HSC Science (Electronics) 11th Standard - Maharashtra State Board Question Bank Solutions for Mathematics and Statistics

Find the number of seating arrangements for 3 men and 3 women to sit around a table so that exactly two women are together.

Four objects in a set of ten objects are alike. Find the number of ways of arranging them in a circular order

Fifteen persons sit around a table. Find the number of arrangements that have two specified persons not sitting side by side.

Answer the following:

There are 12 distinct points A, B, C, ....., L, in order, on a circle. Lines are drawn passing through each pair of points how many lines are there in total.

Answer the following:

There are 12 distinct points A, B, C, ....., L, in order, on a circle. Lines are drawn passing through each pair of points how many lines pass through D.

Answer the following:

There are 12 distinct points A, B, C, ....., L, in order, on a circle. Lines are drawn passing through each pair of points how many triangles are determined by lines.

Answer the following:

There are 12 distinct points A, B, C, ....., L, in order, on a circle. Lines are drawn passing through each pair of points how many triangles have on vertex C.

If 2 sin²θ + 3 sin θ = 0, find the permissible values of cos θ.

In ΔABC, A + B + C = π show that 

cos 2A + cos 2B + cos 2C = –1 – 4 cos A cos B cos C

In ΔABC, A + B + C = π show that

sin A + sin B + sin C = `4cos  "A"/2  cos  "B"/2  cos  "C"/2 `

In ΔABC, A + B + C = π show that

cos A + cos B – cos C = `4cos  "A"/2  cos  "B"/2  sin  "C"/2 - 1`

In ΔABC, A + B + C = π show that

sin²A + sin²B − sin²C = 2 sin A sin B cos C

In ΔABC, A + B + C = π show that

`sin^2  "A"/2 + sin^2  "B"/2 - sin^2  "C"/2 = 1 - 2cos  "A"/2  cos  "B"/2 sin  "C"/2`

In ΔABC, A + B + C = π show that

`tan  "A"/2 tan  "B"/2 + tan  "B"/2 tan  "C"/2 + tan  "C"/2tan  "A"/2` = 1

In ΔABC, A + B + C = π show that

`cot  "A"/2 + cot  "B"/2 + cot  "C"/2 = cot  "A"/2  cot  "B"/2 cot  "C"/2`

In ΔABC, A + B + C = π show that

tan 2A + tan 2B + tan 2C = tan 2A tan 2B tan 2C

In ΔABC, A + B + C = π show that

cos²A +cos²B – cos²C = 1 – 2 sin A sin B cos C

Select the correct option from the given alternatives :

In ∆ABC if cot A cot B cot C > 0 then the triangle is _________

Prove the following:

If sin α sin β − cos α cos β + 1 = 0 then prove cot α tan β = −1

Prove the following:

`cos  (2pi)/15 cos  (4pi)/15cos  (8pi)/15cos  (16pi)/15 = 1/16`