2. SECTION – I Single Correct Answer Type There are 4 parts in this question. Each part has exactly one correct answer.
3. 01 Problem For the tree events A,B and C,P (exactly one of the events A or B occurs)=P(exactly one of the events B or C occurs)=P(exactly one of the events C or A occurs)=p and P (all the three events occur simultaneously)= ,where 0<p<1/2.Then the probability of at least one of the three events A,B and C occurring is a. b. c. d.
4. Problem 02 The angle between a pair of tangents drawn from a point P to the circle The equation of the locus of the point P is a. b. c. d.
6. Problem 04 For positive integers the value of the expression is a real number if and only if a. b. c. d.
7. SECTION – II Fill in the blanks This question contains four incomplete statements. In each part, fill in the blanks so that each of the resulting statements is correct.
8. Problem 01 An ellipse has eccentricity 1/2 and one focus at the point p(1/2,1).Its one directrix is common tangent, nearer to the point P,to the circle and the hyperbola .The equation of the ellipse, in the standard form ,is___________ .
9. Problem 02 If f is an even function defined on the interval (-5,5),then four real values of x satisfying the equation are and __________ .
12. SECTION – III Fill in the blanks This question contains three incomplete statements. In each part, fill in the blanks so that each of the resulting statements is correct.
13. Problem 01 Let denotes the greatest integer function. The domain of f is __________ and the points of discontinuity of in the domain are _______ .
14. Problem 02 The value of expression is an imaginary cube root of unity ,is ____________ .
15. Problem 03 The intercept on the line x=y by the circle .Equation of the circle with AB as a diameter is ___________ .
16. SECTION – IV Fill in the blanks This question contains three incomplete statements. In each part, fill in the blanks so that each of the resulting statements is correct.
17. 01 Problem Let be positive integers such that .The number of solutions all integers satisfying is ___________ .
20. SECTION – V Fill in the blanks This question contains three incomplete statements. In each part, fill in the blanks so that each of the resulting statements is correct.
21. Problem 01 A nonzero vector a is parallel to the line of intersection of the plane determined by the vectors and the plane determined by the vectors .The angle between a and the vector
24. SECTION – VI Fill in the blanks This question three incomplete statements. In each part, fill in the blanks so that each of the resulting statements is correct
25. Problem 01 If band c are two non-collinear unit vectors and a is any vector, then ________ .
