Subject: Maths, asked on 23/10/17

## If the ratio of the sum of the first 12 terms to the sum of the first 18 terms of an AP is 4:9, then find the ratio of the 11th term to 32nd term.

Subject: Maths, asked on 22/10/17

## If a, b, c, d, are in g.p then prove that a2-b2, c2-b2, c2 -d2 are in g.p

Subject: Maths, asked on 22/10/17

## Experts please give me some questions involving sequence and series of complex numbers along with the answer

Subject: Maths, asked on 16/10/17

## Question No. 2 2.  The least value of

Subject: Maths, asked on 16/10/17

## Q. If a, b, c are distinct positive real numbers in G.P. and logca, logbc, logab are in A.P. then find the common difference of this A.P.

Subject: Maths, asked on 16/10/17

## Q. If $\sum _{r=1}^{n}$ Tr = $\frac{n}{8}$( n + 1) (n + 2) (n + 3), then find ​$\sum _{r=1}^{n}$ $\frac{1}{{T}_{r}}$.

Subject: Maths, asked on 16/10/17

## Q. If X1 ,X2, X3, ...Xn are in H.P, then prove that X1 X2 + X2X3 + X3X4 + ... + Xn - 1Xn = (n-1)X1Xn.​

Subject: Maths, asked on 16/10/17

## Q no 15 Q15. The value of  is equal to (A) $\frac{1}{2}-\frac{{3}^{100}}{100\left(101\right)}$                 (B) $\frac{3}{2}-\frac{{3}^{101}}{101\left(102\right)}$ (C) $\frac{3}{2}-\frac{{3}^{100}}{100\left(101\right)}$                 (D) none of these

Subject: Maths, asked on 16/10/17

## Q. If 1.(0!) + 3. (1!) + 7. (2!) + 13.(3!) + 21.(4!) + .....upto terms = (4000)4000! , then the value of n is (A) 4000                   (B) 4001                       (C) 3999                 (D) none of these

Subject: Maths, asked on 16/10/17

## Q no 7 ​Q7. If Sn = , then Sn is equal to       (A) 2n – (n +1)                              (B) n × (n +1) /2       (C) (n2 + 3n +2 )/6                        (D) n – 1 + (1/2n)

Subject: Maths, asked on 16/10/17

## Q. If a, b, c are three positve real numbers, then the minimum value of the expression $\frac{b+c}{a}$ + +  is (A) 1               (B) 2                   (C) 3                 (D) 6

Subject: Maths, asked on 16/10/17

## Q.(i)  If a1, a2, ...., an are n positive real numbers such that a1,a2, .....an = 1, show that ( 1 + a1) (1 + a2) .... (  1+an) $\ge$ 2n . (ii) If n is a positive integer , prove that 2n $>$ 1+ n  ; n $>$ 1.

Subject: Maths, asked on 16/10/17

## Q no 2 Q2. Show that $\frac{{a}_{1}}{{a}_{2}}+\frac{{a}_{2}}{{a}_{3}}+\frac{{a}_{3}}{{a}_{4}}$ ... +  are different positive integers.

Subject: Maths, asked on 16/10/17

## Q. The sum of the series 1 + 2 (1 + 1/n) + 3( 1+1/n)2 + ....$\infty$ is given by (A) n2 + 1           (B) n (n+1)             (C) n ( 1+1/n)2                 (D) n​2

Subject: Maths, asked on 16/10/17

## Qno 6 Q6. Show that (1 + 3–1) ​ (1 + 3–2) ​ (1 + 3–4) ​ (1 + 3–8) ... .

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