1.

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

• infinite number of real roots

• No real root

• exactly one real root

• exactly one 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 true; statement 2 is not a correct explanation for statement 1

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

• Neither I will become a teacher nor 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 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

• an even positive integer

If 100 times the 100^th term of an AP with non zero common difference equals the 50 times its 50^th term, then the 150^th term of this AP is

•  –150

• 150

• times its 50th term

• times its 50th term

In a ∆PQR, if 3 sin P + 4 cos Q = 6 and 4 sin Q + 3 cos P = 1, then the angle R is equal to

• 5π/6

• π/6

• π/4

• π/4

An equation of a plane parallel to the plane x – 2y + 2z – 5 = 0 and at a unit distance from the origin is

• x – 2y + 2z – 3 = 0

• x – 2y + 2z + 1 = 0

• x – 2y + 2z – 1 = 0

• x – 2y + 2z – 1 = 0

If the line 2x + y = k passes through the point which divides the line segment joining the points (1, 1) and (2, 4) in the ratio 3 : 2, then k equals

• 29/5

• 5

• 6

• 6

Let x1, x2, ......, x_n be n observations, and let be their arithmetic mean and σ2 be their variance.
Statement 1: Variance of 2x1, 2x2, ......, 2xn is 4 σ².
Statement 2: Arithmetic mean of 2x1, 2x2, ......, 2xn is 4.

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