11th Maths Important 3 Mark Question Paper

St. Britto Hr. Sec. School - Madurai

11th Maths Important 3 Mark Question Paper-Aug 2020

Time : 1.30 Hours

Part - A

Generic 3 - Answer All Question

Find the nearest point on the line 2x +y = 5 from the origin.

Prove that \(cos\frac { B-C }{ 2 }= \frac { b+c }{ a } sin\frac { A }{ 2 } \)

If n (p(A)) = 1024, n(A\(\cup\)B)=15 and n(p(B))=32, then find n(A\(\cap\)B).

Show that the vectors \(-\hat{i}-2\hat{j}-6\hat{k},2\hat{i}-\hat{j}+\hat{k}\) ,and \(-\hat{i}+3\hat{j}+5\hat{k}\) form a right angled triangle.

If f(x)=2x²+3x-5, then prove that f' (0) + 3 f' (-1) = 0

Consider the functions:(i) y = e^x; (ii) y = log_eX.

Evaluate \(\lim _{ x\rightarrow \pi }{ \frac { \sin { x } }{ x-\pi } } \)

Prove that \(\left| \begin{matrix} 1/{ a }^{ 2 } & bc & b+c \\ 1/{ b }^{ 2 } & ca & c+a \\ 1/{ c }^{ 2 } & ab & a+b \end{matrix} \right| =0\)

If x so large prove that \(\sqrt { { x }^{ 2 }+25 } -\sqrt { { x }^{ 2 }+9 } =\frac { 8 }{ x } \) nearly.

Integrate the following functions with respect to x :\({sin^2x\over 1+cos \ x}\)

Prove that \({{cos\ 2\ x}\over{1+sin\ 2x}}=tan\left( {{\pi}\over{4}}-x \right)\)

If a, b, c are p^th, q^th and r^th terms of an A.P, find the value of\(\begin{vmatrix} a & b & c \\ p & q & r \\ 1& 1 &1 \end{vmatrix}\)

If θ is a parameter, find the equation of the locus of a moving point, whose coordinates are (a(θ-sinθ),a(1-cosθ)).

Write the first 6 terms of the sequences whose nth terms are given below and classify them as arithmetic progression, geometric progression, arithmetic -geometric progression, harmonic progression and none of them \(\frac { 2n+3 }{ 3n+4 } \)

Find the angle between the vectors \(5\hat{i}+3\hat{j}+4\hat{k}\)and\(6\hat{i}-8\hat{j}-\hat{k}\).

Find the equation of the line which passes through the point (- 4, 3) and the portion of the line intercepted between the axes is divided internally in the ratio 5: 3 by this point.

Integrate the following functions with respect to x: e^3x-6

Write the first 6 terms of the sequences whose nth terms are given below and classify them as arithmetic progression, geometric progression, arithmetic -geometric progression, harmonic progression and none of them \(\frac { 3n-2 }{ 3^{n-1} } \)

Solve for x if [x 2 -1] \(\begin{bmatrix} 1&1 &2 \\ -1 & -4 &1 \\ -1 &-1 &-2 \end{bmatrix}\)\(\begin{bmatrix} x \\ 2 \\ 1 \end{bmatrix}\)=0

Evaluate the following limits :
\(\underset{x\rightarrow2}{lim}{{1\over x}-{1\over2}\over x-2}\)

Compute \(lim_{x\rightarrow{0}}[{x^2+x\over x}+4x^3+3]\) .

A student when walks from his house, at an average speed of 6 kmph, reaches his school ten minutes before the school starts. When his average speed is 4 kmph, he reaches his school five minutes late. If he starts to school every day at 8.00 A.M, then find (i) the distance between his house and the school (ii) the minimum average speed to reach the school on time and time taken to reach the school (iii) the time the school gate closes (iv) the pair of straight lines of his path of walk.

Write the first six terms of the sequences given by a₁=4,a_n+1=2na_n.

Evaluate the following limits :
\(\underset{x\rightarrow0}{lim}{\sqrt{1+x}-1\over x}\)

If A₁, B₁, C₁ are the cofactors of a₁, b₂,c₃, respectively, i = 1 to 3 in
|A|=\(\begin{vmatrix} a_1 &b_1 &c_1 \\ a_2 & b_2 &c_2 \\ a_3 & b_3 & c_3 \end{vmatrix}\), show that \(\begin{vmatrix} A_1 &B_1 &C_1 \\ A_2 & B_2 &C_2 \\ A_3 & B_3 & C_3 \end{vmatrix}\) =|A|²

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11th Maths Important 3 Mark Question Paper

St. Britto Hr. Sec. School - Madurai

11th Maths Important 3 Mark Question Paper-Aug 2020

Part - A

Generic 3 - Answer All Question

Find the nearest point on the line 2x +y = 5 from the origin.

Prove that \(cos\frac { B-C }{ 2 }= \frac { b+c }{ a } sin\frac { A }{ 2 } \)

If n (p(A)) = 1024, n(A\(\cup\)B)=15 and n(p(B))=32, then find n(A\(\cap\)B).

