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If X Y Z 0 X Y Z 2 And Theta Is Angle Between Y And Z Then The Value Of 2cosec2 3cot2 Is

1) 11/3 2) 8/3 3) 5/3 4) 1 Answer: 11/3 Solution: Given x+y+z=0 y+z=−x |x| = |y| = |z|= 2 ∣y+z∣=∣x∣ |y+z|2 = |x|2... View Article

If A And B Be Two Unit Vectors Such That Angle Between Them Is 60 Then Ab Is Equal To

1) √5 2) √3 3) 0 4) 1 Answer: (4) 1 Solution: |a-b|2 = |a|2+|b|2-2|a| |b| cosθ Given, θ = 60° Therefore, |a-b|2 = |a|2+|b|2-2|a| |b| cos... View Article

If A I2j3k And B 3ij2k Then The Angle Between The Vectors Ab And Ab Is

1) 60° 2) 90° 3) 45° 4) 55° Answer: (2) 90° Solution: Given, a = i+2j-3k b = 3i-j+2k a+b = 4i+j-k a-b = -2i+3j-5k (a+b).(a-b) =... View Article

If Ai4 Then Aj 2j 3k

1) 12 2) 2 3) 0 4) -12 Answer: (4) -12 Solution: Given, a.i = 4 (a.j)×(2j−3k) =a.(j×(2j−3k)) = a.(−3(j×k)) =−3(a.i) (∵j×k=i) =−3(4) =−12... View Article

Aii Ajjakk Is Equal To

1) a 2) 2a 3) 3a 4) 0 Answer: (1) a Solution: Suppose, a=xi+yj+zk So, (a.i)i+(a.j)j+(a.k)k... View Article

The Unit Vector Perpendicular To Ij And Coplanar With I2j And I3j Is

1) (2i-5j)/√59 2) 2i+5j 3) 1/√2(i+j) 4) i+j Answer: (3) 1/√2(i+j) Solution: Let the unit vector be a = xi+yj As per the given condition, a... View Article

A Force Of Magnitude Of 30n Acting Along Ijk Displaces A Particle From A Point 241 To 352 The Work Done

1) 90J 2) 30J 3) 30/√3 J 4) 20J Answer: (2) 30J Solution: As we know, Work done = Force x displacement Displacement = (3i+5j+2k)-(2i+4j+k)... View Article

If A B 1 And A B 3 Then The Value Of 3a 4b 2a 5b Is

1) –21 2) – (21/2) 3) 21 4) 21/2 Answer: (2) -21/2 Solution: Given, |a| = |b| = 1 |a + b| = √3 |a+b|2 = 3 |a|2+|b|2+2ab = 3 1+1+2ab = 3... View Article

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