VITEEE 2019 :: Mathematics :: General questions

• Mathematics - General questions

At how many points between the interval (-∞, ∞) is the function f (x): sin x is not differentiable

Answer:

Explanation:

The function f (x): sin x is differentiable for all x $\epsilon$ R. Therefore the number of points in the interval (-∞, ∞) where the function is not differentiable are zero.

The position vector of A and B are $2\hat{i}+2\hat{j}+\hat{k}$ and $2\hat{i}+4\hat{j}+4\hat{k}$. The length of the internal bisector of <BOA triangle AOB is

Answer:

Explanation:

We have,

OA = |$2\hat{i}+2\hat{j}+\hat{k}$| = 3;

OB = |$2\hat{i}+4\hat{j}+4\hat{k}$| = 6

Since the internal bisector divides opposite side in the

ratio of adjacent sides

$\frac{AC}{BC} = \frac{3}{6}=\frac{1}{2}$

where OD is the bisector of <BOA .

.'. The position vector of C is

$\frac{2(2\hat{i}+2\hat{j}+\hat{k})+(2\hat{i}+4\hat{j}+4\hat{k})}{2+1} $

=$2\hat{i}+\frac{8}{3}\hat{j}+2\hat{k}$

.'. OD = |$2\hat{i}+\frac{8}{3}\hat{j}+2\hat{k}$|

= $\sqrt{\frac{136}{9}}$

If the lines 3x -4y + 4 = 0 and 6x- 8y-7 = 0 are tangents to a circle, then radius of the circle is

Answer:

Explanation:

The diameter of the circle is the perpendicular distance between the parallel lines (tangents) 3x-4y+ 4 = 0 and3x-4y-$\frac{7}{2}$ = 0

and so it is equal to $\frac{4}{\sqrt{9+16}}+\frac{7/2}{\sqrt{9+16}}=\frac{3}{2}$

Hence radius is $\frac{3}{4}$

$If\omega =\frac{-1 + \sqrt{3i}}{2} $ then $ (3+\omega+\omega^{2})^4$ is

Answer:

Explanation:

Let $\omega =\frac{-1 + \sqrt{3i}}{2}$

Now, 1+ ω + ω² = 0 and  ω³= 1

$then (3+\omega+\omega^{2})^4$ 

= (3+ω+3ω²+2ω-2ω)⁴ =(3+3ω+3ω²-2ω)⁴

= [3(1+2+ω²)-2ω]⁴ = (0-2ω)⁴ = 16ω⁴ = 16ω (ω³ = 1 )

The system of linear equations : x + y+ z = 0,

2x + y - z = 0, 3x +2y = 0 has:

Answer:

Explanation:

The system is a homogeneous system. It has either unique solution or infinite many solution depend on |A|

|A| = $\begin{vmatrix}1& 1 & 1 \\ 2 & 1 & -1 \\ 3 & 2 & 0 \end{vmatrix}$

= 2× 1+ 1(-3)+(4-3) = 2-3+1=0

• Mathematics - General questions