Mathematics | EEE Electrical and Electronics Engineering | TANCET Anna University Online Objective Test

TANCET Anna University EEE Electrical and Electronics Engineering # Mathematics Relations and Functions Prepare / Learn

Q2.

If f (x) = tan x, $- \frac{π}{2} < x < \frac{π}{2}$ and g (x) = $\sqrt{1 - x^{2}}$ , then domain of fog is

A. [−π4,π4]

B. [- 1, 1]

C. (- 1, 1)

D. (−π2,π2)

Answer : Option B
Explaination / Solution:

$\begin{array}{l} f o g (x) = f (g (x)) = f (\sqrt{1 - x^{2}}) \\ \Rightarrow f o g (x) = \tan \sqrt{1 - x^{2}} \end{array}$

and it is defined if

$\begin{array}{l} 1 - x^{2} \geq 0 \\ \Rightarrow x^{2} \leq 1 \\ \Rightarrow - 1 \leq x \leq 1 \end{array}$

TANCET Anna University EEE Electrical and Electronics Engineering # Mathematics Probability Prepare / Learn

Q3. The probability of having atleast one tail in five throws with a coin is

A. 3132

B. 132

C. 1

D. 15

Answer : Option A
Explaination / Solution:
No Explaination.

TANCET Anna University EEE Electrical and Electronics Engineering # Mathematics Engineering Mathematics Prepare / Learn

Q4. Which one of following functions is strictly bounded?

A. 1/X²

B. e^x

C. x²

Answer : Option D
Explaination / Solution:

TANCET Anna University EEE Electrical and Electronics Engineering # Mathematics Relations and Functions Prepare / Learn

Q5. If f (x) =

\sqrt{- x}

, then domain of fof is

A. (−∞,∞)

B. (−∞,0)

C. none of these

D. (0,∞)

Answer : Option C
Explaination / Solution:

$\sqrt{f (x)}$ is defined only if

$f (x)$ will be non negative.

Hence $∴ \sqrt{- f (x)}$ is defined only for 0.

TANCET Anna University EEE Electrical and Electronics Engineering # Mathematics Probability Prepare / Learn

Q6. If E is any event associated with an experiment, then

A. P (E) ≥4 0

B. P (E) ≥1

C. P (E) ≥ 0

D. 0≤P(E)≤r

Answer : Option D
Explaination / Solution:
No Explaination.

TANCET Anna University EEE Electrical and Electronics Engineering # Mathematics Engineering Mathematics Prepare / Learn

Q7. For the function e^x , the linear approximation around x = 2 is

A. (3 - x)e^-2

B. 1 − x

C. [3 + 3√2 - (1 - √2)x]e-2

D. e2

Answer : Option A
Explaination / Solution:

Neglecting higher powers

TANCET Anna University EEE Electrical and Electronics Engineering # Mathematics Relations and Functions Prepare / Learn

Q8. If y = tan

\sqrt{\frac{π}{9} - x^{2}}

then

A. 0≤y≤3

B. −3–√≤y≤3–√

C. none of these

D.
–√0≤y≤3–√

Answer : Option D
Explaination / Solution:

Let $z = \sqrt{\frac{π}{9} - x^{2}}$ and it is defined if

$\begin{array}{l} \frac{π}{9} - x^{2} \geq 0 \\ \Rightarrow x^{2} \leq \frac{π}{9} \end{array}$

$∴ 0 \leq z \leq \frac{π}{3}$

$∴ 0 \leq \tan z \leq \sqrt{3}$

TANCET Anna University EEE Electrical and Electronics Engineering # Mathematics Probability Prepare / Learn

Q9. A and B toss 3 coins. The probability that they both obtain the same number of heads is

A. 316

B. 38

C. 19

D. 516

Answer : Option D
Explaination / Solution:
No Explaination.

TANCET Anna University EEE Electrical and Electronics Engineering # Mathematics Engineering Mathematics Prepare / Learn

Q10. Consider the function f (x) = x − x − . The maximum value of f (x) in the closed interval [− 4, 4] is

A. 18

B. 10

C. -225

D. indeterminate

Answer : Option A
Explaination / Solution:

We have

f (x) = x − x +

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