BOARD ANSWER PAPER : MARCH 2014

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Isabel Powers
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1 BOARD ANSWER PAPER : MARCH 014 ALGEBRA 1 Algebra 1. Attempt any five subquestions from the following: i. Given, t, t 4 1 d t 4 t 1 4 ii. (x + 5) (x ) 0 x or x 0 x 5 or x iii. Since, θ Valueof thecomponent Totalvaluesof allthecomponents measure of central angle (θ) for Bus iv. A coin is tossed. S {H,T} v. Mean ( x ) fixi f i vi. x 10x + 7 x 10x 7 0 is in the standard form.. Attempt any four subquestions from the following: i. The given sequence is 1, 4, 7, 10,. Here, t 1 1, t 4, t 7, t 4 10 t t t t 7 4 t 4 t 10 7 t t 1 t t... constant The difference between two consecutive terms is constant. The given sequence is an A.P. ii. 4x 9 0 (x) () 0 (x ) (x + ) 0 x 0 or x + 0 x or x

2 Board Answer Paper: March 014 iii. Given, equation is 5x + y 4. The point (x, y) (a, ) lies on the graph of the given equation, hence it satisfies the given equation. putting x a and y in the given equation, we get 5(a) + () 4 5a + 4 5a a 5 a iv. The given equations are 7x + 5y 11. (i) and 5x + 7y 1. (ii) Adding (i) and (ii), we get 7x + 5y 11 5x + 7y 1 1x + 1y 4 1(x + y) 4 x + y 4 1 x + y v. When a die is thrown, S {1,,, 4, 5, } n (S) A Event of getting numbers multiple of on the upper face. A {, } n (A) vi. The inter-relation between the measures of central tendency is Mean Mode (Mean Median) 15 9 (15 Median) 15 Median 15 Median Median 15 Median 1. Attempt any three of the following subquestions: i. The given equation is 4x + 7x + 0 Comparing it with ax + bx + c 0, we get a 4, b 7, c x b ± b 4ac a 7± 7 4(4)() (4) 7± 49 7± 17

3 Algebra x or x , 7 17 are the roots of the given equation. ii. The given simultaneous equations are x + y 11. (i) and 7x 4y 9. (ii) Equations (i) and (ii) are in the form ax + by c. D ( 4) (7) D x 9 4 ( 11 4) ( 9) 44 1 D y ( 9) ( 11 7) By Cramer s rule, we get x D x D and y D y D x and y 104 x 1 and y 4 x 1 and y 4 is the solution of the given simultaneous equation. iii. When two coins are tossed, S {HH, HT, TH, TT} n(s) 4 a. A is the event of getting at most one tail. A {HT, TH, HH} n(a) iv. b. D is the event of getting no head. D {TT} n(d) 1 Money (in `) Class interval Class mark x i d i x i A d i x i 5 No. of students Frequency A Total Σf i 5 Σ f i d i 0 fidi d f i f i f i d i [1½]

4 Board Answer Paper: March 014 Mean x A+ d The mean of money collected by a student is `.. v. Price of sugar per kg (in `) Class interval Number of weeks Frequency(f i ) Y Scale: On X- axis: 1 cm ` On Y- axis: 1 cm weeks Number of weeks X 0 Y Price of sugar per kg. (in `) X [] 4

5 Algebra 4. Attempt any two subquestions from the following: i. The instalments are in A.P. Here, S Also, n 1, d 10 Now, S n n [a + (n 1)d] S 1 1 [a + (1 1)( 10)] 1140 [a + 11( 10)] 1140 a a 00 a a 00 a 150 The first instalment is ` 150. ii. Let the three boys be B 1, B, B and the two girls be G 1 and G. A committee of two is to be formed. The sample space is S {B 1 B, B 1 B, B 1 G 1, B 1 G, B B, B G 1, B G, B G 1, B G, G 1 G } n(s) 10 a. Let A be the event that the committee contains at least one girl. A{B 1 G 1, B 1 G, B G 1, B G, B G 1, B G, G 1 G } n(a) 7 P(A) n(a) n(s) 7 10 b. Let B be the event that the committee contains one boy and one girl. B {B 1 G 1, B 1 G, B G 1, B G, B G 1, B G } n(b) P(B) n(b) n(s) 10 5 c. Let C be the event that the committee contains only boys. C {B 1 B, B 1 B, B B } n(c) P(C) n(c) n(s) 10 iii. a. Sales of A ` 1,000 But, sales of A centralanglefor A Total sale Totalsale Total sale ` 7,000. 5

6 Board Answer Paper: March 014 b. Sales of B centralanglefor B Total sale ` 4,000 Sales of C centralanglefor C Total sale ` 1,000 Sales of D centralanglefor D Total sale ` 14,000 c. Salesman B is the salesman with the highest sale. d. The difference between the highest sale and the lowest sale 4,000 14,000 ` 10, Attempt any two of the following subquestions: i. According to the given condition, mt m nt n m[a + (m 1)d] n[a + (n 1)d] ma + md(m 1) na + nd(n 1) ma + m d md na + n d nd ma + m d md na n d + nd 0 (ma na) + (m d n d) (md nd) 0 a(m n) + d(m n ) d(m n) 0 a(m n) + d(m + n) (m n) d(m n) 0 (m n)[a + d(m + n) d] 0 [a+ d(m + n 1)] 0 [Dividing by (m n)] t (m + n) 0 ii. Let the four consecutive natural numbers which are multiple of five be x, x + 5, x + 10, x According to the given condition, x(x + 5) (x + 10) (x + 15) [x(x + 15)] [(x + 5) (x + 10)] (x + 15x) (x + 10x + 5x + 50) (x + 15x) (x + 15x + 50) Let x + 15x a a(a + 50) a + 50a a + 150a 100a a(a + 150) 100(a + 150) 0

7 Algebra (a 100) (a + 150) 0 a or a a 100 or a 150 As x is a natural number. x > 0 x > 0 x + 15x > 0 As x + 15x a a > 0 a 150 a 100 But, a x + 15x x + 15x 100 x + 15x x + 0x 5x x(x + 0) 5(x + 0) 0 (x + 0) (x 5) 0 x or x 5 0 x 0 or x 5 But, x cannot be negative. x 5 x , x and x The four consecutive natural numbers which are multiples of 5 are 5, 10, 15, 0. iii. The given simultaneous equations are 4x + y 4. (i) and y 4x + 4. (ii) From equation (i), y 4 4x y 4 4 x x 0 y 4 0 (x, y) (0, ) (, 4) (, 0) From equation (ii), y 4 x + 4 x 0 y 4 0 (x, y) (0, ) (, 4) (, 0) 7

8 Board Answer Paper: March 014 Y Scale : On both the axes 1 cm 1 unit 10 9 B(0, ) 7 (, 4) 5 4 (, 4) A(, 0) X 1 O(0,0) C(, 0) X 1 Y [] The point of intersection of given lines is (0, ). From the graph, we get ABC, where BO is the height of the triangle and AC is the base. Now, l(ac) 1 cm and l(bo) cm Area of triangle 1 base height Area of ABC 1 l(ac) l(bo) Area of ABC 4 cm

BOARD QUESTION PAPER : JULY 2017 ALGEBRA

BOARD QUESTION PAPER : JULY 2017 ALGEBRA BOARD QUESTION PAPER : JULY 017 ALGEBRA Time : Hours Total Marks : 40 Note: (i) (ii) All questions are compulsory. Use of calculator is not allowed. Q.1 Attempt any five of the following sub - questions