Singapore Maths Olympiad

If it is known that the roots of the equation are all integers, how many distinct roots does the equation have?

x⁵ + 3x⁴ – 4044118x³ – 12132362x² – 12132363x - 2011² = 0

Singapore maths Olympiad

Singapore maths Olympiad

If x = 10000..................................0001000.............................00050
                      2011 times                              2012 times

Which of the following is a perfect square?

a) x - 75  b) x - 25   c) x + 25    d) x + 75

Singapore Maths Olympiad

Singapore maths Olympiad

Singapore Maths Olympiad, Algebra

Singapore maths Olympiad, algebra

 Singapore maths Olympiad

Singapore maths Olympiad algebra

If a, b, and c are real numbers and positive, and if 

a² + ab + b² = 25, 

b² + bc + c² = 49 and 

c² + ca + a² = 64 

Find the value of (a + b + c)^{2                                                        Singapore Maths Olympiad}

Maths Challenging questions

shoot me the answer of this question

Passengers are queuing  outside the Railway Station at a Constant Rate. If the railway authorities open up 3 gates, it takes 9 minutes to clear the queue. If instead the railway authorities were to open 5 gates, the queue would have got cleared in 5 minutes. How many minutes before opening of the gates did the first passenger arrive outside the station.

Problem on CLOCK

The clock gets slower by a minute in one hour. The clock is adjusted to correct time at 7 am. What is the standard time when the clock shows 12 noon.

Problem on CLOCK

At what time will the hour arm and the minute arm coincide. The hour arm is between 7 and 8.

Problems on CLOCK

At what time will the hour arm be diametrically opposite to the minute arm.  The hour arm is between 7 and 8.

Problems on CLOCK

At what times is the angle between the hour arm and the minute arm at 60 degree. The hour arm is between 6 and 7.

Problems on CLOCK

When is the first time, the angle between the minute arm and the hour arm equal to 30o. The hour arm is between 3 and 4.

Problems on CLOCK

What is the angle between the minute arm and the hour arm at 10:30 pm?

JMO / IPM mega / STD IX

Find the area enclosed by the egg. AB is the diameter. AB = BC = AD. O is the centre of the circle. consider the radius AO to be 1 unit.

Answer:

(3 - √2)π - 1

IPM mega final STD VII practice paper

IPM Mega final Question Paper (STD VII)

• What is value of the digits in the units place of the following:

           1 x 3 x 5 x 7 x 9 x 11 x 13 x .............. 2007 x 2009

• nanu and Shruti are running on a circular track. Nanu is at point A and Shruti is at point B. AB represents the diameter of the circular path. If they run in the same direction it will take them 280 secs to meet and if they run in the opposite direction it will take them 40 secs to meet. What is the ratio of speed of Nanu and Shruti.
• If a and b are whole numbers, then find a and b for the following expression:

          3a + 8b = 47

• Between 1 and 2009, how many numbers are multiple of 5 or 7 and 5 and 7?
• Nanu travels from Thane to Mumbai at a constant speed of 20 m/s and then returns from Mumbai to thane at 40/3 m/s. What was the average speed of the vehicle for the whole journey?
• Find the value of 20082009 x 20092008 - 20082008 x 20092009
• How many 3 digit numbers have the sum of the digits equal to 4.
• If nanu travels at 60 km/hr she arrives at 3:00 pm. If she travels at 80 km/hr she arrives at 1:00 pm. What should be her speed if she wishes to arrive at 2:00 pm?
• In the figure given below E and F are the midpoints of AD and DC respectively. ABCD is a rectangle. Find the area of the shaded region.

    

• The distance between 2 points A and B is decreasing by 10% per sec. WHat is the distance remaining in percentage after 3 secs
• At 10% rate of interest per annum, the difference between compound interest and simple interest is Rs 100 for a period of 2 years.What is the Principal?

Answers: 

5, 4:3, a = 5, b = 4, 630 and 57, 57.6 km/hr, 10000, 10, 68 4/7 km/hr, 110 cm2 , 72.9%, Rs 10000

JMO question paper --- STD V / STD VI --- 2015

JMO --- STD V / STD VI --- 2015

puzzle, JMO

There are three temples and one pond before each temple. One person carries some flowers and dips it in the first pond. Number of flowers become 100 times. He then offers some flowers in the first temple.He goes with the balance to second pond and takes a dip. Again the number of flowers increases by 100 times. He offers the same number of flowers at second temple and leaves with the balance  flowers to the third pond. There after the dip the number of flowers increase by 100 times. He offers same number of flowers at temple 3 and nothing remains with him afterwards. So how many flowers did he have in the beginning.

Numbers

Find 4 consecutive prime numbers that add up-to 220.

divisibility

 Let x and y be integers. Prove that (2x + 3y) is divisible by 17 if (9x + 5y) is divisible by 17.