Let `m=t a n3\ a n d\ n=s e c6,\ ` then which of the following statement(s) does/do not hold goods? (a).`m\ &\ n\ ` both are positive (b). `m\ &\ n` both are negative (c).`m` is positive and `n` is negative (d). `m` is negative and `n` is positive

If a ,b ,c in R a n d a b c<0 , then equation b c x^2+(2b+c-a)x+a=0 h a s (a). both positive roots (b). both negative roots (c). real roots (d) one positive and one negative root

Let m and n be 2 positive integers, such that m < n . Which of the following compound inequalities must be true?

(x+1) is a factor of x^n+1 only if (a)n is an odd integer (b) n is an even integer (c )n is a negative integer (d)n is a positive integer

Find the sign of the product if we multiply: i. 2m+1 times (-1) where m is a natural number. ii. 2n positive numbers and 2m+1 negative numbers iii. 2n+1 positive numbers and 2m negative numbers

For 3xx3 matrices M \ a n d \ N , which of the following statement (s) is (are) NOT correct ? Statement - I : N^T M N is symmetricor skew-symmetric, according as M is symmetric or skew-symmetric. Statement - II : M N-N M is skew-symmetric for all symmetric matrices Ma n dN . Statement - III : M N is symmetric for all symmetric matrices M a n dN . Statement - IV : (a d jM)(a d jN)=a d j(M N) for all invertible matrices Ma n dN .

Show that if a and b are relatively prime positive integers, these there exist integers m and n such that a^(m)+b^(n) -=1 (mod ab).

In Figure, B M\ a n d\ D N are both perpendiculars to the segments A C\ a n d\ B M=D N . Prove that A C\ bisects B D .

Let S(M) denote the sum of the digits of a positive integer M written in base 10. Let N be the smallest positive integer such that S(N) = 2017. Find the value of S(5N + 2017)

The number of ordered pairs of positive integers (m,n) satisfying m le 2n le 60 , n le 2m le 60 is

If tantheta=sqrt(n), where n in N ,geq2,t h e nsec2theta is always a rational number (b) an irrational number a positive integer (d) a negative integer