Show that the vectors \(-\hat{i}-2\hat{j}-6\hat{k},2\hat{i}-\hat{j}+\hat{k}\) ,and \(-\hat{i}+3\hat{j}+5\hat{k}\) form a right angled triangle.

If f(x)=2x2+3x-5, then prove that f' (0) + 3 f' (-1) = 0

Consider the functions:(i) y = ex; (ii) y = logeX.

Evaluate \(\lim _{ x\rightarrow \pi }{ \frac { \sin { x } }{ x-\pi } } \)

Prove that \(\left| \begin{matrix} 1/{ a }^{ 2 } & bc & b+c \\ 1/{ b }^{ 2 } & ca & c+a \\ 1/{ c }^{ 2 } & ab & a+b \end{matrix} \right| =0\)

If x so large prove that \(\sqrt { { x }^{ 2 }+25 } -\sqrt { { x }^{ 2 }+9 } =\frac { 8 }{ x } \) nearly.

Integrate the following functions with respect to x :\({sin^2x\over 1+cos \ x}\)

Prove that \({{cos\ 2\ x}\over{1+sin\ 2x}}=tan\left( {{\pi}\over{4}}-x \right)\)

If a, b, c are pth, qth and rth terms of an A.P, find the value of\(\begin{vmatrix} a & b & c \\ p & q & r \\ 1& 1 &1 \end{vmatrix}\)

If θ is a parameter, find the equation of the locus of a moving point, whose coordinates are (a(θ-sinθ),a(1-cosθ)).

Write the first 6 terms of the sequences whose nth terms are given below and classify them as arithmetic progression, geometric progression, arithmetic -geometric progression, harmonic progression and none of them \(\frac { 2n+3 }{ 3n+4 } \)

Find the angle between the vectors \(5\hat{i}+3\hat{j}+4\hat{k}\)and\(6\hat{i}-8\hat{j}-\hat{k}\).

Find the equation of the line which passes through the point (- 4, 3) and the portion of the line intercepted between the axes is divided internally in the ratio 5: 3 by this point.

Integrate the following functions with respect to x: e3x-6

Write the first 6 terms of the sequences whose nth terms are given below and classify them as arithmetic progression, geometric progression, arithmetic -geometric progression, harmonic progression and none of them \(\frac { 3n-2 }{ 3^{n-1} } \)

Solve for x if [x 2 -1] \(\begin{bmatrix} 1&1 &2 \\ -1 & -4 &1 \\ -1 &-1 &-2 \end{bmatrix}\)\(\begin{bmatrix} x \\ 2 \\ 1 \end{bmatrix}\)=0

Evaluate the following limits : \(\underset{x\rightarrow2}{lim}{{1\over x}-{1\over2}\over x-2}\)

Compute \(lim_{x\rightarrow{0}}[{x^2+x\over x}+4x^3+3]\) .

Write the first six terms of the sequences given by a1=4,an+1=2nan.

Evaluate the following limits : \(\underset{x\rightarrow0}{lim}{\sqrt{1+x}-1\over x}\)

If A1, B1, C1 are the cofactors of a1, b2,c3, respectively, i = 1 to 3 in |A|=\(\begin{vmatrix} a_1 &b_1 &c_1 \\ a_2 & b_2 &c_2 \\ a_3 & b_3 & c_3 \end{vmatrix}\), show that \(\begin{vmatrix} A_1 &B_1 &C_1 \\ A_2 & B_2 &C_2 \\ A_3 & B_3 & C_3 \end{vmatrix}\) =|A|2

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Tamilnadu Stateboardszs - Class

If f(x)=2x²+3x-5, then prove that f' (0) + 3 f' (-1) = 0

Consider the functions:(i) y = e^x; (ii) y = log_eX.

If a, b, c are p^th, q^th and r^th terms of an A.P, find the value of\(\begin{vmatrix} a & b & c \\ p & q & r \\ 1& 1 &1 \end{vmatrix}\)

Integrate the following functions with respect to x: e^3x-6

Evaluate the following limits :
\(\underset{x\rightarrow2}{lim}{{1\over x}-{1\over2}\over x-2}\)

Write the first six terms of the sequences given by a₁=4,a_n+1=2na_n.

Evaluate the following limits :
\(\underset{x\rightarrow0}{lim}{\sqrt{1+x}-1\over x}\)

If A₁, B₁, C₁ are the cofactors of a₁, b₂,c₃, respectively, i = 1 to 3 in
|A|=\(\begin{vmatrix} a_1 &b_1 &c_1 \\ a_2 & b_2 &c_2 \\ a_3 & b_3 & c_3 \end{vmatrix}\), show that \(\begin{vmatrix} A_1 &B_1 &C_1 \\ A_2 & B_2 &C_2 \\ A_3 & B_3 & C_3 \end{vmatrix}\) =|A|²