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11th Standard English Medium Business Maths Subject Creative 5 Mark Questions with Solution Part - I

11th Standard

    Reg.No. :
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Business Maths

Time : 00:30:00 Hrs
Total Marks : 50
    10 x 5 = 50
  1. Without expanding show that \(\Delta =\left| \begin{matrix} { cosec }^{ 2 }\theta & { cot }^{ 2 }\theta & 1 \\ { cot }^{ 2 }\theta & { cosec }^{ 2 }\theta & -1 \\ 42 & 40 & 2 \end{matrix} \right| =0\)

  2. In how many ways can the following prizes be given away to a class of 30 students, first and second in mathematics, first and second in physics, first in chemistry and first in English?

  3. Prove that the tangents to the circle x2 + y= 169 at (5,12) and (12,-5) are perpendicular to each other.

  4. Prove that (sin 3x + sin x) sin x + (cos 3x - cos x) cos x = 0.

  5. If the function \(f\left( x \right) =\begin{cases} 6ax+3b\quad if\quad x>1 \\ ax-2b\quad if\quad x<1\quad is\quad continuous\quad at\quad x=1 \\ 15\quad if\quad x=1 \end{cases}\) Find the value of a and b.

  6. Find the maximum and minimum values of x3-6x2+7

  7. A man, deposits Rs.75 at the end of 6 months in a bank which pays interest at 8% compounded semiannually. How much is to his credit at the end of 10 years?

  8. A factory has 3 machines A1, A2, A3 producing 1000, 2000, 3000 bolts per day respectively. A1 produces 1% defectives, A2 produces 1.5% and A3 produces 2% defectives. A bolt is chosen at random and found defective. What is the probability that it comes from machine A1?

  9. Obtain the two regression lines from the following

    X 6 2 10 4 8
    Y 9 11 5 8 7
  10. Reshma wishes to mix two types of food P and Q in such a way that the Vitamin contents of the mixture contain at least 8 units of vitamin A and 11 units of vitamin B. Food P costs Rs.60/kg and Food Q costs Rs.80/kg. Food P contains 3 units 1 kg of vitamin A and 5 units 1 kg of vitamin B while food Q contains 4 units 1 kg of vitamin A and 2 units 1 kg of vitamin B. Determine the minimum cost of the mixture.

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