Commerce (English Medium) कक्षा १२ - CBSE Important Questions for Mathematics

If A = `[(0, 1),(0, 0)]`, then A²⁰²³ is equal to ______.

Number of symmetric matrices of order 3 × 3 with each entry 1 or – 1 is ______.

The value of the determinant `|(6, 0, -1),(2, 1, 4),(1, 1, 3)|` is ______.

The value of |A|, if A = `[(0, 2x - 1, sqrt(x)),(1 - 2x, 0, 2sqrt(x)),(-sqrt(x), -2sqrt(x), 0)]`, where x ∈ R⁺, is ______.

Given that A is a square matrix of order 3 and |A| = –2, then |adj(2A)| is equal to ______.

Differentiate the following function with respect to x: `(log x)^x+x^(logx)`

If `y=log[x+sqrt(x^2+a^2)]` show that `(x^2+a^2)(d^2y)/(dx^2)+xdy/dx=0`

If x = a sin t and `y = a (cost+logtan(t/2))` ,find `((d^2y)/(dx^2))`

Differentiate x^sinx+(sinx)^cosx with respect to x.

If y=2 cos(logx)+3 sin(logx), prove that `x^2(d^2y)/(dx2)+x dy/dx+y=0`

If x=α sin 2t (1 + cos 2t) and y=β cos 2t (1−cos 2t), show that `dy/dx=β/αtan t`

If x cos(a+y)= cosy then prove that `dy/dx=(cos^2(a+y)/sina)`

Hence show that `sina(d^2y)/(dx^2)+sin2(a+y)(dy)/dx=0`

If x = a sin 2t (1 + cos 2t) and y = b cos 2t (1 – cos 2t) then find `dy/dx `

Find the value of `dy/dx " at " theta =pi/4 if x=ae^theta (sintheta-costheta) and y=ae^theta(sintheta+cos theta)`

If x = cos t (3 – 2 cos² t) and y = sin t (3 – 2 sin² t), find the value of dx/dy at t =4/π.

if `x^y + y^x = a^b`then Find `dy/dx`

Find the values of a and b, if the function f defined by 

If `y = sin^-1 x + cos^-1 x , "find"  dy/dx`

If e^y ( x +1)  = 1, then show that  `(d^2 y)/(dx^2) = ((dy)/(dx))^2 .`

Find `(dy)/(dx) , if y = sin ^(-1) [2^(x +1 )/(1+4^x)]`