Title XI - maths - chapter 10 - Solutions Pair of Straight Lines)-iii.pdf ✅

X-Mathematics e-Techno Text Book Nishith Multimedia India (Pvt.) Ltd. 54 PAIR OF STRAIGHT LINES Worksheet -1 PAIR OF STRAIGHT LINES LEVEL-1 SINGLE CORRECT CHOICE TYPE: 1. Key : 1 Sol. Required equation is (2x + y) (x + 2y) = 0 2 2     2x 5xy 2y 0 2. Key : 3 Sol.     2 2 2 2 3x 5xy 2y 0 3x 3xy 2xy 2y 0 3x x y 2y x y 0                      x y 3x 2y 0; x y 0; 3x 2y 0   3. Key : 3 Sol.     2 2 2 a b 1 1 2 1 1 cos cos 4 2 2 3 a b 4h 1 1 16                   4. Key : 1 Sol. Sum of the slopes 5 5 1   MULTI CORRECT CHOICE TYPE: 5. Key : 1, 3 Sol.    2 2 2 2 6x xy 4cy 3x 4y kx 3y 3kx 9xy 4kxy 12y            2 2             3kx xy 9 4k 12y ; 3k 6 k 2; 12 4c c 3 REASONING TYPE: 6. Key : 1 Sol.   2 2 a b cos a b 4h      COMPREHENSION TYPE: 7. Key : 4 Sol. 2 2 x 3xy 4y 0    ;     2 2 2 2 a b 1 4 3 3 cos a b 4h 3 25 9 34 1 4 4 2                     8. Key : 3
X-Mathematics e-Techno Text Book Nishith Multimedia India (Pvt.) Ltd. 55 Sol. 2 2 2x 7xy 3y 0    ;   2 2 a b 5 5 5 1 cos a b 4h 1 49 50 5 2 2           1 cos 2 4       9. Key : 2 Sol. 2 2 3x 11xy 3y 0    ; 9 9 7 cos tan 9 121 130 9        MATRIX MATCH TYPE: 10. Key: 1)q; 2)r; 3)s; 4)p a)    2 2 2 2 ax 2hxy by k y m x y m x k y m xy m xy m m x 1 2 2 1 1 2                2 2 2 2 1 2 1 2 a 2h b x xy y k m m x xy m m y b b                  ii) 1 2 1 2 1 2 2h 1 1 2h m m b m m m m a a b        iii) 1 2 1 2 a 2h m m : m m b b     iv)     2 2 2 2 1 2 1 2 1 2 2 2 4h 4a h ab m m m m 4m m 4 b b b               2 1 2 2 h ab m m b     LEVEL-2 SINGLE CORRECT CHOICE TYPE: 11. Key : 3 Sol. Sum of the slopes = 4 (Product of the slopes) 2c 1 4 2c 4 c 2 7 7          12. Key : 1, 2, 3 Sol. 2 2 3x 8xy 3y 0    ; a = 3, b = – 3, h = – 4 1 2 1 2 2h 8 8 a m m ; m m 1 b 3 3 b           
X-Mathematics e-Techno Text Book Nishith Multimedia India (Pvt.) Ltd. 56 2 1 2 2 h ab 2 16 9 10 10 m m b 3 3 3           LEVEL-3 SINGLE CORRECT CHOICE TYPE: 13. Key : 1 Sol. 2y cosec 4yz 1 2 x 2y cosec 2y cosec 1 2 2                         y cosec y cot ; x y cosec cot    The two lines are x y cosec cot 0        and x y cosec cot 0        MATRIX MATCH TYPE: 14. Key: 1)p; 2)q; 3)r; 4)s Sol. 1) 2 2 2x 5xy 2y 0    ; 5 h 2  5 a 2, h , b 2 2    2 25 2 25 16 2 4 2 h ab 3 4 2 tan a b 4 4 4          2) 2 2 2x 5xy 2y 0    a = b = 2, 5 h 2    2 2 a b 4 4 cos 0 25 5 a b 4h         3) 2 xy y 0   ; a = 0, b = 1, 1 h 2    2 2 2 a b 1 1 1 cos cos sin 1 cos a b 4h 1 1 2 2                 4) 2 2 x 7xy 12y 0    a = 1, b = 12, 7 h 2   2 169 1 sin 1 cos 1 170 170       
X-Mathematics e-Techno Text Book Nishith Multimedia India (Pvt.) Ltd. 57 36 3 2cos 3sin 39 170 170 4sin 5cos 69 4 65 170 170            LEVEL-4 SINGLE CORRECT CHOICE TYPE: 15. Key : 1 Sol. Required equation is 0 0     y tan30 x y tan60 x 0             x xy 2 2 2 2 y y 3 x 0 y 3 xy x 0 x y 3 4xy 3 3                        REASONING TYPE: 16. Key : 3 LEVEL-5 SINGLE CORRECT CHOICE TYPE: 17. Key : 2 COMPREHENSION TYPE: 18. Key : 1 Sol. A – B = 0 is   2 2 2 2 2x 20xy 8y 2x 4xy 3y       2 2 2 2 2 2 2x 20xy 8y 2x 4xy 3y 4x 24xy 11y                2 2 4x 2xy 22xy 11y 2x 2x y 11y 2x y 2x y 2x 11y           19. Key : 3 Sol.     2 2 2 2 ab x y a b xy 0     ; 2 2 2 2 abx b xy a xy aby 0     bx ax by ay ax by 0         ; ax by bx ay 0      20. Key : 3 Sol. 2 2 x 2xy sec y 0     ; 2 2 y 2xy sec x 0     2 2 2 2xsec 4x sec 4x y 2      ; 2 y xsec x sec 1       y x sec x tan      y xsec x tan or xsec x tan              y x tan sec and y x sec tan              Worksheet -2 PAIR OF STRAIGHT LINES