IMO - Mock Test...

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

Rules:
(i) If an even number is followed by another even number, they are to be added.
(ii) If an even number is followed by a prime number, they are to be multiplied.
(iii) If an odd number is followed by an even number, the even number is to be subtracted from the odd number.
(iv) If an odd number is followed by another odd number, the first number is to be added to the square of the second number.
(v) If an even number is followed by a composite odd number, the even number is to be divided by the odd number.

Kalyani is mother-in-law of Veena who is sister-in-law of Ashok. Dheeraj is father of Sudeep, the only brother of Ashok. How is Kalyani related to Ashok?

Inspector Jatin travelled 400 metres from his police station. He then turned left and travelled 500 metres straight, after which he turned left again and travelled 400 metres straight. Then, he turned right and walked another 600 metres straight. How far is he from the police station?

Select the correct water image of given combination of letters and numbers.

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Select a figure from the options which satisfies the condition of placement of dots as in Fig. (X).

Select a figure from among the options which will continue the same series as established by the five Problem Figures P, Q, R, S and T.

Study the following information carefully and answer the question given below.
P, Q, R, S, T, V and W are Seven passengers and I, II, III are three different vehicles. There are at least two passengers in each vehicle I, II and III and one of them is a lady. There are two engineers, two doctors and three teachers among them. R is lady doctor and she does not travel with the pair of sisters P and V. Q, a male engineer travels with only W, a teacher in vehicle I. S is a male doctor. Two persons belong to same profession do not travel in the same vehicle. P is not an engineer and travels in vehicle II.

How many lady members are there amongst them?

Rita stands third in a row of twenty students, arranged in ascending order of heights. Five new students join the group, all taller than Rita. What will be Rita's position if the students are now arranged in descending order of their heights?

Select a figure from the options which will complete the pattern in Fig. (X).

If RUST = 9-6-8-7 and BOARD = 25-12-26-9-23, then how will you code "BEAT"?

Which of the following Venn diagrams best represents the relationship amongst, ''Honesty, Intelligence, and Aptitude''?

The letters in the word ULTRAVIOLET are arranged in the alphabetical order and each letter is assigned a numerical value equal to its serial number as in the English alphabet. What will be the difference between the sum of odd-positioned numbers and that of even-positioned numbers?

A cube of side 10 cm is colored red with a 2 cm wide green strip along all the sides on all the faces. Now, the cube is cut into 125 smaller cubes of equal size. How many cubes have three green faces each?

Code the group of digits as per the scheme and conditions given below.



Conditions:
(i) If the first as well as the last digit is odd their codes are to be interchanged.
(ii) If the first digit is even and the last digit is odd both are to be coded by the code for odd digit.
(iii) If the last digit is '0' it is to be coded by 'X'.
(iv) If the first as well as the last digit is even both are to be coded by '-'.

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A set of three figures X, Y and Z shows a sequence of folding of a piece of paper. Figure (Z) shows the manner in which the folded paper has been cut. Select the figure from the options which would resemble the unfolded form of paper.

The points, whose abscissa and ordinate have different signs, lie in quadrants _______.

Which of the following is a true statement?

The value of 3 is

The expression 2x³ + ax² + bx + 3, where a and b are constants, has a factor of x - 1 and leaves a remainder of 15 when divided by x + 2. Find the values of a and b, respectively.

In the given figure, AOB is a straight line and AOX₃ = 57°, X₁OX₄ = 97°, X₃OB = 123° and X₄OB = 68°. Find AOX_1.

Find the value of .

Which of the following statements is INCORRECT?

The degree of the polynomial 3x² + 12 - + 12x + 4 is

'L', 'B' and 'H' of a cuboid are increased, decreased and increased by 1%, 3% and 2%, respectively. The volume of the cuboid will ______.

The area of the triangle formed by 2x + 3y = 6 and the coordinate axes is ________.

The perimeter of a triangle is 6p² - 4p + 9 and two of its sides are p² - 2p + 1 and 3p² - 5p + 3. Find the third side of the triangle.

In the given figure, ABCD is a rectangle. BD = BE, BED = 40° and EDA = 260°. Find CDB.

In the given figure, line l is II line BC and D is the mid-point of BC.
If area (ABC) = x × area (EDC), then find the value of x.

