Class 11th

The position of a moving car at time t is given by f(t)=at²+bt+c, t>0, where a,b and c are real numbers greater than 1. Then the average speed of the car over the time interval [t?,t?] is attained at the point:

If α, β are roots of the equation x² + 5√2x + 10 = 0, α > β and P? = α? - β? for each positive integer n, then the value of (P?P? + 5√2P?P?)/(P?P? + 5√2P?²) is equal to……….

Consider the following frequency distribution:
| Class: | 10-20 | 20-30 | 30-40 | 40-50 | 50-60 |
|---|---|---|---|---|---|
| Frequency: | α | 110 | 54 | 30 | β |
If the sum of all frequencies is 584 and median is 45, then |α - β| is equal to…….

The ratio of the coefficient of the middle term in the expansion of (1+x)²? and the sum of the coefficients of two middle terms in expansion of (1+x)¹? is…….

Four point masses, each of mass m, are fixed at the corners of a square of side l. The square is rotating with angular frequency ω, about an axis passing through one of the corners of the square and parallel to its diagonal, as shown in the figure. The angular momentum of the square about this axis is:

How are alkanes used in real life?

A ray of light coming from the point (2,2√3) is incident at an angle 30° on the line x=1 at the point A. The ray gets reflected on the line x=1 and meets x-axis at the point B. Then, the line AB passes through the point:

The term independent of 'x' in the expression of [(x+1)/(x²/³ - x¹/³ + 1) - (x-1)/(x-x¹/²)]¹?, where x ≠ 0, 1 is equal to…….

Shown in the figure is a hollow icecream cone (it is open at the top). If its mass is M, radius of its top, R and height, H, then its moment of inertia about its axis is:

There are 5 students in class 10, 6 students in class 11 and 8 students in class 12. If the number of ways, in which 10 students can be selected from them so as to include at least 2 students from each class and at most 5 students from the total 11 students of class 10 and 11 is 100k, then k is equal to…….