11th Maths Monthly Test - 4 ( Binomial Theorem, Sequences and Series)

St. Britto Hr. Sec. School - Madurai

11th Maths Monthly Test - 4 ( Binomial Theorem, Sequences and Series)-Aug 2020

Time : 2.30 Hours

Part - A

Generic 2 - Answer All Question

Find the middle term in \({ \left( x-\frac { 1 }{ 2y } \right) }^{ 10 }\)

Evaluate 98⁴ .

Expand \(\left( { 2x }^{ 2 }-\frac { 3 }{ x } \right) ^{ 3 }\)

Write the n^th term of the following sequences
\(\frac { 1 }{ 2 } ,\frac { 2 }{ 3 } ,\frac { 3 }{ 4 } ,\frac { 4 }{ 5 } ,\frac { 5 }{ 6 } \)

Find the sum of first n terms of the series 1²+3²+5²+...

Using binomial theorem, indicate which of the following two number is larger (1.01)^1000000 ,10,000

Compute 102⁴

Find a negative value of m if the Co-efficient of x² in the expansion of (1+x)m ,|x|<1 is 6

Write the first 6 terms of the sequences whose n^th term a_n given below
\({ a }_{ n }=\begin{cases} n+1\quad if\quad n\quad is\quad odd \\ n\quad \quad if\quad n\quad is\quad even \end{cases}\)

Find \(\sum_{k=1}^{n}{1\over k(k+1)}.\)

Part - B

Generic 3 - Answer All Question

If n is a postive integer, show that 9ⁿ⁺¹ - 8n - 9 is always divisible by 64

Prove that \(\sqrt { \frac { 1-x }{ 1+x } } \) is approximately equal to 1 - x + \(\frac{x^2}{2}\) when x is very small.

If the m^th term of a H.P. is n and n^th term is m, then show that its p^th term is \(\frac{mn}{p}\).

Find \(\sum_{1}^{\infty}{\frac{1}{(k+1)(k+2)}}\).

Find the coefficient of \(\frac{1}{x^{17}}\) in the expansion of \((x^{4}-\frac{1}{x^{3}})^{15}\).

Part - C

Generic 5 - Answer All Question

In a certain town, a viral disease caused severe health hazards upon its people disturbing their normal life. It was found that on each day, the virus which caused the disease spread in Geometric Progression. The amount of infectious virus particle gets doubled each day, being 5 particles on the first day. Find the day when the infectious virus particles just grow over 1,50,000 units?

Find the Co-efficient of x⁴ in the expansion (1+x³)⁵⁰ \(\left( { x }^{ 2 }+\frac { 1 }{ { x }^{ 3 } } \right) ^{ 5 }\)

The product of three increasing numbers in GP is 5832. if we add 6 to the second number and 9 to the third number, then resulting number form an AP. Find the numbers in GP

Find \(\sqrt {4+x^2}-\sqrt {4-x^2}\) when x is small.

Find the general terms and sum to n terms of the sequence 1, \(\frac{4}{3},\frac{7}{9},\frac{10}{27},....\)

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11th Maths Monthly Test - 4 ( Binomial Theorem, Sequences and Series)

St. Britto Hr. Sec. School - Madurai

11th Maths Monthly Test - 4 ( Binomial Theorem, Sequences and Series)-Aug 2020

Part - A

Generic 2 - Answer All Question

Find the middle term in \({ \left( x-\frac { 1 }{ 2y } \right) }^{ 10 }\)

Evaluate 984 .

Expand \(\left( { 2x }^{ 2 }-\frac { 3 }{ x } \right) ^{ 3 }\)

Write the nth term of the following sequences \(\frac { 1 }{ 2 } ,\frac { 2 }{ 3 } ,\frac { 3 }{ 4 } ,\frac { 4 }{ 5 } ,\frac { 5 }{ 6 } \)

Find the sum of first n terms of the series 12+32+52+...

Using binomial theorem, indicate which of the following two number is larger (1.01)1000000 ,10,000

Compute 1024

Find a negative value of m if the Co-efficient of x2 in the expansion of (1+x)m ,|x|<1 is 6

Write the first 6 terms of the sequences whose nth term an given below \({ a }_{ n }=\begin{cases} n+1\quad if\quad n\quad is\quad odd \\ n\quad \quad if\quad n\quad is\quad even \end{cases}\)

Find \(\sum_{k=1}^{n}{1\over k(k+1)}.\)

Part - B

Generic 3 - Answer All Question

If n is a postive integer, show that 9n+1 - 8n - 9 is always divisible by 64

Prove that \(\sqrt { \frac { 1-x }{ 1+x } } \) is approximately equal to 1 - x + \(\frac{x^2}{2}\) when x is very small.

If the mth term of a H.P. is n and nth term is m, then show that its pth term is \(\frac{mn}{p}\).

Find \(\sum_{1}^{\infty}{\frac{1}{(k+1)(k+2)}}\).

Find the coefficient of \(\frac{1}{x^{17}}\) in the expansion of \((x^{4}-\frac{1}{x^{3}})^{15}\).

Part - C

Generic 5 - Answer All Question

Find the Co-efficient of x4 in the expansion (1+x3)50 \(\left( { x }^{ 2 }+\frac { 1 }{ { x }^{ 3 } } \right) ^{ 5 }\)

The product of three increasing numbers in GP is 5832. if we add 6 to the second number and 9 to the third number, then resulting number form an AP. Find the numbers in GP

Find \(\sqrt {4+x^2}-\sqrt {4-x^2}\) when x is small.

Find the general terms and sum to n terms of the sequence 1, \(\frac{4}{3},\frac{7}{9},\frac{10}{27},....\)

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Tamilnadu Stateboardszs - Class

Evaluate 98⁴ .

Write the n^th term of the following sequences
\(\frac { 1 }{ 2 } ,\frac { 2 }{ 3 } ,\frac { 3 }{ 4 } ,\frac { 4 }{ 5 } ,\frac { 5 }{ 6 } \)

Find the sum of first n terms of the series 1²+3²+5²+...

Using binomial theorem, indicate which of the following two number is larger (1.01)^1000000 ,10,000

Compute 102⁴

Find a negative value of m if the Co-efficient of x² in the expansion of (1+x)m ,|x|<1 is 6

Write the first 6 terms of the sequences whose n^th term a_n given below
\({ a }_{ n }=\begin{cases} n+1\quad if\quad n\quad is\quad odd \\ n\quad \quad if\quad n\quad is\quad even \end{cases}\)

If n is a postive integer, show that 9ⁿ⁺¹ - 8n - 9 is always divisible by 64

If the m^th term of a H.P. is n and n^th term is m, then show that its p^th term is \(\frac{mn}{p}\).

Find the Co-efficient of x⁴ in the expansion (1+x³)⁵⁰ \(\left( { x }^{ 2 }+\frac { 1 }{ { x }^{ 3 } } \right) ^{ 5 }\)