Science (English Medium) कक्षा १२ - CBSE Question Bank Solutions

If `intx^3/sqrt(1 + x^2) "d"x = "a"(1 + x^2)^(3/2) + "b"sqrt(1 + x^2) + "C"`, then ______.

`int (x + 3)/(x + 4)^2 "e"^x  "d"x` = ______.

If A and B are invertible matrices of the same order, then (AB)^-1 is equal to ____________.

If `"x = a sin"  theta  "and  y = b cos"  theta, "then"  ("d"^2 "y")/"dx"^2` is equal to ____________.

If y `= "Ae"^(5"x") + "Be"^(-5"x") "x"  "then"  ("d"^2 "y")/"dx"^2` is equal to ____________.

Find: `int logx/(1 + log x)^2 dx`

Evaluate: `int_(-1)^2 |x^3 - 3x^2 + 2x|dx`

The value of `int_2^3 x/(x^2 + 1)`dx is ______.

If A, B are non-singular square matrices of the same order, then (AB^–1)^–1 = ______.

If A and B are invertible square matrices of the same order, then which of the following is not correct?

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

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

Evaluate : `∫_0^(π/2)(sin^2 x)/(sinx+cosx)dx`

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`

Evaluate :`int_0^(pi/2)(2^(sinx))/(2^(sinx)+2^(cosx))dx`

If x = a cos θ + b sin θ, y = a sin θ − b cos θ, show that `y^2 (d^2y)/(dx^2)-xdy/dx+y=0`

Find the second order derivative of the function.

x² + 3x + 2

Find the second order derivative of the function.

x²⁰

Find the second order derivative of the function.

x . cos x

Find the second order derivative of the function.

log x