TS ICET 27th July 2022 Shift-1

The number of multiples of 7 occurring between 100 and 10000 is

$$\frac{4 \tan 150^{\circ} + \sin 240^{\circ}}{5 \cos 330^{\circ} + 3 \cot 225^{\circ}} = m + n\sqrt{3} \Rightarrow m + n$$ =

$$\tan 20^{\circ} = x \Rightarrow \frac{\tan 259^{\circ} + \tan 340^{\circ}}{\tan 200^{\circ} - \tan 110^{\circ}}$$

In a triangle ABC, $$\tan \frac{A}{2}. \tan \frac{B}{2} + \tan \frac{B}{2} . \tan \frac{C}{2}.\tan \frac{A}{2}$$ =

If $$\cos \theta = \frac{-5}{13}$$ and $$\theta$$ is not in $$3^{rd}$$ quadrant, then $$\tan \frac{\theta}{2}$$ =

The angle of elevation of the top of a tower when observed from the top of a tree of height 10m on a river side is $$45^{\circ}$$ and the angle of depression of the reflection of the top of the tower in the river is $$60^{\circ}$$, then the height of the tower, in meters, is

A right angled triangle ABC is right angled at B. If AB = 3 cm, BC = 4 cm, then the length of the altitude from B to AC is

In ABC, $$\angle BCA = 90^{\circ}$$ and CD is perpendicular to AB. If AD = 4cm and BD = 9 cm, then the length of CD (in cm) is

If the lengths of the two diagonals of a rhombus are 10 cm and 24 cm, then the perimeter of the rhombus (in cm), is

The sides of a rectangle are in the ratio 6 : 5 and its area is 1470 $$cm^{2}$$. Then the perimeter of the rectangle, in cm, is