List of top Mathematics Questions on Mathematical Logic asked in MHT CET

If $p, q$ are true statements and $r$ is false statement, then which of the following is correct.

Negation of the statement $\forall x \in R, x^2+1=0$ is

If the symbolic form of the switching circuit is \( \sim p \vee ( p \wedge \sim q) \vee q \), then the current flows through the circuit only if:

Evaluate the integral \( \int_0^5 \frac{dx}{x^2 + 2x + 10} \)

If \( CP \) and \( CD \) is a pair of semi-conjugate diameters of the ellipse \( \frac{x^2}{a^2} + \frac{y^2}{b^2} = 1 \), then \( CP^2 + CD^2 = \)

The differential equation of all lines perpendicular to the line \[ 5x + 2y + 7 = 0 \text{ is} \]

The logical expression \( [p \wedge (q \vee r)] \vee [\neg r \wedge \neg q \wedge p] \) is equivalent to

Evaluate the integral \[ \int \frac{dx}{\cos 2x - \cos^2 x} \]

The verbal statement of the same meaning, of the statement 'If the grass is green then it rains in July' is

If \[ \frac{x}{\sqrt{1 + x^2}} + \frac{y}{\sqrt{1 + y^2}} = 0, \quad x \neq y, \text{ then } (1 + x^2)^2 \frac{dy}{dx} = \]

Write the statement in symbolic form 'Sandeep neither likes tea nor coffee but enjoys a soft drink'. Where \( p \): Sandeep likes tea, \( q \): Sandeep likes coffee, \( r \): Sandeep enjoys a soft drink

If \((\sim p \wedge q)\rightarrow r\) is false, then the truth values of \(p,q,r\) respectively are