Question

PARTA
Answer ALL the 10 questions
10 X 1=10
1.
On N the set of natural numbers,
a *b = L.C.M of a and b. Find the identity
for in N.
5.
If y = sin(ax+b), find
dy
dx
2.
Write the range of f(x) = cos-1x.
6.
Evaluate: sec? (7 - 4x)dx.
4 3
y
3.
IT
Find the values of x, y
7.
х
5
Find *, if for a unit vector ā,
(x-).(+a)=12.
5
and z.
8.
If a line has the direction ratios - 18, 12, -4
then what are its direction cosines?
4.
Evaluate the determinant
0 sin a - cos a:
1-sina 0
sin ß
COS O
-sinß
0
9.
Define constraints in Linear Programming
Problem.
10. A fair die is rolled. If
E = {1,2,4,6), F={1,3), find P(EIF).
PART-B:
Answer any TEN questions
10 X 220​

Answer 1

Answer:

5.

using chain rule,

$\frac{dy}{dx} = \frac{d(sin(ax + b))}{d(ax + b)} . \frac{d(ax + b)}{dx} \\ =a \: \: cos(ax + b)$

2. Given f(x)=cos^−1 x

The domain of f(x) is equivalent to the range of values of x for which f(x) exists

Let f(x)=θ , we get x=cosθ

The range of cosθ is [−1,1]

Therefore the range of x is [−1,1]

Hence, the domain of f(x) is [−1,1]

9. Constraints The linear inequalities or equations or restrictions on the variables of a linear programming problem are called constraints. The conditions x ≥ 0, y ≥ 0 are called non-negative restrictions. In the above example, the set of inequalities (1) to (4) are constraints.