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SECTION "B" (Short Answer Question) Marks: 30
NOTE: Answer any SIX (06) questions from this section. All questions carry equal marks.
2. If A = {1, 2, 3, 4}, then find the power set A.
3. If a: b = c: d = e: f then show that:
a2b + c2d + e2fab2 + cd2 + ef2 = a + c + eb + d + f
4. Prove that
√1 + cosθ1 - cosθ = sinθ1 - cosθ (cosθ ≠ 1)
5. If two chords of a circle are congruent, then they will be equidistant from the centre. Prove it.
6. A ladder makes an angle of 60° with the ground and reaches a height of 6cm on the wall. Find the length of the ladder.
7. Resolve 11 - 3x(x - 1)(x + 3) into partial fraction.
8. If the angles subtended by two chords of a circle (or congruent circles) at the centres (corresponding centres) are equal, the chords are equal. Prove it.
9. Find the value of m, if the roots of the equation x2 - 5x + 2m = 0 differ by 1.
10. The marks obtained by students in a subject (out of 50) are given in the following grouped table. Find Mode.
| Marks | 25 - 29 | 30 - 34 | 35 - 39 | 40 - 44 | 45 - 49 |
| No. of Students | 9 | 18 | 35 | 17 | 5 |
11. If two arcs of a circle are congruent then the corresponding chords are equal. Prove it.
—OR— Find variance of number of absentees in a class for last seven days: 3, 5, 3, 2, 4, 1, 8
SECTION "C"; (Detailed –Answer Question) (30)
NOTE: Attempt any THREE (03) questions from this Section. All questions carry equal marks.
12. Find the inverse of the matrix by adjoint method:
A =
| 1 | 0 | 1 |
| -4 | 1 | -1 |
| 6 | -2 | 1 |
13. If two triangles are similar, the squares of their corresponding sides are proportional. Prove it.
14. In a right-angled triangle, the square of the length of hypotenuse is equal to sum of the square of the length of the other two sides. Prove it.
15. Draw an inscribed circle of ΔABC in which mAB = 7cm, m∠B = 60° and mBC = 6cm. (Also write steps of construction)
16. The internal bisectors of an angle of a triangle divides the sides opposite to it in the ratio of the sides containing the angle. Prove it.
16. (OR) If two circles touch internally, the distance between their centres is equal to the difference of their radii. Prove it.
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