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

Integrate the functions:

cot x log sin x

Integrate the functions:

`sin x/(1+ cos x)`

Integrate the functions:

`(sin x)/(1+ cos x)^2`

Integrate the functions:

`1/(1 + cot x)`

Integrate the functions:

`1/(1 - tan x)`

Integrate the functions:

`sqrt(tanx)/(sinxcos x)`

Integrate the functions:

`(1+ log x)^2/x`

Integrate the functions:

`((x+1)(x + logx)^2)/x`

Integrate the functions:

`(x^3 sin(tan^(-1) x^4))/(1 + x^8)`

`(10x^9 + 10^x log_e 10)/(x^10 + 10^x)  dx` equals:

`int (dx)/(sin^2 x cos^2 x)` equals:

Of the students in a school, it is known that 30% have 100% attendance and 70% students are irregular. Previous year results report that 70% of all students who have 100% attendance attain A grade and 10% irregular students attain A grade in their annual examination. At the end of the year, one student is chos~n at random from the school and he was found ·to have an A grade. What is the probability that the student has 100% attendance? Is regularity required only in school? Justify your answer

Prove that `tan {pi/4 + 1/2 cos^(-1)  a/b} + tan {pi/4 - 1/2 cos^(-1)  a/b} = (2b)/a`

Often it is taken that a truthful person commands, more respect in the society. A man is known to speak the truth 4 out of 5 times. He throws a die and reports that it is a six. Find the probability that it is actually a six.

Do you also agree that the value of truthfulness leads to more respect in the society?

if A =  `((2,3,10),(4,-6,5),(6,9,-20))`, Find `A^(-1)`. Using `A^(-1)` Solve the system of equation `2/x + 3/y +10/z = 2`; `4/x - 6/y + 5/z = 5`; `6/x + 9/y - 20/z = -4`

Solve the following equation for x:  `cos (tan^(-1) x) = sin (cot^(-1)  3/4)`

Prove that `3sin^(-1)x = sin^(-1) (3x - 4x^3)`, `x in [-1/2, 1/2]`

Find the shortest distance between the lines `vecr = (4hati - hatj) + lambda(hati+2hatj-3hatk)` and `vecr = (hati - hatj + 2hatk) + mu(2hati + 4hatj - 5hatk)`

Suppose a girl throws a die. If she gets 1 or 2 she tosses a coin three times and notes the number of tails. If she gets 3,4,5 or 6, she tosses a coin once and notes whether a ‘head’ or ‘tail’ is obtained. If she obtained exactly one ‘tail’, what is the probability that she threw 3,4,5 or 6 with the die ?

Show that the function f: ℝ → ℝ defined by f(x) = `x/(x^2 + 1), ∀x in R`is neither one-one nor onto. Also, if g: ℝ → ℝ is defined as g(x) = 2x - 1. Find fog(x)