Class 9 Exam  >  Class 9 Tests  >  Number System - Olympiad Level MCQ, Class 9 Mathematics - Class 9 MCQ

Number System - Olympiad Level MCQ, Class 9 Mathematics - Class 9 MCQ


Test Description

25 Questions MCQ Test - Number System - Olympiad Level MCQ, Class 9 Mathematics

Number System - Olympiad Level MCQ, Class 9 Mathematics for Class 9 2024 is part of Class 9 preparation. The Number System - Olympiad Level MCQ, Class 9 Mathematics questions and answers have been prepared according to the Class 9 exam syllabus.The Number System - Olympiad Level MCQ, Class 9 Mathematics MCQs are made for Class 9 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for Number System - Olympiad Level MCQ, Class 9 Mathematics below.
Solutions of Number System - Olympiad Level MCQ, Class 9 Mathematics questions in English are available as part of our course for Class 9 & Number System - Olympiad Level MCQ, Class 9 Mathematics solutions in Hindi for Class 9 course. Download more important topics, notes, lectures and mock test series for Class 9 Exam by signing up for free. Attempt Number System - Olympiad Level MCQ, Class 9 Mathematics | 25 questions in 25 minutes | Mock test for Class 9 preparation | Free important questions MCQ to study for Class 9 Exam | Download free PDF with solutions
Number System - Olympiad Level MCQ, Class 9 Mathematics - Question 1

Find the remainder when 73 x 75 x 78 x 57 x 197 x 37 is divided by 34.

Detailed Solution for Number System - Olympiad Level MCQ, Class 9 Mathematics - Question 1

⇒ (73 x 75 x 78 x 57 x197 x 37) / 34

⇒ (5 x 7 x 10 x 23 x 27 x 3) / 34

[We have taken individual remainder, which means if 73 is divided by 34 individually, it will give remainder 5, 75 divided 34 gives remainder 7 and so on.]

⇒ (5 x 7 x 10 x 23 x 27 x 3)/34

⇒ (35 x 30 x 23 x 27) / 34 [Number Multiplied]
⇒ (35 x 30 x 23 x 27) / 34

⇒ (1 x -4 x -11 x -7) / 34

[We have taken here negative as well as positive remainder at the same time. When 30 divided by 34 it will give either positive remainder 30 or negative remainder -4. We can use any one of negative or positive remainder at any time.]

⇒ (1 x -4 x -11 x  -7) / 34

⇒ (28 x -11) / 34

⇒ (-6 x -11) / 34

⇒  66 / 34

⇒ R = 32.


Required remainder = 32.

Number System - Olympiad Level MCQ, Class 9 Mathematics - Question 2

Arrange in descending order √8,  ∛81 , ∛250 

1 Crore+ students have signed up on EduRev. Have you? Download the App
Number System - Olympiad Level MCQ, Class 9 Mathematics - Question 3

The value of x in    is :-

Detailed Solution for Number System - Olympiad Level MCQ, Class 9 Mathematics - Question 3

(3x+ 1)^1/4 = 2

=> 3x+ 1 = (2²)²

=> 3x+ 1 = 16

=> 3x = 16-1

=> 3x = 15

=> x = 5

Number System - Olympiad Level MCQ, Class 9 Mathematics - Question 4

Value of (256)0.16 x (256)0.09=?

Detailed Solution for Number System - Olympiad Level MCQ, Class 9 Mathematics - Question 4

(256)0.16 x (256)0.09 = (256)(0.16 + 0.09)

   = (256)0.25

   = (256)(25/100)

   = (256)(1/4)

   = (44)(1/4)

   = 44(1/4)

   = 41

   = 4

Number System - Olympiad Level MCQ, Class 9 Mathematics - Question 5

Which one of the following is a rational number ?

Detailed Solution for Number System - Olympiad Level MCQ, Class 9 Mathematics - Question 5

(√2)= 2 which is a rational number

Number System - Olympiad Level MCQ, Class 9 Mathematics - Question 6

The value of x in   is :-

Detailed Solution for Number System - Olympiad Level MCQ, Class 9 Mathematics - Question 6

(4x -7 )^1/3 -5 =0

(4x -7)^1/3 = 5

4x -7 = 5³

4x -7 =125

4x = 125 +7

4x = 132 

x = 132/4

 x = 33

 

Number System - Olympiad Level MCQ, Class 9 Mathematics - Question 7

Which of the following is not an improper fraction :-

Detailed Solution for Number System - Olympiad Level MCQ, Class 9 Mathematics - Question 7

In proper fraction, the  numerator is greater than it's denominator whereas in improper fraction denominator is greater than numerator.

