11th Standard Syllabus & Materials

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11th Standard Maths English Medium Free Online Test One Mark Questions with Answer Key 2020 - Part Seven

Published on: 11/11/2020

Download Tamil Nadu 11th Standard Maths question papers, model tests, one-mark questions, important questions, and public exam papers in PDF format. Free study materials and answer keys for TN State Board students.

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Std: 11th Standard - Maths

chapter: - Model Question paper

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Questions:

Multiple Choice Question

10 x 1 = 10

The value of \(\sqrt [ 4 ]{ { (-2) }^{ 4 } } =\) _______.

(a)

(b)

-2

(c)

(d)

-4

If a and b are chosen randomly from the set {1,2,3,4} with replacement, then the probability of the real roots of the equation \(x^2+ax+b=0\) is

(a)

\({3\over 16}\)

(b)

\({5\over 16}\)

(c)

\({7\over 16}\)

(d)

\({11\over 16}\)

\(\int x^2 e^{\frac{x}{2}} d x\) is

(a)

\( x^2e^{x\over2}-4xe^{x\over2}-8e^{x\over2}+c\)

(b)

\( 2x^2e^{x\over2}-8xe^{x\over2}-16e^{x\over2}+c\)

(c)

\( 2x^2e^{x\over2}-8xe^{x\over2}+16e^{x\over2}+c\)

(d)

\( x^2{e^{x\over2}\over 2}-{xe^{x\over2}\over 4}+{e^{x\over2}\over 8}+c\)

\(\int \frac{x^2+\cos ^2 x}{x^2+1} \operatorname{cosec}^2 x d x\) is

(a)

cot x + sin ^-1x + c

(b)

-cot x + tan^-1x + c

(c)

-tan x + cot^-1x + c

(d)

-cot x - tan^-1x + c

The value of x, for which the matrix A = \(\begin{bmatrix} e^{x-2}& e^{7+x} \\ e^{2+x} & e^{2x+3} \end{bmatrix}\) is singular

(a)

(b)

(c)

(d)

If sin θ = sin \(\alpha\), then the angles θ and \(\alpha\) are related by _______________

(a)

\(\theta=n\pi\pm\alpha\)

(b)

\(\theta=2n\pi+(-1)^n\alpha\)

(c)

\(\alpha=n\pi\pm(-1)^n\theta\)

(d)

\(\theta=(2n+1)\pi+\alpha\)

Logarithm of 144 to the base 2\(\sqrt{3}\) is ___________

(a)

(b)

(c)

(d)

If the roots of x²-bx + c = 0 are two consecutive integer,then b²- 4c is ___________

(a)

(b)

(c)

(d)

none of these

cos 6x - cos 8x = _______________

(a)

2 sin 7x sin x

(b)

sin 7x sin x

(c)

\(\frac { 1 }{ 2 } \)sin 7x + sin x

(d)

\(\sqrt { 2 } \) sin7x sin x

10.

If A = {(x,y) : y = e^x, x∈R} and B = {(x,y) : y = e^-x, x ∈ R} then n(A∩B) is

(a)

Infinity

(b)

(c)

(d)

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Answers Key:

Multiple Choice Question

10 x 1 = 10

(a)
2

\(n(S)=n(A \times A) \quad=16\)
\(\text {To find } n(A)\)
\(\text {Let } a=4, b=1 \text { then } a^{2}-4 b \text { is }\)
A = 1,b = 1 then 16 - 4 > 0
b = 2. then 16 - 8 > 0
b=3 then 16-L2>0
b = 4 then 16 - 16 = 0
Let Q = 3,b = 1 thg,l, 9-4 > 0
b = 2 then 9 - 8 > 0
Let a = 2,b = l then 4 - 4 > 0
n(A).= 7,
\(P(A)=\frac{n(A)}{n(S)}=\frac{7}{16}\)

Applying Bernoulli's formula
\(\int x^{2} e^{x / 2} d x =x^{2}\left(\frac{e^{x / 2}}{1 / 2}\right)-2 x\left(\frac{e^{x / 2}}{1 / 2 \times 1 / 2}\right)+2\left(\frac{e^{x / 2}}{1 / 2 \times 1 / 2 \times 1 / 2}\right)+c \)
\(=2 x^{2} e^{x / 2}-8 x e^{x / 2}+16 e^{x / 2}+c \)

\(\int \frac{x^{2}+\cos ^{2} x}{x^{2}+1} \operatorname{cosec}^{2} x d x \)
\(=\int \frac{x^{2}+\left(1-\sin ^{2} x\right)}{x^{2}+1} \times \frac{1}{\sin ^{2} x} d x \)
\(=\int \frac{\left(x^{2}+1\right)-\sin ^{2} x}{\left(x^{2}+1\right) \sin ^{2} x} d x \)
\(=\int\left(\frac{1}{\sin ^{2} x}-\frac{1}{x^{2}+1}\right) d x \)
\(=\int\left(\operatorname{cosec}^{2} x-\frac{1}{x^{2}+1}\right) d x \)
\(=-\cot x-\tan ^{-1} x+c \)

\(|A|=0 \quad \text { [since } A \text { is singular] }\)
\(\left|\begin{array}{ll} e^{x-2} & e^{7+x} \\ e^{2+x} & e^{2 x+3} \end{array}\right| =0 \)
\(e^{x-2+2 x+3}-e^{2+x+7+x} =0 \)
\(e^{3 x+1} =e^{9+2 x} \)
\(3 x+1 =9+2 x \)
\(x =8 \)