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

`"tan"^-1 1/3 + "tan"^-1 1/5 + "tan"^-1 1/7 = "tan"^-1 1/8 =` ____________.

If tan^-1 2x + tan^-1 3x = `pi/4,` then x is ____________.

If `"tan"^-1 (("x" - 1)/("x" + 2)) + "tan"^-1 (("x" + 1)/("x" + 2)) = pi/4,` then x is equal to ____________.

The value of cot^-1 9 + cosec^-1 `(sqrt41/4)` is given by ____________.

If A is a square matrix, then A – A’ is a ____________.

For any square matrix A, AA^T is a ____________.

If A `= [("cos x", - "sin x"),("sin x", "cos x")]`, find AAT.

If the matrix A `= [(5,2,"x"),("y",2,-3),(4, "t",-7)]` is a symmetric matrix, then find the value of x, y and t respectively.

If a matrix A is both symmetric and skew-symmetric, then ____________.

The matrix `[(0,5,-7),(-5,0,11),(7,-11,0)]` is ____________.

The matrix A `=[(0,1),(1,0)]` is a ____________.

The matrix `[(0,-5,8),(5,0,12),(-8,-12,0)]`  is a ____________.

If `[(1,2),(3,4)],` then A² - 5A is equal to ____________.

If A `= [(0,1,1),(1,0,1),(1,1,0)] "then"  ("A"^2 - 3"I")/2 =` ____________.

Evaluate the determinant `Delta = abs (("log"_3  512, "log"_4  3),("log"_3  8, "log"_4  9))`

`abs(("cos"  15°, "sin"  15°),("sin"  75°, "cos"  75°))`

Find the minor of 6 and cofactor of 4 respectively in the determinant `Delta = abs ((1,2,3),(4,5,6),(7,8,9))`

The differential coefficient of `"tan"^-1 ((sqrt(1 + "x") - sqrt (1 - "x"))/(sqrt (1+ "x") + sqrt (1 - "x")))` is ____________.

A manufacturing company makes two types of television sets; one is black and white and the other is colour. The company has resources to make at most 300 sets a week. It takes Rs 1800 to make a black and white set and Rs 2700 to make a coloured set. The company can spend not more than Rs 648000 a week to make television sets. If it makes a profit of Rs 510 per black and white set and Rs 675 per coloured set, how many sets of each type should be produced so that the company has maximum profit? Formulate this problem as a LPP given that the objective is to maximise the profit

In a LPP, the linear function which has to be maximised or minimised is called a linear ______ function.