SECTION ·A’ MULTIPLE CHOICE QUESTION

1. Choose the correct answer for each from the given options:

Mathematics Solved 2012 MCQS

SECTION “B” (SHORT-ANSWER QUESTIONS)

2. If U = {x/x∈N . x ≤ 10}. A = (2, 4, 6, 8, 10} B = {3, 6, 9, 10} Prove that {A ∪ B} = A ∩ B

ANSWER:

ANSWER

Simplify

ANSWER

Question Answer

ANSWER

Question Answer

6. Resolve into factors. r² (s – t) + s²(t² – r) + e (r – s)

ANSWER: Please see Q.no.6 of 2014.

7. The sum of three consecutive odd numbers is 909. Find the numbers

ANSWER

The sum of these three odd no. will be
X + (x + 2) + (x + 4)
According to given condition
X + x + 2 + x + 4 = 909
3x + 6 = 909
3x = 909 – 6
3x = 903
x = 903/3
1st odd no. is x = 301
2nd no. is x + 2 = 301 + 2 = 303
Then the 3rd odd no.
X + 4 or 301 + 4 = 305
The three odd no. are 301, 303, 305

Question Answer

9. By using Cramer’s rule, solve the

equation  2x + 5y = 9
4x – 2y = 1

ANSWER:

ANSWER

10. Find the solution set with the help of
quadratic equation. 2b² – 7b + 5 = 0

ANSWER: Please see Q.no.9of 2014.

11. Prove that the sum of the three angles of a triangle is equal to 180º.

ANSWER: Please see Q.no.15of 2014.

12. Find the relation independent of ‘t’ from the following equation 

equation

ANSWER

Similarly

similarly

This is an equation independent of t

13. If a transversal intersect two parallel lines, the alternate angles so formed are congruent. Prove it.

ANSWER

Question

Prove that a = b = c

ANSWER

15. If two sides of a triangle are congruent, the angles opposite to them are also congruent. Prove it.

ANSWER

Proof:

statement bwt reasons

16. Prove that cotβ + tanβ = cotβ sec² β.

ANSWER

SECTION’c’ (DETAILED- ANSWER QUESTION)

Question Answer

ANSWER

16. Find the Solution set of the following equations graphically. (Find four ordered pairs of each equation).
4x – y -10 = 0
3x + 5y -19 = 0

Answer

graph

19. In a correspondence of triangles if three sides of one triangle are congruent to the corresponding three sides of the other, the two triangles are congruent. Prove it.

Answer

Proof:

statements reasons

20.(a) Marks obtained by some students In computer science exam. are given below. Find Median of their numbers

Question

ANSWER:

Answer

(b) Find the factors of X³ – X² – 14x + 24 with the help of remainder theorem.

Answer

21. Draw the transverse common tangents of the two circles with the radII 3cm and 2cm, when the distance b/e their centers
Is 6cm. Write down the steps of construction.

figure

Steps of Construction:

(1) Draw a straight line AB = 6cm
(2) With centre A draw a circle of radius 3 cm and with centre B draw a circle of radius 2 cm.
(3) With centre A draw a big circle of radius 3 + 2 = 5cm
(4) Bisect AB at 0 and with centre 0 and radius = mOA or m OB draw a 4th circle intersecting the big circle at Q and R.
(5) Join A to Q and R, intersecting the given circle at 5 & 5′
(6) Draw BT parallel to AQ and BT’ parallel to AR
(7) Join 5 and T and extend on either sides similarly join 5′ and T’ and extend on either sides. In this way 5T and SiT’ are the required transverse common tangents.