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

If the statement p, q are true statement and r, s are false statement then determine the truth value of the following:

∼ [(∼ p ∧ r) ∨ (s → ∼ q)] ↔ (p ∧ r)

Find the separate equation of the line represented by the following equation:

x² + 2xy tan α - y² = 0

Find the combined equation of the pair of a line passing through the origin and perpendicular to the line represented by following equation:

5x² - 8xy + 3y² = 0 

Find the combined equation of the pair of a line passing through the origin and perpendicular to the line represented by the following equation:

5x² + 2xy - 3y² = 0 

Find the combined equation of the pair of a line passing through the origin and perpendicular to the line represented by the following equation:

xy + y² = 0 

Find the combined equation of the pair of a line passing through the origin and perpendicular to the line represented by the following equation:

3x² − 4xy = 0 

If A = {3, 5, 7, 9, 11, 12}, determine the truth value of the following.

∃ x ∈ A such that x – 8 = 1

If A = {3, 5, 7, 9, 11, 12}, determine the truth value of the following.

∀ x ∈ A, x² + x is an even number

If A = {3, 5, 7, 9, 11, 12}, determine the truth value of the following.

∃ x ∈ A such that x² < 0

If A = {3, 5, 7, 9, 11, 12}, determine the truth value of the following.

∀ x ∈ A, x is an even number.

If A = {3, 5, 7, 9, 11, 12}, determine the truth value of the following.

∃ x ∈ A such that 3x + 8 > 40

If A = {3, 5, 7, 9, 11, 12}, determine the truth value of the following.

∀ x ∈ A, 2x + 9 > 14

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Auxiliary equation of 2x² + 3xy - 9y² = 0 is

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If two lines ax² + 2hxy + by² = 0 make angles α and β with X-axis, then tan (α + β) = _____.

If the slope of one of the two lines given by `"x"^2/"a" + "2xy"/"h" + "y"^2/"b" = 0` is twice that of the other, then ab : h² = ______.

The joint equation of the lines through the origin and perpendicular to the pair of lines 3x² + 4xy – 5y² = 0 is _______.

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If the equation 3x² – 8xy + qy² + 2x + 14y + p = 1 represents a pair of perpendicular lines, then the values of p and q are respectively ______.

The area of triangle formed by the lines x² + 4xy + y² = 0 and x - y - 4 = 0 is ______.

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The combined equation of the coordinate axes is

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If h² = ab, then slopes of lines ax² + 2hxy + by² = 0 are in the ratio