Functions - Maharashtra Board STD 11 Science Maths Questions - Vidyadip

Question types

Functions question types

336 questions across 6 question groups — pick any mix to generate a Maths paper with step-by-step answer keys.

336

Questions

6

Question groups

5

Question types

MCQ

Solve the following Question.(1 Marks)

Solve the Following Question.(2 Marks)

Solve the Following Question.(3 Marks)

Solve the Following Question.(4 Marks)

Solve the Following Question.(5 Marks)

Sample Questions

Functions questions

One sample from each question group in this chapter. Select any group above to see the full set with answer keys.

Q 1MCQ1 Mark

The domain and range of $f(x)=2-|x-5|$ are

A
$R+,(-\infty, 1]$
✓
$R,(-\infty, 2]$
C
$R,(-\infty, 2)$
D
$R+,(-\infty, 2]$

Answer: B.

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Q 2MCQ1 Mark

The domain of $\frac{1}{|x|-x}$, where $[\mathrm{x}]$ is greatest integer function is

A
$\mathrm{R}$
B
$\mathrm{Z}$
✓
$R-Z$
D
$Q-\{0\}$

Answer: C.

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Q 3MCQ1 Mark

If $f(x)=2 x^2+b x+c$ and $f(0)=3$ and $f(2)=1$, then $f(1)$ is equal to

A
$-2$
✓
$0$
C
$1$
D
$2$

Answer: B.

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Q 4MCQ1 Mark

Let the function $f$ be defined by $f(x)=\frac{2 x+1}{1-3 x}$ then $f^{-1}(x)$ is:

✓
$\frac{x-1}{3 x+2}$
B
$\frac{x+1}{3 x-2}$
C
$\frac{2 x+1}{1-3 x}$
D
$\frac{3 x+2}{x-1}$

Answer: A.

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Q 5MCQ1 Mark

If $f: R \rightarrow R$ is defined by $f(x)=x^3$, then $f^{-1}(8)$ is equal to:

✓
$\{2\}$
B
$\{-2.2\}$
C
$\{-2\}$
D
$(-2.2)$

Answer: A.

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Q 6Solve the following Question.(1 Marks)1 Mark

Find $f(x)$,
if$g(x)=1+\sqrt{x}$ and $f[g(x)]=3+2 \sqrt{x}+x$.

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Q 7Solve the following Question.(1 Marks)1 Mark

Find the range of the following function : $f(x)=1+2 x+4 x$

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Q 8Solve the following Question.(1 Marks)1 Mark

Find the range of the following function : $f(x)=[x]-x$

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Q 9Solve the following Question.(1 Marks)1 Mark

Find the range of the following function : $f(x)=\frac{1}{1+\sqrt{x}}$

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Q 10Solve the following Question.(1 Marks)1 Mark

Find the range of the following function : $f(x)=\frac{x}{9+x^2}$

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Q 11Solve the Following Question.(2 Marks)2 Marks

Find $f(x)$, if
$g(x)=x^2+x-2$ and (gof) $(x)=4 x^2-10 x+4$

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Q 12Solve the Following Question.(2 Marks)2 Marks

Find (fog) (x) and (gof) (x) : $f(x)=\frac{x}{x+1}, g(x)=\frac{x}{1-x}$

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Q 13Solve the Following Question.(2 Marks)2 Marks

Find (fog) (x) and (gof) (x) : $f(x)=e^x, g(x)=\log x$

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Q 14Solve the Following Question.(2 Marks)2 Marks

Find the domain of the following functions.
$\mathrm{f}(\mathrm{x})=\sqrt{x-x^2}+\sqrt{5-x}$

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Q 15Solve the Following Question.(2 Marks)2 Marks

Find the domain of the following functions.$f(x)=\sqrt{1-\sqrt{1-\sqrt{1-x^2}}}$

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Q 16Solve the Following Question.(3 Marks)3 Marks

Find (fof) ( $x$ ) if : $f(x)=\frac{2 x+1}{3 x-2}$

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Q 17Solve the Following Question.(3 Marks)3 Marks

Find (fof) ( $x$ ) if : $f(x)=\frac{x}{\sqrt{1+x^2}}$

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Q 18Solve the Following Question.(3 Marks)3 Marks

Find the domain of the following functions.$f(x)=\sqrt{\log \left(x^2-6 x+6\right)}$

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Q 19Solve the Following Question.(3 Marks)3 Marks

If $\frac{\log _2 a}{4}=\frac{\log _2 b}{6}=\frac{\log _2 c}{3 k}$ and $a^3 b^2 c=1$, find the value of $k$.

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Q 20Solve the Following Question.(3 Marks)3 Marks

Show that $7 \log \left(\frac{15}{16}\right)+6 \log \left(\frac{8}{3}\right)+5 \log \left(\frac{2}{5}\right)+\log \left(\frac{32}{25}\right)=\log 3$

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Q 21Solve the Following Question.(4 Marks)4 Marks

Find the value of $\frac{3+\log _{10} 343}{2+\frac{1}{2} \log _{10}\left(\frac{49}{4}\right)+\frac{1}{2} \log _{10}\left(\frac{1}{25}\right)}$

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Q 22Solve the Following Question.(5 Marks)5 Marks

Solve the following for $x$, where $|x|$ is modulus function, $[x]$ is the greatest integer function, $\{x\}$ is a fractional part function.$\left|x^2-9\right|+\left|x^2-4\right|=5$

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Q 23Solve the Following Question.(5 Marks)5 Marks

Solve: $\sqrt{\log _2 x^4}+4 \log _4 \sqrt{\frac{2}{x}}=2$

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