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JMO Sample Papers 2012 with Answers, Solutions, KVS JMO Question Papers.
JMO Sample Papers 2012 - I:-
1. If four times the reciprocal of the circumference of a circle equals the diameter of the circle, then the area of the circle is …………..
2. If a=1000, b=100, c=10, and d=1, then (a+b+c-d) + (a+b-c+d) + (a-b+c+d)+(-a+b+c+d) is equal to …….
3. When the base of a triangle is increased by 10% and the altitude to the base is decreased by 10%, the change in area is ……….
4. If the sum of two numbers is 1, and their product is 1, then the sum of their cubes is ……………
5. If x = find the value of log3x.
6. If and find the value of x-y.
7. Find the number of digits in the number 22005 x 52000 when written in full.
8.Find the remainder when 22005 is divided by 13.
9. A polynomial p (x) leaves a remainder three when divided by x – 1 and a remainder five when divided by x-3. Find the remainder when p(x) is divided by (x-1) (x-3).
10. Find two numbers, both lying between 60 and 70, each of which is exactly divides 243-1.
11. In triangle ABC the medians AM and CN to the sides BC and AB, respectively intersect in the point O.P is the mid-point of side AC, and MP intersects CN in Q. If the area of triangle OMQ is 24 cm2, find the area of triangle ABC.
12. The base of a pyramid is an equilateral triangle of side length 6 cm. The other edges of the pyramid are each of length cm. Find the volume of the pyramid.
x-1 | + | x | + | x + 1 | = x + 2
14.Find the greatest number of four digits which when divided by 3, 5, 7, 9 leaves remainders 1, 3, 5, 7 respectively.
15. A printer numbers the pages of a book starting with 1. He uses 3189 digits in all. How many pages does the book have ?
16. ABCD is a parallelogram. P, Q, R and S are points on sides AB, BC, CD and DA respectively such that AP=DR. If the area of the parallelogram is 16 cm2, find the area of the quadrilateral PQRS.
18. ABC is a right angle triangle with B = 90o. M is the mid point of AC and BM = cm. Sum of the lengths of sides AB and BC is 30 cm. Find the area of the triangle ABC.
19. Without actually calculating, find which is greater : 31 11 or 17 14
20. Show that there do not exist any distinct natural numbers a, b, c, d such that a3 + b3 = c3 + d3 and a + b = c + d
21. Find the largest prime factor of : 312 + 212 – 2.66
22. Find the smallest multiple of ‘15’ such that each digit of the multiple is either ‘0’ or ‘8’.
23. At the end of year 2002. Ram was half as old as his grandfather. The sum of years in which they were born is 3854. What is the age of Ram at the end of year 2003?
24. Find the area of the largest square, which can be inscribed in a right angle triangle with legs ‘4’ and ‘8’ units.
25. In a Triangle the length of an altitude is 4 units and this altitude divides the opposite side in two parts in the ratio 1:8. Find the length of a segment parallel to altitude which bisects the area of the given triangle.
Central Board of Secondary Education - CBSE is a Board of Education for public and private schools, under the Union Government of India.
CBSE affiliates all Jawahar Navodaya Vidyalayas, all Kendriya Vidyalayas, private schools, all the schools in the NCT of Delhi and Foreign Schools.
The board conducts final examinations every spring for All India Senior School Certificate Examination (AISSCE) for Class 10 and 12.The board also annually conducts the AIEEE exam for admission to undergraduate courses in engineering and architecture in numerous colleges spread over India.
Central Board of Secondary Education
PS-1-2, Institutional Area,
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