The orthocenter, incenter, circumcentre and centroid of a triangle coincide, the triangle is :

1. scalene

2. isosceles

3. equilateral

4. right angled

If PT is tangent to the circle at point T and PAB is secant of this circle. Then which of the following statements is true ?

1. PT² = PA × AB

2. PT² = TB × PA

3. PT² = PA × PB

4. PT² = PB × TB

Two men A and B have a choice to buy ₹ 100 shares. A buys shares at ₹ 120 per share and 5% dividend. B buys shares at ₹ 150 per share and 8% dividend. Which of the two men A and B gets the better return, if the nominal value of both the shares is ₹ 100?

1. A

2. B

3. both get equal returns

4. cannot say

Assertion (A) : The numbers 8, 10, 12, x and 15 are in ascending order of their values. If the mean of their observations is equal to their median, the value of x is 15.

Reason (R) : If the number of observations is n, their mean = $\dfrac{\text{Sum of observations}}{n}$ and median (if n is odd) = value of the $\Big(\dfrac{n + 1}{2}\Big)^{\text{th}}$ observation

1. A is true, R is true

2. A is true, R is false

3. A is false, R is true

4. A is false, R is false