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AlgebraQuestion and Answers: Page 328

Question Number 32541 Answers: 2 Comments: 0

Coefficient of x^5 in the expansion of (x^2 −x−2)^5 is

$C o e f f i c i e n t o f x^{5} i n t h e e x p a n s i o n$ $o f {(x^{2} - x - 2)}^{5} i s$

Question Number 32532 Answers: 0 Comments: 3

If a,b,c are 3 positive numbers in an A.P and T= ((a+8b)/(2b−a))+((8b+c)/(2b−c)). Then the value of T^( 2 ) is ? Ans. given is 361.

$I f a, b, c a r e 3 p o s i t i v e n u m b e r s i n a n$ $A . P a n d$ $T = \frac{a + 8 b}{2 b - a} + \frac{8 b + c}{2 b - c} .$ $T h e n t h e v a l u e o f T^{2} i s ?$ $A n s . g i v e n i s 361 .$

Question Number 32494 Answers: 0 Comments: 0

Question Number 32446 Answers: 1 Comments: 0

Question Number 32441 Answers: 1 Comments: 0

Question Number 32524 Answers: 0 Comments: 0

(1/2)x^2 +(√2)=

$\frac{1}{2} x^{2} + \sqrt{2} =$

Question Number 32424 Answers: 1 Comments: 0

Question Number 32395 Answers: 0 Comments: 1

1+1

$1 + 1$

Question Number 32334 Answers: 0 Comments: 1

p is apolynomial having n roots (x_i ) with x_i ≠xj for i≠j calculate Σ_(k=1) ^n (1/(1−x_k )) .

$p i s a p o l y n o m i a l h a v i n g n r o o t s (x_{i}) w i t h x_{i} \neq x j f o r$ $i \neq j c a l c u l a t e \sum_{k = 1}^{n} \frac{1}{1 - x_{k}} .$

Question Number 32333 Answers: 0 Comments: 1

decompose F(x) = (1/((1−x)^2 (1−x^2 ))) inside R(x).

$d e c o m p o s e F (x) = \frac{1}{{(1 - x)}^{2} (1 - x^{2})} i n s i d e R (x) .$

Question Number 32332 Answers: 0 Comments: 0

calculate Σ_(p=1) ^n (p/(1+p^2 +p^4 )) .

$c a l c u l a t e \sum_{p = 1}^{n} \frac{p}{1 + p^{2} + p^{4}} .$

Question Number 32331 Answers: 0 Comments: 0

p is a polynomial having n simples roots (x_i )_(1≤i≤n) prove that Σ_(k=1) ^n (1/(p^′ (x_k ))) =0

$p i s a p o l y n o m i a l h a v i n g n s i m p l e s r o o t s {(x_{i})}_{1 ⩽ i ⩽ n}$ $p r o v e t h a t \sum_{k = 1}^{n} \frac{1}{p^{^{'}} (x_{k})} = 0$

Question Number 32330 Answers: 0 Comments: 1

let p_n (x)=(x+1)^(6n+1) −x^(6n+1) −1 with n integr prove that ∀n (x^2 +x+1)^2 divide p_n (x).

$l e t p_{n} (x) = {(x + 1)}^{6 n + 1} - x^{6 n + 1} - 1 w i t h n i n t e g r$ $p r o v e t h a t \forall n {(x^{2} + x + 1)}^{2} d i v i d e p_{n} (x) .$

Question Number 32326 Answers: 0 Comments: 0

simplify Σ_(k=p) ^(2p) (C_k ^p /2^k ) .

$s i m p l i f y \sum_{k = p}^{2 p} \frac{C_{k}^{p}}{2^{k}} .$

Question Number 32242 Answers: 1 Comments: 0

A company manufactures two types of products; X ($4.50 profit per item x) and Y ($3.00 profit per item y). These items are built using both machine time and manual labour. The X product requires 3 hours of machine time and two hours of manual labour. The Y product requires 3 hours of machine time and no manual labour. If the week′s supply of manual labour is limited to 8 hours and machine time to 15 hours, write down all inequalities involving x and y.

