Arts (English Medium) इयत्ता १२ - CBSE Question Bank Solutions

The Relation between the height of the plant (y in cm) with respect to exposure to sunlight is governed by the following equation y = 4x - `1/2 x^2` where x is the number of days exposed to sunlight.

If the height of the plant is 7/2 cm, the number of days it has been exposed to the sunlight is ______.

Find the vector and the cartesian equations of the plane containing the point `hati + 2hatj - hatk` and parallel to the lines `vecr = (hati + 2hatj + 2hatk) + s(2hati - 3hatj + 2hatk)` and `vecr = (3hati + hatj - 2hatk) + t(hati - 3hatj + hatk)`

If A = [a_ij] is a skew-symmetric matrix of order n, then ______.

If `[(2, 0),(5, 4)]` = P + Q, where P is symmetric, and Q is a skew-symmetric matrix, then Q is equal to ______.

Number of symmetric matrices of order 3 × 3 with each entry 1 or – 1 is ______.

The value of |A|, if A = `[(0, 2x - 1, sqrt(x)),(1 - 2x, 0, 2sqrt(x)),(-sqrt(x), -2sqrt(x), 0)]`, where x ∈ R⁺, is ______.

Prove that, for any three vector `veca,vecb,vecc [vec a+vec b,vec b+vec c,vecc+veca]=2[veca vecb vecc]`

Two schools P and Q want to award their selected students on the values of discipline, politeness and punctuality. The school P wants to award Rs x each, Rs y each and Rs z each for the three respective values to its 3, 2 and 1 students with a total award money of Rs 1,000. School Q wants to spend Rs 1,500 to award its 4, 1 and 3 students on the respective values (by giving the same award money for the three values as before). If the total amount of awards for one prize on each value is Rs 600, using matrices, find the award money for each value.
Apart from the above three values, suggest one more value for awards.

A school wants to award its students for the values of Honesty, Regularity and Hard work with a total cash award of Rs 6,000. Three times the award money for Hard work added to that given for honesty amounts to Rs 11,000. The award money given for Honesty and Hard work together is double the one given for Regularity. Represent the above situation algebraically and find the award money for each value, using matrix method. Apart from these values, namely, Honesty, Regularity and Hard work, suggest one more value which the school must include for awards.

A trust invested some money in two type of bonds. The first bond pays 10% interest and second bond pays 12% interest. The trust received Rs 2,800 as interest. However, if trust had interchanged money in bonds, they would have got Rs 100 less as interest. Using matrix method, find the amount invested by the trust. Interest received on this amount will be given to Helpage India as donation. Which value is reflected in this question?

If `A=[[2,3],[5,-2]]` then write A^-1

Show that the four points A(4, 5, 1), B(0, –1, –1), C(3, 9, 4) and D(–4, 4, 4) are coplanar.

Find λ, if the vectors `veca=hati+3hatj+hatk,vecb=2hati−hatj−hatk and vecc=λhatj+3hatk`  are coplanar.

Find the inverse of each of the matrices, if it exists. [`(1, -1),(2,3)`]

Find the inverse of each of the matrices, if it exists.` [(2,1),(1,1)]`

Find the inverse of each of the matrices, if it exists.

`[(1,3),(2,7)]`

Find the inverse of each of the matrices, if it exists. 

`[(2,3),(5,7)]`

Find the inverse of each of the matrices, if it exists.

`[(2,7),(1,4)]`

Find the inverse of each of the matrices, if it exists.

`[(2,5),(1,3)]`

Find the inverse of each of the matrices, if it exists.

`[(3,1),(5,2)]`