11th Maths Important 5 Mark Question Paper

St. Britto Hr. Sec. School - Madurai

11th Maths Important 5 Mark Question Paper-Aug 2020

Time : 2.00 Hours

Part - A

Generic 5 - Answer All Question

Evaluate the following integrals\(\int {x^2\over x^2+5}dx\)

If θ is a parameter, find the equation of the locus of a moving point, whose coordinates are x=a cos³, y=a sin³ θ.

Find the separate equation of the following pair of straight lines.
(i) 3x² + 2xy - y² = 0
(ii) 6(x -1)² + 5(x -1)(y - 2)-4(y - 2)² = 0
(iii) 2x² -xy - 3y² - 6x + 19y - 20 = 0

If 22 P_r+1:20 P_r+2=11 : 52 find r.

Express each of the following as a sum or difference. sin 5\(\theta\) sin 4\(\theta\)

If the first two terms of a H. P are \(\frac { 2 }{ 5 } \) and\(\frac { 12 }{ 13 } \) respectively, find the largest term of the H.P.

Prove that \(sec(\frac{3\pi}{2}-\theta)sec(\theta-\frac{5\pi}{2})+tan(\frac{5\pi}{2}+\theta)tan(\theta-\frac{3\pi}{2}=-1\)

Solve : \({ log }_{ 2 }x-3{ log }_{ \frac { 1 }{ 2 } }x=6\)

Each of the digits 1, 1, 2, 3, 3 and 4 is written on a separate card. The six cards are then laid out in a row to form a 6-digit number.
(i) How many distinct 6-digit numbers are there?
(ii) How many of these 6-digit numbers are even?
(iii) How many of these 6-digit numbers are divisible by 4?

A number of four different digits is formed with the use of the digits 1,2,3,4 and 5 in all possible ways. Find the following
(i) How many such numbers can be formed?
(ii) How many of these are even?
(iii) How many of these are exactly divisible by 4?

If A + B + C = \(\pi\), prove the following
cos A + cos B + cos C = 1 + 4 sin \(({A\over 2})\)sin \(({B\over 2})\)sin\(({C\over 2})\)

Solve the following equations cot\(\theta \) +cosec\(\theta \)=\(\sqrt { 3 } \)

Solve for x:\(\frac { x-2 }{ 3x+1 } >\frac { x-3 }{ 3x-2 } \)

Solve\(\sqrt{3}\) sin \(\theta\) - cos \(\theta\) =\(\sqrt{2}\)

Two integers are selected at random from integers 1 to 11. If the sum is even, find the probability that both the numbers are odd.

Evaluate \(\int { \frac { 1 }{ { x }^{ \frac { 1 }{ 2 } }+{ x }^{ \frac { 1 }{ 3 } } } } \)dx

A ripple tank demonstrates the effect of two water waves being added together. The two waves are described by h = 8 cos t and h = 6 sin t, where t ∊ [0, 2π) is in seconds and h is the height in millimeters above still water. Find the maximum height of the resultant wave and the value of that which it occurs.

Resolve the following rational expressions into partial fractions.
\({{1}\over{x^2-a^2}}\)

Determine the roots of the equation \(\begin{vmatrix} 1 &4 &2 0 \\ 1 & -2 & 5 \\ 1 &2x &5x^2 \end{vmatrix}=0\)

Find the equation of the lines passing through the point of intersection lines 4x - y + 3 = 0 and 5x + 2y + 7 = 0
(i) through the point (-1, 2)
(ii) Parallel to x - y + 5 = 0
(iii) Perpendicular to x - 2y + 1 = 0.

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11th Maths Important 5 Mark Question Paper

St. Britto Hr. Sec. School - Madurai

11th Maths Important 5 Mark Question Paper-Aug 2020

Part - A

Generic 5 - Answer All Question

Evaluate the following integrals\(\int {x^2\over x^2+5}dx\)

If θ is a parameter, find the equation of the locus of a moving point, whose coordinates are x=a cos3, y=a sin3 θ.

Find the separate equation of the following pair of straight lines. (i) 3x2 + 2xy - y2 = 0 (ii) 6(x -1)2 + 5(x -1)(y - 2)-4(y - 2)2 = 0 (iii) 2x2 -xy - 3y2 - 6x + 19y - 20 = 0

If 22 Pr+1:20 Pr+2=11 : 52 find r.

