Grade 10 Olympiad – Tuyển chọn câu hỏi Olympiad lớp 10
Table Of Contents
Grade 10 Olympiad
Week 1
Choose correct answer(s) from the given choices
(1) Find the next term of given sequence.
11, 38, 139, 542, 2251, ….
a. 13003 b. 9870
c. 9878 d. 9883
(2) The sum of the first n odd natural numbers is 100. Find the value of n.
a. 10 b. 11
c. 12 d. 9
(3) Faces of a cube are marked with 1,2,3,4,5 and 6. If two views of cube are as shown below, what will be there on the face opposite to face 2?
a. 5 b. 3
c. 6 d. 1
(4) Find the next term of given sequence ..
24, 25, 29, 38, 54, ….
a. 80 b. 79
c. 72 d. 83
(5) Solve quadratic equation {x^2} + \left( {\frac{a}{{a + b}} + \frac{{a + b}}{a}} \right)x + 1 = 0
Fill in the blanks
(6) For a positive integer k we write
(1 + x)(1 + 2x)(1 + 3x)…(1 + kx) = a0 + a1x + a2x2 + … + akxk , where a0, a1,…ak are the coefficients of the polynomial. If a0 + a1 + a2 + … + ak−1 is divisible by 4511, the smallest possible value of k is ………
Answer the questions
(7) How many zeroes do the numbers 91 × 90 × 89 × …3 × 2 × 1 ends with ?
(8) If the 70th element of an arithmetic progression is 721 and the 50th element is 521, then what is the 6th element?
(9) Simplify\frac{{2{{\sin }^3}\theta - \sin \theta }}{{\cos \theta - 2{{\cos }^3}\theta }}
(10) In the following diagram rectangle represents women, triangle represents engineers, circle represents urban and square represents government employees. Find number of women who are urban.
Week 2
Choose correct answer(s) from the given choices
(1) The sum of the n consecutive natural numbers starting from 3 is 75. Find the value of n.
a. 10 b. 11
c. 12 d. 9
(2) What is the probability that a leap year will contain 53 Mondays?
a. \frac{1}{{52}}
b. \frac{2}{{7}}
c. \frac{1}{{7}}
d. \frac{2}{{366}}
(3) How many zeroes do the numbers 22 × 21 × 20 × …3 × 2 × 1 ends with?
a. 5 b. 12
c. 4 d. 10
Fill in the blanks
(4) If 2sinθ – cosθ = 2, the value of sinθ + 2cosθ = ……….
(5) The second smallest prime factor of \frac{{{1^3} + 1}}{{1 + 1}} + \frac{{{2^3} + 1}}{{2 + 1}} + \frac{{{3^3} + 1}}{{3 + 1}} + ... + \frac{{{{771}^3} + 1}}{{771 + 1}} is ……………
Answer the questions
(6) Coin A is flipped 3 times and coin B is flipped 5 times. What is the probability that the number of heads obtained from flipping the two coins is the same?
(7) Faces of a cube are marked with 1,2,3,4,5 and 6. Two views of cube are as shown below, if face 4 is opposite to face 6, what will be there on the top when 5 is at the bottom?
(8) Solve quadratic equation x2 + 7x – (p2 + 3p – 10) = 0 using factorization.
(9) Solve quadratic equation a2b2x2 + b2x – a2x – 1 = 0 using factorization.
(10) If secθ + tanθ = q, find value of secθ in terms of q.
Week 3
Choose correct answer(s) from the given choices
(1) The sum of the first 10 terms of an arithmetic progression is 265. The sum of the first 20 terms is 1030. What is the sum of the first 30 terms of the AP?
a. 2300 b. 2295
c. 2290 d. 1295
(2) The sum of the first n odd natural numbers is 36. Find the value of n.
a. 8 b. 5
c. 7 d. 6
(3) Solve quadratic equation x2 + 9 x – (p2 + 3p – 18) = 0 using factorization.
a. x = (p + 6) ,or x = -(p – 3)
b. x = -(p + 6) ,or x = p – 3
c. x = (p – 6) ,or x = p + 3
d. x = -(p + 6) ,or x = -(p – 3)
(4) Find the next term of given sequence.
15, 48, 153, 486, 1539, ….
a. 4863 b. 4852
c. 5103 d. 4860
Fill in the blanks
(5) The sum of the last two digits of the integer 1! + 2! + 3! + … + 2514! is ………….
Answer the questions
(6) Simplify:
(7) Solve quadratic equation x2 + 4 x – (p2 + 2p – 3) = 0 using factorization.
(8) How many integers satisfy the inequality x2 – 13 x < – 36.
(9) There are a total of 9 chocolates – 3 each in the flavors of coffee, cherry and grape. There are also 4 children. If each child is allowed to choose their own favorite flavor, what is the probability that all of them will get flavors of their choice?
(10) Faces of a cube are marked with A, B, C, D, E and F. If two views of cube are as shown below, what will be there on the face opposite to face C ?
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