IMO - Mock Test...

Two rows of numbers are given. The resultant of each row is to be worked out separately based on the following rules, and the question below the rows of numbers is to be answered. The operations of numbers in each row progress from left to right.

Rules:
(i) If an odd number is followed by another odd number, they are to be multiplied.
(ii) If an even number is followed by another even number, the first number is to be divided by the second even number.
(iii) If an even number is followed by the perfect square of an odd number, the first number is to be subtracted from the second number.
(iv) If an odd number is followed by an even number, the two are to be added.
(v) If an even number is followed by an odd number which is not a perfect square, the square of the odd number is to be added to the even number.

Pointing to a woman in a photograph, a man says, ''She is the grandmother of the son of my daughter-in-law's mother-in-law.'' How is the woman related to the man?

A man travelled 400 metres straight from his office. He then turned left and travelled 500 metres straight, after which he turned left again and travelled 400 metres straight. Finally, he turned right and walked another 600 metres straight. How far is he from his office?

Select the correct mirror image of the given Fig. (X) if the mirror is placed along MN.

Select a figure from the options which satisfies the same conditions of placement of the dots as in Figure (X).

There is a definite relationship between figures (1) and (2). Establish a similar relationship between figures (3) and (4) by selecting a suitable figure from the options that would replace the question mark (?) in figure (4).

Read the following information carefully and answer the question given below it.

(i) There is a group of six persons A, B, C, D, E and F in a family. They are Psychologist, Manager, Lawyer, Jeweler, Doctor and Engineer.
(ii) The doctor is the grandfather of F who is a Psychologist.
(iii) The Manager D is married to A.
(iv) C, the Jeweler, is married to the Lawyer.
(v) B is the mother of F and E.
(vi) There are two married couples in the family.

How is A related to E?

Arun is fifth from the left end and Navin is twelfth from the right end in a row of children. If Navin shifts by three places towards Arun, he becomes tenth from the left end. How many children are there in the row?

Select a figure, from among the options, which when placed in the blank space of Fig. (X) would complete the pattern.

If 'Book' is called 'Pen', 'Pen' is called 'Paper', 'Paper' is called 'Eraser', 'Eraser' is called 'Scale' and 'Scale' is called 'Calculator', then with which does a student write?

Select a figure from the options that illustrates the relationship amongst ''pigeons, birds, dogs''.

If the first and the second letters of the word MISJUDGEMENTS are interchanged with the last and the second last letters respectively, and similarly the third and the fourth letters are interchanged with the third last and the fourth last letters respectively, and so on, then what will be the fifth letter to the right of the third letter from the left end?

Two positions of a dice are given below. When 1 dot is at the top, which number will be at the bottom?

Directions: In the following question, the symbols @, ©, $ and % are used with the different meanings as given below:

A $ B means 'A is not smaller than B'.
A @ B means 'A is neither smaller than nor equal to B'.
A © B means 'A is neither smaller than nor greater than B'.
A % B means 'A is neither greater than nor equal to B'.

Now, assuming the following statements to be true, find out which of the three conclusions, I, II and III given below them is/are definitely true and give your answer accordingly.

Statements:
K © P, P @ Q, Q $ R
Conclusions:
I. K @ R
II. R % P
III. Q % K

Select a number which will replace the question mark (?) in the number pattern given below.

Find the remainder when 2x³ - 9x² + x + 12 is divided by 2 + 3x.

In which quadrant does the point P(x, y) lie if xy < 0?

If x² + = 98, find the value of x³ + .

The factors of 8a³ + b³ - 6ab + 1 are

Evaluate: (2x - y + 3z)(4x² + y² + 9z² + 2xy + 3yz - 6xz)

A box of chocolates contains 5 chocolates with hard centre and 4 with soft centre. Amit takes a chocolate, selected at random, from the box and eats it. Ajay then takes a chocolate, selected at random, from the box. Find the probability that Amit and Ajay both choose a chocolate with hard centre.

In the given figure, ABC has sides AB = 7.5 cm, AC = 6.5 cm and BC = 7 cm. On the base BC, a parallelogram DBEC of area same as that of ABC is constructed. Find the height DF of the parallelogram.

The number of dimensions a point has is

A solid iron rectangular block of dimensions (2.2 m × 1.2 m × 1 m) is cast into a hollow cylindrical pipe of internal radius 35 cm and thickness 5 cm. Find the length of the pipe.

In the given figure, ABCD and ABEF are two cyclic quadrilaterals. If BCD = 110°, then BEF is equal to

Simplify:

The figure below is the net of a prism made up of identical triangles. What is the total area of the faces of the prism if the side of the square is 6 cm?

The mean of 25 numbers is 8. If 2 is added to each number, what will be the new mean?

Euclid stated that all right angles are equal to each other in the form of a/an

In the given figure,

(i) AB BF and EF BF
(ii) AC = BC
(iii) KD is perpendicular to BC and DE.


Find the measure of x.

If 2^x = 4^y = 8^z and , then the value of z is

Each edge of a cube is increased by 50%. Find the percentage increase in the surface area of the cube.

What is the area of the shaded part in the given figure? (Take )

In the given figure, AB II CD and EF II DQ. Determine PDQ, AED and DEF, respectively.

The pie chart shows the grades attained by a group of students in a common test.



If 240 students sat for the common test and those who obtained grades D and E failed the test, then how many students passed the test?

The taxi fare in a city is Rs. 25 for first kilometre and Rs. 10.5 for next each subsequent kilometre. A traveller is charged Rs. 109 as the fare. How many kilometres did he travel?

A bookseller procures 40 books for 3200 and sells them at a profit equal to the selling price of 8 books. What is the selling price of one dozen books, if the price of each book is same?

Four years ago, the average age of a family of 6 members was 25 years. Meanwhile, a child was born in the family; still the average age of the whole family is same today. The present age of the child is

A moneylender borrows money at 4% p.a. and pays interest at the end of the year. He lends it at 6% p.a. compounded half-yearly and receives the interest at the end of the year. Thus, he gains Rs. 104.50 a year. The amount of money he borrows is

A certain factory employed 600 men and 400 women and the average wage was Rs. 25.50 per day. If a woman got Rs. 5 less than a man, then what were the daily wages of a man and a woman, respectively?

Three lightships flash simultaneously at 6:00 a.m. The first lightship flashes every 12 seconds, the second lightship every 30 seconds and the third lightship every 66 seconds. At what time will the three lightships next flash together?

A man earns Rs. 20 on the first day and spends Rs. 15 on the next day. He again earns Rs. 20 on the third day and spends Rs. 15 on the fourth day. If he continues to save like this, then how soon will he have Rs. 60 in hand?

The price of a car depreciates in the first year by 25%, in the second year by 20%, in the third year by 15% and so on. The final price of the car after 3 years(in Rs.), if the present cost of the car is 10,00,000 is

A car travelling at of its usual speed covers 42 km in 1 hour 40 mins 48 secs. What is the usual speed of the car?

Cubical boxes of volume 15,625 cm³ each are put in a cubical store of side 2.5 m.

(i) How many such boxes can be put in the store?
(ii) What are the dimensions of the box?

Consider the figure below.



The ratio of the area of I to that of II is 8 : 1. The area of III is as much as the area of II. If the difference between the area of I and area of II is 252 cm², then

(P) Area of I
(Q) Area of II + III

Which of the following statements is INCORRECT?

Fill in the blanks.

(P) Any point lying on x-axis is of the form ______.
(Q) The abscissa of a point on y-axis is _______.
(R) The point at which the two coordinate axes meet is called the ________.
(S) The perpendicular distance of the point (4, 5) from x-axis is ________.
(T) The perpendicular distance of the point (3, 7) from y-axis is ________.

Following are the steps of construction of PQR, given that QR = 3 cm, PQR = 45° and QP - PR = 2 cm.
Arrange them and select the correct option.

(i) Make an angle XQR = 45° at point Q of base QR.
(ii) Join SR and draw the perpendicular bisector of SR say AB.
(iii) Draw the base QR of length 3 cm.
(iv) Let bisector AB intersects QX at P. Join PR.
(v) Cut the line segment QS = QP - PR = 2 cm from the ray QX.

Select the correct option.

Statement 1: (x + y)³ = x³ + y³ + 3xy(x + y) and (x² + y²) = (x + y)² + 2xy

Statement 2: If x² + = 7, then the value of x³ + = 18