1. One Mark Questions

2. Choose the Correct Answer 1.If p is true and q is false then which of the following is not true? (a) ~ p is true (b) p  q is true (c) p  q is false (d) p  q is true 2.Given E (X + c) = 8 and E (X – c) = 12 then the value of c is (a) – 2 (b) 4 (c) – 4 (d) 2

3. Choose the Correct Answer 3.In 5 throws of a die, getting 1 or 2 is a success. The mean number of successes is (a) 5/3 (b) 3/5 (c) 5/9 (d) 9/5 4.If f (x) is a p.d.f of a normal distribution with mean  then is (a) 1 (b) 0.5 (c) 0 (d) 0.25

4. Choose the Correct Answer 5.If X is a discrete random variable then P(X  a) (a) P(X < a) (b) 1 – P(X  a) (c) 1 – P(X < a) (d) 0 6.A particular integral of (D 2 – 4D + 4) y = e 2x is (a) (b) x e 2x (c) x e –2x (d)

5. Choose the Correct Answer 7.The order and degree of the differential equation y’ + (y’’) 2 = (x + y’’) 2 are (a) 1, 1 (b) 1, 2 (c) 2, 1 (d) 2, 2 8.Which of the following is a contradiction? (a) p  q (b) p  q (c) p  –q (d) p  –q

6. Choose the Correct Answer 9.The order of [7] in (Z 9, + 9 ) is (a) 9 (b) 6 (c) 3 (d) 1

7. Choose the Correct Answer 10.Which of the following is correct? (a) An element of a group can have more than one inverse. (b) If every element of a group is its own inverse, then the group is Abelian. (c) The set of all 2  2 real matrices forms a group under matrix multiplication. (d) (a * b) –1 = a –1 * b –1 for all a, b  G

8. Choose the Correct Answer 11.The volume generated by rotating the triangle with vertices at (0, 0), (3, 0) and (3, 3) about x-axis is (a) 18  (b) 2  (c) 36  (d) 9 

9. Choose the Correct Answer 12.The arc length of the curve y = f(x) from x = a and x = b is (a) (b) (c) (d)

10. Choose the Correct Answer 13.The surface area of the solid of revolution of the region bounded by y = 2x, x = 0 and x = 2 about x – axis is (a) 8  5  (b) 2  5  (c)  5  (d) 4  5 

11. Choose the Correct Answer 14.The differential equation obtained by eliminating a and b from y = a e 3x + b e –3x is (a) (b) (c) (d)

12. Choose the Correct Answer 15.The integrating factor of is (a) e x (b) log x (c) (d) e –x

13. Choose the Correct Answer 16.Which of the following function is increasing in (0,  ) (a) e x (b) 1/x (c) – x 2 (d) x –2 17.One of the critical numbers of x 3/5 (4 – x) is (a) 0 (b) 4 (c) 4/3 (d) 3/5

14. Choose the Correct Answer 18.The percentage error in the 11 th root of the number 28 is approximately ----------- times the percentage error in 28. (a) 1/28 (b) 1/11 (c) 11 (d) 28 19.The curve 9y 2 = x 2 (4 – x 2 ) is symmetrical about (a) y – axis (b) x – axis (c) y = x (d) both the axes

15. Choose the Correct Answer 20.The value of is (a) (b) (c) 0(d) 21.The line 5x – 2y + 4k = 0 is a tangent to 4x 2 – y 2 = 36 then k is (a) (b) (c) (d)

16. Choose the Correct Answer 22.The eccentricity of the hyperbola with asymptotes x + 2y – 5 = 0, 2x – y + 5 = 0 is (a) 3 (b)  2 (c)  3 (d) 2 23.The point of contact of the tangent y = mx + c and the parabola y 2 = 4ax is (a) (b) (c) (d)

17. Choose the Correct Answer 24.The slope of the normal to the curve y = 3x 2 at the point whose x co-ordinate is 2 is (a) (b) (c) (d) 25.If s = t 3 – 4t 2 + 7, the velocity when the acceleration is zero is (a) m/ sec (b) – m / sec (c) m / sec (d) – m / sec

18. Choose the Correct Answer 26.The polar form of the complex number (i 25 ) 3 is (a) cos + i sin (b) cos  + i sin  (c) cos  – i sin  (d) cos – i sin 27.z 1 = 4 + 5i, z 2 = - 3 + 2i then is (a) (b) (c) (d)

19. Choose the Correct Answer 28.The value of is (a) | z |(b) | z | 2 (c) 2| z |(d) 2| z | 2 29.If a = 3 + i and z = 2 – 3i then the points on the Argand diagram representing az, 3az and – az are (a) vertices of a right triangle (b) vertices of an equilateral triangle (c) vertices of an isosceles triangle (d) collinear

20. Choose the Correct Answer 30.The radius of the director circle of the conic 9x 2 + 16y 2 = 144 is (a)  7 (b) 4 (c) 3 (d) 5 31.If, then the area of the quadrilateral PQRS is (a) 5  3 (b) 10  3 (c) 5  3/2 (d) 3/2

21. Choose the Correct Answer 32.If and then a unit vector perpendicular to and is (a) (b) (c) (d)

22. Choose the Correct Answer 33.The point of intersection of the lines and is (a) (2, 1, 1) (b) (1, 2, 1) (c) (1, 1, 2) (d) (1, 1, 1) 34.The distance from the origin to the plane is (a) (b) (c) (d)

23. Choose the Correct Answer 35.If,, are three mutually perpendicular unit vectors, then | + + | = (a) 3 (b) 9 (c) 3  3(d)  3 36.If A = [2 0 1], then the rank of AA T is (a) 1 (b) 2 (c) 3 (d) 0

24. Choose the Correct Answer 37.If the matrix has an inverse then the value of k is (a) k is any real number(b) k = – 4 (c) k  – 4 (d) k  4 38.If A is a matrix of order 3, then det (KA) is (a) k 3 det (A) (b) k 2 det (A) (c) k det (A) (d) det (A)

25. Choose the Correct Answer 39.Every homogeneous system (a) is always consistent (b) has only trivial solution (c) has infinitely many solution (d) need not be consistent

26. Choose the Correct Answer 40.If and are two unit vectors and  is the angle between them, then( + ) is a unit vector if (a) (b) (c) (d)