One mark questions are quick and easy to score. Here are the most important one mark questions from the Samacheer syllabus for 11th Maths. Students can practice with this question paper to score more. In this question paper, one marks are questions are taken based on the book back, creative questions and repeatedly asked questions.

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Questions:

Multiple Choice Question

50 x 1 = 50

\(\int { \frac { x }{ 4+{ x }^{ 4 } } } \) dx is equal to________+c.

(a)

\(\frac { 1 }{ 4 } \) tan^-1 (x²)

(b)

\(\frac { 1 }{ 4 } \) tan^-1 \(\left( \frac { { x }^{ 2 } }{ 2 } \right) \)

(c)

\(\frac { 1 }{ 2 } \) tan^-1 \(\left( \frac { { x }^{ 2 } }{ 2 } \right) \)

(d)

none of these

\(\int { { tan }^{ 3 } } 2sec2x\) dx = ___________+c.

(a)

\(\frac { 1 }{ 6 } \) sec³ 2x

(b)

\(\frac { 1 }{ 6 } \) sec³2x - \(\frac { 1 }{ 2 } \) sec 2x

(c)

\(\frac { 1 }{ 2 } \) sec 2x

(d)

\(\frac { 1 }{ 6 } \) sec³ 2x + \(\frac { 1 }{ 2 } \) sec 2x

A flash light has 8 batteries out of which 3 are dead. If 2 batteries are selected without replacement and tested, the probability that both are dead is

(a)

\(\frac { 3 }{ 28 } \)

(b)

\(\frac { 1 }{ 14 } \)

(c)

\(\frac { 9 }{ 64 } \)

(d)

\(\frac { 33 }{ 56 } \)

A bag contains 5 black balls, 4 white balls and 3 red balls. If a ball is selected at random, the probability that it is black or red ball is

(a)

\(\frac { 1 }{ 3 } \)

(b)

\(\frac { 1 }{ 4 } \)

(c)

\(\frac { 5 }{ 12 } \)

(d)

\(\frac { 2 }{ 3 } \)

The slop of the curve \(y={ x }^{ 3 }-7{ x }^{ 2 }+5x+10\) at x=1 is

(a)

(b)

-6

(c)

(d)

\(\lim _{ x\rightarrow \frac { \pi }{ 2 } }{ \frac { \sin { x } }{ x } } =\)

(a)

\(\pi \)

(b)

\(\frac { \pi }{ 2 } \)

(c)

\(\frac { 2 }{ \pi } \)

(d)

Choose the correct or the most suitable answer from the given four alternatives.
If, \(y=a+b{ x }^{ 2 }\) where a, b are arbitrary constants, then ____

(a)

\(\frac { d^{ 2 }y }{ d{ x }^{ 2 } } =2xy\)

(b)

\(x\frac { d^{ 2 }y }{ d{ x }^{ 2 } } ={ y }_{ 1 }\)

(c)

\(x\frac { d^{ 2 }y }{ d{ x }^{ 2 } } -\frac { dy }{ dx } +y=0\)

(d)

\(x\frac { d^{ 2 }y }{ d{ x }^{ 2 } } =2xy\)

Choose the correct or the most suitable answer from the given four alternatives.
If \(y=\log _{ a }{ x } \) then \(\frac { dy }{ dx } \) is ______

(a)

\(\frac { 1 }{ x } \)

(b)

\(\frac { 1 }{ x\log _{ e }{ a } } \)

(c)

\(\log { _{ e }^{ a } } \)

(d)

\(\frac { 1 }{ \log _{ a }{ x } } \)

The value of \(\left| \begin{matrix} x+1 & x+2 & x+a \\ x+2 & x+3 & x+b \\ x+3 & x+4 & x+c \end{matrix} \right| \) =_____________ 0, where a, b, c are in AP is

(a)

(x+1)(x+2)(x+3)

(b)

(c)

(d)

(x+a)(x+b)(x+c)

10.

A matrix which is not a square matrix is called a_________matrix.

(a)

singular

(b)

non-singular

(c)

non-square

(d)

rectangular

11.

If m is a number such that m \(\le\) 5, then the probability that quadratic equation 2x² + 2mx + m + 1 = 0 has real roots is

(a)

\({1\over 5}\)

(b)

\({2\over 5}\)

(c)

\({3\over 5}\)

(d)

\({4\over 5}\)

12.

