$$ if \ {1\over x}+x=4,$$ then find $${1\over x^2}+x^2$$

A spherical metallic shell with 6 cm external radius weighs 6688 g. What is the thickness of the shell if the density of metal is 10.5 g per cm3? (Take л = 22/7)

The angles of triangle are in the ratio 3:4:5 the measure of the largest angle of the triangle is

The ratio of the marks of Kamlesh in the examination of two subjects English and Mathematics is 7 : 11. If he got 20 marks more in Mathematics than in English, then how many marks did he get in English?

On a sum Rina earn a interest of Rs. 1519 at S.I. in 7 years at 7% p.a. Find the sum.

If p = 99, then value of p(p² + 3p + 3) is

In ∆PQR, ∠Q=90°. If cot $$R={1\over 3}$$, then what is the value of $${secP(cosR+sinP)\over cosec \ R(sinR-cosecP)} $$?

Directions : In an Institution there are 800 students. Students use different modes of transport for going to the institution and return. The given pie diagram represents the requisite data. Study the diagram carefully and answer the questions.

If the total amount spent by the Government during the year was ₹ 3,00,000 crores, the amount spent on state development exceeds that on sports by