CBSE 12 Maths Question Paper-2023 Set-5

Let R be a relation in the set N given by R = {(a, b): a = b-2, b > 6}. Then

If A=[[5,x],[y,0]] and A=Aᵀ, where Aᵀ is the transpose of the matrix A, then

sin[(π/3)+sin⁻¹(1/2)] is equal to

If for a square matrix A, A²-A+I=O, then A⁻¹ equals

If |[[a,3,4],[1,2,1],[1,4,1]]|=0, then the value of a is

If f(x)=|cos x|, then f(3π/4) is

If x=A cos 4t + B sin 4t, then d²x/dt² is equal to

The function f(x)=[x], where [x] denotes the greatest integer less than or equal to x, is continuous at

The function f(x)=x³+3x is increasing in interval

∫(from -1 to 1) |x-2|/(x-2)dx, x≠2 is equal to

∫(sec x)/(sec x - tan x) dx equals

The order and the degree of the differential equation (1+3(dy/dx))²=4(d³y/dx³) respectively are:

If →a·ı^ = →a·(ı^ + ɵ^) = →a·(ı^ + ɵ^ + k^) = 1, then →a is

Five fair coins are tossed simultaneously. The probability of the events that atleast one head comes up is

If for any two events A and B, P(A)=4/5 and P(A∩B)=7/10, then P(B/A) is equal to

The angle between the lines 2x=3y=-z and 6x=-y=-4z is

Let A={3,5}. Then number of reflexive relations on A is

If A=[[1,0],[2,1]] and B=[[x,0],[1,1]], and A=B², then x equals

If A=[aₒₗ] is a square matrix of order 2 such that aₒₗ = {1, when i ≠ j; 0, when i = j} then A² is

The value of the determinant |[[6,0,-1],[2,1,4],[1,1,3]]| is

The derivative of x²⁾ w.r.t x is

The interval in which the function f(x)=2x³+9x²+12x-1 is decreasing, is

The function f(x)=x|x|, x ∈ R is differentiable

The value of ∫(from 0 to π/4)(sin 2x)dx is

The sum of the order and the degree of the differential equation d/dx((dy/dx)³) is

Two vectors →a=a₁ı^+a₂ɵ^+a₃k^ and →b=b₁ı^+b₂ɵ^+b₃k^ are collinear if

A unit vector ı̂, makes equal and acute angles with the coordinate axes. The projection of the vector →b=5ı^+7ɵ^-⁽^ on the vector →a is

If any line makes angles 90°, 135° and 45° with x, y and z-axis respectively, then its direction cosines are: