IMO - Mock Test

Result

IMO - Mock Test - 1

Score
-
out of -
Rank
-
out of -

TIME Taken - -

SHARING IS CARING

If our Website helped you a little, then kindly spread our voice using Social Networks. Spread our word to your readers, friends, teachers, students & all those close ones who deserve to know what you know now.

Weekly Quiz Competition

Question 1
1 / -0

If '×' stands for 'addition', '÷' stands for 'subtraction', '+' stands for 'multiplication' and '-' stands for 'division', then which of the following equations is correct?

A
204 - 17 + 13 × 12 ÷ 4 = 164

B
204 - 17 + 13 ÷ 12 × 4 = 164

C
204 ÷ 17 × 13 + 12 - 4 = 164

D
204 ÷ 17 - 13 + 12 × 4 = 164

Solution

204 - 17 + 13 × 12 ÷ 4 means 204 ÷ 17 × 13 + 12 - 4

= 12 × 13 + 12 - 4 = 164
Question 2
1 / -0

Find the odd one out from the given options.

A
Earth

B
Jupiter

C
Sun

D
Saturn

Solution

Except option (3), all the others are planets.
Question 3
1 / -0

An A.P. consists of 53 terms. If the last term and the first term be 216 and 8 respectively, then find the value of 48^th term.

A
176

B
196

C
200

D
7340

Solution

Given, n = 80, a1 = 8, a53 = 216

Now, a1 + 52d = 216

8 + 52d = 216

52d = 216 - 8

52d = 208

d = 4

Hence, a48 = a1 + 47d = 8 + 47(4)

a48 = 196
Question 4
1 / -0

What will be the H.C.F of three numbers which are in ratio of 3 : 5 : 7 and their L.C.M is 1575?

A
9

B
12

C
15

D
60

Solution

Let the numbers be 3X, 5X and 7X.

Then, the L.C.M is 105X.

So, 105X = 1575

=> X = 15

So, the numbers are 3 x 15, 5 x 15 and 7 x 15.

So, H.C.F is 15.
Question 5
1 / -0

The point which divides the line joining (1, 2) and (3, 4) internally in the ratio of 1 : 1 lies in which quadrant?

A
First quadrant

B
Second quadrant

C
Third quadrant

D
Fourth quadrant

Solution

Since the coordinates of both points are positive, the line joining them lies in the first quadrant. The division of the line in the ratio of 1 : 1 means the mid-point of this line also, therefore, lies in the first quadrant, with both coordinates positive.
Question 6
1 / -0

x = 17¹² + 10¹² and y = 16⁶ + 9⁶. If x - y is divided by 13, then the remainder is R₁ and if it is divided by 14, then the remainder is R₂. What is (R₁, R₂)?

A
(0, 0)

B
(0, 1)

C
(1, 0)

D
(1, 1)

Solution

x - y = 17¹²+ 10¹² - 16⁶ - 9⁶
x - y = 17¹² + 10¹² - 4¹² - 3¹²
x - y = (17¹² - 4¹²) + (10¹² - 3¹²)
17¹² - 4¹² is divided by 17 - 4 = 13 and 10¹² - 3¹² is divided by 10 + 3 = 13
So, R₁ = 0
x - y can also be written as
x - y = (17¹² - 3¹²) + (10¹² - 4¹²)
Now, both (17¹² - 3¹²) and (10¹² - 4¹²) are divided by 14.
So, R₂= 0
Question 7
1 / -0

If the LCM of two whole numbers is twice their HCF, then what is the ratio of the larger number to the smaller number?

A
3 : 1

B
2 : 1

C
3 : 2

D
4 : 1

Solution

Suppose, k is the HCF of the two numbers. Then, the numbers are ak and bk.
The LCM of these two numbers is 2k.
We know: Product of the numbers = HCF × LCM
ak × bk = HCF × LCM
ak × bk = k × (2k)
⇒ ab = 2
This is possible only if either a = 1, b = 2 or a = 2, b = 1.
So, the required ratio of larger to smaller number = 2/1= 2 : 1
Question 8
1 / -0

On 2^nd July 1985, it was Wednesday. The day of the week on 2^nd July, 1984 was

A
Wednesday

B
Tuesday

C
Monday

D
Thursday

Solution

There are 365 days between 2^nd July, 1984 and 2^nd July, 1985.
In 365 days, there are 52 weeks and 1 odd day.
If 2^nd July, 1985 was a Wednesday, then
2^nd July, 1984 was the day that comes before Wednesday which means Tuesday.
Question 9
1 / -0

Rina participated in a quiz which consisted of 30 questions, out of which some were multiple choice questions and the rest were subjective questions. Each multiple choice question carried 2 marks and each subjective question carried 5 marks. The quiz was of 75 marks. Find out the number of multiple choice questions asked in the quiz.

