MCQ (Single Correct Answer)

1

The range of the function $$f(x) = {\log _e}\sqrt {4 - {x^2}} $$ is given by

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2

The function $$f(x) = \log \left( {{{1 + x} \over {1 - x}}} \right)$$ satisfies the equation

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3

The equation ex + x $$-$$ 1 = 0 has, apart from x = 0

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4

A mapping from IN to IN is defined as follows:

$$f:IN \to IN$$

$$f(n) = {(n + 5)^2},\,n \in IN$$

(IN is the set of natural numbers). Then

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5

The domain of definition of the function $$f(x) = \sqrt {1 + {{\log }_e}(1 - x)} $$ is

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6

The domain of the function $$f(x) = \sqrt {{{\cos }^{ - 1}}\left( {{{1 - |x|} \over 2}} \right)} $$ is

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7

For what values of x, the function $$f(x) = {x^4} - 4{x^3} + 4{x^2} + 40$$ is monotone decreasing?

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8

The minimum value of $$f(x) = {e^{({x^4} - {x^3} + {x^2})}}$$ is

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9

The period of the function f(x) = cos 4x + tan 3x is

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10

The even function of the following is

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11

If f(x + 2y, x $$-$$ 2y) = xy, then f(x, y) is equal to

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12

If $g(f(x))=|\sin x|$ and $f(g(x))=(\sin \sqrt{x})^2$, then

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13

If $f(x)=\frac{3 x-4}{2 x-3}$, then $f(f(f(x)))$ will be

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14

Let $u+v+w=3, u, v, w \in \mathbb{R}$ and $f(x)=u x^2+v x+w$ be such that $f(x+y)=f(x)+f(y)+x y$, $\forall x, y \in \mathbb{R}$. Then $f(1)$ is equal to

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15

If $f(x)$ and $g(x)$ are two polynomials such that $\phi(x)=f\left(x^3\right)+x g\left(x^3\right)$ is divisible by $x^2+x+1$, then

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16

Let $$\mathrm{f}: \mathbb{R} \rightarrow \mathbb{R}$$ be a function defined by $$\mathrm{f}(x)=\frac{\mathrm{e}^{|x|}-\mathrm{e}^{-x}}{\mathrm{e}^x+\mathrm{e}^{-x}}$$, then

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17

For every real number $$x \neq-1$$, let $$\mathrm{f}(x)=\frac{x}{x+1}$$. Write $$\mathrm{f}_1(x)=\mathrm{f}(x)$$ & for $$\mathrm{n} \geq 2, \mathrm{f}_{\mathrm{n}}(x)=\mathrm{f}\left(\mathrm{f}_{\mathrm{n}-1}(x)\right)$$. Then $$\mathrm{f}_1(-2) \cdot \mathrm{f}_2(-2) \ldots . . \mathrm{f}_{\mathrm{n}}(-2)$$ must be

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18

The equation $$2^x+5^x=3^x+4^x$$ has

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19

In the interval $$( - 2\pi ,0)$$, the function $$f(x) = \sin \left( {{1 \over {{x^3}}}} \right)$$.

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20

Domain of $$y = \sqrt {{{\log }_{10}}{{3x - {x^2}} \over 2}} $$ is

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21

Let $$f(x) = {(x - 2)^{17}}{(x + 5)^{24}}$$. Then

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22

Let $$f(n) = {2^{n + 1}}$$, $$g(n) = 1 + (n + 1){2^n}$$ for all $$n \in N$$. Then

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23

The maximum value of $$f(x) = {e^{\sin x}} + {e^{\cos x}};x \in R$$ is

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24

$$f:X \to R,X = \{ x|0 < x < 1\} $$ is defined as $$f(x) = {{2x - 1} \over {1 - |2x - 1|}}$$. Then

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25
Let f : R $$\to$$ R be given by f(x) = | x2 $$-$$ 1 |, x$$\in$$R. Then,
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26
f(x) is real valued function such that 2f(x) + 3f($$-$$x) = 15 $$-$$ 4x for all x$$\in$$R. Then f(2) =
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27
Consider the functions f1(x) = x, f2(x) = 2 + loge x, x > 0. The graphs of the functions intersect
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28
Given that f : S $$\to$$ R is said to have a fixed point at c of S if f(c) = c. Let f : [1, $$\infty$$) $$\to$$ R be defined by f(x) = 1 + $$\sqrt x $$. Then
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29
Let $$f(x) = 1 - \sqrt {({x^2})} $$, where the square root is to be taken positive, then
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30
The domain of $$f(x) = \sqrt {\left( {{1 \over {\sqrt x }} - \sqrt {x + 1} } \right)} $$ is
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31
Let $$A = \{ x \in R: - 1 \le x \le 1\} $$ and $$f:A \to A$$ be a mapping defined by $$f(x) = x\left| x \right|$$. Then f is
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32
Let $$f(x) = \sqrt {{x^2} - 3x + 2} $$ and $$g(x) = \sqrt x $$ be two given functions. If S be the domain of fog and T be the domain of gof, then
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33
Let $$f:R \to R$$ be defined by $$f(x) = {x^2} - {{{x^2}} \over {1 + {x^2}}}$$ for all $$x \in R$$. Then,
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34
Consider the function f(x) = cos x2. Then,
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35
Let a > b > 0 and I(n) = a1/n $$-$$ b1/n, J(n) = (a $$-$$ b)1/n for all n $$ \ge $$ 2, then
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36
The domain of definition of $$f(x) = \sqrt {{{1 - |x|} \over {2 - |x|}}} $$ is
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37
If f : R $$ \to $$ R be defined by f (x) = ex and g : R $$ \to $$ R be defined by g(x) = x2. The mapping gof : R $$ \to $$ R be defined by (gof) (x) = g[f(x)] $$\forall $$x$$ \in $$R. Then,
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38
For 0 $$ \le $$ p $$ \le $$ 1 and for any positive a, b; let I(p) = (a + b)p, J(p) = ap + bp, then
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39
Let $$f:R \to R$$ be such that f is injective and $$f(x)f(y) = f(x + y)$$ for $$\forall x,y \in R$$. If f(x), f(y), f(z) are in G.P., then x, y, z are in
WB JEE 2017
40
Let $$f(x) = {x^{13}} + {x^{11}} + {x^9} + {x^7} + {x^5} + {x^3} + x + 19$$. Then, f(x) = 0 has
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Subjective

MCQ (More than One Correct Answer)

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