RD Sharma Chapter 1 : Number System Exercise 1.1 Solutions Are the following statements true or false? Give your reasons for your answer. (i) Every whole number is a natural number. (ii) Every integer is a rational number (iii) Every rational number is an integer (iv) Every natural number is a whole number. (v) Every […]
RD Sharma Chapter 5 : Algebra of Matrices Multiple Choice Question Solutions If A = [[i, 0], [0, i]], n∈N, then A^4n equals Watch Solution If A = [[1, 0, 0], [0, 1, 0], [a, b, -1]], then A^2 is equal to Watch Solution If A and B are two matrices such that AB = A
RD Sharma Chapter 5 : Algebra of Matrices Very Short Question Answer Solutions If A = [[2, 1, 4], [4, 1, 5]] and B = [[3, -1], [2, 2], [1, 3]]. Write the orders of AB and BA. Watch Solution If A is an m×n matrix and B is n×p matrix does AB exist ? If
RD Sharma Chapter 5 : Algebra of Matrices Exercise 5.5 Solutions If A=[[2, 3], [4, 5]], prove that A – A^T is skew-symmetric matrix. Watch Solution If A = [[3, -4], [1, -1]], show that A – A^T is a skew-symmetric matrix. Watch Solution If the matrix A = [[5, 2, x], [y, z, -3], [4,
RD Sharma Chapter 5 : Algebra of Matrices Exercise 5.4 Solutions Let A = [[2, -3],[-7, 5]] and B=[[1, 0],[2, -4]], verify that (2A)^T = 2A^T Watch Solution Let A = [[2, -3], [-7, 5]] and B = [[1, 0], [2, -4]], verify that (A + B)^T = A^T + B^T Watch Solution Let A =
RD Sharma Chapter 5 : Algebra of Matrices Exercise 5.3 Solutions Compute the indicated product : [[a, b], [-b, a]] [[a, -b], [b, a]] Watch Solution Compute the indicated product : [[1, -2], [2, 3]] [[1, 2, 3], [-3, 2, -1]] Watch Solution Compute the indicated product : [[2, 3, 4], [3, 4, 5], [4, 5,
RD Sharma Chapter 5 : Algebra of Matrices Exercise 5.2 Solutions Compute the following sums: [[3, -2], [1, 4]]+[[-2, 4] [1, 3]] Watch Solution Compute the following sums: [[2, 1, 3], [0, 3, 5], [-1, 2, 5]] + [[1, -2, 3], [2, 6, 1], [0, -3, 1]] Watch Solution Let A=[[2, 4], [3, 2]], B=[[1, 3],
RD Sharma Chapter 4 : Inverse Trigonometric Function Very Short Type Questions (VSAQs) Solutions Write the value of sin^-1(-√3/2) + cos^-1(-1/2) Watch Solution Write the difference between maximum and minimum values of sin^-1x for x ∈[-1,1] Watch Solution If sin^-1x+sin^-1y + sin^-1z = 3π/2, then write the value of x + y + z. Watch Solution
RD Sharma Chapter 5 : Algebra of Matrices Exercise 5.1 Solutions If a matrix has 8 elements, what are the possible orders it can have ? What if it has 5 elements ? Watch Solution If A = [aij] = [[2,3,-5],[1,4,9],[0,7,-2]] and B = [bij] = [[2,-1],[-3,4],[1,2]] then find (i) a22 + b21 (ii) a11b11 +
RD Sharma Chapter 4 : Inverse Trigonometric Function Multiple Choice Questions (MCQs) Solutions If tan^-1{(√1+x^2)-(√1-x^2)/(√1+x^2)+(√1-x^2)} = α, then x^2= Watch Solution The value of tan{cos^-1(1/5√2) – sin^-1(4/17)} is Watch Solution 2tan^-1{cosec(tan^-1x) – tan(cot^-1x)} is equal to Watch Solution If cos^-1(x/a) + cos^-1(y/b) = α, then x^2/a^2 – (2xy/ab)cosα + y^2/b^2 = Watch Solution The positive integral