ISC (Commerce) इयत्ता १२ - CISCE Important Questions

Using the matrix method, solve the following system of linear equations:

`2/x + 3/y + 10/z` = 4, `4/x - 6/y + 5/z` = 1, `6/x + 9/y - 20/z` = 2.

 If x=a sin 2t(1+cos 2t) and y=b cos 2t(1−cos 2t), find `dy/dx `

If y = e^ax. cos bx, then prove that

`(d^2y)/(dx^2) - 2ady/dx + (a^2 + b^2)y` = 0

Show that the semi-vertical angle of the cone of the maximum volume and of given slant height is `cos^(-1)(1/sqrt3)`

Show that the height of the cylinder of maximum volume, that can be inscribed in a sphere of radius R is `(2R)/sqrt3.`  Also, find the maximum volume.

Prove that the semi-vertical angle of the right circular cone of given volume and least curved surface is \[\cot^{- 1} \left( \sqrt{2} \right)\] .

If logy = tan^–1 x, then show that `(1+x^2) (d^2y)/(dx^2) + (2x - 1) dy/dx = 0 .`

Evaluate `∫_0^(3/2)|x cosπx|dx`

Evaluate:

\[\int \cos^{-1} \left(\sin x \right) \text{dx}\]

Find the particular solution of the differential equation:

2y e^x/y dx + (y - 2x e^x/y) dy = 0 given that x = 0 when y = 1.

Prove by vector method, that the angle subtended on semicircle is a right angle.

If the direction cosines of a line are `(1/c, 1/c, 1/c)` then ______.

 Find the equation of the lines passing through the point (2, 1, 3) and perpendicular to the lines

A monopolist's demand function is `x = 60 - p/5`. At what level of output will marginal revenue be zero?

For 50 students of a class, the regression equation of marks in statistics (X) on the marks in accountancy (Y) is 3y – 5x + 180 = 0. The mean marks in accountancy is 44 and the variance of marks in statistics is `(9/16)^(th)` of the variance of marks in accountancy. Find the mean marks in statistics and the correlation coefficient between marks in the two subjects.

What is rehabilitation?

Explain the following term in cricket:

Sight screen

Explain the following term in cricket:

Bump ball

Explain the following term in cricket:

An appeal

Explain the following term:

Technical foul