How many natural numbers up to 2001 are divisible by 3,4 but not by 5? a) 768 b) 801 c) 934 d) 1067 Sol: Divisible by 3 till 2001 = 667 Divisible by 4 till 2001 = 500 Divisible by 12 till 2001 = 166 ⇒ Divisible by 3, 4 = 667 + 500 – […]
How many natural numbers up to 2001 are divisible by 3,4 but not by 5 Read More »
How many pairs of positive integers(of m,n) satisfy the equation m² + 105 = n² a) 2 b) 3 c) 4 d) 5 Sol: m² – n² = 105 (m – n) (n + m) = 105 105 = 3 × 35 ⇒ m = 19, n = 16 105 = 5 × 21 ⇒
How many pairs of positive integers(of m,n) satisfy the equation m² + 105 = n² Read More »
The value of the expression (cos⁶θ + sin⁶θ – 1)(tan²θ + cot²θ + 2) is: (a) 0 (b) -1 (c) -3 (d) 1 Sol:
The value of the expression (cos⁶θ + sin⁶θ – 1)(tan²θ + cot²θ + 2) is Read More »
If a³ + b³ = 110 and a + b = 5, then (a + b)² – 3ab is equal to: a) 52 b) 32 c) 42 d) 22 Sol: a + b = 5 a³ + b³ = 110 ⇒ (a + b) (a² + b² – ab) = 110 a² + b² –
If a³ + b³ = 110 and a + b = 5, then (a + b)² – 3ab is equal to Read More »
The base of a prism is in the shape of an equilateral triangle. If the perimeter of the base is 18.45 cm and the height of the prism is 32 cm, then what is the volume (in cm³) of the prism? a) 180√3 b) 324.8√3 c) 434 d) 524 Sol: Perimeter = 18.45 cm Side
The average marks of four students together is 60%. The average marks of Ram, Dev, Atul and Pankaj individually are 46%, 52%, 70% and 82% respectively. If the average marks of Ram and Dev together is 49% and that of Dev and Atul together is 60%. What is the ratio of number obtained by Ram
A tank of petrol contains 300 litres of pure petrol initially, Every time a seller sells out 60 litres from the container and replaces each time with 60 liters of kerosene. After replacing the liquid with kerosene 4th time, the total amount of kerosene (in l t) in the mi xture i s? a)122.88 b)
A swimming pool is fitted with three pipes, the 1st two pipes working simultaneously can fill the pool in the same as the 3rd pipe alone, the 2nd pipe alone fills the pool 5 hours faster than 1st pipe and 4 hours slower than 3rd pipe. In what time 2nd and 3rd pipe together fill
A, B and C complete a work in 12,15 and 18 days respectively if they start work together till the whole work complete. Find the share of wages of A,B and C out of he total wages of 1443 Rs? a)220,390,385 b) 285,390,362 c) 362,585,390 d) 585,468,390 Sol: A + B + C = 37
The average of P numbers is Q4, the average of Q numbers is P 4. The average of (P+Q) number is? a) QP b) PQ(P2 + Q2) c) PQ(P2+Q2-PQ) d) P2+Q2 Sol: Sum of P number = PQ⁴ Sum of Q number = QP⁴ (P + Q) = PQ⁴ + QP⁴
