Solve x ( x + 5 ) ( x + 7 ) ( x + 12 ) = - 150
[6 marks]Solve the following system of linear equations using Cramer’s rule x + y + z = 4, 2x - 3y + 4z = 33 and 3x -2y -2z =
[2 marks]Solve the following simultaneous equations x2 + y2 = 185 ; x + y = 19
[5 marks]Solve by Matrix Inversion method. -3x + 6x -11x =123 3x - 4x + 6x = -5123 4x - 8x + 13x = -17123
[14 marks]Using theorems prove that x y z |x2 y2 z2 |= xyz (x - y) ( - z ) (z – x ) x3 y3 z
[3 marks]Atwo digit number is four times the sum and three times the product of its digits. Find the number.
[5 marks]Calculate the mean and standard deviation from the following data Age 20-30 30-40 40-50 50-60 60-70 70-80 80-90 No. of 3 61 132 153 140 51 members
[2 marks]Calculate the mode and median for the following data. Class 0-10 10-20 20-30 30-40 40-50 Frequency 10 14 19 17 13
[5 marks]The number Nof bacteria in a culture grew at the rate proportional to N. The value of Nwas initially 100 and increased to 332 in one hour. What will be the value of Nafter 1.5 hours?
[5 marks]Do as directed
[6 marks]Find the value of tan 22 1°/2 (ii) Evaluate tan 13𝜋12
[ marks]Cos + Sin = √2 Cos , show that Cos - Sin = √2 Sin
[5 marks]Prove that cos4A – sin4A = 1 – 2sin2A
[5 marks]If sin 𝛼 = 1 and cos𝛽 = 3 and if 0 α, β 𝜋 , then prove that α+ β = 𝜋 . √5 √10 2
[4 marks]Solve (xy2 +x)dx+(yx2 +y)dy = 0
[5 marks]Apopulation grows at the rate of 8% per year. How long does it take for the population to double? Q. 6 (a) If xy = ex - y, prove that dy/dx = log x /(log ex)2
[6 marks]Evaluate: ∫ 3x−5 x2−x−2
[5 marks]Solve : (x2 – y2) dy =2xy dx
[5 marks]In a group of students there are 4 girls and 6 boys. In how many ways a committee of five members can be formed such that I. There are at least 3 girls II. There are at the most 3 boys in the committee.
[6 marks]Find the equation of the line passing through the points (2, 3) and (5, -2).
[5 marks]Find the area of the triangle whose vertices are (4, 4), (3, -2), (-3, 16).
[5 marks]