HSC Arts (English Medium) १२ वीं कक्षा - Maharashtra State Board Question Bank Solutions for Mathematics and Statistics

Write the negation of the following.

All-natural numbers are whole numbers.

Write the negation of the following.

∀ n ∈ N, n² + n + 2 is divisible by 4.

Write the negation of the following.

∃ x ∈ N such that x – 17 < 20

Using the rule of negation write the negation of the following with justification.

∼ q → p

Using the rule of negation write the negation of the following with justification.

p ∧ ∼ q

Using the rule of negation write the negation of the following with justification.

p ∨ ∼ q

Using the rule of negation write the negation of the following with justification.

(p ∨ ∼ q) ∧ r

Using the rule of negation write the negation of the following with justification.

p → (p ∨ ∼ q)

Using the rule of negation write the negation of the following with justification.

∼ (p ∧ q) ∨ (p ∨ ∼ q)

Using the rule of negation write the negation of the following with justification.

(p ∨ ∼ q) → (p ∧ ∼ q)

Using the rule of negation write the negation of the following with justification.

(∼ p ∨ ∼ q) ∨ (p ∧ ∼ q)

Select and write the correct answer from the given alternative of the following question:

The negation of inverse of ∼p → q is ________.

The negation of p ∧ (q → r) is ________.

Write the negation of the following:

∀ n ∈ A, n + 7 > 6.

Write the negation of the following:

∃ x ∈ A, such that x + 9 ≤ 15.

Write the negation of the following:

Some triangles are equilateral triangle.

Find the distance of the point `4hat"i" - 3hat"j" + hat"k"` from the plane `bar"r".(2hat"i" + 3hat"j" - 6hat"k")` = 21.

Find the distance of the point (1, 1 –1) from the plane 3x +4y – 12z + 20 = 0.

Solve the following:

Find the distance of the point `3hat"i" + 3hat"j" + hat"k"` from the plane `bar"r".(2hat"i" + 3hat"j" + 6hat"k")` = 21.

Solve the following :

Find the distance of the point (13, 13, – 13) from the plane 3x + 4y – 12z = 0.