Number System - Olympiad Level MCQ, Class 9 Mathematics - Question 8

Let N = 1421*1423*1425. What is the remainder when N is divided by 12?

Detailed Solution for Number System - Olympiad Level MCQ, Class 9 Mathematics - Question 8

1421 = 118*12 + 5 = 12k + 5, where k = 118.

1423 = 12k + 7

1425 = 12k + 9

N = (12k + 5)(12 k + 7)(12k + 9)

When N is divided by 12, the remainder is same as the remainder, when 5 * 7 * 9 = 315 is divided by 12.

5 * 7 * 9 = 35 * 9 = 315 

315 = 312 + 3 = 12 * 26 + 3 

The remainder is 3.

Number System - Olympiad Level MCQ, Class 9 Mathematics - Question 9

Find the least number which will leaves remainder 5 when divided by 8, 12, 16 and 20.

Detailed Solution for Number System - Olympiad Level MCQ, Class 9 Mathematics - Question 9

We have to find the Least number, therefore we find out the LCM of 8, 12, 16 and 20.
8 = 2*2*2;
12 = 2*2*3;
16 = 2*2*2*2;
20 = 2*2*5;
LCM = 2*2*2*2*3*5 = 240;
This is the least number which is exactly divisible by 8, 12, 16 and 20.
Thus,
required number which leaves remainder 5 is,
240+5 = 245.

Number System - Olympiad Level MCQ, Class 9 Mathematics - Question 10

The value of :  .  

Number System - Olympiad Level MCQ, Class 9 Mathematics - Question 11

 The binary equivalent of (1011.011)10 is equal to

Detailed Solution for Number System - Olympiad Level MCQ, Class 9 Mathematics - Question 11

1 * 23 + 0 * 22 + 1 * 21 + 0 * 2^-1 +1 * 2^-2 + 1 * 2^-3 = 11.375
Hence, (1011.011)10 = 11.375

Number System - Olympiad Level MCQ, Class 9 Mathematics - Question 12

If pqr = 1, then     is equal to :-

Detailed Solution for Number System - Olympiad Level MCQ, Class 9 Mathematics - Question 12

LHS = 1/[1 + p + q⁻¹] + 1/[1 + q + r⁻¹] + 1/[1 + r + p⁻¹] 

1/[1 + p + q⁻¹] = 1/[1 + p + 1/q] = q/ [q + pq + 1] -------(1)

1/[1 + q + r⁻¹] = 1/[1 + q + 1/r ]
= 1/[1 + q + pqr/r ] {from pqr = 1}
= 1/[1 + q + pq] = 1/[q + pq + 1] --------(2)

1/[1 + r + p⁻¹] = pqr/[pqr + r + pqr/p] 
= pqr/[pqr + r + qr] = pq/[pq + 1 + q] ------(3)

Add equations (1), (2) and (3) 
q[1 + pq + q] + 1/[q + pq + 1] + PQ/[pq + 1 + q] 
= [1 + pq + q]/[1 + pq + q] = 1 
Hence , LHS = RHS proved

Number System - Olympiad Level MCQ, Class 9 Mathematics - Question 13

What is the sum of all two digit numbers that gives a remainder of 3 when they are divided by 7?

Detailed Solution for Number System - Olympiad Level MCQ, Class 9 Mathematics - Question 13

The two digit number which gives a remainder of 3 when divided by 7 are:

10, 17, 24 94.

Now, these number are in AP series with 

1st Term, a = 10; 

Number of Terms, n = 13;

Last term, L = 94 and

Common Difference, d = 7.

Sum,

= n*(a+L)/2

= 13*52 = 676.

