Class 11th

The shortest distance between the lines (x-1)/0 = (y+1)/-1 = z/1 and x+y+z+1=0, 2x-y+z+3=0 is:

lim(x→1) ∫₁ˣ (t-1)² cos(t²)dt / ((x-1)sin(x-1))

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…….