Class 11th

The number of solutions of the equation sin x = cos² x in the interval (0, 10) is

Let 3, 6, 9, 12,…. upto 78 terms and 5, 9, 13, 17,…. upto 59 terms be two series. Then, the sum of the terms common to both the series is equal to

Let   $n\ge 5$  be an integer. If 9ⁿ – 8n – 1 = 64α and 6ⁿ – 5n – 1 = 25β, then α - β is equal to

Negation of the Boolean statement $\left(p\vee q\right)\Rightarrow \left(\left(\sim r\right)\vee p\right)$ is equivalent to

From the base of a pole of height 20 meter, the angle of elevation of the top of tower is 60°. The pole subtends an angle 30° at the top of the tower. Then the height of the tower is

From the base of a pole of height 20 meter, the angle of elevation of the top of tower is 60°. The pole subtends an angle 30° at the top of the tower. Then the height of the tower is

The number of values of $a\in N$ such that the variance of 3, 7, 12, a, 43 a is a natural number is

The probability that a relation R from $\left\{x,y\right\}to\left\{x,y\right\}$  is both symmetric and transitive, is equal to

Let a triangle ABC be inscribed in the circle $x^2-\sqrt[]{2}\left(x+y\right)+y^2=0$ such that $\angle BAC=\frac{\pi }{2}.$ If the length of side AB is $\sqrt[]{2},$ then the area of the $\Delta ABC$ is equal to

Let P : y² = 4ax, a > 0 be a parabola with focus S. Let the tangents to the parabola P make an angle of  with the line y = 3x + 5 touch the parabola P at A and B. Then the value of a for which A, B and S are collinear is