11th Maths Important 2 Mark Question Paper

St. Britto Hr. Sec. School - Madurai

11th Maths Important 2 Mark Question Paper-Aug 2020

Time : 1.30 Hours

Part - A

Generic 2 - Answer All Question

Suppose that a boat travels 10 km from the port towards north and then turns 60 to its left. If the boat travels further 8 km, how far from the port is the boat?

Evaluate the following: ¹⁰⁰C₉₉

Expand: sin(A + B + C).

A group consists of 4 girls and 7 boys. In how many ways can a team of 5 members be selected, if the team has atleast one boy and one girl

Find the domain and range of the real valued function f(x)=\(\frac{5-x}{x-5}\).

Evaluate the following limits :
\(\underset{\sqrt x\rightarrow3}{lim}{x^2-81\over \sqrt x-3}\)

If A+B+C=180⁰ ,prove that sin²A+sin²B-sin²C=2 sin A sin B cos C

Represent graphically the displacement of 30 km 60° west of north

Express each of the following sum or difference as a product.sin 50° + sin 20°.

Check whether the following functions are one to one and onto.
\(f:N\cup(2,-1,0)\rightarrow N\) defined by f(x) =x + 3.

Differentiate the following:\(y={3\sqrt{1+x^3}}\)

For what value of k is the function \(f\left( x \right) =\begin{cases} \frac { \sin { 5x } }{ 3x } \quad if\quad x\neq 0 \\ k,\quad \quad \quad if\quad x=0 \end{cases}\) is continuous at x = 0.

If ¹⁵C_r: ¹⁵C_r-1 = 11:5 find r.

To travel from a place A to place B, there are two different bus routes B₁, B₂, two different train routes T₁ and one air route A₁. From place B to place C there is one bus route say B₁, two different train routes T'₁: T'₂ and one air route A₁ .Find the number of routes of commuting from place A to place C via place without using similar mode of transportation.

Prove that sin (30^o + \(\theta\)) + cos (60^o + \(\theta\))

If \(\vec{a}=\hat{i}+2\hat{j}+3\hat{k}\) , \(\vec{b}=-\hat{i}+2\hat{j}+\hat{k}\)and\(\vec{c}=3\hat{i}+\hat{j}\) .Find \(\lambda\)so that \(\vec{a}+\lambda \vec{b}\) is perpendicular to \(\vec{c}\).

Differentiate the following with respect to x :\(y=(x-{1\over x})^2\)

Find the value \(\lambda\) for which the vectors \(\overrightarrow{a}\) and \(\overrightarrow{b}\) are perpendicular, where \(\overrightarrow{a}=2\hat{i}+\lambda\hat{j}+\hat{k}\) and \(\overrightarrow{b}=\hat{i}-2\hat{j}+3\hat{k}\)

Find the value of \(\frac { 8! }{ 5!\times 2! } \).

Show that the function f:N➝N given by f(x)=2x is one-one but not onto.

Integrate the following with respect to x\({x\over \sqrt{1+x^2}}\)

Integrate the following with respect to x: 5x⁴

Prove that \(2n{ C }_{ n }=\frac { { 2 }^{ n }\times 13\times ...(2n-1) }{ n! } \) .

State whether the following sets are finite or infinite.
{x \(\in \) Z:x is even and less than 10}

If A+B+C=180⁰ ,prove that sin(B+C-A) + sin(C+A-B) + sin(A+B-C)= 4 sinA sinB sinC

Find the square root of 9-4\(\sqrt{5}\)

Integrate the following with respect to x: sec²(3+4x)

\(f(x)=tan \ x \ at \ x={\pi\over 2}.\)

Show that the function f:R➝R given by f(x)=x² is neuther one-one nor onto.

A box contains 5 different red and 6 different white balls. In how many ways 6 balls be selected so that are atleast 2 balls of each colour.

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11th Maths Important 2 Mark Question Paper

St. Britto Hr. Sec. School - Madurai

11th Maths Important 2 Mark Question Paper-Aug 2020

Part - A

Generic 2 - Answer All Question

Suppose that a boat travels 10 km from the port towards north and then turns 60 to its left. If the boat travels further 8 km, how far from the port is the boat?