Express each of the following as a sum or difference. sin 5\(\theta\) sin 4\(\theta\)

If the first two terms of a H. P are \(\frac { 2 }{ 5 } \) and\(\frac { 12 }{ 13 } \) respectively, find the largest term of the H.P.

Prove that \(sec(\frac{3\pi}{2}-\theta)sec(\theta-\frac{5\pi}{2})+tan(\frac{5\pi}{2}+\theta)tan(\theta-\frac{3\pi}{2}=-1\)

Solve : \({ log }_{ 2 }x-3{ log }_{ \frac { 1 }{ 2 } }x=6\)

Each of the digits 1, 1, 2, 3, 3 and 4 is written on a separate card. The six cards are then laid out in a row to form a 6-digit number. (i) How many distinct 6-digit numbers are there? (ii) How many of these 6-digit numbers are even? (iii) How many of these 6-digit numbers are divisible by 4?

A number of four different digits is formed with the use of the digits 1,2,3,4 and 5 in all possible ways. Find the following (i) How many such numbers can be formed? (ii) How many of these are even? (iii) How many of these are exactly divisible by 4?

If A + B + C = \(\pi\), prove the following cos A + cos B + cos C = 1 + 4 sin \(({A\over 2})\)sin \(({B\over 2})\)sin\(({C\over 2})\)

Solve the following equations cot\(\theta \) +cosec\(\theta \)=\(\sqrt { 3 } \)

Solve for x:\(\frac { x-2 }{ 3x+1 } >\frac { x-3 }{ 3x-2 } \)

Solve\(\sqrt{3}\) sin \(\theta\) - cos \(\theta\) =\(\sqrt{2}\)

Two integers are selected at random from integers 1 to 11. If the sum is even, find the probability that both the numbers are odd.

Evaluate \(\int { \frac { 1 }{ { x }^{ \frac { 1 }{ 2 } }+{ x }^{ \frac { 1 }{ 3 } } } } \)dx

Resolve the following rational expressions into partial fractions. \({{1}\over{x^2-a^2}}\)

Determine the roots of the equation \(\begin{vmatrix} 1 &4 &2 0 \\ 1 & -2 & 5 \\ 1 &2x &5x^2 \end{vmatrix}=0\)

Find the equation of the lines passing through the point of intersection lines 4x - y + 3 = 0 and 5x + 2y + 7 = 0 (i) through the point (-1, 2) (ii) Parallel to x - y + 5 = 0 (iii) Perpendicular to x - 2y + 1 = 0.

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Tamilnadu Stateboardszs - Class

If θ is a parameter, find the equation of the locus of a moving point, whose coordinates are x=a cos³, y=a sin³ θ.

Find the separate equation of the following pair of straight lines.
(i) 3x² + 2xy - y² = 0
(ii) 6(x -1)² + 5(x -1)(y - 2)-4(y - 2)² = 0
(iii) 2x² -xy - 3y² - 6x + 19y - 20 = 0

If 22 P_r+1:20 P_r+2=11 : 52 find r.

Each of the digits 1, 1, 2, 3, 3 and 4 is written on a separate card. The six cards are then laid out in a row to form a 6-digit number.
(i) How many distinct 6-digit numbers are there?
(ii) How many of these 6-digit numbers are even?
(iii) How many of these 6-digit numbers are divisible by 4?

A number of four different digits is formed with the use of the digits 1,2,3,4 and 5 in all possible ways. Find the following
(i) How many such numbers can be formed?
(ii) How many of these are even?
(iii) How many of these are exactly divisible by 4?

If A + B + C = \(\pi\), prove the following
cos A + cos B + cos C = 1 + 4 sin \(({A\over 2})\)sin \(({B\over 2})\)sin\(({C\over 2})\)

Resolve the following rational expressions into partial fractions.
\({{1}\over{x^2-a^2}}\)

Find the equation of the lines passing through the point of intersection lines 4x - y + 3 = 0 and 5x + 2y + 7 = 0
(i) through the point (-1, 2)
(ii) Parallel to x - y + 5 = 0
(iii) Perpendicular to x - 2y + 1 = 0.