In a library, 50% of a total number of books is of Marathi. The books of English are 1/3 rd of Marathi books. The books on mathematics are 25% of English books. The remaining 560 books are of other subjects. What is the total number of books in the library?

Solve the following equations.

(1) 17 (x + 4) + 8 ( x + 6) = 11( x +5) + 15 (x +3)

Complete the activity according to the given steps.

(1) Draw rhombus ABCD. Draw diagonal AC.

(2) Show the congruent parts in the figure by identical marks.

(3) State by which test and in which correspondence ∆ ADC and ∆ ABC are congruent.

(4) Give reason to show ∠DCA ≅ ∠BCA, and ∠DAC ≅ ∠BAC

(5) State which property of a rhombus is revealed from the above steps.

The shape of a farm is a quadrilateral. Measurements taken of the farm, by naming its corners as P, Q, R, S in order are as follows. l(PQ) = 170 m, l(QR) = 250m, l(RS) = 100 m, l(PS) = 240 m, l(PR) = 260 m.

Find the area of the field in a hectare (1 hectare = 10,000 sq.m)

Divide the polynomial (6x³ + 11x² - 10x - 7) by the binomial (2x + 1). Write the quotient and the remainder.