NDA MATHEMATICS QUIZ - 7

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Question 1:

Consider the function $f (x) = {\begin{cases} \frac{a^{[x]} + x}{[x] + x} x \neq 0 \\ log a at x = 0 \end{cases}$ is?

फलक पर विचार करें $f (x) = {\begin{cases} \frac{a^{[x]} + x}{[x] + x} x \neq 0 \\ log a at x = 0 \end{cases}$ फिर $f (x)$ है

f (x)

is continuous at x = 0

f (x)

,x = 0 पर निरंतर है

f (x)

exists at x = 0

f (x)

, x = 0 . पर मौजूद है

Both (a) and (b) are correct

Neither of (a) and (b) are correct

Question 2:

If $f (x) = \cos (\log x)$ then

$f (x y) + f (\frac{x}{y})$ equals.

अगर $f (x) = \cos (\log x)$ फिर

$f (x y) + f (\frac{x}{y})$ बराबरी.

f (x) . f (y)

f (x) . f (y)

2 f (x) \cdot f (y)

2 f (x) \cdot f (y)

3 f (x) \cdot f (y)

3 f (x) \cdot f (y)

f (x) + f (y)

f (x) + f (y)

Question 3:

The function defined by

f (x) = \frac{3 x}{\frac{2}{x}} + 1 + 2 c

, when

x \neq 0 = 0, x = 0

then

f^{'} (0)

f (x) = \frac{3 x}{\frac{2}{x}} + 1 + 2 c

द्वारा परिभाषित फलन, जब

x \neq 0 = 0, x = 0

तब

f^{'} (0)

Exists

is equal to 0

is equal to 1

does not create

Question 4:

The function $y = \cos^{- 1} (\sin x)$ is not differentiable at:

फलक $y = \cos^{- 1} (\sin x)$ यहां पर अवकलनीय नहीं है:

x = π

x = π

x = π / 2

x = π / 2

x = 2 π

x = 2 π

x = - 2 π

x = - 2 π

Question 5:

Domain of definitin of The function $f (x) = \log_{x (x^{2} + 1)} (x^{2} - 5 x + 6)$ will be

समारोह की परिभाषा का डोमेन $f (x) = \log \log_{x (x^{2} + 1)} (x 2 - 5 x + 6)$ होगा.

(3, \infty)

(3, \infty)

2, \infty)

2, \infty)

(2, \infty) - {1}

(2, \infty) - {1}

(0, 2) U (3 \infty)

(0, 2) U (3 \infty)

Question 6:

The function $y = x - \tan^{- 1} x$ decreases in the interval.

फलन $y = x - \tan^{- 1} x$ अंतराल में घटता है।

(- \infty, 0)

(- \infty, 0)

(- 1, \infty)

(- 1, \infty)

(- \infty, \infty) - (0)

(- \infty, \infty) - (0)

None of these

Question 7:

${Lt}_{x \to 0} (\cos x)^{1 / x 3}$ equals:

${Lt}_{x \to 0} (\cos x)^{1 / x 3}$ बराबर है:

1.0

0.0

\frac{1}{e}

\frac{1}{e}

- 1

- 1

Question 8:

$lim_{x \to \infty} (\frac{1}{e^{x} - 1} - \frac{1}{x})$ . . . . . . .

${Lim}_{x \to 0} (\frac{1}{e^{x} - 1} - \frac{1}{x})$ . . . . . . .

- \frac{1}{3}

- \frac{1}{3}

- \frac{1}{2}

- \frac{1}{2}

- 1

- 1

- 2

- 2

Question 9:

$lim_{n \to \infty} (\frac{1}{3.4} + \frac{1}{4.5} + \frac{1}{5.6} + \dots \dots$ up to $\infty)$ is:

माना $n \to \infty (\frac{1}{3.4} + \frac{1}{4.5} + \frac{1}{5.6} + \dots . \infty$ तक $)$ है:

0.0

1.0

\frac{1}{2}

\frac{1}{2}

\frac{1}{3}

\frac{1}{3}

Question 10:

A funciton $f (x)$ be defined in such a way that

$f^{'} (x) = \frac{x^{3}}{3} + c x + 2$ where

$f (0) = 0$ and $f (6) = 210$ then the value of $c$ is.

एक फलन $f (x)$ इस तरह से परिभाषित किया जा सकता है कि

$f (x) = \frac{x 3}{3} + c x + 2$ कहाँ पे

$f (0) = 0$ तथा $f (6) = 210$ तो का मान $C$ है.