If in $∆\mathrm{ABC}$, r₁ < r₂ < r₃, then :

• a < b < c

• a > b > c

• b > a < c

• a < c < b

In a $∆\mathrm{ABC}$, if 3a = b + c, then $\cot \left(\frac{\mathrm{B}}{2}\right)\cot \left(\frac{\mathrm{C}}{2}\right)$ is equal to :

• 1

• 2

• 3

• 4

If in a triangle, if b = 20, c = 21 and $\sin \left(\mathrm{A}\right) = \frac{3}{5}$, then a is equal to

• 12

• 13

• 14

• 15

A tower subtends angles $\mathrm{\alpha }, 2\mathrm{\alpha } \mathrm{and} 3\mathrm{\alpha }$ respectively at points A, B and C, all lying on a horizontal line through the foot of the tower,then $\frac{\mathrm{AB}}{\mathrm{BC}}$ is equal to :

• $\frac{\sin \left(3\mathrm{\alpha }\right)}{\sin \left(2\mathrm{\alpha }\right)}$

• $1 + 2\cos \left(2\mathrm{\alpha }\right)$

• $2\cos \left(2\mathrm{\alpha }\right)$

• $\frac{\sin \left(2\mathrm{\alpha }\right)}{\sin \left(\mathrm{\alpha }\right)}$

5.

A bag X contains 2 white and 3 black balls and another bag Y contains 4 white and 2 black balls. One bag is selected at random and a ballis drawn from it. Then, the probability for the ball chosen be white, is :

• $\frac{2}{15}$

• $\frac{7}{15}$

• $\frac{8}{15}$

• $\frac{14}{15}$

For a poisson variate X, if P(X = 2) = 3P(X = 3), then the mean of X is :

• 1

• $\frac{1}{2}$

• $\frac{1}{3}$

• $\frac{1}{4}$

A random variate X takes the values 0, 1, 2, 3 and its mean is 1.3. If P(X = 3) = 2P(X = 1) and P(X = 2) = 0.3, then P(X = 0) is equal to :

• 0.1

• 0.2

• 0.3

• 0.4

The co-ordinate axes are rotated through an angle 135°. If the co-ordinates of a point P inthe new system are known to be (4, - 3), then the co-ordinates of P in the original system are :

• $\left(\frac{1}{\sqrt{2}}, \frac{7}{\sqrt{2}}\right)$

• $\left(\frac{1}{\sqrt{2}}, - \frac{7}{\sqrt{2}}\right)$

• $\left(- \frac{1}{\sqrt{2}}, - \frac{7}{\sqrt{2}}\right)$

• $\left(- \frac{1}{\sqrt{2}}, \frac{7}{\sqrt{2}}\right)$

The point P is equidistant from A(1, 3), B(- 3, 5)and C(5, - 1), then PA is equal to

• 5

• $5\sqrt{5}$

• 25

• $5\sqrt{10}$

If the lines 4x + 3y - 1 = 0, x - y + 5 = 0 and kx + 5y - 3 are concurrent, then k is equal to

• 4

• 5

• 6

• 7