Science (English Medium) Class 12 - CBSE Important Questions

A is a square matrix with ∣A∣ = 4. then find the value of ∣A. (adj A)∣.

Using properties of determinants, find the value of x for which
`|(4-"x",4+"x",4+"x"),(4+"x",4-"x",4+"x"),(4+"x",4+"x",4-"x")|= 0`

Using matrices, solve the following system of linear equations :

x + 2y − 3z = −4
2x + 3y + 2z = 2
3x − 3y − 4z = 11

If A = [a_ij] is a skew-symmetric matrix of order n, then ______.

If A is a square matrix of order 3, |A′| = −3, then |AA′| = ______.

If A is a square matrix of order 3 and |A| = 5, then |adj A| = ______.

If A = `[(2, -3, 5),(3, 2, -4),(1, 1, -2)]`, find A^–1. Use A^–1 to solve the following system of equations 2x − 3y + 5z = 11, 3x + 2y – 4z = –5, x + y – 2z = –3

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 ______.

if `y=x^x` find `(dy)/(dx)`

Differentiate `tan^(-1)(sqrt(1-x^2)/x)` with respect to `cos^(-1)(2xsqrt(1-x^2))` ,when `x!=0`

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`