The equation of the circle passing through the foci of the ellipse  and having centre at (0,3) is 

• x²+y²-6y-7 =0

• x²+y²-6y+7 =0

• x²+y²-6y-5 =0

• x²+y²-6y-5 =0

A multiple choice examination has 5 questions. Each question has three alternative answers of which exactly one is correct. The probability that a student will get 4 or more correct answers just by guessing is

• 17/3⁵

• 13/3⁵

• 11/3⁵

• 11/3⁵

The x-coordinate of the incentre of the triangle that has the coordinates of mid points of its sides as (0, 1) (1, 1) and (1, 0) is

The term independent of  x in  is 

• 4

• 120

• 18

• 18

Let Tn be the number of all possible triangles formed by joining vertices of an n-sided regular polygon. If T_n+1 − T_n = 10, then the value of n is

• 7

• 5

• 10

• 10

16.

If z is a complex number of unit modulus and argument θ, then arg  is equal to

• -θ

• π/2-θ

• θ

• θ

ABCD is a trapezium such that AB and CD are parallel and BC⊥CD. If ∠ADB = θ, BC = p and CD = q,then AB is equal to

Given A circle, 2x² + 2y²= 5 and parabola,  
Statement I An equation of a common tangent to these curves is 
Statement II If the line  is the common tangent, then m satisfies m⁴-3m²+2 =0

• Statement I is true,  Statement II is true; Statement II is a correct explanation for statement I

• Statement I is true, Statement II is true; Statement II is not a correct explanation for statement I

• Statement I is true, Statement II is false

• Statement I is true, Statement II is false

The expression  can be written as

• sin A cos A+1

• sec A cosec A+1

• tan A + cot A

• tan A + cot A

All the students of a class performed poorly in Mathematics. The teacher decided to give grace marks of 10 to each of the students. Which of the following statistical measures will not change even after the grace marks were given?

• Mean

• Median

• Mode

• Mode