If A and B are two events such that A ⊂ B and P(B)\(\neq o\), then which of the following is correct?

(a)

\(P(A/B)={P(A)\over P(B)}\)

(b)

P(A/B)

(c)

P(A/B)\(\ge\)P(A)

(d)

P(A/B)>P(B)

13.

A man has 3 fifty rupee notes, 4 hundred rupees notes, and 6 five hundred rupees notes in his pocket. If 2 notes are taken at random, what are the odds in favour of both notes being of hundred rupee denomination?

(a)

1:12

(b)

12:1

(c)

13:1

(d)

1:13

14.

\(\int \sin \sqrt{x} d x\) is

(a)

\(2(-\sqrt{x}cos\sqrt{x}+sin\sqrt{x})+c\)

(b)

\(2(-\sqrt{x}cos\sqrt{x}-sin\sqrt{x})+c\)

(c)

\(2(-\sqrt{x}sin\sqrt{x}-cos\sqrt{x})+c\)

(d)

\(2(-\sqrt{x}sin\sqrt{x}+cos\sqrt{x})+c\)

15.

\(\int \frac{e^{6 \log x}-e^{5 \log x}}{e^{4 \log x}-e^{3 \log x}} d x\) is

(a)

x+c

(b)

\({x^3\over 3}+c\)

(c)

\({3\over x^3}+c\)

(d)

\({1\over x^2}+c\)

16.

The number of points in R in which the function \(f(x)=|x-1|+|x-3|+sin \ x\) is not differentiable, is

(a)

(b)

(c)

(d)

17.

If y = cos (sin x²), then \({dy\over dx}\) at x = \(\sqrt{\pi\over 2}\) is

(a)

-2

(b)

(c)

\(-2\sqrt{\pi\over 2}\)

(d)

18.

\(lim_{\alpha \rightarrow {\pi/4}}{sin \alpha -cos \alpha \over \alpha -{\pi\over 4}}\) is

(a)

\(\sqrt{2}\)

(b)

\(1\over \sqrt{2}\)

(c)

(d)

19.

The vectors \(\overrightarrow{a}-\overrightarrow{b},\overrightarrow{b}-\overrightarrow{c},\overrightarrow{c}-\overrightarrow{a}\) are

(a)

parallel to each other

(b)

unit vectors

(c)

mutually perpendicular vectors

(d)

coplanar vectors.

20.

If \(\triangle\) = \(\begin{vmatrix} a&b &c \\ x & y & z \\ p &q &r \end{vmatrix}\), then \(\begin{vmatrix} ka&kb &kc \\ kx & ky & kz \\k p &kq &kr \end{vmatrix}\) is

(a)

\(\triangle\)

(b)

k\(\triangle\)

(c)

3k\(\triangle\)

(d)

k³\(\triangle\)

21.

The locus of a point which is collinear with the points (a, 0) and (0, b) is ______________

(a)

x + y = 1

(b)

\(\frac{x}{a}+\frac{y}{b}=1\)

(c)

x + y = ab

(d)

\(\frac{x}{a}-\frac{y}{b}=1\)

22.

The angle between the lines 2x - y + 5 = 0 and 3x + y + 4 = 0 is ______________

(a)

45⁰

(b)

30⁰

(c)

60⁰

(d)

90⁰

23.

Area of triangle ABC is _______________

(a)

\(\frac{1}{2}\)ab cos C

(b)

\(\frac{1}{2}\)ab sin C

(c)

\(\frac{1}{2}\)ab cos B

(d)

\(\frac{1}{2}\)bc sin B

24.

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)

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

25.

Which one of the following is false?

(a)

A⋂(BΔ\C) = (A ⋂ B)Δ(A ∩ C)

(b)

A∩(B - C) = (A ∩B) \ (A∩C)

(c)

(A U B), = A' ∩ B'

(d)

(A \ B) U B = A ⋂ B

26.

Which one of the following statements is false? The graph of the function \(f(x)={1\over x}\)

(a)

exist is the first and third quadrant only

(b)

is a reciprocal function

(c)

is defined at x = 0

(d)

it is symmetric about y = x and y = - x.

27.

