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

 Show that the function `f(x) = |x-4|, x ∈ R` is continuous, but not diffrent at x = 4. 

Evaluate : `int(x1+x^2)/(1+x^4)dx`

Solve the differential equation  `dy/dx = (x + y+2)/(2(x+y)-1)`

 Evaluate: `int_-6^3 |x+3|dx`

Solve the following system of linear equation using matrix method: 
`1/x + 1/y +1/z = 9`

`2/x + 5/y+7/z = 52`

`2/x+1/y-1/z=0`

Draw a rough sketch and find the area bounded by the curve x² = y and x + y = 2.

Find the equation of the regression line of y on x, if the observations (x, y) are as follows : 
(1,4),(2,8),(3,2),(4,12),(5,10),(6,14),(7,16),(8,6),(9,18)
Also, find the estimated value of y when x = 14.

Write the negation of the following statements :
(a) Radha likes tea or coffee.
(b) `∃x cc` R such that x + 3 ≥ 10.

If A = `[(1,2), (1,3)]`, find A² - 3A

If y – 2x – k = 0 touches the conic 3x² – 5y² = 15, find the value of k. 

Prove that `1/2 "cos"^(-1) ((1-"x")/(1+"x")) = "tan"^-1 sqrt"x"`

A problem is given to three students whose chances of solving it are `1/4, 1/5` and `1/3` respectively. Find the probability that the problem is solved.

If a + ib = `("x" + "iy")/("x" - "iy"),` prove that `"a"^2 +"b"^2 = 1` and `"b"/"a" = (2"xy")/("x"^2 - "y"^2)`

If A, B and C are the elements of Boolean algebra, simplify the expression (A’ + B’) (A + C’) + B’ (B + C). Draw the simplified circuit.

Find the coordinates of the centre, foci and equation of directrix of the hyperbola x² – 3y² – 4x = 8.

The two lines of regressions are x + 2y – 5 = 0 and 2x + 3y – 8 = 0 and the variance of x is 12. Find the variance of y and the coefficient of correlation.

For the given lines of regression, 3x – 2y = 5 and x – 4y = 7, find:
(a) regression coefficients b_yx and b_xy
(b) coefficient of correlation r (x, y)

Calculate the Spearman’s rank correlation coefficient for the following data and interpret the result: 

A pair of dice is thrown. What is the probability of getting an even number on the first die or a total of 8?

Solve the differential equation:

`"x"("dy")/("dx")+"y"=3"x"^2-2`