Very Short Answer on Binomial Theorem Class 11 OP Malhotra Exe-13C ISC Maths Solutions Ch-13. In this article you would learn to solve hard questions easily on Binomial Theorem. Step by step solutions of latest textbook has been given as latest syllabus. Visit official Website CISCE for detail information about ISC Board Class-11.
Binomial Theorem Class 11 OP Malhotra Very Short Answer ISC Math Solutions Ch-13
| Board | ICSE |
| Publications | S Chand |
| Subject | Maths |
| Class | 11th |
| Chapter-13 | Binomial Theorem |
| Writer | OP Malhotra |
| Exe-13(C) | Very Short Answer Type Questions. |
Very Short Answer on Binomial Theorem
OP Malhotra ISC Class 11 Maths Solutions
Que-1: How many terms are there in the expansion of
(i) ((2x + y3)4)7) (ii) ((x2 + 6y5)1/3)15
Sol: (i) = (2x + y³)²⁸
→ Number of terms = 28 + 1
= 29
(ii) (x² + 6y⁵)⁵
→ Number of terms = 5 + 1
= 6
Que-2: The number of terms in the expansion of (1 + x)2n − (1 − x)2n is ……………
Sol: (1+x)²ⁿ − (1−x)²ⁿ removes even powers
→ terms = n
Que-3: Answer true or false: The number of terms in the expansion of (a + b)n, where x ∈ N, is less than the power of n.
Sol: Number of terms in (a+b)ⁿ
= n+1
Statement: n+1 < n
→ False
Que-4: Expand (1 − 2x)5.
Sol: (1−2x)⁵
= 1 − 10x + 40x² − 80x³ + 80x⁴ − 32x⁵
Que-5: Find the 4th term in the expansion of (x − 2y)12.
Sol: General term = Tr+1 = C(n,r)an−rbr
4th term
⇒ r = 3
T₄ = C(12,3) x⁹ (-2y)³
= -1760x⁹y³
Que-6: Find the 9th term in the expansion of (3x − 1/2x)8, x ≠ 0.
Sol: 9th term
r = 8
T₉ = C(8,8) (3x)⁰ (-1/2x)⁸
= 1 / (256x⁸)
Que-7: Find the coefficient of x5 in the expansion of (x + 3)8.
Sol: Coefficient of x⁵ in (x+3)⁸
= C(8,5)3³
= 56 × 27
= 1512
Que-8: Find the constant term in the expansion of (x − 1/x)6.
Sol: Constant term in (x − 1/x)⁶ occurs when powers cancel
r=3
Term = C(6,3)(−1)³ = -20
Que-9: Find the middle term in the expansion of (x − 3y)8.
Sol: Total terms = 9 → middle term = 5th
T₅ = C(8,4)x⁴(-3y)⁴
= 5670 x⁴y⁴
Que-10: Find the middle term in the expansion of (3 − x3/6)7.
Sol: Total terms = 8
→ middle terms = 4th and 5th
Que-11: Write the coefficient of the middle term in the expansion of (1 − x)50.
Sol: Middle coefficient of (1−x)⁵⁰
= -C(50,25)
Que-12: Write the general term in the expansion of (x2 − y)6.
Sol: General term of (x²−y)⁶
Tr+1 = C(6,r)(x²)6−r(−y)r
Que-13: The ratio of the coefficients of xp and xq in the expansion of (1 + x)p+q is ……………..
Sol: Coefficient ratio of xᵖ and xᑫ in (1+x)p+q
= C(p+q,p) : C(p+q,q)
= 1 : 1
Que-14: The largest coefficient in the expansion of (1 + x)30 is ……………..
Sol: Largest coefficient in (1+x)³⁰ occurs at middle
= C(30,15)
Que-15: The coefficient of a−6b4 in the expansion of (1/a − 2b/3)10 is ……………..
Sol: Term containing a⁻⁶b⁴ in (1/a − 2b/3)¹⁰
r = 4
Coefficient = C (10,4) (-2/3)⁴
–: End Binomial Theorem Class 11 OP Malhotra Exe-13C ISC Maths Ch-13 Solutions :–
Return to :- OP Malhotra ISC Class-11 S Chand Publication Maths Solutions
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