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, \((a,b)=\)

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?

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

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…

Given below are two statements in the context of throwing two different dice together: Statement (I): The probability that the two numbers obtained have even sum, is 0.50. Statement (II): The probability that the two numbers obtained have even product is 0.75. In light of the abo…

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 statemen…

If the eight-digit number 5a32465b is divisible by 88, then 2a + 5b =

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

Given below are two statements, one is labelled as Assertion (A) and other one labelled as Reason (R). Assertion (A): Sum of first hundred even natural numbers divisible by 5 is 45050. Reason (R): Sum of first n-terms of an Arithmetic Progression is given by…