Statement-I : If , then

is equal to

is equal to-

Statement The sum of the series 1+(1+2+4)+(4+6+9)+(9+12+16)+…+(361+380+400) is 8000.
Statement - II : , for any natural number n.

If in a frequently distribution, the mean and median are 21 and 22 respectively, then its mode is approximately.

The negation of the statement "If I become a teacher, then I will open a school", is :

The value of the definite integral is

So here we used the concept of integrals and simplified it. We can also solve it manually but it will take lot of time to come to final answer hence we used the minimum and maximum method which makes problem to solve easily. So the answer is non of these.

Suppos ef, f' andf'' are continuous on[0, e] and that then the value of

ther

If is a point on the circle whose centre is on the x-axis and which touches the line x+y=0 at (2,-2), then the greatest value of a is

Equation of the circle of radius is

In the adjoining figure, the circle meets the sides of an equilateral triangle at six points. If AG=2,GF=13,FC=1 and HJ=7, then DE=

Two circles of unequal radii intersect in two distinct points P and Q. A line through P cuts 1st circle at A and 2nd circle at B. Let M be the mid point of AB. If the line MQ meets the 1st circle at X and the second circle at Z then M divides XZ internally in the ratio.

A circle touches the lines and has unit radius. If the centre of this circle lies in the first quadrant, then one possible equation of this circle is

From a point R(5, 8) two tangents RP and RQ are drawn to a given circle S = 0 whose radius is 5. If circumcentre of the triangle PQR is (2, 3), then the equation of circle S = 0 is

PA and PB are tangents to a circle S touching S at points A and B.C is a point on S in between A and B as shown in the figure. LCM is a tangent to S intersecting PA and PB in points L and M respectively.Then the perimeter of the triangle PLM depends on