HSC Commerce Class 11 - Tamil Nadu Board of Secondary Education Question Bank Solutions for Business Mathematics and Statistics

Prove that:

cos 20° cos 40° cos 80° = `1/8`

Prove that:

tan 20° tan 40° tan 80° = `sqrt3`.

Prove that:

(cos α – cos β)² + (sin α – sin β)² = 4 sin² `((alpha - beta)/2)`

Prove that:

sin A sin(60° + A) sin(60° – A) = `1/4` sin 3A

Prove that:

sin (A – B) sin C + sin (B – C) sin A + sin(C – A) sin B = 0

Prove that:

2 cos `pi/13` cos \[\frac{9\pi}{13} + \text{cos} \frac{3\pi}{13} + \text{cos} \frac{5\pi}{13}\] = 0

Prove that:

`(cos 2"A" - cos 3"A")/(sin "2A" + sin "3A") = tan  "A"/2`

Prove that:

`(cos 7"A" +cos 5"A")/(sin 7"A" −sin 5"A")` = cot A

Prove that cos 20° cos 40° cos 60° cos 80° = `3/16`.

Evaluate-

cos 20° + cos 100° + cos 140°

Evaluate:

sin 50° – sin 70° + sin 10°

If cos A + cos B = `1/2` and sin A + sin B = `1/4`, prove that tan `(("A + B")/2) = 1/2`

If sin(y + z – x), sin(z + x – y), sin(x + y – z) are in A.P, then prove that tan x, tan y and tan z are in A.P.

If cosec A + sec A = cosec B + sec B prove that cot`(("A + B"))/2` = tan A tan B.

If tan θ = `1/sqrt5` and θ lies in the first quadrant then cos θ is:

The following data pertains to the marks in subjects A and B in a certain examination. Mean marks in A = 39.5, Mean marks in B = 47.5 standard deviation of marks in A = 10.8 and Standard deviation of marks in B = 16.8. coefficient of correlation between marks in A and marks in B is 0.42. Give the estimate of marks in B for the candidate who secured 52 marks in A.

X and Y are a pair of correlated variables. Ten observations of their values (X, Y) have the following results. ∑X = 55, ∑XY = 350, ∑X² = 385, ∑Y = 55, Predict the value of y when the value of X is 6.

Find the line regression of Y on X

Using the following information you are requested to

1. obtain the linear regression of Y on X
2. Estimate the level of defective parts delivered when inspection expenditure amounts to ₹ 82
   ∑X = 424, ∑Y = 363, ∑X² = 21926, ∑Y² = 15123, ∑XY = 12815, N = 10.
   Here X is the expenditure on inspection, Y is the defective parts delivered.

The following information is given.

Coefficient of correlation between X and Y is `8/15`. Find

1. The regression Coefficient of Y on X
2. The most likely value of Y when X = ₹ 100.