$A company manufactures two types of products;$ $X ($ 4.50 profit per item x) and Y ($ 3.00 profit per$ $item y) . These items are built using both machine$ $time and manual labour . The X product requires$ $3 hours of machine time and two hours of manual$ $labour . The Y product requires 3 hours of machine$ $time and no manual labour . If the {week}^{'} s supply of$ $manual labour is limited to 8 hours and machine$ $time to 15 hours, write down all inequalities$ $involving x and y .$

Question Number 32239 Answers: 1 Comments: 0

Find the sum of the coefficients of all the integral power of x in the expansion of (1+2(√x))^(40) .

$F i n d t h e s u m o f t h e c o e f f i c i e n t s$ $o f a l l t h e i n t e g r a l p o w e r o f x i n t h e$ $e x p a n s i o n o f {(1 + 2 \sqrt{x})}^{40} .$

Question Number 32208 Answers: 0 Comments: 0

Question Number 32203 Answers: 0 Comments: 5

Number of solutions of the equation z^3 +(([3(z^− )^2 ])/(∣z∣))=0 where z is a complex no.

$N u m b e r o f s o l u t i o n s o f t h e e q u a t i o n$ $z^{3} + \frac{[3 {(\bar{z})}^{2}]}{∣ z ∣} = 0 w h e r e z i s a c o m p l e x n o .$

Question Number 32184 Answers: 1 Comments: 0

If one vertex of the triangle having maximum area that can be inscribed in the circle ∣z−i∣=5 is 3−3i, then find other vertices of triangle.

$I f o n e v e r t e x o f t h e t r i a n g l e h a v i n g$ $m a x i m u m a r e a t h a t c a n b e i n s c r i b e d$ $i n t h e c i r c l e ∣ z - i ∣= 5 i s 3 - 3 i, t h e n$ $f i n d o t h e r v e r t i c e s o f t r i a n g l e .$

Question Number 32181 Answers: 1 Comments: 1

Intercept made by the circle zz^− +a^− z+az^− +r=0 on the real axis on complex plane is :−

$I n t e r c e p t m a d e b y t h e c i r c l e$ $z \bar{z} + \bar{a z} + a \bar{z} + r = 0 o n t h e r e a l a x i s o n$ $c o m p l e x p l a n e i s : -$

Question Number 32160 Answers: 1 Comments: 0

If z=cosθ+isinθ is a root of equation a_0 z^n +a_1 z^(n−1) +a_2 z^(n−2) +.....+a_(n−1) z+a_n =0 then prove that: i) a_0 +a_1 cos θ+a_2 cos 2θ+.....+a_n cos nθ=0 ii) a_1 sin θ + a_2 sin 2θ+....+a_n sin nθ=0.

$I f z = c o s θ + i s i n θ i s a r o o t o f e q u a t i o n$ $a_{0} z^{n} + a_{1} z^{n - 1} + a_{2} z^{n - 2} + . . . . . + a_{n - 1} z + a_{n} = 0$ $t h e n p r o v e t h a t :$ $i) a_{0} + a_{1} \cos θ + a_{2} \cos 2 θ + . . . . . + a_{n} \cos n θ = 0$ $i i) a_{1} \sin θ + a_{2} \sin 2 θ + . . . . + a_{n} \sin n θ = 0 .$

Question Number 32159 Answers: 1 Comments: 2

Express the following in a+ib form: (((cos x+isin x)(cos y+isin y))/((cosa+isin a)(cosb+isinb))).

$E x p r e s s t h e f o l l o w i n g i n a + i b f o r m :$ $\frac{(\cos x + i \sin x) (\cos y + i \sin y)}{(c o s a + i \sin a) (c o s b + i s i n b)} .$

Question Number 32142 Answers: 0 Comments: 0

Question Number 32132 Answers: 0 Comments: 0

∫(1/((x+1)ln(x)))dx=?

$\int \frac{1}{(x + 1) l n (x)} d x = ?$

Question Number 32110 Answers: 1 Comments: 0

If y=1+x^2 +x^3 and x=1+α, where α is small, show that y≈3+5α. Hence, find the increase in y when x is increased from 1 to 1.02

$If y = 1 + x^{2} + x^{3} and x = 1 + α, where α is small, show$ $that y \approx 3 + 5 α . Hence, find the increase in y when$ $x is increased from 1 to 1.02$

Question Number 32099 Answers: 1 Comments: 0

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