Given below are two statements: Statement (I): The difference, the sum and the product of two numbers are in the ratio 1 : 5 : 12. The product of the two numbers is 18. Statement (II): The last digit in the decimal representation of \(2^{91}\) is 6. In light of the above statements, choose the most appropriate answer from the options given below.

\(k^2-1\) is divisible by 8, if k is

Given below are two statements: Statement (I): The volume of a right circular cylinder of base radius 7 cm and height 10 cm is 1540 cm\(^2\) (Take \(\pi=\frac{22}{7}\)). Statement (II): Total surface area of the cylinder having radius of base 14 cm and height 30 cm, is 3872 cm…

The total number of seconds in P weeks, P days, P hours, P minutes and P seconds is.

Sonali buys 2 Pen Drives A and B and their cost price is in the ratio of 5 : 6 respectively. If she sells them on 10% profit each, she earns total profit of ₹ 22. What will be her total profit, if she sells Pen Drive A on 20 % loss and Pen Drive B on 30% profit?

Given below are two statements: Statement (I): \((x^2+3x+1)=(x-2)^2\) is not a quadratic equation. Statement (II): The nature of roots of the quadratic equation \(x^2+2x\sqrt{3}+3=0\) are real and equal. In light of the above statements, choose the most appropriate answer from th…

The expression \(2x^3+ax^2+bx+3\), where a and b are constants, has a factor of \(x-1\) and leaves a remainder of 15 when divided by \(x+2\). Then, \((a,b)=\)

The number of integral solutions of the equation \(7\left(y+\frac{1}{y}\right)-2\left(y^2+\frac{1}{y^2}\right)=9\) is

A 30 metre deep well, with diameter 7 metre is dug and the earth from digging is evenly spread out to form a platform of size 22 metre by 14 metre. The height of the platform is