SSC CGL Tier-2 01-December-2016 Maths

ABC is an isosceles triangle inscribed in a circle. If $$AB = AC = 12\surd5$$ and $$BC = 24  cm$$ then radius of circle is

ABC is an isosceles triangle where AB = AC whichis circumscribed abouta circle. If P is the point where the circle touches the side BC, then which of the following is true ?

If D and E are the mid points of AB and AC respectively of $$\triangle$$ABC, then the ratio of the areas of ADE and BCED is ?

O is the circumcentre of the isosceles $$\triangle$$ABC. Given that AB = AC = 17 cm and BC = 6 cm. The radius of the circle is

$$B_1$$ is a point on the side $$AC$$ of $$\triangle ABC$$ and $$B_1B$$ is joined. line is drawn through A parallel to $$B_1B$$ meeting $$BC$$ at $$A_1$$ and another line is drawn through $$C$$ parallel to $$B_1B$$ meeting $$AB$$ produced at $$C_1$$. Then

The value of the expression $$(1 + \sec 22^\circ + \cot 68^\circ)(1 - \cosec 22^\circ + \tan 68^\circ)$$is

If $$x \sin^3 \theta + y \cos^3 \theta = \sin \theta \cos \theta  and  x \sin \theta - y \cos \theta = 0$$, then the value of $$x^2 + y^2$$ equals

If $$\sec \theta + \tan \theta = m (>1)$$, then the value of $$\sin \theta  is  (0^\circ < \theta < 90^\circ)$$

If $$(a^2 - b^2)\sin \theta + 2ab \cos \theta = a^2 + b^2$$, then $$\tan \theta =$$

A person from the top of a hill observes a vehicle moving towards him at a uniform speed. It takes 10 minutes for the angle of depression to change from $$45^\circ$$ to $$60^\circ$$. After this the time required by the vehicle to reach the bottom of the hill is