The length of perpendicular from the origin to a line is 12 and the line makes an angle of 120° with the positive direction of y-axis. then the equation of line is ______________

(a)

\(x+y\sqrt 3=24\)

(b)

\(x+y=12\sqrt 2\)

(c)

x + y = 24

(d)

\(x+y=12\sqrt 3\)

28.

If ⁿC₁₀ = ⁿC₆, then ⁿC₂ = _________

(a)

(b)

(c)

120

(d)

240

29.

A candidate is required to answer 7 question out of 12 questions, which are divided into two groups each containing 6 questions. He is not permitted to attempt more than 5 questions from either group. Find the number of different ways of doing questions.

(a)

779

(b)

781

(c)

780

(d)

782

30.

If an A.P the sum of terms equidistant from the beginning and end is equal to ______________

(a)

first term

(b)

second term

(c)

sum of first and last term

(d)

last term

31.

Let \(\alpha\) and \(\beta\) are the roots of a quadratic equation px² + qx + r = 0 then ___________

(a)

\(\alpha +\beta=-{p\over r}\)

(b)

\(\alpha\beta={p\over r}\)

(c)

\(\alpha +\beta={-q\over p}\)

(d)

\(\alpha \beta =r\)

32.

Find the point of intersection of the lines 2x²+ xy -y²- 5x + 3y + 2 = 0 ______________

(a)

(-1, -1)

(b)

(1, 1)

(c)

(1, 0)

(d)

(0, 1)

33.

Expansion of \(log(\sqrt \frac{1+x}{1-x})\) is ______________

(a)

\(x+\frac{x^3}{3}+\frac{x^5}{5}+...\)

(b)

\(1.\frac{x^2}{2}+\frac{x^4}{4}+...\)

(c)

\(1-x+\frac{x^2}{2}+\frac{x^3}{5}+...\)

(d)

\(x-\frac{x^2}{3}+\frac{x^3}{3}+...\)

34.

The quadratic equation whose roots are tan 75° and cot 75° is _______________

(a)

x²+4x+ 1 = 0

(b)

4x²-x+ 1 = 0

(c)

4x²+ 4x - 1 = 0

(d)

x² - 4x + 1 = 0

35.

is _________

(a)

\(\lfloor{n}(n+2)\)

(b)

(c)

(d)

none of these

36.

If \(f:[-2,2]\rightarrow A\) is given by f(x) = 3³ then f is onto, if A is ___________

(a)

[3, 3]

(b)

(3, 3)

(c)

[-24,24]

(d)

(-24, 24)

37.

The series for log \(\left( \frac { 1+x }{ 1-x } \right) is\) ______________

(a)

\(x+\frac { { x }^{ 3 } }{ 3 } +\frac { { x }^{ 5 } }{ 5 } +...+\infty \)

(b)

\(2\left[ x+\frac { { x }^{ 3 } }{ 3 } +\frac { { x }^{ 5 } }{ 5 } +...+\infty \right] \)

(c)

\(\frac { { x }^{ 2 } }{ 2 } +\frac { { x }^{ 4 } }{ 4 } +\frac { { x }^{ 6 } }{ 6 } +...+\infty \)

(d)

\(2\left[ \frac { { x }^{ 2 } }{ 2 } +\frac { { x }^{ 4 } }{ 4 } +\frac { { x }^{ 6 } }{ 6 } +...+\infty \right] \)

38.

If the two straight lines x + (2k -7)y + 3 = 0 and 3kx + 9y - 5 = 0 are perpendicular then the value of k is

(a)

k = 3

(b)

\(k=\frac13\)

(c)

\(k=\frac23\)

(d)

\(k=\frac32\)

39.

The first and last term of an A.P. are 1 and 11. If the sum of its terms is 36, then the number of terms will be ______________

(a)

(b)

(c)

(d)

40.

The number of ways to average the letters of the word CHEESE are _________

(a)

120

(b)

240

(c)

720

(d)

41.

Which of the following equation is the locus of (at², 2at)

(a)

\(\frac{x^2}{a^2}-\frac{y^2}{b^2}=1\)

(b)

\(\frac{x^2}{a^2}+\frac{y^2}{b^2}=1\)

(c)

x²+ y²= a²

(d)

y²= 4ax

42.

The value of the series\(\frac { 1 }{ 2 } +\frac { 7 }{ 4 } +\frac { 13 }{ 8 } +\frac { 19 }{ 16 } +\).....is

(a)

(b)

(c)

(d)

43.

