List of top Mathematics Questions on Geometry asked in GATE XH- C3, GATE XH-C1

Consider a square field ABCD. The diagonal AC is 50 meter. The cost of laying grass in the field is Rs. 5 per square-meter. The total cost for laying grass in the field ABCD is Rs. ________________ (rounded off to two decimal places).
Consider a square field ABCD. The diagonal AC is 50 meter. The cost of laying grass in the field is Rs. 5 per square-meter. The total cost for laying grass in the field ABCD is Rs. ________________ (rounded off to two decimal places).

A logician proves that \((P \land Q) \rightarrow (P \lor Q)\) is a tautology in the following steps: 

i. \((P \land Q) \rightarrow (P \lor Q)\) 
ii. \(\langle X \rangle \langle OP \rangle (P \lor Q)\) 
iii. \((\neg P \lor P \lor Q \lor \neg Q)\) 
iv. \(T\) (TRUE) 

Other symbols are standard logic operators: \(\neg\) stands for NEGATION; \(\land\) for AND; \(\lor\) for OR; and \(\rightarrow\) for IMPLIES. 

Which of the following is/are the set of correct values of \(X\) and \(OP\)?

Consider the predicate calculus expression, \(\forall x\, P(x) \rightarrow \exists x\, P(x)\). Which of the following English sentences with respect to a club called Sunshine is/are equivalent to this predicate calculus expression?
A square with sides of length $6\,\text{cm$ is given. The boundary of the shaded region is defined by two semi-circles whose diameters are the sides of the square, as shown. The area of the shaded region is \underline{\hspace{1cm}} $\text{cm}^2$.} \includegraphics[width=0.35\linewidth]{image10.png}