Science (English Medium) Class 12 - CBSE Question Bank Solutions for Mathematics

if  `vec"a"= 2hat"i" + 3hat"j"+ hat"k", vec"b" = hat"i" -2hat"j" + hat"k" and vec"c" = -3hat"i" + hat"j" + 2hat"k", "find" [vec"a" vec"b" vec"c"]`

Find the maximum and minimum of the following functions : f(x) = `logx/x`

A rod of 108 m long is bent to form a rectangle. Find it’s dimensions when it’s area is maximum.

The matrix A = `[(0, 0, 5),(0, 5, 0),(5, 0, 0)]` is a ______.

If A and B are matrices of same order, then (3A –2B)′ is equal to______.

If two matrices A and B are of the same order, then 2A + B = B + 2A.

For the non singular matrix A, (A′)^–1 = (A^–1)′.

AB = AC ⇒ B = C for any three matrices of same order.

If A = `[(3, -4),(1, 1),(2, 0)]` and B = `[(2, 1, 2),(1, 2, 4)]`, then verify (BA)² ≠ B²A² 

Show by an example that for A ≠ O, B ≠ O, AB = O

Given A = `[(2, 4, 0),(3, 9, 6)]` and B = `[(1, 4),(2, 8),(1, 3)]` is (AB)′ = B′A′? 

If X and Y are 2 × 2 matrices, then solve the following matrix equations for X and Y.

2X + 3Y = `[(2, 3),(4, 0)]`, 3Y + 2Y = `[(-2, 2),(1, -5)]`

Let f(x) = x|x|, for all x ∈ R. Discuss the derivability of f(x) at x = 0

If y = tan(x + y), find `("d"y)/("d"x)`

If y = tanx + secx, prove that `("d"^2y)/("d"x^2) = cosx/(1 - sinx)^2`

Differentiate `tan^-1 (sqrt(1 - x^2)/x)` with respect to`cos^-1(2xsqrt(1 - x^2))`, where `x ∈ (1/sqrt(2), 1)`

Let f(x)= |cosx|. Then, ______.

Differential coefficient of sec (tan^–1x) w.r.t. x is ______.

If u = `sin^-1 ((2x)/(1 + x^2))` and v = `tan^-1 ((2x)/(1 - x^2))`, then `"du"/"dv"` is ______.