SSC CGL Tier-2 12th September 2019 Maths

If $$3(\cot^2 \phi - \cos \phi) = \cos^2 \phi, 0^\circ < \phi < 90^\circ$$, then the value of $$(\tan^2 \phi + \cosec^2 \phi + \sin^2 \phi)$$ is:

A hemispherical bowl of internal diameter 36 cm is full of a liquid. This liquid is to be filled into cylindrical bottles each of radius 3 cm and height 12 cm. How many such bottles are required to empty the bowl?

If $$(5x + 1)^3 + (x - 3)^3 + 8(3x - 4)^3 = 6(5x + 1)(x - 3)(3x - 4)$$,$$ then $$x$$ is equal to:

The average of 33 numbers is 74. The average of the first 17 numbers is 72.8 and that of the last 17 numbers is 77.2. If the $$17^{th}$$ number is excluded, then what will be the average of the remaining numbers (correct to one decimal place)?

A solid cube is cut into three cuboids of same volumes. Whatis the ratio of the surface area of the cube to the sum of the surface areas of any two of the cuboids so formed?

If $$\frac{\sin^2 \phi - 3 \sin \phi + 2}{\cos^2 \phi} = 1$$ where $$0^\circ < \phi < 90^\circ$$, then what is the value of $$(\cos 2 \phi + \sin 3 \phi + \cosec 2 \phi)$$?

A loan has to be returned in two equal yearly instalments each of ₹44,100. If the rate of interest is 5% p.a.. compounded annually, then the total interest paid is:

A sum of ₹x is divided among A, B and C suchthat the ratio of the shares of A and B is 6 : 7 and that of B and is 3 : 2. If the difference between the shares of A andC is ₹540, then the value of x is:

The sides $$PQ$$ and $$PR$$ of $$\triangle PQR$$ are produced to points $$S$$ and $$T$$, respectively. The bisectors of $$\angle SQR$$ and $$\angle TRQ$$ meet at $$U$$. If $$\angle QUR = 79^\circ$$, then the measure of $$\angle P$$ is:

The value of $$\frac{\sin (78^\circ + \theta) - \cos (12^\circ - \theta) + (\tan^2 70^\circ - \cosec^2 20^\circ)}{\sin 25^\circ \cos 65^\circ + \cos 25^\circ \sin 65^\circ}$$ is: