The average of five consecutive positive integers is n. If the next two integers are also included, the average of all these integers will

• increase by 1.5

• increase by 1

• remain the same

• remain the same

If a hemisphere is melted and four spheres of equal volume are made, the radius of each sphere will be equal to

• th of the radius of the hemisphere

• radius of the hemisphere

•  of the radius of the hemisphere
•  of the radius of the hemisphere

If a shopkeeper wants to give 20% discount on a toy, he has to sell it for Rs.300. If he sells it at Rs. 405, then his gain percent is

• 5%

• 4%

• 8%

• 8%

The average age of 30 students of a class is 14 years 4 months. After admission of 5 new students in the class the average becomes 13 years 9 months. The youngest one of the five new students is 9 years 11 months old. The average age of the remaining 4 new students is

• 11 years 2 months

• 13 years 6 months

• 12 years 4 months

• 12 years 4 months

AD is perpendicular to the internal bisector of  of Δ ABC. DE is drawn through D and Parallel to BC to meet AC at E. If the length of AC is 12 cm, then the length of AE (in cm.) is

• 3

• 8

• 4

• 4

The unit digit in the product (2467)¹⁵³ x (341)¹⁷² is

• 7

• 8

• 4

• 4

67.

There is a wooden sphere of radius  The surface area of the largest possible cube cut out from the sphere will be

• 864 cm²

• 

• 462 cm²

• 462 cm²

If a + b = 1, find the value of a³ + b³ - ab - (a² - b²)².

• -1

• 1

• 0

• 0

If , then the value of tan θ is (θ is acute)

A cylinder with base radius 8 cm and height 2cm is melted to form a cone of height 6 cm. The radius of the cone will be

• 6 cm

• 8 cm

• 4 cm

• 4 cm