If l + m + n=0, which of the following conditions must l, m and n satisfy so that the system of simultaneous linear equations x + 3y -4z = l, 2x - y - z = m, x + y - 2z = n has at least one ?

If 2x – ky + z = 0 is a factor of 9y²– z² – 2xz + 6xy, then the value of k is equal to

A ship 55 kms. From the shore springs a leak which admits 2 tones of water in 6 min; 80 tones would suffer to sink her, but the pumps can throw out 12 tones an hour. Find the average rate of sailing that she may just reach the shore as she begins to sink.

. If the roots, x₁,and x₂, of the quadratic equation x² - 2x + c = 0 also satisfy the equation 7_x2 - 4_x1 = 47, then which of the following is true?

A man purchased 40 fruits; apples and oranges for Rs 17. Had he purchased as many as oranges as apples and as many apples as oranges, he would have paid Rs 15. Find the cost of one pair of an apple and an orange

A singles tennis tournament is held, in which 30 men participated. If a player is eliminated as soon as he loses a match, how many matches are required to determine the winner

P lent Rs.600 to Q for 2 years and Rs.150 to R for 4 years and received altogether from both Rs.90 as interest. Find the rate of interest, simple interest being calculated

For prime numbers p and q, p + q = 102 and p > q. What is the least possible value of p − q?

If a₁ = 1 and a_n+1 = 2a_n + 5, n = 1, 2 ...., then a₁₀₀ is equal to :

If x + y = 2, then the value of x⁴ + y⁴ – x³ y² – x² y³+16xy is equal to