Fill in the blanks:

If a straight line falling on two straight lines make the interior angles on the same side of it, taken together are ____ than two right angles, then the two straight lines, if produced indefinitely, meet on that side on which the sum of angles is less than ____ right angles.

From the given information, find the probability of people with ages 60, 61 and 64 who can drive.

Factors: x⁴ + 5x³ + 5x² - 5x - 6

A certain distance is covered at a certain speed (s₁). If half of this distance is covered in double the time at speed (s₂). Find the ratio of the two speeds. Also, if s₁ is 60 km/hr, then find s₂.

'Lines are parallel if they do not intersect' is stated in the form of

The two circles shown below have radii x and 3x. A point is chosen, at random, inside the larger circle. Find, in its simplest fractional form, the probability that this point is in the shaded area.

Number of players participating in three different games in five different schools.



Number of players participating in Kho-Kho from School-4 is what percent of number of players participating in hockey from School-2?

The population of a town was 1,60,000 three years ago. If it had increased by 3%, 2.5% and 5% in the last three years, then find its present population.

The sides of a quadrangular field, taken in order are 26 m, 27 m, 7 m and 24 m respectively. The angle contained by the last two sides is a right angle. Find its area.

A alone can complete a work in 16 days and B alone in 12 days. Starting with A, they work on alternate days. The total work will be completed in ______________

A triangular park in a city has dimensions 100 m × 90 m × 110 m. A contract is given to a company for planting grass in the park at the rate of Rs. 4,000 per hectare. Find the amount to be paid to the company.
(Take = 1.414)

Eight people are planning to share equally the cost of a rental car. If one person withdraws from the arrangement and the others share equally the entire rental of the car, then the share of each of the remaining persons is increased by ___________ of the original share.

The taxi charges in a city comprise of a fixed charge, together with the charge of the distance covered. For a journey of 16 km, the charges paid are Rs. 156 and for a journey of 24 km, the charges paid are Rs. 204.

What will a person have to pay for travelling a distance of 30 km?

If 6 years are subtracted from the present age of Gagan and is divided by 18, then the present age of his grandson Anup is obtained. If Anup is 2 years younger to Madan whose age is 5 years, then what is Gagan's present age?

A trader purchases 70 kg of tea at Rs. 15 per kg and 30 kg of tea at Rs. 18.50 per kg. If the packing charges are 2%, then at what price he must sell the mixture of two to gain 15%?

The population of a city had increased successively at the rate of 6%, 4% and 2% per annum during last three years. If its present population is 11,24,448, then what was its population three years ago?

The cost price of an article A is Rs. 160 and selling price of another article B is Rs. 240. If the selling price of A be equal to the cost price of B, then the profit after selling A is 20%. What is the profit on B?

The figure below is made up of one big circle, two identical medium circles and two identical small circles.
The ratio of the radius of the small circle to the radius of the medium circle is 2 : 3.

(a) What is the total area of the unshaded part in the figure?
(b) What fraction of the big circle is shaded?

Study the statements carefully.

Statement I: If P(x) is a polynomial of degree 1 and ax + b is a factor of P(x), then we have P = 0.
Statement II: If P(x) is a polynomial of degree 1, then polynomial (x - a) (x - b) is a factor of P(x), if P (a) = 0 and P (b) = 0.

ABCDE.... is part of a regular polygon which has interior angles of 160°. CDLM is a square.



Find the value of x and y respectively.

State True (T) or False (F).

(P) In a ABC, if E is the midpoint of median AD, then ar(BED) = ar(ABC).
(Q) A parallelogram and a rectangle on the same base and between the same parallels are equal in area.
(R) If a triangle and a parallelogram are on the same base and between the same parallels, then the ratio of the area of the triangle to the area of the parallelogram is 1 : 2.
(S) If in a trapezium ABCD, it is given that AB || DC and the diagonals AC and BD intersect at O, then, ar (AOB) = ar (COD).

A, B, C are three sets of values of x:

A: 2, 3, 7, 1, 3, 2, 3
B: 7, 5, 9, 12, 5, 3, 8
C: 4, 4, 11, 7, 2, 3, 4

Which one of the following statements is correct?