Free Printable QUIZ(M-IV)

1.

Show that z = f(x²+y²) is a solution of

a)

yp-xq = 0

b)

yq-xp = 0

c)

p - q = 0

d)

q - p = 0

2.

Solution of (D-5D'+1)² = 0 is

a)

z = e^-xf₁(y+5x)+x e^-xf₁(y+5x)

b)

z = e^-xf₁(y+5x)+ e^-xf₁(y+5x)

c)

z = e^-xf₁(y-5x)+x e^-xf₁(y-5x)

d)

z = e^-xf₁(y-5x)+e^-xf₁(y-5x)

3.

Find the solution of xp + yq = z.

a)

$f\left(\frac{x}{y},\frac{y}{z}\right)=0$

b)

$f\left(\frac{x}{y^2},\frac{y}{z^2}\right)=0$

c)

$f\left(\frac{x^2}{y},\frac{y^2}{z}\right)=0$

d)

$f\left(\frac{1}{y},\frac{1}{z}\right)=0$

4.

$PI\ of\ \left(D^2-D'^2\right)z=\cos\left(x+y\right)$

a)

$\frac{x}{2}\cos\left(x+y\right)$

b)

$\frac{x}{2}\sin\left(x+y\right)$

c)

$x\sin\left(x+y\right)$

d)

$x\cos\left(x+y\right)$

5.

Two Dimension Wave equation is

a)

$0=\frac{1}{c^2}\left(\frac{\partial^2u}{\partial x^2}+\frac{\partial^2u}{\partial y^2}\right)$

b)

$\frac{\partial^{ }u}{\partial t^{ }}=\frac{1}{c^2}\left(\frac{\partial^2u}{\partial x^2}+\frac{\partial^2u}{\partial y^2}\right)$

c)

$\frac{\partial^2u}{\partial t^2}=\frac{1}{c^2}\left(\frac{\partial^2u}{\partial x^2}+\frac{\partial^2u}{\partial y^2}\right)$

d)

None of these

6.

Radio Equations are

a)

$\frac{\partial^2V}{\partial x^2}=LC\frac{\partial^2V}{\partial t^2}\ and\ \frac{\partial^2I}{\partial x^2}=LC\frac{\partial^2I}{\partial t^2}$

b)

$\frac{\partial^2V}{\partial x^2}=RC\frac{\partial^2V}{\partial t^2}\ and\ \frac{\partial^2I}{\partial x^2}=RC\frac{\partial^2I}{\partial t^2}$

c)

$\frac{\partial^{ }V}{\partial x^{ }}=LC\frac{\partial^{ }V}{\partial t^{ }}\ and\ \frac{\partial^2I}{\partial x^2}=LC\frac{\partial^2I}{\partial t^2}$

d)

$\frac{\partial^2V}{\partial x^2}=LC\frac{\partial^2V}{\partial t^2}\ and\ \frac{\partial I}{\partial x}=LC\frac{\partial I}{\partial t}$

7.

Classify the following Partial Differential Equation. $\frac{\partial^2u}{\partial x^2}+3\frac{\partial^2x}{\partial x\partial y}+\frac{\partial^2u}{\partial y^2}=0$

a)

Parabolic

b)

Hyperbolic

c)

Elliptic

d)

None of these

8.

$\frac{\partial^2u}{\partial x^2}+\frac{\partial^2u}{\partial y^2}=0$

Name the equation

a)

Laplace Equation

b)

Heat Equation

c)

Wave Equation

d)

Submarine Equation

9.

Formula of measure of Kurtosis is

a)

$\beta_1=\frac{\mu_3^2}{\mu_2^2}$

b)

$\beta_1=\frac{\mu_3^2}{\mu_2^3}$

c)

$\beta_2=\frac{\mu_4^2}{\mu_2^3}$

d)

$\beta_2=\frac{\mu_4}{\mu_2^2}$

10.

The first four central moments of a distribution are 0, 2.5, 0.7 and 18.75. comment on the kurtosis of the distribution.

a)

$\beta_2=3,\ Mesokurtic$

b)

$\beta_2=3,\ Leptokurtic$

c)

$\beta_2=3,\ platykurtic$

11.

$y=a+bx$

Write the normal equation for the curve.

a)

$\sum_{ }^{ }y=na+b\sum_{ }^{ }x\ and\ \sum_{ }^{ }xy=a\sum_{ }^{ }x+b\sum_{ }^{ }x^2\$

b)

$\sum_{ }^{ }xy=na+b\sum_{ }^{ }x^2\ and\ \sum_{ }^{ }x^2y=a\sum_{ }^{ }x+b\sum_{ }^{ }x^3$

c)

$\sum_{ }^{ }y=a+b\sum_{ }^{ }x\ and\ \sum_{ }^{ }xy=\sum_{ }^{ }x+b\sum_{ }^{ }x^2$

d)

$\sum_{ }^{ }y=a+b\sum_{ }^{ }x\ and\ \sum_{ }^{ }xy=a\sum_{ }^{ }x+\sum_{ }^{ }x^2$

12.

If covariance between x and y variables is 10 and the variance of x and y are respectively 16 and 9, find the coefficient of correlation.

a)

0.73

b)

0.63

c)

0.83

d)

0.53

13.

The total area under the curve of p.d.f of a Normal curve is

a)

0

b)

0.5

c)

1

d)

0.8

14.

The mean and variance of Binomial distribution are

a)

np, npq

b)

p, pq

c)

np, np

d)

np, nq

15.

If P(X=0)=P(X=1)=k in a Poisson variate X, then what is k?

a)

e

b)

1/e

c)

0

d)

1

16.

What is the chance that a leap year should have fifty three Sundays?

a)

1/7

b)

2/7

c)

3/7

d)

4/7

17.

What is alternate hypothesis if null hypothesis is H₀=µ=50?

a)

H₁=µ=50

b)

H₁= µ ≠ 50

c)

H₁= µ > 50

d)

H₁= µ < 50

18.

If the critical value of Z is 1.96, what is the significance level of two tailed test?

a)

5%

b)

1%

c)

10%

d)

2.5%

19.

When a true null hypothesis is rejected, what is the error made, known with?

a)

Type II error

b)

Type I error

20.

What is test statistics for testing null hypothesis, when sample size n is small?

a)

t-test

b)

Z-test

c)

F- test

QUIZ(M-IV)

Total questions: 20

Worksheet time: 27mins

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