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if a(1),a(2),…….a(n),……. form a G.P. and...

if `a_(1),a_(2),…….a_(n),…….` form a G.P. and `a_(1) gt 0 ,` for all `I ge 1`
`|{:(log a_(n),,loga_(n)+loga_(n+2),,log a_(n+2)),(log a_(n+3),,log a_(n+3)+log a_(n+5),,log a_(n+5)),(log a_(n+6),,log_(n+6)+loga_(n+8),,log a_(n+8)):}|`

A

2

B

4

C

0

D

1

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C
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If a_(n) gt a_(n-1) gt …. gt a_(2) gt a_(1) gt 1 , then the value of "log"_(a_(1))"log"_(a_(2)) "log"_(a_(3))…."log"_(a_(n)) is equal to

If a_(n+1)=a_(n-1)+2a_(n) for n=2,3,4, . . . and a_(1)=1 and a_(2)=1 , then a_(5) =

If a_(1)=5 and a_(n)=1+sqrt(a_(n-1)), find a_(3) .

If a_(1)=3 and a_(n)=2a_(n-1)+5 , find a_(4) .

Let a_(1),a_(2),a_(3), …, a_(10) be in G.P. with a_(i) gt 0 for i=1, 2, …, 10 and S be te set of pairs (r, k), r, k in N (the set of natural numbers) for which |(log_(e)a_(1)^(r)a_(2)^(k),log_(e)a_(2)^(r)a_(3)^(k),log_(e)a_(3)^(r)a_(4)^(k)),(log_(e)a_(4)^(r)a_(5)^(k),log_(e)a_(5)^(r)a_(6)^(k),log_(e)a_(6)^(r)a_(7)^(k)),(log_(e)a_(7)^(r)a_(8)^(k),log_(e)a_(8)^(r)a_(9)^(k),log_(e)a_(9)^(r)a_(10)^(k))| = 0. Then the number of elements in S is

If A_(n)=2A_(n-1)+3 for all n ge1 , and A_(4)=45 , what is A_(1) ?

( 1 + x + x^(2))^(n) = a_(0) + a_(1) x + a_(2) x^(2) + …+ a_(2n) x^(2n) , then a_(0) + a_(1) + a_(2) + a_(3) - a_(4) + … a_(2n) = .

VMC MODULES ENGLISH-MATRICES AND DETERMINANTS -JEE MAIN ARCHIVE
  1. If a^2+b^2+c^2=-2a n df(x)= |1+a^2x(1+b^2)x(1+c^2)x(1+a^2)x1+b^2x(1+c...

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  2. The system of equations alphax+y+z=alpha-1, x+alphay+z=alpha-1 ...

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  3. if a(1),a(2),…….a(n),……. form a G.P. and a(1) gt 0 , for all I ge 1 ...

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  4. Let A=[(0,0,-1),(0,-1,0),(-1,0,0)] Then only correct statement about t...

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  5. Let A=[(1,-1,1),(2,1,-3),(1,1,1)] and 10 B=[(4,2,2),(-5,0,alpha),(1,-2...

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  6. If the system of linear equations {:(x+2ay+az=0),(x+3by+bz=0),(x+4cy...

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  7. If A=[{:(a,b),(b,a):}] and A^(2)=[{:(alpha, beta),(beta, alpha):}] the...

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  8. If omega is a non-real cube root of unity and n is not a multiple o...

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  9. if a,b,c are positive and are the pth qth and rth terms respectively ...

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  10. If one of the cube roots of 1 be omega, then |(1,1+omega^2,omega^2),(...

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  11. If A is a symmetric matrix and B is a skew-symmetric matrix such that ...

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  12. The total number of matrices A = [{:(0, 2y, 1), (2x, y, -1), (2x, -y,...

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  13. Let A={:(cosalpha,-sinalpha),(sinalpha,cosalpha):},(ainR) such that A...

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  14. Let P=[(1, 0, 0),(3, 1, 0),(9, 3, 1)]Q=[q(ij)] and Q=P^5+I3 then (q21+...

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  15. Let A = ((0,2q,r),(p,q,-r),(p,-q,r)). If A A^(T) = I(3), then |p| is

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  16. The value of theta lying between 0 and pi/2 and satisfying the equatio...

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  17. The sum of the real roots of the equation |{:(x, -6, -1), (2, -3x, x...

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  18. If Delta(1) =|{:(x, sin theta, cos theta),(-sin theta, -x, 1),(cos the...

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  19. If [{:(1, 1), (0,1):}]*[{:(1, 2), (0,1):}]*[{:(1, 3), (0,1):}]cdotcdot...

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  20. Let alpha and beta be the roots of the equation x^(2) + x + 1 = 0. ...

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