mathematics Question Bank - Sarthaks eConnect

If an integer p is chosen at random in the interval `0<=p<=5`, The probability that the roots of the equation `x^2+px+p/4+1/2=0` are real is

Total number of six-digit numbers in which all and only odd digits appear is -

If all the permutations of the letters in the word 'OBJECT' are arranged (and numbered serially)
in alphabetical order as in a dictinonary, then the `717^(th)` word is-

If `|Z_1|=|Z_2|=|Z_3|=1` and `Z_1+Z_2+Z_3=0` then area of the triangle whose vertices are `Z _1,Z_2,Z_3` is-

If `a_1, a_2,...... a_15` are in A.P. and `(a_1 + a_8 + a_15) = 15`. The `a_2 + a_3 + a_8 + a_13 + a_14 = ??`

If `log_(1/2) (x^2 – 5x + 7)` > 0, then exhaustive range of values of x is

Statement-I : Statement p `=>`q and ~q is true. then p is false
Statement-II : Statement `p ->(q -> P)` is equivalent to `p ->`(p `^^` q)

The standard deviation of the set of first n natural numbers is -

If A & B are two square matrices such that `B = – A ^(–1)BA, then (A + B)^2` is equal to

20 teachers of a school either teach maths or physics, 12 of them teach mathematics while 4 teach both the subjects. Then the number of teachers teaching only physics is -

Let the sets A = {2, 4, 6, 8,....} and B = {3, 6, 9, 12,....}, and n(A) = 200, n(B) = 250. then -

Equation of incircle of equilateral triangle ABC, where B = (2, 0), C =(4, 0) and A lies in fourth quadrant is -

If the angle between tangents drawn to `x^2+y^2 –2x –4y+1=` 0 at the points where it is cut by the line y = 2x + c, is `pi/ 2`, then

A straight line passing through P(3, 1) meet the coordinate axes at A and B. It is given that distance of this straight line from the origin 'O' is maximum Area of triangle OAB is equal to

A line is drawn perpendicular to line y = 5x, meeting the co-ordinate axes at A and B. If the are of `triangle`OAB is 10 sq. units, where O is the origin, then the equation of drawn line is -

If f(x) `= cos x – cos^2 x + cos^3 x – ... oo, then int f (x)dx` is equal to -

If y = 2x – 3 is a tangent to the parabola `y^2 =4a(x-1/3)`, then 'a' is equal t-

Statement-I : f(x) =2cosx+3sinx ; g(x) `=sin^-1( x/sqrt13)-tan^-1 (3/2)`both are increasing for `x in (0,pi/2)`

Statement-II : If f(x) is increasing then`f^(–1)` (x) is also increasing

Statement-I : minimum value of `3log_10 x – log_x0.001` is 6
Statement-II : `f(x)+1/f(x)>=2` for all + ve function.

Recent questions and answers in mathematics