Today is our topic of discussion Binomial Expansion exercises – 10.2
Binomial Expansion exercises – 10.2
1. In the expansion of (1 + 2x + x²)³
(i) Number of terms is 4
(ii) Second term is 6x
(iii) Last term is is x^6
Which one is correct?
1) i, ii
2) i, iii
3) ii, iii
4) i, ii and iii
2. If (r+1)th term is free of x what is the value of r?
1) 0
2) n/2
3) n
4) 2n
3. If n = 4, then which one is the fourth term?
1) 4
2) 4x
3) 4/x
4)4/x²
4. The coefficients of expansion of (x + y)^5 are:
1) 5, 10, 10,5
2) 1,5, 10, 10, 5, 1
3) 10,5,5, 10
4) 1,2,3,3,2,1
5. In the expansion of (1 – x) * (1 + x/2) ^ 8 the coefficient of x is
1) -1
2)1/2
3) 3
4) -1/2
6. What is the x-free term in the expansion of (x² + 1/x²))^4 ?
1) 4
2) 6
3) 8
4) 0
7. Ordering the coefficients of the expansion of (x + y) ^ 4 we get,
8. Expand each of these:
1) (2 + x²)^5
2) (2 – 1/2x)^6
9. Determine the first four terms of these 1) (2 + 3x) ^ 6 (4 – 1/(2x)) ^ 5
10. If determine p, r and s. (p – 1/2 * x) ^ 6 =r-96x+sx^ 2 +***,
11. Determine the coefficient of x ^ 3 in the expansion of (1 + x/2) ^ 8
12. Expand 2+x/4^6 up to x³ in ascending power of x. Find the approximate value of (1.9975)^6 up to four decimal places.
13. Using binomial theorem, find the value of (1.99)^5 up to four decimal places.
14. In the expansion of (1 + x/4)^n coefficients of 3rd term is the double of the coefficient of the 4th term. Find the value of n. Also, determine the number of terms and middle term of the expansion.
15. 1) In the expansion of (2k- x/2)^5 .
( 2) In the expansion of (x² + of k. coefficient of 2³ is 160, find the value
16. A=(1+x)^7 and B = (1-x)^8
1) Determine the expansion of A using Pascal’s Triangle.
2) Expand B upto four terms. Use the result to find the value of (0.99)8 upto four decimal places.
3) Determine the coefficient of x7 in the expansion of AB.
17. (A+B)^x is an algebraic expression.
1) If A = 1, B = 2 and n = 5, determine the expansion of the expression using Pascal’s Triangle.
2) If B = 3 and n = 7, in the expansion of the expression, coefficient of x4 is 22680. Determine A.
3) If A = 2 and B = 1, then the coeffecients of 5th and 6th terms of the expansion are same. Determine the value of n
18. If a1, a2, a3 a4 are four consecutive terms in the expansion of (1 + x)”, then prove that a1 + a3 202 = a1 + a2 a3 + as a2+ a3
19. Which one is bigger? 9950 + 10050 or 10150?
See more:
- Exponential and Logarithmic Function exercises – 9.2
- Define specific heat capacity, thermal capacity and water equivalent with their units
