\(\frac { tan\theta }{ sec\theta } +\frac { tan\theta }{ sec\theta +1 } \) is equal to

It S₁ denotes the total surface area of a sphere of radius r and S₂ denotes the total surface area of a cylinder of base radius r and height 2r, then ___________

Find the slope of the line 2y = x + 8 ____________

In a triangle, the internal bisector of an angle bisects the opposite side. Find the nature of the triangle.

\(\frac { { x }^{ 2 }+7x12 }{ { x }^{ 2 }+8x+15 } \times \frac { { x }^{ 2 }+5x }{ { x }^{ 2 }+6x+8 } =\_ \_ \_ \_ \_ \_ \_ \_ \_ \)

Given a₁ = -1, \(a=\frac { { a }_{ n } }{ n+2 } \), then a₄ is ____________

If f(x) = mx + n, when m and n are integers f(-2) = 7, and f(3) = 2 then m and n are equal to ___________

The mean of first first 10 odd natural number is ___________

If cos9∝ = sin∝ and 9∝ < 90^o, then the value of tan t∝ is

If a letter is chosen at random from the English alphabets {a, b,...,z}, then the probability that the letter chosen precedes x

Kamalam went to play a lucky draw contest. 135 tickets of the lucky draw were sold. If the probability of Kamalam winning is \(\frac{1}{9}\), then the number of tickets bought by Kamalam is

The angle of elevation of a cloud from a point h metres above a lake is \(\beta \). The angle of depression of its reflection in the lake is 45°. The height of location of the cloud from the lake is

Two persons are standing ‘x’ metres apart from each other and the height of the first person is double that of the other. If from the middle point of the line joining their feet an observer finds the angular elevations of their tops to be complementary, then the height of the shorter person (in metres) is

If the sequence t₁, t₂, t₃... are in A.P. then the sequence t₆, t₁₂, t₁₈,.... is 

The next term of the sequence \(\frac { 3 }{ 16 } ,\frac { 1 }{ 8 } ,\frac { 1 }{ 12 } ,\frac { 1 }{ 18 } \), ..... is

When proving that a quadrilateral is a parallelogram by using slopes you must find

When proving that a quadrilateral is a trapezium, it is necessary to show

In figure CP and CQ are tangents to a circle with centre at O. ARB is another tangent touching the circle at R. If CP = 11 cm and BC = 7 cm, then the length of BR is

The two tangents from an external points P to a circle with centre at O are PA and PB. If \(\angle APB\) = 70^o then the value of \(\angle AOB\) is

The height and radius of the cone of which the frustum is a part are h₁ units and r₁ units respectively. Height of the frustum is h₂ units and radius of the smaller base is r₂ units. If h₂ : h₁ = 1:2 then r₂ : r₁ is

The volume (in cm³) of the greatest sphere that can be cut off from a cylindrical log of wood of base radius 1 cm and height 5 cm is

If g = {(1,1), (2,3), (3,5), (4,7)} is a function given by g(x) = αx + β then the values of α and β are

Let f(x) = \(\sqrt { 1+x^{ 2 } } \) then

For the given matrix A = \(\left( \begin{matrix} 1 \\ 2 \\ 9 \end{matrix}\begin{matrix} 3 \\ 4 \\ 11 \end{matrix}\begin{matrix} 5 \\ 6 \\ 13 \end{matrix}\begin{matrix} 7 \\ 8 \\ 15 \end{matrix} \right) \) the order of the matrix A^T is

The number of points of intersection of the quadratic polynomial x² + 4x + 4 with the X axis is