SSC CGL 6 June 2019 Shift-2

The efficiencies of A, B and C are in the ratio 5 : 3: 8. Working together they can complete a work in 30 days. A and B worked together for 20 days. The remaining work will be completed by C alone in:

If $$\frac{\cos^2 \theta}{\cot^2 \theta - \cos^2 \theta} = 3, 0^\circ < \theta < 90^\circ$$, then the value of $$\cot \theta + \cosec \theta$$ is:

In $$\triangle$$ABC with sides 6 cm, 7 cm and 8 cm,the angle bisector of the largest angle divides the opposite side into two segments. What is the length of the shorter segment?

The distance between two stations A and B is 800 km. A train X starts from A and moves towards B at 40 km/h and another train Y starts from B and moves towards A at 60 km/h. How far from A will they cross each other ?

If $$2x^2 + y^2 + 6x - 2xy + 9 = 0$$, then the value of $$(4x^3 - y^3 + x^2y^2)$$ is:

The vertices of a $$\triangle$$PQR lie on a circle with centre O. SR is a tangent to the circle at the point R. If QR bisects the $$\angle$$ORS, then what is the measure of $$\angle$$RPQ?

In a circle with centre O, ACBO is a parallelogram where C is a point on the minor arc AB. What is the measure of AOB?

If $$\sin \theta = 4 \cos \theta$$, then what is the value of $$\sin \theta \cos \theta$$ ?

ABCD is a parallelogram in which diagonals AC and BD intersect at O. AE and DF are perpendiculars on BC at E and F, respectively. Which of the following is NOT true?

The average of twelve numbers is 46. The average of the first four numbers is 43 and that of the last five numbers is 49.4.The $$5^{th}$$ and the $$6^{th}$$ numbers are respectively 4 and 6 more than the $$7^{th}$$ number. What is the average of the $$5^{th}$$ and the $$7^{th}$$ numbers?