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Soumyadeep Kar

Subject: Maths, asked on 31/12/17

$P r o v e t h a t \sum_{r = 1}^{m} \frac{(m + 1) (r - 1) m^{r - 1}}{r ({}^{m}C_{r})} = m^{m} - 1$

Amitesh Kumar

Subject: Maths, asked on 28/12/17

Please fast

$7 . I f {(1 + x)}^{n} = \sum_{r = 0}^{n} C r X^{r}, (1 + \frac{C_{1}}{C_{0}}) (1 + \frac{C_{2}}{C_{1}}) . . . . . . . . (1 + \frac{C_{n}}{C_{n - 1}}) i s e q u a l t o (a) \frac{n^{n - 1}}{(n - 1)!} (b) \frac{{(n + 1)}^{n - 1}}{(n - 1)!} (c) \frac{{(n + 1)}^{n}}{n!} (d) \frac{{(n + 1)}^{n + 1}}{n!}$

Amitesh Kumar

Subject: Maths, asked on 28/12/17

Plz fast

Amitesh Kumar

Subject: Maths, asked on 28/12/17

Please fast

$7 . I f {(1 + x)}^{n} = \sum_{r = 0}^{n} C r X^{r}, (1 + \frac{C_{1}}{C_{0}}) (1 + \frac{C_{2}}{C_{1}}) . . . . . . . . (1 + \frac{C_{n}}{C_{n - 1}}) i s e q u a l t o (a) \frac{n^{n - 1}}{(n - 1)!} (b) \frac{{(n + 1)}^{n - 1}}{(n - 1)!} (c) \frac{{(n + 1)}^{n}}{n!} (d) \frac{{(n + 1)}^{n + 1}}{n!}$

Amitesh Kumar

Subject: Maths, asked on 28/12/17

Plz fast
Q). The expansion ${\{x + {(x^{3} - 1)}^{1 / 2}\}}^{5} + {\{x - {(x^{3} - 1)}^{1 / 2}\}}^{5}$ is a polynomial of degree
(a) 5
(b) 6
(c) 7
(d) 8

Kshitiz Anand

Subject: Maths, asked on 27/12/17

Qno 12

Q12. Coefficient of x²⁹ in the polynomial

$(x - \frac{1}{1 \times 3}) (x - \frac{2}{1 \times 3 \times 5}) (x - \frac{3}{1 \times 3 \times 5 \times 7}) . . . . . . . (\frac{30}{1 \times 3 \times . . . . . \times 61})$ is

$(A) \frac{1}{2} (1 - \frac{1}{1 \times 3 \times . . . . . \times 61}) (B) \frac{1}{2} + \frac{1}{1 \times 3 \times . . . . . \times 61} (C) - \frac{1}{2} (1 - \frac{1}{1 \times 3 \times . . . . . \times 61}) (D) \frac{29}{1 \times 3 \times . . . . . \times 61}$

Kshitiz Anand

Subject: Maths, asked on 27/12/17

Question number 14

$14 . T h e h i g h e s t p o w e r o f 18 c o n t a i n e d i n^{50} C_{25} i s (A) 3 (B) 0 (C) 1 (D) 2$

Amitesh Kumar

Subject: Maths, asked on 27/12/17

Q.5. If $a_{n} = \sum_{r = 0}^{n} \frac{1}{{}^{n}C_{r}}$ , find the value of $\sum_{r = 0}^{n} \frac{r}{{}^{n}C_{r}}$ .

Amitesh Kumar

Subject: Maths, asked on 27/12/17

Q.1. The value of $\sum_{r = 0}^{10} \cdot {}^{10}C_{r} \cdot 3^{r} \cdot {(- 2)}^{10 - r}$ is

Yayati

Subject: Maths, asked on 20/12/17

$I f (x^{2} + x - 3)^{279} = a_{0} + a_{1} x + a_{2} x^{2} + a_{558} x^{558} f i n d a_{0} + a_{1} + a_{2} + a_{3} + . . . . . . + a_{558}$

Priyanka

Subject: Maths, asked on 19/12/17

Solve this:

Priyanka

Subject: Maths, asked on 19/12/17

Find the term independent of x

$(4 + x + 7 x^{2}) {(x - \frac{3}{x})}^{11}$

Tarunvir Singh

Subject: Maths, asked on 16/12/17

Please do 13th question

Q13. The -coefficient of x⁷⁰ in the product (x – 1) (x² – 2) (x³ –3) (x⁴ – 4) ......(x¹²–12) is

(a) 4 (b) 6 (c) 8 (d) 12

Tarunvir Singh

Subject: Maths, asked on 16/12/17

Please do 9th question:

9. The term independent of 'x' in the expansion of ${(9 x - \frac{1}{3 \sqrt{x}})}^{18}, x > 0, i s α t i m e s t h e c o r r e s p o n d i n g b i n o m i a l c o e f f i c i e n t . T h e n' α' i s$

$(a) 3 (b) \frac{1}{3} (c) - \frac{1}{3} (d) 1$

Tarunvir Singh

Subject: Maths, asked on 16/12/17

Find the coefficientof x^70 in series (x-1)(x^2-2)and ao on till (x^12-1)

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