**1. X can do a piece of work in 20 days and Y can do it in 10 days. They started together, but after 6 days X leaves off. Y will do the rest work in**

**(a) 1 day**

(b) 2 days

(c) 7/3 days

(d) 3 days

**Sol.**

**(X + Y)’s 6 days’ work = 6 * (1/20 + 1/10) = 9/10**

**Remaining work = 1 – 9/10 = 1/10**

**1/10 work is done 2y Y in 10 * 1/10 = 1 day**

**2. If each side of a rectangle is increased by 50%, its area will increase by**

**(a) 125%**

(b) 75%

(c) 100%

(d) 225%

**Sol.**

**Original area = l × b**

**New area =3/2 l×3/2 b=9/4 lb**

**Increase % =(9/4 lb – lb)/lb×100%**

**= 125%**

**3. Ratio of angles of linear pair is 8 : 1 then measure of each angle is**

(a) 80°, 10°

(b) 120°, 15°

**(c) 160°, 20°**

(d) 200°, 25°

**Sol.**

**Let angles be 8x and x**

**8x + x = 180**

**x = 20° then angles are 160° and 20°**

**4.60% of that the students in a school are boys. If the number of girls in the school is 300, then the number of boys is-**

(a) 300

**(b) 450**

(c) 500

(d) 750

**Sol:**

**Here 40% are girl in a school.**

**40%=300**

**60%=300× 60/40**

**=450**

**5. The circumference of the base of a right circular cylinder is 44 cm and its height is 15 cm. The volume (〖in cm〗^3 ) of the cylinder is (use π=22/7)**

(a) 770

(b) 1155

(c) 1540

**(d) 2310**

**Sol.**

**Radius of cylinder =44/2π=44/(2 × 22/7)=7 cm**

**∴ Volume of cylinder**

**=πr^2 h=22/7×7×7×15=2310 〖cm〗^3**

**6. In a polyhedron, if the number of faces, edges and vertices are denoted by F, E and V respectively, then according to Euler’s formula**

**(a) F+V-E=2**

(b) F-V+E=2

(c) F-V-E=2

(d) F+V=E-2

**Sol.**

**In, Polygon the number of faces, edges and vertices are denoted by F,E and V respectively. According to Euler’s formul a.**

**(F+V-E=2)**

**7. The ratio of the length to the breadth of a rectangle is 2 : 1. Its perimeter is 60 cm, find its area.**

(a) 250 sq cm

**(b) 200 sq cm**

(c) 300 sq cm

(d) 205 sq cm

**Sol.**

**2(2x + x) = 60 cm**

**⇒ x = 10 cm**

**∴ Area = 2x**

**x = 2(100) = 200 cm2**

**8. If x^2+1/x^2 =34, then find the value of x+1/x**

(a) 4

**(b) 6**

(c) 8

(d) 17

**Sol.**

**x^2+1/x^2 =34**

**⇒ (x+1/x)^2-2×1/x=34**

**[a^2+b^2=(a+b)^2=2ab]**

**⇒ (x+1/x)^2=36**

**⇒ x+1/x=6**

**9. The value of 5-(2 1/2-3/4)+(3 1/2-1 1/4) is**

(a) 4 1/2

**(b) 5 1/2**

(c) 5 1/4

(d) 3 1/2

**Sol.**

**5-[5/2-3/4]+[7/2-5/4]=5-[(10 – 3)/4]+[(14 – 5)/4]=5-7/4+9/4**

**=(20 – 7 + 9 )/4=22/4=11/2=5 1/2**

**10. One-fourth of a pizza was eaten by Renu. The rest was equally distributed among 12 children. What part of the pizza did each of these children get?**

**(a) 1/16**

(b) 1/32

(c) 3/16

(d) 1/8

**Sol.**

**Pizza remaining = 3/4**

**Pizza that single child get = (3/4) × (1/12)=1/16**