A
5

B
13

C
15

D
25

Solution

Let the number of MCQs be m.
So, number of subjective questions = 30 - m
Also, as the question paper is of 75 marks, we have 2m + 5(30 - m) = 75
Or, m = 25
Question 10
1 / -0

On a busy day, 2000 sweets were sold by a confectionery. Total amount collected on that day was Rs. 9600. If the cost of mint flavoured sweets is Rs. 8/sweet, the cost of chocolate sweets is Rs 4/sweet, then how many mint sweets and chocolates sweets were sold that day?

A
400, 1600

B
200, 1800

C
825, 1650

D
1000, 1000

Solution

Number of sweets sold = 2000

Cost of mint sweet = Rs. 8, and cost of chocolate sweet = Rs. 4.

Let x be number of mint sweets sold, and y be the number of chocolate sweets sold.

x + y = 2000 (i)

and, 8x + 4y = 9600 (ii)

Multiplying the equation (i) by 4 and subtracting from eq. (ii)

4x = 9600 - 8000

4x = 1600 , Hence x = 400

Putting the value in equation (i),

400 + y = 2000

y = 2000 - 400 = 1600

Hence, the number of mint sweets sold = 400, and number of chocolate sweets sold = 1600
Question 11
1 / -0

Three plots having areas 132, 204 and 228 square metres are to be sub-divided into equal sized flower beds. If the breadth of a bed is 3 metres, then find the maximum length that each bed can have.

A
18 metres

B
12 metres

C
3 metres

D
4 metres

Solution

HCF of 132, 204 and 228 = 2 × 2 × 3 = 12
Area of the bed = 12 square metres
Breadth of each bed = 3 metres
Length of each bed = 12 ÷ 3 = 4 metres
Question 12
1 / -0

A pencil is cylindrical in shape with a length of 20 cm and a cross-sectional radius of 1 cm. It is sharpened using a good sharpener on both the sides such that the shape on either end of the cylindrical pencil is that of a right circular cone with a height of 3 cm. If there is no change in the net length of the pencil due to sharpening, what is the volume of the material that was removed from the pencil to sharpen the edges?

A
6π cm³

B
5π cm³

C
4π cm³

D
2π cm³

Solution

nitial volume of pencil = 1² ^_π 20 = 20^_πcm³
Volume of pencil after sharpening = 2 × (volume of cone) + volume of middle cylinder
= 2 ×1/3^_π (1)²(3) + ^_π π1² ^_×14
= 2^_π + 14^_π = 16^_π cm³
Thus, volume of material chiselled = 20^_π – 16^_π = 4^_π cm³
Question 13
1 / -0

Two farmers Ravi and Ram have 40 goats in total. They sell their goats at different prices, but each of them receives the same amount of money. If Ravi had sold his goats at Ram's price, he would have received Rs. 5,400. If Ram had sold his goats at Ravi's price, he would have received Rs. 2,400. How many goats does Ravi have in total?

A
16

B
18

C
24

D
28

Solution

Assume Ravi and Ram have n and 40 – n goats, respectively.
Ravi's selling price = Rs. x, and Ram's selling price = Rs. y
So, xn = y (40 – n) ...(1) (As given)
If prices are interchanged,
then ny = 5400 ...(2)
And, x (40 – n) = 2400 …(3)
Solving (1), (2) and (3), we get n = 24.

User

Question Analysis

Correct -
Wrong -
Skipped -

My Perfomance

Score
-
out of -
Rank
-
out of -

Re-Attempt Weekly Quiz Competition

IMO - Mock Test - 1

Result

IMO - Mock Test - 1

Score

-

Rank

-

SHARING IS CARING

Question 1

204 - 17 + 13 × 12 ÷ 4 = 164

204 - 17 + 13 ÷ 12 × 4 = 164

204 ÷ 17 × 13 + 12 - 4 = 164

204 ÷ 17 - 13 + 12 × 4 = 164

Solution

Question 2

Earth

Jupiter

Sun

Saturn

Solution

Question 3

176

196

200

7340

Solution

Question 4

9

12

15

60

Solution

Question 5

First quadrant

Second quadrant

Third quadrant

Fourth quadrant

Solution

Question 6

(0, 0)

(0, 1)

(1, 0)

(1, 1)

Solution

Question 7

3 : 1

2 : 1

3 : 2

4 : 1

Solution

Question 8

Wednesday

Tuesday

Monday

Thursday

Solution

Question 9

5

13

15

25

Solution

Question 10

400, 1600

200, 1800

825, 1650

1000, 1000

Solution

Question 11

18 metres

12 metres

3 metres

4 metres

Solution

Question 12

6π cm3

5π cm3

4π cm3

2π cm3

Solution

6π cm³

5π cm³

4π cm³

2π cm³