The equation e^sinx-e^-sinx -4 = 0 has

• infinite number of real roots

• No real root

• exactly one real root

• exactly four real roots

B.

No real root

Statement 1: The sum of the series 1 + (1 + 2 + 4) + (4 + 6 + 9) + (9 + 12 + 16) + ...... + (361 + 380 +400) is 8000.
Statement 2: , for any natural number n.

• Statement 1 is false, statement 2 is true

• Statement 1 is true, statement 2 is true; statement 2 is a correct explanation for statement 1

• Statement 1 is true, statement 2 is true; statement 2 is not a correct explanation for statement 1

• Statement 1 is true, statement 2 is false

The negation of the statement “If I become a teacher, then I will open a school” is

• I will become a teacher and I will not open a school

• Either I will not become a teacher or I will not open a school

• Neither I will become a teacher nor I will open a school

• I will not become a teacher or I will open a school

Statement I An equation of a common tangent to the parabola  and the ellipse 2x² +y² =4 is .
Statement II If the line  is a common tangent to the parabola  and the ellipse 2x² +y² =4, then m satisfies m⁴ +2m² =24

• Statement 1 is false, statement 2 is true

• Statement 1 is true, statement 2 is true; statement 2 is a correct explanation for statement 1

• Statement 1 is true, statement 2 is true; statement 2 is not a correct explanation for statement 1

• Statement 1 is true, statement 2 is false

C.

Statement 1 is true, statement 2 is true; statement 2 is not a correct explanation for statement 1

If n is a positive integer, then  is

• an irrational number

• an odd positive integer

• an even positive integer

• a rational number other than positive integers

A.

an irrational number

Adding both the binomial expansions above, we get

It is the irrational number because of odd power of  appears in each of the terms.