(2+x+x3)5=a0+a1x+.....+a15x15. find the value of a0+2a1+a2+2a3....+2a15

Sail E0 Webinar

Question

(2 + x + x^{3})^{5} = a_{0} + a_{1} x + . . . . . + a_{15} x^{15}

. find the value of

a_{0} + 2 a_{1} + a_{2} + 2 a_{3} . . . . + 2 a_{15}

Answer: Option B
:
B
At x=1

a_{0} + a_{1} + . . . . . + a_{15} = 4^{5} . . . . . . . . . . . . . (1)

At x= -1

a_{0} - a_{1} + . . . . . . - a_{15} = 0................. (2)

(1)-(2)

= 2 a_{1} + 2 a_{3} . . . . . . .2 a_{15} = 4^{5} . . . . . . . . . (3)

(\frac{[(1) + (2)]}{2}) = a_{0} + a_{2} . . . = \frac{4^{5}}{2} . . . . . . . . (4)

(3)+(4)

= a_{0} + 2 a_{1} + a_{2} + 2 a_{3} . . . . + 2 a_{15} = 4^{5} + [\frac{4^{5}}{2}] = 1536.

Was this answer helpful ?

Next Question

Submit Solution

More Questions on This Topic :

Question 1. Let f(x) = 24x+2 for x ϵ Real numbers. Find out the value of f(12001) + f(22001)+ ...... + f(20002001)....

Question 2. There are two women participating in a chess tournament. Every participant played two games with the other participants.....men played with the women. How many games were played?

Question 3. The set of all positive integers is the union of 2 disjoint subsets {f(1),f(2),f(3),...}& {g(1),g(2),g(3),...}, wher....f(1)<f(2)<f(3)<.....& g(1)<g(2)<g(3)<...... g(n)=f(f(n))+1 for n = 1,2,3,...... What is the value of g(1)?

Question 4. ABCABC is a six digit number where A,B,C are three consecutive natural numbers. Find the remainder when ABCABC is divide....numbers. Find the remainder when ABCABC is divided by 1001?

Question 5. PQR is a right angled triangle with PQ=8, QR=6, QT as altitude. If a circle is drawn with QT as diameter, what is the ar....as diameter, what is the area of the shaded region?

Question 6. A company has to construct a flyover. It deployed 10 men who can finish the work 30 days each working 8 hrs a day. After....Also assume that it rains only during the working hours.

Question 7. The infinite sum 513+55132+555133+5555134+..... equals ....

Question 8. Sum to p terms of the series 12+(12+32)+(12+32+52)+.... is ....

Question 9. In a college, 35% of the students play at least two out of three games- Cricket, Hockey and Football. Football is played....any game, what percentage of the students play only Football?

Question 10. If x2−gx+3=0 and 2x2−6x+g=0 have a common root, then find the value(s) of the common root.....common root, then find the value(s) of the common root.

Chapter 1 - GLOBAL STEEL SCENARIO & INDIAN STEEL INDUSTRY Part 1 : (13-04-2024) INDUSTRY AND COMPANY AWARENESS (ICA)

Direction Sense Test Part 1 Reasoning (Hindi)

Chapter 1 - RMHP / OHP / OB & BP Part 1 : (14-02-2024) GPOE

Cube & Cuboid Part 1 Reasoning (Hindi)

Data Interpretation (DI) Basic Concept Reasoning (Hindi)

Counting Figures Part 1 Counting Of Straight Lines Reasoning (Hindi)

Sail E0 free webinar Webinars

Real Numbers Part 7 Class 10 Maths

Real Numbers Part 1 Class 10 Maths

Polynomials Part 1 Class 10 Maths

DSP Combined 1 Free Revision Test SAIL JO E-0

GPOE / GPA Combined 1 Free Revision Test SAIL JO E-0

BSP Plant Specific Review Test SAIL JO E-0

BSL Combined 1 Free Revision Test SAIL JO E-0

GFM Combined 1 Free Revision Test SAIL JO E-0