For a > 0, let the curves C1 : y2 = ax and C2 : x2 = ay intersect at origin O and a point P. Let the line x = b (0 < b < a) intersect the chord OP and the x-axis at points Q and R, respectively. If the line x = b bisects the area bounded by the curves, C1 and C2, and the area of $$\Delta$$OQR = {1 \over 2}, then 'a' satisfies the equation :

Negation of the statement : $$\sqrt{5}$$ is an integer or 5 is an irrational is :

Consider the statement : ‘‘For an integer n, if n3 – 1 is even, then n is odd.’’ The contrapositive statement of this statement is :

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

The statement $$\left(p\to \left(q\to p\right)\right)\to \left(p\to \left(p\vee q\right)\right)$$ is :

The negation of the Boolean expression x $$\leftrightarrow$$ ~ y is equivalent to :

Contrapositive of the statement : ‘If a function f is differentiable at a, then it is also continuous at a’, is:

Given the following two statements: $$\left(S_1\right):\left(q\vee p\right)\to \left(p\leftrightarrow \sim q\right)$$ is a tautology $$\left(S_2\right):\sim q\wedge \left(\sim p\leftrightarrow q\right)$$ is a fallacy. Then:

Let p, q, r be three statements such that the truth value of (p $$\wedge$$ q) $$\to$$ ($$\sim$$q $$\vee$$ r) is F. Then the truth values of p, q, r are respectively :

Which of the following is a tautology ?

The contrapositive of the statement "If I reach the station in time, then I will catch the train" is :

If p $$\to$$ (p $$\wedge$$ ~q) is false, then the truth values of p and q are respectively :

Which of the following statements is a tautology?

Which one of the following is a tautology?

Let A, B, C and D be four non-empty sets. The contrapositive statement of "If A $$\subseteq$$ B and B $$\subseteq$$ D, then A $$\subseteq$$ C" is :

The logical statement (p $$\Rightarrow$$ q) $$\Lambda$$ ( q $$\Rightarrow$$ ~p) is equivalent to :

The proposition p $$\to$$ ~ (p $$\wedge$$ ~q) is equivalent to :

Amount of solar energy received on the earth’s surface per unit area per unit time is defined a solar constant. Dimension of solar constant is :

Dimensional formula for thermal conductivity is (here K denotes the temperature):

A quantity x is given by \left( {{{IF{v^2}} \over {W{L^4}}}} \right) in terms of moment of inertia I, force F, velocity v, work W and Length L. The dimensional formula for x is same as that of :