$\frac{\left(1+\tan ^{2} \mathrm{~A}\right) \cot \mathrm{A}}{\operatorname{cosec}^{2} \mathrm{~A}}$ is equal to

The value of (tan35° tan45° tan55°) is (tan35° tan45° tan55°) dk eku fdruk gS \

In what ratio does the point T (3, 0) divide the segment joining the points S (4, –2) and U (1, 4)?

If secθ + tanθ = 2 then the value of sec T is ;fn secT + tanT = 2

What is the angle in radian through which a pendulum swings and its length is 75 cm and the tip describes an arc of length 21 cm.

The radius of two circles are 5cm and 3cm, the distance between their centres is 24 cm. Then the length of the transverse common tangent is

A, B and C together can complete a work in 20 days. A and B together can complete the same work in 30 days. Then C alone can complete the same work in how many days?

Which of the following numbers is completely divisible by 99?

In what ratio, the line joining (–1, 1) and (5, 7) is divided by the line x + y = 4 ?

The simplified value of

$\frac{\frac{1}{3} \cdot \frac{1}{3} \cdot \frac{1}{3}+\frac{1}{4} \cdot \frac{1}{4} \cdot \frac{1}{4}+\frac{1}{5} \cdot \frac{1}{5} \cdot \frac{1}{5}-3 \cdot \frac{1}{3} \cdot \frac{1}{4} \cdot \frac{1}{5}}{\frac{1}{3} \cdot \frac{1}{3}+\frac{1}{4} \cdot \frac{1}{4}+\frac{1}{5} \cdot \frac{1}{5}-\left(\frac{1}{3} \cdot \frac{1}{4}+\frac{1}{4} \cdot \frac{1}{5}+\frac{1}{5} \cdot \frac{1}{3}\right)}$ is