Free Printable FasTrack Mathematics for Engineering Aspirants

1.

The domain of

\sin^{-1}\left(\log_3\left(\frac{x}{3}\right)\right)is

a)

[1,9]

b)

[-1,9]

c)

[-9,1]

d)

[-9,-1]

2.

The inverse of a function

f(x)=\frac{5x-3}{2x+1}\ is

a)

$\frac{-x-3}{2x+5}$

b)

$\frac{-x-3}{2x-5}$

c)

$\frac{-x+3}{2x-5}$

d)

inverse does not exists

3.

If f(2)=4 and f'(2)=4 then

\lim_{x\rightarrow2\ }

\frac{xf\left(2\right)-2f\left(x\right)}{x-2}

is

a)

2

b)

-2

c)

-4

d)

4

4.

The slope of the tangent at the point (a,a) on the curve

y^2=\frac{x^3}{2a-x}

, where a>0 is

a)

1

b)

2

c)

-1

d)

-2

5.

The value of the integral

\int_{-4}^4\left(x^2-3+\cot x\right)dx\ is

a)

$2\left(\frac{28}{3}+\sin4\right)$

b)

$2\left(\frac{28}{3}+\cos4\right)$

c)

$\frac{58}{3}+\sin4$

d)

$2\left(\frac{58}{3}+\sin4\right)$

6.

Let [.] denote the greatest integer function then the value of $\int_0^{1.5}x\left[x^2\right]dx\ is$

a)

$\frac{7}{4}$

b)

$\frac{1}{4}$

c)

$\frac{3}{4}$

d)

$\frac{5}{4}$

7.

$If\ \frac{\text{dy}}{\text{dx}}=y\$ and y(0)=2 then y(ln2) is

a)

13

b)

-2

c)

4

d)

5

8.

The degree and order of the differential equation of the family of all parabolas whose axis is X-axis are respectively

a)

(1,2)

b)

(3,2)

c)

(2,3)

d)

(2,1)

9.

Let X and Y be two events such that

P(X)=1/3 , P(X/Y)=1/2 and P(Y/X)=2/5. Then ……

a)

$P\left(\frac{\overline{X}}{Y}\right)=\frac{1}{2}$

b)

$P\left(X\cap Y\right)=\frac{1}{5}$

c)

$P\left(X\ \cup Y\right)=\frac{2}{5}$

d)

$P\left(Y\right)=\frac{4}{15}$

10.

All the students of a class performed poorly in mathematics. The teacher decided to give marks of 10 to each of the students. Which of the following statistical measures will not change even after the grace marks were given?

a)

mean

b)

median

c)

mode

d)

variance

FasTrack Mathematics for Engineering Aspirants

Total questions: 10

Worksheet time: 50mins

Similar Resources on Wayground