The area (in sq. units) of the region A = {(x, y) : x2 $$\le$$ y $$\le$$ x + 2} is

Let S($$\alpha$$) = {(x, y) : y2 $$\le$$ x, 0 $$\le$$ x $$\le$$ $$\alpha$$} and A($$\alpha$$) is area of the region S($$\alpha$$). If for a $$\lambda$$, 0 < $$\lambda$$ < 4, A($$\lambda$$) : A(4) = 2 : 5, then $$\lambda$$ equals

The area (in sq. units) of the region bounded by the parabola, y = x2 + 2 and the lines, y = x + 1, x = 0 and x = 3, is

The area (in sq. units) in the first quadrant bounded by the parabola, y = x2 + 1, the tangent to it at the point (2, 5) and the coordinate axes is :

The area (in sq. units) of the region bounded by the curve x2 = 4y and the straight line x = 4y – 2 is :

If the area enclosed between the curves y = kx2 and x = ky2, (k > 0), is 1 square unit. Then k is -

The area of the region A = {(x, y) : 0 $$\le$$ y $$\le$$x |x| + 1 and $$-$$1 $$\le$$ x $$\le$$1} in sq. units, is :

The area (in sq. units) bounded by the parabolae y = x2 – 1, the tangent at the point (2, 3) to it and the y-axis is :

For any two statements p and q, the negation of the expression p $$\vee$$ (~p $$\wedge$$ q) is :

The Boolean expression ~(p $$\Rightarrow$$ (~q)) is equivalent to :

If the truth value of the statement p $$\to$$ (~q $$\vee$$ r) is false (F), then the truth values of the statements p, q, r are respectively :

The negation of the Boolean expression ~ s $$\vee$$ (~r $$\wedge$$ s) is equivalent to :

Which one of the following Boolean expressions is a tautology?

If p $$\Rightarrow$$ (q $$\vee$$ r) is false, then the truth values of p, q, r are respectively :-

Which one of the following statements is not a tautology?

The contrapositive of the statement "If you are born in India, then you are a citizen of India", is :

The expression $$\sim$$ ($$\sim$$ p $$\to$$ q) is logically equivalent to :

The Boolean expression ((p $$\wedge$$ q) $$\vee$$ (p $$\vee$$ $$\sim$$ q)) $$\wedge$$ ($$\sim$$ p $$\wedge$$ $$\sim$$ q) is equivalent to :

Contrapositive of the statement " If two numbers are not equal, then their squares are not equal." is :

If q is false and p $$\wedge$$ q $$\leftrightarrow$$ r is true, then which one of the following statements is a tautology ?