The number of five digit telephone numbers having at least one of their digits repeated is

(a)

90000

(b)

10000

(c)

30240

(d)

69760

44.

\(\sqrt [ 4 ]{ 11 } \) is equal to ___________

(a)

\(\sqrt [ 8 ]{ 11^{ 2 } } \)

(b)

\(\sqrt [ 8 ]{ 11^{ 4 } } \)

(c)

\(\sqrt [ 8 ]{ 11^{ 8 } } \)

(d)

\(\sqrt [ 8 ]{ 11^{ 6 } } \)

45.

If cosec x + cot x = \(\frac { 11 }{ 2 } \) then tan x = ___________

(a)

\(\frac { 21 }{ 22 } \)

(b)

\(\frac { 15 }{ 16 } \)

(c)

\(\frac { 44 }{ 117 } \)

(d)

\(\frac { 117 }{ 44 } \)

46.

The number of roots of (x + 3)⁴+ (x + 5)⁴= 16 is

(a)

(b)

(c)

(d)

47.

The solution set of the following inequality |x-1| \(\ge\) |x-3| is

(a)

[0, 2]

(b)

\([2,\infty)\)

(c)

(0, 2)

(d)

\((-\infty,2)\)

48.

\(\left( 1+cos\frac { \pi }{ 8 } \right) \left( 1+cos\frac { 3\pi }{ 8 } \right) \left( 1+cos\frac { 5\pi }{ 8 } \right) \left( 1+cos\frac { 7\pi }{ 8 } \right) \) =

(a)

\(\frac { 1 }{ 8 } \)

(b)

\(\frac { 1 }{ 2 } \)

(c)

\(\frac { 1 }{ \sqrt { 3 } } \)

(d)

\(\frac { 1 }{ \sqrt { 2 } } \)

49.

The shaded region in the adjoining diagram represents.

(a)

A\B

(b)

B\A

(c)

AΔB

(d)

50.

The inverse of f(x) = \(\begin{cases} x\quad if\quad x<1 \\ { x }^{ 2 }\quad if\quad 1\le x\le 4 \\ 8\sqrt { x } \quad if\quad x>4 \end{cases}\) is

(a)

\({ f }^{ -1 }(x)=\begin{cases} x\quad if\quad x<1 \\ \sqrt { x } \quad if\quad 1\le x\le 16 \\ \frac { { x }^{ 2 } }{ 64 } \quad if\quad x>16 \end{cases}\)

(b)

\({ f }^{ -1 }(x)=\begin{cases} -x\quad if\quad x<1 \\ \sqrt { x } \quad if\quad 1\le x\le 16 \\ \frac { { x }^{ 2 } }{ 64 } \quad if\quad x>16 \end{cases}\)

(c)

\({ f }^{ -1 }(x)=\begin{cases} { x }^{ 2 }\quad if\quad x<1 \\ \sqrt { x } \quad if\quad 1\le x\le 16 \\ \frac { { x }^{ 2 } }{ 64 } \quad if\quad x>16 \end{cases}\)

(d)

\({ f }^{ -1 }(x)=\begin{cases} { 2x }\quad if\quad x<1 \\ \sqrt { x } \quad if\quad 1\le x\le 16 \\ \frac { { x }^{ 2 } }{ 8 } \quad if\quad x>16 \end{cases}\)

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Answers Key:

Multiple Choice Question

50 x 1 = 50

(b)
\(\frac { 1 }{ 4 } \) tan^-1 \(\left( \frac { { x }^{ 2 } }{ 2 } \right) \)

(b)
\(\frac { 1 }{ 6 } \) sec³2x - \(\frac { 1 }{ 2 } \) sec 2x

(a)
\(\frac { 3 }{ 28 } \)

(d)
\(\frac { 2 }{ 3 } \)

(b)
-6

(b)
\(x\frac { d^{ 2 }y }{ d{ x }^{ 2 } } ={ y }_{ 1 }\)

(b)
\(\frac { 1 }{ x\log _{ e }{ a } } \)

10.

(d)
rectangular

11.