Number System - Olympiad Level MCQ, Class 9 Mathematics - Question 14

The exponential form of    is :- 

Number System - Olympiad Level MCQ, Class 9 Mathematics - Question 15

If A =    , then the value of   is :-

Number System - Olympiad Level MCQ, Class 9 Mathematics - Question 16

If x =  and y = 1, the value of  is :-

Number System - Olympiad Level MCQ, Class 9 Mathematics - Question 17

If a = , b =  then value of a3 + b3 is :-

Number System - Olympiad Level MCQ, Class 9 Mathematics - Question 18

 ÷  =

Number System - Olympiad Level MCQ, Class 9 Mathematics - Question 19

If 2x = 3y = 6-z, then  is equal to :-

 

Detailed Solution for Number System - Olympiad Level MCQ, Class 9 Mathematics - Question 19

Let 2= 3y = 6 -z = k
⇒ 2x = k

Similarly, 

Number System - Olympiad Level MCQ, Class 9 Mathematics - Question 20

If ax = b, by = c and cz = a, then the value of xyz is :-

Detailed Solution for Number System - Olympiad Level MCQ, Class 9 Mathematics - Question 20

From the following, we need to find the values of x,y, and z:

a x =b , b y =c , c z =a

From ax =  b, we get x  =b/a -------------------------- (i)
From by = c, we get y  =c/b ---------------------------(ii)
From cz = a, we get z = c/a ---------------------------(iii)

Multiplying the left hand sides and right hand sides of (i), (ii) and (iii) we get
xyz=(b/a)*(c/b)*(c/a)

When we simplify, we find that xyz=1. Hence proved.

Number System - Olympiad Level MCQ, Class 9 Mathematics - Question 21

Solution set of the equation |x – 2| = 5 is :-

Number System - Olympiad Level MCQ, Class 9 Mathematics - Question 22

Three numbers are in ratio 1:2:3 and HCF is 12. The numbers are:

Detailed Solution for Number System - Olympiad Level MCQ, Class 9 Mathematics - Question 22

Let the required numbers be x, 2x and 3x. Then, their H.C.F. = x. So, x = 12  ∴  The numbers are 12, 24 and 36  

Number System - Olympiad Level MCQ, Class 9 Mathematics - Question 23

The minimum value of the expression |17x – 8 | – 9 is :-

Detailed Solution for Number System - Olympiad Level MCQ, Class 9 Mathematics - Question 23

Let's say the following polynomial be f(x) .

f(x) = | 17x - 8 | - 9 .

We know that Modulus value can be 0 at least and at most positive infinite. 

So, | 17x - 8 | = 0

17x - 8 = 0 
x = 8/17 .

Now, Finding 

f min ( x) = | 17(8/17)-8 | - 9 
= 0 - 9 
= -9.

Therefore, The minimum value of | 17x - 8 | - 9 is -9.

Number System - Olympiad Level MCQ, Class 9 Mathematics - Question 24

If 2a – 9 = b + a, then the value of (|a – b| + |b – a|) is :-

Detailed Solution for Number System - Olympiad Level MCQ, Class 9 Mathematics - Question 24

The correct option is Option A.

2a - 9 = b + a 

=> 2a - a = b + 9 

=> a = b + 9 

Now, |a-b| + |b-a|

= √a² + b² +√b² + a²

= √(b+9)² + b² +√b² + (b+9)²

= b + 9 + b + b + b + 9

= 4b +18

Number System - Olympiad Level MCQ, Class 9 Mathematics - Question 25

If the decimal number is a fraction then its binary equivalent is obtained by ________ the number continuously by 2.

Detailed Solution for Number System - Olympiad Level MCQ, Class 9 Mathematics - Question 25

On multiplying the decimal number continuously by 2, the binary equivalent is obtained by the collection of the integer part. However, if it’s an integer, then it’s binary equivalent is determined by dividing the number by 2 and collecting the remainders.

Information about Number System - Olympiad Level MCQ, Class 9 Mathematics Page
In this test you can find the Exam questions for Number System - Olympiad Level MCQ, Class 9 Mathematics solved & explained in the simplest way possible. Besides giving Questions and answers for Number System - Olympiad Level MCQ, Class 9 Mathematics, EduRev gives you an ample number of Online tests for practice

Top Courses for Class 9

Download as PDF

Top Courses for Class 9