Evaluate the following: 100C99

Expand: sin(A + B + C).

A group consists of 4 girls and 7 boys. In how many ways can a team of 5 members be selected, if the team has atleast one boy and one girl

Find the domain and range of the real valued function f(x)=\(\frac{5-x}{x-5}\).

Evaluate the following limits : \(\underset{\sqrt x\rightarrow3}{lim}{x^2-81\over \sqrt x-3}\)

If A+B+C=1800 ,prove that sin2A+sin2B-sin2C=2 sin A sin B cos C

Represent graphically the displacement of 30 km 60° west of north

Express each of the following sum or difference as a product.sin 50° + sin 20°.

Check whether the following functions are one to one and onto. \(f:N\cup(2,-1,0)\rightarrow N\) defined by f(x) =x + 3.

Differentiate the following:\(y={3\sqrt{1+x^3}}\)

For what value of k is the function \(f\left( x \right) =\begin{cases} \frac { \sin { 5x } }{ 3x } \quad if\quad x\neq 0 \\ k,\quad \quad \quad if\quad x=0 \end{cases}\) is continuous at x = 0.

If 15Cr: 15Cr-1 = 11:5 find r.

Prove that sin (30o + \(\theta\)) + cos (60o + \(\theta\))

If \(\vec{a}=\hat{i}+2\hat{j}+3\hat{k}\) , \(\vec{b}=-\hat{i}+2\hat{j}+\hat{k}\)and\(\vec{c}=3\hat{i}+\hat{j}\) .Find \(\lambda\)so that \(\vec{a}+\lambda \vec{b}\) is perpendicular to \(\vec{c}\).

Differentiate the following with respect to x :\(y=(x-{1\over x})^2\)

Find the value \(\lambda\) for which the vectors \(\overrightarrow{a}\) and \(\overrightarrow{b}\) are perpendicular, where \(\overrightarrow{a}=2\hat{i}+\lambda\hat{j}+\hat{k}\) and \(\overrightarrow{b}=\hat{i}-2\hat{j}+3\hat{k}\)

Find the value of \(\frac { 8! }{ 5!\times 2! } \).

Show that the function f:N➝N given by f(x)=2x is one-one but not onto.

Integrate the following with respect to x\({x\over \sqrt{1+x^2}}\)

Integrate the following with respect to x: 5x4

Prove that \(2n{ C }_{ n }=\frac { { 2 }^{ n }\times 13\times ...(2n-1) }{ n! } \) .

State whether the following sets are finite or infinite. {x \(\in \) Z:x is even and less than 10}

If A+B+C=1800 ,prove that sin(B+C-A) + sin(C+A-B) + sin(A+B-C)= 4 sinA sinB sinC

Find the square root of 9-4\(\sqrt{5}\)

Integrate the following with respect to x: sec2(3+4x)

\(f(x)=tan \ x \ at \ x={\pi\over 2}.\)

Show that the function f:R➝R given by f(x)=x2 is neuther one-one nor onto.

A box contains 5 different red and 6 different white balls. In how many ways 6 balls be selected so that are atleast 2 balls of each colour.

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Tamilnadu Stateboardszs - Class

Evaluate the following: ¹⁰⁰C₉₉

Evaluate the following limits :
\(\underset{\sqrt x\rightarrow3}{lim}{x^2-81\over \sqrt x-3}\)

If A+B+C=180⁰ ,prove that sin²A+sin²B-sin²C=2 sin A sin B cos C

Check whether the following functions are one to one and onto.
\(f:N\cup(2,-1,0)\rightarrow N\) defined by f(x) =x + 3.

If ¹⁵C_r: ¹⁵C_r-1 = 11:5 find r.

Prove that sin (30^o + \(\theta\)) + cos (60^o + \(\theta\))

Integrate the following with respect to x: 5x⁴

State whether the following sets are finite or infinite.
{x \(\in \) Z:x is even and less than 10}

If A+B+C=180⁰ ,prove that sin(B+C-A) + sin(C+A-B) + sin(A+B-C)= 4 sinA sinB sinC

Integrate the following with respect to x: sec²(3+4x)

Show that the function f:R➝R given by f(x)=x² is neuther one-one nor onto.