ISC (Arts) Class 12 - CISCE Question Bank Solutions for Mathematics

Draw a rough sketch of the curve y² = 4x and find the area of region enclosed by the curve and the line y = x.

Find the value of λ for which the four points with position vectors `6hat"i" - 7hat"j", 16hat"i" - 19hat"j" - 4hat"k" , lambdahat"j" - 6hat"k"  "and"  2hat"i" - 5hat"j" + 10hat"k"` are coplanar.

Find the equation of the standard ellipse, taking its axes as the coordinate axes, whose minor axis is equal to the distance between the foci and whose length of the latus rectum is 10. Also, find its eccentricity. 

Find the equation of the parabola with latus-rectum joining points (4, 6) and (4, -2).

Sketch the graphs of the curves y² = x and y² = 4 – 3x and find the area enclosed between them. 

The price of relatives and weights of a set of commodities are given below:

If the sum of the weights is 40 and the weighted average of price relatives index number is 122, find the numerical values of x and y.

Construct 3 yearly moving averages from the following data and show on a graph against the original data: 

Find the area of the region bound by the curves y = 6x – x² and y = x² – 2x 

Find a unit vector perpendicular to each of the vectors `veca + vecb  "and"  veca - vecb  "where"  veca = 3hati + 2hatj + 2hatk and vecb = i + 2hatj - 2hatk` 

The order and degree of `((dy)/(dx))^3 - (d^3y)/(dx^3) + ye^x` = 0 are ______.

The power of highest ordered derivative when all the derivatives are made free from negative and/or fractional indices if any is called ______ of the differential equation

The order and degree of the differential equation `[1 + ((dy)/(dx))^2] = (d^2y)/(dx^2)` are ______.

The degree of the differential equation `("d"^2"y")/("dx"^2) + 3("dy"/"dx")^2 = "x"^2 (("d"^2"y")/("dx"^2))^2` is:

Using integration, find the area of the region bounded between the line x = 4 and the parabola y² = 16x.

A relation R on (1, 2, 3) is given by R = {(1, 1), (2, 2), (1, 2), (3, 3), (2, 3)}. Then the relation R is ______.

If the following function is continuous at x = 2 then the value of k will be ______.

f(x) = `{{:(2x + 1",", if x < 2),(                 k",", if x = 2),(3x - 1",", if x > 2):}`

An edge of a variable cube is increasing at the rate of 10 cm/sec. How fast will the volume of the cube increase if the edge is 5 cm long? 

If `|veca| = 3, |vecb| = sqrt(2)/3` and `veca xx vecb` is a unit vector then the angle between `veca` and `vecb` will be ______.

If A(1, 2, – 3) and B(– 1, – 2, 1) are the end points of a vector `vec("AB")` then find the unit vector in the direction of `vec("AB")`.

If `hata` is unit vector and `(2vecx - 3hata)*(2vecx + 3hata)` = 91, find the value of `|vecx|`.