HSC Science (Computer Science) 12th Standard Board Exam - Maharashtra State Board Question Bank Solutions for Mathematics and Statistics

Fill in the blanks :

Inverse of statement pattern p ↔ q is given by –––––––––.

Write the converse, inverse, contrapositive of the following statement.

If a man is bachelor, then he is happy.

Write the dual of the following.

(~p ∧ q) ∨ (p ∧ ~q) ∨ (~p ∧ ~q)

Find the principal solutions of the following equation:

sin 2θ = `− 1/(sqrt2)`

Find the principal solutions of the following equation:
tan 5θ = -1

Find the principal solutions of the following equation:

cot 2θ = 0.

The acute angle between the lines represented by x² + xy = 0 is ______.

The false statement in the following is ______.

Find the measure of the acute angle between the lines given by x² − 4xy + y² = 0 

Find the value of h, if the measure of the angle between the lines 3x² + 2hxy + 2y² = 0 is 45°. 

If θ is the acute angle between the lines given by ax² + 2hxy + by² = 0 then prove that tan θ = `|(2sqrt("h"^2) - "ab")/("a" + "b")|`. Hence find acute angle between the lines 2x² + 7xy + 3y² = 0 

Write the converse and contrapositive of the following statements.

“If a function is differentiable then it is continuous”

If the angle between the lines represented by ax² + 2hxy + by² = 0 is equal to the angle between the lines 2x² − 5xy + 3y² = 0, then show that 100(h² − ab) = (a + b)²

Write the dual of the following

(p ˄ ∼q) ˅ (∼p ˄ q) ≡ (p ˅ q) ˄ ∼(p ˄ q)

The value of x, y, z for the following system of equations x + y + z = 6, x − y+ 2z = 5, 2x + y − z = 1 are ______

System of equations x + y = 2, 2x + 2y = 3 has ______

If A = `[(2, 0),(0, 1)]` and B = `[(1),(2)]`, then find the matrix X such that A⁻¹X = B.

Transform `[(1, 2, 4),(3, -1, 5),(2, 4, 6)]` into an upper triangular matrix by using suitable row transformations

Solve the following by inversion method 2x + y = 5, 3x + 5y = −3

Three chairs and two tables cost ₹ 1850. Five chairs and three tables cost ₹2850. Find the cost of four chairs and one table by using matrices