Group B [6 x 5 = 30]
Attempt any six questions.
11. In an examination, 27% of the students failed in Mathematics and 31% failed in statistics. If 6% of the students failed in both subjects, find the percentage of the students
a. failed in examination.
b. passed in both subjects.
12. i. If A = [-3, 1) and B = [-2, 4]. Find A – B with graphical representation in a real line. [2.5]
ii. Rewrite – 3 < x < 4 by using the modulus sign. [2.5]
13. Let f:R R and g:R
R be defined by f(x) = 2x + 1 and g (x) = 3x – 1, find
i. gof (x) ii. fog (x) iii. f-1 o g [1 + 1 + 3]
14. Sum to n terms of the series 1.3 + 3.5 + 5.7 + ………………… [5]
15. Prove that:
16. Find the centre, vertices, eccentricity, foci and length of major axis of the ellipse:
25x2 + 4y2 = 100.
17. The letters of the word ‘ STRANGE’ are to be shuffled to form different words such that
a. the vowels always come together.
b. the vowels may occupy only the odd positions.
Group C [2 x 10 = 20]
Attempt any two questions
18. If arithmetic mean, geometric mean and harmonic mean between tow unequal positive numbers are A, G, H respectively, then prove that:
i. (G.M)2 = A.M. H.M.
ii. A.M. > G.M. > H.M.
19. a. Define scalar product of two vectors in space. By vector method, Prove in any ABC
that: c = a cos B + b cos A.
b. Find the area of the parallelogram determined by the vectors + 2
+ 3
and
– – 2
+
.
20. Find the equation of a circle passing through the points (1, 2), (3, 1) and (-3, -1).
