No. of Printed Pages: 6
IBET-0211
DIPLOMA IN CIVIL ENGINEERING (DCLE(G» I
DIPLOMA IN MECHANICAL ENGINEERING
(DME) I DCLEVI I DMEVII DELVI I DECVI I
DCSVI/ACCLEVI I ACMEVIIACELVI I
ACECVI I ACCSVI

00542
Term-End Examination December, 2016
BET-021 MATHEMATICS -II
Time hours Maximum Marks: 70
Note: Question no. 1 is compulsory. Attempt any four questions out of the remaining questions no. 2 to 7. Use of calculator is permitted.

1. Select the correct answer from the four alternatives. 7xl=7 x^3 2x^2 x 1/2 0 2 1
If x cos y sin t equal) t (or equal then the value of dy/dx at t T/4 is

(a) 1

(b) 0 infinity


(iii) Integral dx is equal to
log x c

(b) e^x c

(c) calculator

(d) None of these

(iv) Integral dx (The upper and lower limits are 2 and is equal to 4

(b) 0

(d) 8 If a ib then
a 4/5 b a 4/5 b a b a 3/5 b 4/5

(vi) If A and B are square matrices of the same order, then

det AB =det A . det B. False True Sometimes True None of these

(vii) According to De Moivre's theorem,

(cos 8 i sin 8 =cos n8 i sin n8 is true if n is a positive integer if n is a negative integer if n is an integer if n depends upon the value of 8
Fill in the blanks 7xl=7 Let A =[aij]2x2 and aij then A2 is equal to
lim a x^n a^n equal to If (cos 8 i sin then r is 8 is Integral (log x dx) A particle moves along a straight line according to the formula s =12t where s is in meter and t is in seconds. Its acceleration is The central value of a set of observations is called Points of maxima and minima for the function

f(x) x^5 5x^4 5x^3 1 are Differentiate (sin x)^COS x with respect to x. Find the angle between the curves

f(x) 4 x^2 and x^2 7 7

3. Evaluate

Integral tan^-1 Evaluate

Integral The upper and lower limits are 1 and 0

4. If Z1 and Z2 are two complex numbers, then

show that Mod (Zl z2) equal) Mod(z1) Mod(z2)· Find the different values of(1 . 7 7


5. Check the continuity of the following function at x 0

f(x) 2x-1 if x<0

2x 1 if equal 0

(b) Show that the matrix A 4 -6 1
1
4 11

is invertible. Find adj(A) and 7 7

6. Calculate the mean and median of the following data using step deviation method:

Number of workers Wages per week up to
12 15
30 30
65 45
107 60
157 75
202 90
222 105
230 120 Find the standard deviation of the following data:

38,70,48,34,42,55,63,46,54,44 7 7

7. Evaluate Integral (sin x sin x cos x )dx. The upper and lower limits are 0 and T/2
If A and Bare invertible square matrices of the same order, then show that AB is also invertible and 7 7