\(m \leq 5\)
\(2 x^{2}+2 m x+m+1>0\)
For real roots
\(4 m^{2}-8(m+1)>0 \)
\(4 m^{2} - 8 m-8>0 \)
\(m^{2}-2 m-2>0 \)
\(\text {Then } m \text { can be } 5,4,3\)
\(n(S)=5 ,n(A)=3 ,P(A)=\frac{3}{5} \)

12.

\(P(A / B)=\frac{P(A \cap B)}{P(B)}=\frac{P(A)}{P(B)}[\because A \subset B \Rightarrow A \cap B=A]\)

13.

Fifty rupee note = 3
Hundred rupee note = 4
500 rupee note = 6
Totsl = 13
\(\mathrm{n}(\mathrm{S})=13 \mathrm{C}_{2}=78\)
\(\text {No. of ways the event to occur }=4\)
\(n(A)=4 C_{2}=6\)
\(\text {No. of ways the event not to occur }=72\)
The odds of event are a:b
\(6: 72 \Rightarrow 1: 12\)

14.

\(\text { Let } \sqrt{x}=t\)
\(\text { Then } x=t^{2}\)
\(\therefore \frac{d x}{d t}=2 t\)
\(\therefore d x=2 t d t\)
\(\therefore \int \sin \sqrt{x} d x=\int \sin t \times 2 t d t\)
\(=2 \int t \sin t d t\)
\(\text { Applying Bernoulli's formula }\)
\(=2[t(-\cos t)-1(-\sin t)]+c\)
\(\text { Putting } t=\sqrt{x}\)
\(=2[-\sqrt{x} \cos \sqrt{x}+\sin \sqrt{x}]+c\)

15.

\(\int \frac{e^{6 \log x}-e^{5 \log x}}{e^{4 \log x}-e^{3 \log x}} d x =\int \frac{x^{6}-x^{5}}{x^{4}-x^{3}} d x \)
\(=\int \frac{x^{2}\left(x^{4}-x^{3}\right)}{x^{4}-x^{3}} d x \)
\(=\int x^{2} d x=\frac{x^{3}}{3}+c \)

16.

\(f(x)=|x-1|+|x-3|+\sin x\)
\(\text { Since } \sin x \text { is differentiable everywhere }\)

At x = 1 and x = 3. The graph admit cups.
\(\therefore\) The derivative is not exist.
\(\therefore\) The number of points in R is 2.

17.

\(y =\cos \left(\sin x^{2}\right) \)
\(\frac{d y}{d x} =-\sin \left(\sin x^{2}\right) \cos \left(x^{2}\right)(2 x) \)
\(\text { At } x =\sqrt{\pi / 2}, \frac{d y}{d x}=-\sin \sin \left(\frac{\pi}{z}\right) \cos (\pi / 2) 2(\sqrt{\pi / 2}) \)
\(=(\sin 1)(0) 2\left(\frac{\sqrt{\pi}}{2}\right)=0 \quad[\because \cos \pi / 2=0] \)

18.

We know that,
\(\sin \alpha-\cos \alpha =\sqrt{2}\left[\frac{1}{\sqrt{2}} \sin \alpha-\frac{1}{\sqrt{2}} \cos \alpha\right] \)
\(=\sqrt{2}\left[\cos \frac{\pi}{4} \sin \alpha-\sin \frac{\pi}{4} \cos \alpha\right] \)
\(=\sqrt{2} \sin \left(\alpha-\frac{\pi}{4}\right) \)
\(\therefore \lim _{\alpha \rightarrow \frac{\pi}{4}} \frac{\sin \alpha-\cos \alpha}{\alpha-\frac{\pi}{4}} =\lim _{\alpha-\frac{\pi}{4} \rightarrow 0} \frac{\sqrt{2} \sin \left(\alpha-\frac{\pi}{4}\right)}{\left(\alpha-\frac{\pi}{4}\right)}=\sqrt{2} \)

19.

(d)
coplanar vectors.

20.

\(\left|\begin{array}{lll} k a & k b & k c \\ k x & k y & k z \\ k p & k q & k r \end{array}\right|=k^{3}\left|\begin{array}{lll} a & b & c \\ x & y & z \\ p & q & r \end{array}\right|=k^{3} \Delta\)
\(\text { Take } k \text { from } R_{1}, R_{2}, R_{3}\)

21.

(b)
\(\frac{x}{a}+\frac{y}{b}=1\)

22.

(a)
45⁰

23.

