Free Printable quiz

1.

$\frac{\text{d}}{\text{d}x}\sqrt{e^{\sqrt{x}}}$

a)

$\frac{e^{\sqrt{x}}}{2\sqrt{x}}$

b)

$e^{\sqrt{x}}$

c)

$\frac{e^{\sqrt{x}}}{4\sqrt{xe^{\sqrt{x}}}}$

d)

$\frac{e^{\sqrt{x}}}{\sqrt{x}}$

2.

the equation of the tangent to the curve y=f(x) at (x1,y1) is given by

a)

y-y1=f'(x) (x-x1)

b)

$y-y1=\frac{-1}{f\left(x\right)}\left(x-x1\right)$

c)

$y-y1=\frac{1}{f'\left(x\right)}\left(x-x1\right)$

d)

$y-y1=\frac{-1}{f'\left(x\right)}\left(x-x1\right)$

3.

let f be a continuous on[a,b] and differentiable on (a,b) then function is increasing if

a)

f'(x)>0

b)

f''(x)>0

c)

f(x)>0

d)

f''(x)=0

4.

all the points of discontinuity of greatest integer function defined by f(x) =[x] , where [x] denote the greatest integer less than or equal to x .

a)

all real numbers

b)

all rational no.

c)

all integers

d)

al natural no.

5.

let A be a non singular square matrix of order n then

\left|agjA\right|

is equal to

a)

$\left|A^{ }\right|^n$

b)

$\left|A\right|^n-1$

c)

$\left|A\right|^{n-1}$

d)

$\left|A\right|^{n-2}$

6.

if

\left|A\right|

is a matrix of order 3 and

A_{ij}

is coafactor of

a_{ij}

,then value of

\left|A\right|

is given by

a)

$a_{11}A_{31}+a_{12}A_{32}+a_{13}A_{33}$

b)

$a_{11}A_{11}+a_{12}A_{12}+a_{13}A_{13}$

c)

$a_{21}A_{11}+a_{22}A_{12}+a_{23}A_{13}$

d)

none of above

7.

$\cos^{-1}\left(-x\right)$ =

a)

$\cos^{-1}\left(x\right)$

b)

$-\cos^{-1}\left(x\right)$

c)

$\pi+\cos^{-1}\left(x\right)$

d)

$\pi-\cos^{-1}\left(x\right)$

8.

The greatest integer function f(x) =[x] is

a)

One one

b)

Onto

c)

Bijective

d)

Neither one one nor onto

9.

If A= matrix (row. 1 $\left(\alpha\ \ \ \ \beta\right)$ And row.2 $\left(\gamma\ \ \ -\alpha\right)$ ) such that $A^2$ = I then

a)

$1-\alpha^2\ +\beta\gamma\ =0$

b)

$1+\alpha^2+\beta\gamma_{ }=0$

c)

$1-\alpha^2-\beta\gamma\ =0$

d)

$1+\alpha^2-\beta\gamma=0$

10.

If A is a matrix of order n $\times$ n then adj (adjA) =

a)

$\left|A^{ }\right|^{n—2}A$

b)

$\left|A^n-1\right|A$

c)

$\left|A\right|^{n^{ }}A$

d)

$\left|A\right|^{n–1}A$

11.

Let A = matrix row.1. ( $1\ \ \ Sin\theta\ \ \ 1$ ) Row.2. ( $-Sin\theta\ \ \ \ 1\ \ \ Sin\theta$ ). Row.3. ( $-1\ \ \ \ -Sin\theta\ \ \ \ \ 1$ ), where $0\le\theta\le2\pi$ Then

a)

Det(A) = 0

b)

Det(A) $\in$ (2, $\infty$ )

c)

Det(A) $\in$ (2,4)

d)

Det(A) $\in$ [2,4]

12.

If A = matrix. Row.1.. ( 2. -1. 1) row.2. ( -1. 2. -1) row .3. (1. -1. 2 ) then $A^{-1}$

a)

$\frac{1}{5}\ matrix\left[\ row.1\left(1\ \ \ \ 3\ \ \ \ 1\right)\right]$

row.2 (3 1 -1)

row.3 (3 3 -1)]

b)

Not defined because A is singular

c)

$\frac{1}{4}\ matrix\ \left[\ row1..\ \left(3\ \ 1\ \ \ -1\right)\ \right]$

row 2..(1 3 1)
row3..(-1 1 -3)]

d)

Non of the above

13.

find the equation of normal to the curve $y^2$ =4x at the point (1,2)

a)

x+y+3=0

b)

x+y=3

c)

x-y-3=0

d)

x+y=2

14.

find the interval in which the function f given by f(x) =sinx+cosx , $0\le x\le2\pi$ is strictly increasing or strictly decreasing.

a)

f is strictly increasing [0 , $\frac{\pi}{4}$ )

b)

f is strictly decreasing ( $\frac{\pi}{4},\frac{5\pi}{4}$ )

c)

f is strictly increasing ( $\frac{5\pi}{4},2\pi$ )

d)

all of the above

15.

$find\ the\ values\ of\ a\ and\ b\ if\ \ f\left(x\right)\ is\$ continuous function , f(x)= 5 if x $\le$ 2; f(x) =ax+b when 2 $<x<10$ ; f(X) =21 when x $\ge$ 10

a)

a=1,b=1

b)

a=2,b=2

c)

a=1,b=2

d)

a=2,b=1

16.

find $\frac{dy}{dx}$ if xy= $e^{\left(x-y\right)}$

a)

$\frac{x\left(y+1\right)}{y\left(x+1\right)}$

b)

$\frac{y\left(x-1\right)}{x\left(y+1\right)}$

c)

$\frac{y\left(x+1\right)}{x\left(y+1\right)}$

d)

$\frac{x\left(x-1\right)}{y\left(y+1`\right)}$

17.

$\tan^{-1}\ \frac{1}{5}+\tan^{-1}\ \frac{1}{7}$ + $\tan^{-1}\ \frac{1}{3}+\tan^{-1}\ \frac{1}{8}$ =

a)

$\frac{\pi}{3}$

b)

$\frac{\pi}{4}$

c)

$\frac{\pi}{2}$

d)

$\pi$

18.

$\tan^{-1}\ \frac{a\cos x-b\sin x}{b\cos x+a\sin x}$ simplify ,if $\frac{a}{b}\tan x>-1$

a)

$\tan^{-1}\ \frac{b}{a}\ -\tan^{-1}x$

b)

$\tan^{-1}\ \frac{a}{b}-x$

c)

$\frac{a}{b}-\tan^{-1}x$

d)

$\tan^{-1\ }\ \frac{a}{b}$

19.

the slope of tangent to the curve x= $t^2$ +3t-8 ,y= $2t^2$ -2t-5 at the point (2,-1) is

a)

$-\frac{6}{7}$

b)

$\frac{6}{7}$

c)

$\frac{7}{6}$

d)

$\frac{22}{7}$

20.

absolute maximum value of the function f(x)= $12x^{\frac{4}{3}}-6x^{\frac{1}{3}}$ ,x $\in$ [-1,1]

a)

18

b)

16

c)

$\frac{1}{8}$

d)

$\frac{-9}{4}$

quiz

Total questions: 20

Worksheet time: 40mins

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