Let `S(k)=1+3+5+.....+(2k-1)=3+k^2` . Which of the following is true ?

Let S(k) = 1 + 3 + 5 +...+ (2k -1) = 3 + k^2 . Then which of the following is true ?

If (tan3A)/(tanA)=k(k!=1) then which of the following is not true? (a) (cosA)/(cos3A)=(k-1)/2 (b) (sin3A)/(sinA)=(2k)/(k-1) (c) (cot3A)/(cotA)=1/k (d) none of these

If 12x=k is the directrix of parabola y^2 + 4y+3x=0 , then which of the following true? (A) k=25 (B) k=0 (C) k=5 (D) k=15

(2(4k+1))/(3)ge(k(6+5)-3)/(2) Which of the following correctly describes the possible values of k in the inequality above?

Let alpha,beta and gamma be the roots of the equation x^(3)-x-1=0 . If P_(k)=(alpha)^(k)+(beta)^(k)+(gamma)^(k),kge1 , then which one of the following statements is not true?

Let S_(k) , where k = 1,2 ,....,100, denotes the sum of the infinite geometric series whose first term is (k -1)/(k!) and the common ratio is (1)/(k) . Then, the value of (100^(2))/(100!) +sum_(k=2)^(100) | (k^(2) - 3k +1) S_(k)| is....

yltx+k_(1) ygt2x+k_(2) Suppose that on a coordinate plane (0, 0) is a solution to the system of inequalities given above. Which of the following conclusions about k_(1) and k_(2) must be true?

Find the value of 'k' for which the following matrices are invertible ? (i) |{:(6,k),(-2,1):}| (ii) |{:(0,k,3),(1,-2,2),(4,3,-1):}|

Let S_k,k=1, 2, …. 100 denote the sum of the infinite geometric series whose first term is (k-1)/(K!) and the common ration is 1/k then the value of (100)^2/(100!)+ Sigma_(k=1)^(100) |(k^2-3k+1)S_k| is ____________

Let A and B be two fixed points and P , another point in the plane, moves in such a way that k_(1)PA+k_(2)PB=k_(3) , where k_(1) , k_(2) and k_(3) are real constants. The locus of P is Which one of the above is not true ?