10 5 Root 2 Is

(1) 125√10 (2) 25√2 (3) 125 (4) 125√2 Solution: Here a = √2 Common ratio, r = √5 nth term of GP = arn-1 7th term = √2×√56... View Article

The Nth Term Of The Series 2 By 1 Fact 7 By 2 Fact Is

(1) n(3n-1)/2(n)! (2) n(3n+1)/2(n)! (3) n(3n)/2(n)! (4) none of these Solution: Given series 2/1! + 7/2! + 15/3! + 26/4! + … Here... View Article

11 Sq Plus 12 Sq Plus 13 Sq Plus 20 Sq Equal

1) 2481 2) 2483 3) 2485 4) 2487 Solution: Sum of squares n natural numbers = n(n+1)(2n+1)/6 112 + 122 + 132 +...202 = (12 + 22 +... View Article

First Term Of 11th Term Of The Following Groups 1 2 3 4 5 Is

(1) 89 (2) 97 (3) 101 (4) 123 Solution: Given groups (1), (2,3,4), (5,6,7,8,9)... In each group the numbers are in AP with common... View Article

The Sum Of N Terms Of 2n 1 Plus 2 2n 3 Plus 3 2n 5 Is Eq

(1) (n+1)(n+2)/6 (2) n(n+1)(n+2)/6 (3) n(n+1)(2n+3) (4) n(n+1)(2n+1)/6 Solution: Given series (2n-1) + 2(2n-3) + 3(2n-5) +...n... View Article

If Nth Term Of A Series Be 3 N N 1 Then The Sum Of N Terms Of The Series Is

(1) (n2+n)/3 (2) (n3+8n)/3 (3) (n2+8n)/5 (4) (n2-8n)/3 Solution: Given nth term of the series, tn = 3 + n(n-1) = 3+n2-n Sum, S =... View Article

11 Cube Plus 12 Cube 20 Cube

(1) Is divisible by 5 (2) Is an odd integer divisible by 5 (3) Is an even integer which is not divisible by 5 (4) Is an odd integer... View Article