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

Find a vector of magnitude 20 units parallel to the vector `2hati + 5hatj + 4hatk`.

A company sells hand towels at ₹ 100 per unit. The fixed cost for the company to manufacture hand towels is ₹ 35,000 and variable cost is estimated to be 30% of total revenue. What will be the total cost function for manufacturing hand towels?

XYZ company plans to advertise some vacancies. The Manager is asked to suggest the monthly salary for these vacancies based on the years of experience. To do so, the Manager studies the years of service and the monthly salary drawn by the existing employees in the company.

Following is the data that the Manager refers to:

1. Find the regression equation of monthly salary on the years of service.
2. If a person with 13 years of experience applies for a job in this company, what monthly salary will be suggested by the Manager?

The graph of the function f is shown below.

Of the following options, at what values of x is the function f NOT differentiable?

Consider the graph `y = x^(1/3)`

Statement 1: The above graph is continuous at x = 0

Statement 2: The above graph is differentiable at x = 0

Which of the following is correct?

There are three machines and 2 of them are faulty. They are tested one by one in a random order till both the faulty machines are identified. What is the probability that only two tests are needed to identify the faulty machines?

Find a vector of magnitude 9 units and perpendicular to the vectors.

`veca = 4hati - hatj + hatk` and `vecb = -2hati + hatj - 2hatk`

The value of `dy/dx` if y = |x – 1| + |x – 4| at x = 3 is ______.

Using the method of integration, find the area of the triangular region whose vertices are (2, -2), (4, 3) and (1, 2).

Determine the value of 'k' for which the following function is continuous at x = 3

`f(x) = {(((x + 3)^2 - 36)/(x - 3),  x != 3), (k,  x = 3):}`

The binary operation *: R x R → R is defined as a *b = 2a + b Find (2 * 3)*4

Draw a rough sketch of the curve and find the area of the region bounded by curve y² = 8x and the line x =2.

Sketch the graph of y = |x + 4|. Using integration, find the area of the region bounded by the curve y = |x + 4| and x = –6 and x = 0.

Find the shortest distance between the lines `vec r = hat i + 2hat j + 3 hat k +  lambda(2 hat i +  3hatj +  4hatk)` and `vec r =  2hat i +  4 hat j + 5 hat k +  mu (4hat i + 6 hat j +  8 hat k)`

The average cost function, AC for a commodity is given by AC = `x + 5 + 36/x` in terms of output x. Find

1) The total cost, C and marginal cost, MC as a function of x.

2) The outputs for which AC increases

`f(x)=(x^2-9)/(x - 3)` is not defined at x = 3. what value should be assigned to f(3) for continuity of f(x) at = 3?

A 13 m long ladder is leaning against a wall, touching the wall at a certain height from the ground level. The bottom of the ladder is pulled away from the wall, along the ground, at the rate of 2 m/s. How fast is the height on the wall decreasing when the foot of the ladder is 5 m away from the wall?

Evaluate:  `int (x(1+x^2))/(1+x^4)dx`

If `veca` and `vecb` are non- collinear vectors, find the value of x such that the vectors `barα = (x - 2)veca + vecb` and `barβ = (3+2x)bara - 2barb` are collinear.

Discuss the continuity of the function f at x = 0

If f(x) = `(2^(3x) - 1)/tanx`, for x ≠ 0

         = 1,   for x = 0