For in [5, 7]

The value of 'c' in Lagrange's mean value theorem for in [0, 1] is

The value of 'c' in Lagrange's mean value theorem for in [0, 2] is

The equation represents

The polar equation of the circle whose end points of the diameter are and is

The radius of the circle is

The adjoining figure shows the graph of Then –

Graph of y = ax² + bx + c = 0 is given adjacently. What conclusions can be drawn from this graph –

Here we can see that the graph was given to us and us to take out the conclusion from that since we have the options available so I would suggest you to always start to check from the options because by the use of options we can see how easily we concluded this question.

For the quadratic polynomial f (x) = 4x² – 8kx + k, the statements which hold good are

The graph of the quadratic polynomial y = ax² + bx + c is as shown in the figure. Then :

The roots (also called as zeros, y = 0) of the quadratic equation  are given by x =  . The quantity  is called the discriminant of the equation and determines the nature of its roots.
If   ≥ 0, the roots are real.
If   = 0, the roots are real and equal.
If   < 0, the roots are complex and conjugates of each other.

The greatest possible number of points of intersections of 8 straight line and 4 circles is :

The students can make an error if they don’t know about the formula for calculating the number of points as mentioned in the hint which is as follows
The number point of intersection between two lines can be counted by finding the number of ways in which two lines can be selected out of the lot as two lines can intersect at most one point.
The number point of intersection between two circles can be counted by finding the number of ways in which two circles can be selected out of the lot multiplied by 2 as two circles can intersect at most two points.
The number point of intersection between two circles can be counted by finding the number of ways in which one circle and one line can be selected out of the lot multiplied by 2 as one circle and one line can intersect at most two points.

How many different nine digit numbers can be formed from the number 223355888 by rearranging its digits so that the odd digits occupy even position ?

Here we have obtained the total number of 9 digit numbers using the given digits. While finding the number of ways to arrange the odd digits in 5 even places, we have divided the 4! by 2! because the digit 3 were occurring two times and the digit 5 were occurring 2 times. Here we can make a mistake by conserving the number of even digits 4 and the number of odd digits 5, which will result in the wrong answer.

A person predicts the outcome of 20 cricket matches of his home team. Each match can result either in a win, loss or tie for the home team. Total number of ways in which he can make the predictions so that exactly 10 predictions are correct, is equal to :

The foot of the perpendicular from the point on the line is

The point of intersection of the lines is

The line passing through and perpendicular to is