Advance Mathematics for SSC Exams Set-2

1. [2^(16) – 1] is divisible by
(a) 11
(b) 13
(c) 17
(d) 19
2. When a number is divided by 24, the remainder is 16. The remainder when the same number is divided by 12 is
(a) 3
(b) 4
(c) 6
(d) 8

3. A number, when divided by 136, leaves remainder 36. If the same number is divided by 17, the remainder will be
(a) 9
(b) 7
(c) 3
(d) 2

4. Find the altitude of a rhombus whose area is 420cm2 and perimeter 140cm.

5. Find the maximum value of (sinA.cosB)5+5?

6.A cylindrical rod of length h is method and cast into a cone of base radius twice that of the cylinder. What is the height of the cone?
(a) 3h/4
(b) 4h/3
(c) 2h
(d) h/2

7.If C1 is right circular cone with base radius r1 cm and height h1 cm and C2 is a right circular cylinder with base radius r2 cm and height h2 cm and if r1 : r2 = 1 : n (where n is a positive integer) and their volumes are equal, then which one of the following is correct?
(a) h1 = 3nh2
(b) h1 = 3n^2 h2
(c) h1 = 3h2
(d) h1 = n^2h2

8.The perimeter of a rhombus is 40 cm and the measure of an angle is 60, then the area of it is:
(a) 1000 √3 cm^2
(b) 50 √3 cm^2
(c) 160 √3 cm^2
(d) 100 cm^2

9.A right angled isosceles triangle is inscribed in a semi-circle of radius 7cm. The area enclosed by the semi-circle but exterior to the triangle is :
(a) 14 cm^2
(b) 28 cm^2
(c) 44 cm^2
(d) 68 cm^2

10.The area of the square with AC as a side is 128 cm^2. What is the sum of the areas of semicircles drawn on AB and AC as diameters, given ABC is an isosceles right angled triangle and AC is its hypotenuse.
(a) 32 π cm^2
(b) 16π cm^2
(c) 16 cm^2
(d) 32 cm^2

6.(a) ; Let the radius of cylinder be r and radius of cone be R
R = 2r
According to question,
Volume of cylinder = Volume of cone
πr^2 h=1/3 πR^2 H
r^2 h=1/3 π(2r)^2 H
H = 3h/4