Mathematics Tes...

On [1, e], the least and greatest values of f(x) = x² log x is :

One vertex of the equilateral triangle with centroid at the origin and one side as x + y – 2 = 0 can be

The value of 'a' for which both the roots of the equation (1−a²)x²+2ax−1=0 lie between 0 and 1 are given by

For all real values of a and b, lines (2a + b)x + (a + 3b)y + (b - 3a) = 0 and mx + 2y + 6 = 0 are concurrent, then m is equal to

The coefficient of x⁵ in the expansion of (1 + x)²¹ + (1 +x)²² +.......+(1 + x)³⁰  is

The locus of the centers of the circles which cut the circles x²+y²+4x−6y+9=0 and x²+y²−5x+4y−2=0 orthogonally is :

If triangle has vertices (1, 1, 1), (2, 2, 2), (1, 1, y) and the area equal to$$cosec(π/4)sq. units. Find the value of y is/are

Two towns A and B are 60 km apart. A school is to be built to serve 150 students in town A and 50 students in town B. If the total distance to be travelled by all 200 students is to be as small as possible, then the school should be built at :

The area bounded by $y=\frac{\sin x}{x}$,x-axis and x = 0, $\text{x}=$$\frac{\mathrm{\pi }}{4}$ ; x=0,x=$\frac{\pi }{4}$

The equation of the line passing through (1, 1, -1) and perpendicular to the plane x - 2y - 3z = 7 is :