Maths NCERT Exemplar Solutions Class 11th Chapter Four

Let the position vectors of points 'A' and 'B' be i+j+k and 2i+j+3k, respectively. A point 'P' divides the line segment AB internally in the ratio λ:1(λ>0). If O is the origin and OB.OP - 3|OA*OP|² = 6, then λ is equal to 

For a positive integer n, (1+x/2)? is expanded in increasing powers of x. If three consecutive coefficients in this expansion are in the ratio 2:5:12, then n is equal to

Let [t] denote the greatest integer less than or equal to t. Then the value of ∫?²|2x-[3x]|dx is

If the variance of the terms in an increasing A.P. b?,b?,b?,.,b? is 90, then the common difference of this A.P. is 

If y = Σ? kcos?¹{ (3/5)coskx - (4/5)sinkx }, then dy/dx at x=0 is 

The angle of elevation of the top of a hill from a point on the horizontal plane passing through the foot of the hill is found to be 45°. After walking a distance of 80 meters towards the top, up a slope inclined at an angle of 30° to the horizontal plane, the angle of elevation of the top of the hill becomes 75°. Then the height of the hill (in metres) is [numerical value].

Let AD and BC be two vertical poles at A and B respectively on a horizontal ground. If AD=8m, BC=11m and AB=10m; then the distance (in meters) of a point M on AB from the point A such that MD²+MC² is minimum is [numerical value].

If a and b are unit vectors, then the greatest value of √3|a+b|+|a-b| is [numerical value].

Let f:R→R be defined as f(x)={x⁵sin(1/x)+5x², x<0; 0, x=0; xcos(1/x)+x, x>0}. The value of λ for which f"(0) exists, is [numerical value].

Set A has m elements and Set B has n elements. If the total number of subsets of A is 112 more than the total number of subsets of B, then the value of m.n is [numerical