Free Printable Aptitude

1.

a)

b)

c)

d)

2.

If u=x^y then u_xy is

a)

y^x-1(1+xlogy)

b)

x^y-1(1-ylogx)

c)

x^y-1(1+ylogx)

d)

y^x-1(1-xlogy)

3.

$If\ u=\frac{y}{z}+\frac{z}{x}\ then\ the\ value\ of\ x\frac{\partial u}{\partial x}+y\frac{\partial u}{\partial y}+z\frac{\partial u}{\partial z\ }is$

a)

1

b)

2

c)

-1

d)

0

4.

$If\ x=e^u+e^{-v}\ and\ y=e^{-u}-e^vthen\ the\ value\ of\ \ \frac{\partial x}{\partial u}+\frac{\partial y}{\partial v}$

a)

$-\left(e^u-e^v\right)$

b)

$e^u-e^v$

c)

$e^{-u}+e^{-v}$

d)

$e^u+e^{-v}$

5.

$The\ value\ of\ the\ integral\ \int_{ }\frac{\log x}{x}dx\ is\ equal\ to\$

a)

$\log\left(\log x\right)+c$

b)

$\frac{\left(\log x\right)^2}{2}+c$

c)

$2\log x+c$

d)

None

6.

$The\ value\ of\ \int\ \frac{x}{x^2-1}dx\ is$

a)

$\log\left(x^2-1\right)+c$

b)

$\frac{1}{2}\log\left(x^2-1\right)+c$

c)

$\log\left(x+1\right)+c$

d)

$None$

7.

$The\ value\ of\ the\ integral\ \int_0^1\frac{1}{1+x^2}dx\ is$

a)

1

b)

$\frac{\pi}{2}$

c)

$\frac{\pi}{4}$

d)

$\frac{1}{2}$

8.

$The\ PI\ of\ \left(D^2+1\right)y=e^{-x}\ is\$

a)

$A\cos x+B\sin x$

b)

$\frac{1}{2}e^{-x}$

c)

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

d)

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

9.

$The\ PI\ of\ \left(3D^2+5D\right)y=8\ is$

a)

$\frac{8x}{5}$

b)

$\frac{8}{5}$

c)

$\frac{8x}{11}$

d)

$\frac{8}{11}$

10.

If 1±2i , 1±2i are the roots of auxiliary equations corresponding to a fourth order homogeneous linear differential equation f(D)=0,then the solution is

a)

y=e^x((A+Bx)cos2x+(C+Dx)sin2x)

b)

y=e^2x((A+Bx)cos2x+(C+Dx)sin2x)

c)

y=(A+Bx)cos2x+(C+Dx)sin2x

d)

y=e^x(Acos2x+Bsin2x)

Aptitude

Total questions: 10

Worksheet time: 5mins

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