(b)
\(\frac{1}{2}\)ab sin C

24.

25.

(d)
(A \ B) U B = A ⋂ B

26.

27.

(a)
\(x+y\sqrt 3=24\)

28.

29.

30.

31.

32.

(b)
(1, 1)

33.

(a)
\(x+\frac{x^3}{3}+\frac{x^5}{5}+...\)

34.

(d)
x² - 4x + 1 = 0

35.

(a)
\(\lfloor{n}(n+2)\)

36.

37.

(b)
\(2\left[ x+\frac { { x }^{ 3 } }{ 3 } +\frac { { x }^{ 5 } }{ 5 } +...+\infty \right] \)

38.

\(\text { Slope of first line }=\frac{-1}{(2 k-7)}\)
\(\text { Slope of second line }=\frac{-3 k}{9}\)
\(\text { They are perpendicular } \mathrm{m}_{1} \mathrm{~m}_{2}=-1\)
\(\frac{3 k}{9(2 k-7)} =-1 \)
\(k =-3(2 k-7) \)
\(k =-6 k+21 \)
\(7 k =21 \)
\(k=3 \)

39.

(b)
6

40.

(a)
120

41.

\(\left(a t^{2}, 2 a t\right) \Rightarrow x=a t^{2}, \quad y=2 a t\)
\(y^{2} =4 a^{2} t^{2} \)
\(=4 a^{2}\left(\frac{x}{a}\right) \)
\(y^{2} =4 a x \)

42.

\(\mathrm{a} =1, \quad \mathrm{~d}=6, \quad \mathrm{r}=\frac{1}{2} \)
\(\mathrm{~S}_{\infty} =\frac{a}{1-\mathrm{r}}+\frac{\mathrm{dr}}{(1+\mathrm{r})^{2}} \)
\(=\frac{1}{1-\frac{1}{2}}+\frac{6 \times \frac{1}{2}}{\left(\frac{1}{2}\right)^{2}} \)
\(=2+(3 \times 4)=14 \)

43.

The number of five digit telephone numbers which can be formed using the digits 0,1,2.... 9 is 10⁵.
The number of 5 digit numbers which has none of their digit repeated is ¹⁰P₅, = 30240
The required number of telephone. number is 10⁵ =- 30240 = 69,760

44.

(a)
\(\sqrt [ 8 ]{ 11^{ 2 } } \)

45.

46.

(a)
4

47.

(b)
\([2,\infty)\)

48.

\(\left(2 \cos ^{2} \frac{\pi}{16}\right)\left(2 \cos ^{2} \frac{3 \pi}{16}\right)\left(2 \cos ^{2} \frac{5 \pi}{16}\right)\left(2 \cos ^{2} \frac{7 \pi}{16}\right) \)
\(=2^{4}\left[\cos \frac{\pi}{16} \cos \frac{3 \pi}{16} \cos \frac{5 \pi}{16} \cos \frac{7 \pi}{16}\right]^{2} \)
\(=\left(\cos \frac{8 \pi}{16}+\cos \frac{6 \pi}{16}\right)^{2}\left(\cos \frac{8 \pi}{16}+\cos \frac{2 \pi}{16}\right)^{2} \)
\(=\left(\cos \frac{6 \pi}{16}\right)^{2}\left(\cos \frac{2 \pi}{16}\right)^{2} \)
\(=\left\{\frac{1}{2}\left[\cos \frac{8 \pi}{16}+\cos \frac{4 \pi}{16}\right]\right\}^{2} \)
\(=\frac{1}{4} \cdot \frac{1}{2}=\frac{1}{8} \)

49.

50.

\(\text { i) Let } y=x \text { then } x=y \Rightarrow f^{-1}(x)=x\)
\(\text { ii) Let } y=x^{2} \text { then } y=\sqrt{x} \Rightarrow f^{-1}(x)=\sqrt{x}\)
\(\text { iii) Let } y=8 \sqrt{x} \text { then } \frac{y^{2}}{64}=x \Rightarrow \mathrm{f}^{-1}(x)=\frac{x^{2}}{64}\)
\(\therefore \mathrm{f}^{-1}(x)= \begin{cases}x & x<1 \\ \sqrt{x} & 1 \leq x \leq 16 \\ \frac{x^{2}}{64} & x>16\end{cases}\)