Mathematics Times – July 2019

Sequence and Series 1.For each positive real number , let A be the set of all natural numbers n such that sin n 1 sin( ) n ...

Let a i j k  6 3 6     and d i j k       . Suppose that a b c    where b  is parallel to d  and c  is p ...

3.Suppose (c)  ˆ (d) may or may not be equal to ˆ a a a 1 , , , , 2 3 a 2012 are integers arranged on a circle. Each numbe ...

[2011] [2010] [2010] Suppose log logab ba c .The smallest possible integer value of c for all a b, 1 is [2011] ...

2.Sol: Given that 3 2 4 1 ( ) n k ak bk ck d n       3 2 4 1 1 1 1 n n n n k k k k a k b k c k d n            ...

a 0  0 so 3 1^2010 n 2 a  . As we have 3 1^5  mod (11), that is 32010 (3 ) 15 402 mod(11). Therefore 3 1 0^2010   mod(11 ...

So that 1 cos 3    and finally, we get cos^11 3          . 5.Sol: Given that v v v v1 2 3 4, , ,     are unit v ...

we get a c b       and also, we have b c c a       That is a c c c a           after simplyfing , we get ...

3.Sol: Miscellaneous 1.Sol: 2.Sol: 3.Sol: 1 2 3 x x x ... xn n       and 2 2 2 x x 1 2 ... xn n      Also given mean ...

: (1) Number of scalene triangles: 13 3 283 3        (2) Number of isosceles triangle: 13 2 4 152 2         ...

in the n-gon. An n-gon will have exterior angles of 360 n (the sum of all the exterior angles must add up to 360 degrees). Consi ...

Therefore there are four distinct pairs, that satisfy the simultaneous equations. 6.Sol: In general ,we obtain , for n n^3    ...

11.Sol: 12.Sol: the smallest possible integer value of c is 2. 11.Sol: Rewrite the given equation cos 1 sin^7  ^4  Since sin ...

32 DETERMINANTS [ONLINE QUESTIONS] The number of values of k for which the system of linear equations, ( 2) 10k x y k   kx k ...

(a) Both the statements are true (b) Both the statements are false (c) Statement-I is true, but Statement-II is false. (d) State ...

Statement-1: Statement-2: (a) Statement-1 is true; Statement-2 is false. (b) Statement-1 is true; Statement-2 is true; Statement ...

If 5 is equal to : [2016] (a) 4 (b) 13 (c) (c) 51 63 84 72       (d) 51 84 63 72       3 2 a b A        an ...

If (b) f'' 2 f' 2 0  (c) f'' 2 f' 2 4  (d) f^2 f' 2 f'' 2 0  2 15 2 15 y x x   1   x x 1 , ...

16.Let (a) 1 3 (b) 1 3  (c)^1 13  (d)^1 13 f x x x g x  ,  sinx and h x gof x   . Then [2014] (a) 17.Let for h x ...

CONTINUITY & DIFFERENTIABILITY [ONLINE QUESTIONS] b 2. b 3. c 4. b 5. b d 7. a 8. d 9. c 10. b d 12. b 13. b 14. c 15. a c ...