Mathematics Tes...

The function \(f: R \rightarrow[-1,1]\) defined by \(f(x)=\frac{|x|}{1+|x|}, x \in R\) is:

Directions: The following question has four choices, out of which ONE or MORE are correct.

The equation(s) of the straight line(s) passing through the point (3, -2) and inclined at 60° to the line √3x + y = 1 is/are:

Find the differential equation of the family of ellipse such that its centre is on the origin:

Directions: The following question has four choices, out of which ONE or MORE are correct. The point(s) of discontinuity of the function \(f(x)=\left[\frac{6 x}{\pi}\right] \cos \left[\frac{3 x}{\pi}\right],\) where \([y]\) denotes the largest integer less than or equal to \(y\), is/are:

Directions: The following question has four choices, out of which ONE or MORE are correct. Let \(P M\) be a perpendicular from the point \(P(1,2,3)\) to \(x\) -y plane. If OP makes an angle \(\theta\) with the positive direction of z-axis and OM makes an angle \(\phi\) with the positive direction of \(x\) -axis, where 0 is the origin \((\theta\) and \(\phi\) are acute angles \(),\) then:

If the sum of odd coefficients of \((1+z)^{5}\) is \(x,\) find the number of solutions of \(a+b+c+d=x\) where\(-x

The distance of the point (3,8,2) from the line

\(\frac{x-1}{2}=\frac{y-3}{4}=\frac{z-2}{3}\)

measured parallel to the plane \(3 x+2 y-2 z+15=0\) is-

The value of \(\int_{0}^{1} X(1-X)^{99} d x\) is:

The number of values of k for which the system of equations (k + 1) x + 8y = 4k and kx + (k + 3)y = 3k - 1 has infinitely many solutions is:

Directions: The following question has four choices, out of which ONE or MORE are correct.

The value(s) of 'k' for which the planes kx + 4y + z = 0, 4x + ky + 2z = 0 and 2x+ 2y + z = 0 intersect in a straight line is/are:

Directions: The following question has four choices, out of which ONE or MORE are correct.

If OT and ON are perpendiculars dropped from the origin to the tangent and normal to the curve x = a sin³ t, y = a cos³ t at an arbitrary point, then:

The eccentricity of an ellipse with its centre at the origin is 1/2. If one of the directrix is x = 4, then the equation of the ellipse is:

If the area of a triangle with vertices (-3, 0), (3, 0) and (0, k) is 9 square units, then what is the value of k?