IMO - Mock Test...

Select the correct water image of the given figure.

The question consists of a set of three figures P, Q and R showing a sequence of folding a piece of paper. Figure (R) shows the manner in which the folded paper has been cut. Select the figure from the options which would most closely resemble the unfolded form of figure (R).

Select a letter which replaces the question mark (?), if the same rule is followed either row-wise or column-wise.

In a certain code language, the word CONFUSED is written as EMNBEFTV. How will the word SECLUDED be written in that language?

lf 'P + Q' means 'P is the mother of Q', 'P Q' means 'P is the brother of Q', 'P # Q' means 'P is the father of Q' and 'P * Q' means 'P is the sister of Q', then how is L related to O in 'K L + M # N * O'?

Which of the following Venn diagrams best represents the relationship among Women, Boys and Students?

There is a certain relationship between figures (i) and (ii). Establish a similar relationship between figures (iii) and (iv) by selecting a suitable figure from the options which will replace '?' in figure (iv).

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 of numbers is to be answered. The operations on numbers progress from left to right.

Rules:
(i) If a 2-digit even number is followed by another even number, then the first one is to be divided by the second one.
(ii) If an even number is followed by a prime number, then the two are to be multiplied.
(iii) If an odd number is followed by another odd number, then the two are to be added.
(iv) If a 3-digit number is followed by a 2-digit number which is a perfect square, then the second number is to be subtracted from the first number.
(v) If a 3-digit number is followed by another 3-digit number which is not a perfect square, then the first number is to be divided by the second one.



If m is the resultant of the first row, then what will be the resultant of the second row?

Select a figure from the options which is exactly embedded in Fig. (X) as one of its parts.

Three figures (X), (Y) and (Z) show a sequence of folding of a sheet of paper. Figure (Z) shows the manner in which the folded paper has been cut. Select a figure from the options which represents the unfolded form of figure (Z).

Sonali walks 20 m North. Then she turns right and walks 30 m. Then she again turns right and walks 35 m. In which direction and how many metres away is she from her original position?

If the interchange of signs '×' and '-' is made in each of the following options, then which of the following is correct?

Find the minimum number of straight lines required to make the given figure.

Directions: Study the following information carefully and answer the question.

(i) A, B, C, D, E, F and G are playing cards sitting around a circular table.
(ii) D is not the immediate neighbour of C and E.
(iii) A is the immediate neighbour of B and C.
(iv) G, who is second to the left of D, is the immediate neighbour of E and F.

What is the position of C?

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

In the given figure, line RT is drawn parallel to SQ. If QPS = 100°, PQS = 40°, PSR = 85° and QRS = 70°, then QRT = _______.

If a number 54x49y is divisible by 90, then what is the value of ?

Which of the following is equal to 25?

If 540 is 10% of y and z% of y is 16,200, then find the value of y and z respectively.

In a rectangle, if the difference between the sum of adjacent sides and the diagonal is one-fourth the length of longer side, then 7 times the length of longer side is ______ times the length of shorter side.

Which of the following statements is/are incorrect?

Find the smallest whole number that must be subtracted from 899 to make it a perfect cube.

The numerator and the denominator of a rational number are in the ratio 5 : 7. When 6 is added to both the numerator and denominator, the ratio becomes 4 : 5. What is the rational number?

Factorise: 25(x + y)² - 36(x - 2y)²

To construct a unique parallelogram, the minimum number of measurements required is ________.

Which of the following rational numbers does not lie between and ?

Simplify:

The difference between compound interest and simple interest on a sum for 2 years at 8% p.a. is Rs. 768. Find the sum.

Which of the following equations have x = 12, as its solution?

How much more does the family spend on clothing than on savings?

How much does the family spend on rent, food and clothing in a year, if the expenditure is same throughout the year?

If (a² + b²)³ = (a³ + b³)² and ab 0, then is equal to ______.

Using Euler's formula, find the value of P, Q and R.

Three cuboids of dimensions 20 cm × 30 cm × 130 cm, 50 cm × 60 cm × 70 cm and 40 cm × 70 cm × 80 cm are melted to form a cube. Find the side of the cube formed.

Solve for x:
(i) 2(x + 5) - (x - 6) = 3(x + 7) - 3
(ii) (3x + 4)² + (3x - 2)² = (6x + 5) (3x - 2) + 12

A farmer has a field in the shape of an isosceles trapezium whose perimeter is 215 m. One of its non-parallel sides is 50 m. What is the sum of its parallel sides?

Shalini tosses a biased coin 98 times, and head is obtained 56 times. If the coin is tossed at random, then what is the probability of getting a tail?

A sugar factory has annual sales of 3,72,00,00,000 kg of sugar. Express this quantity in the standard form.

A shopkeeper fixes the marked price of a pair of shoes 45% above its cost price. What is the percentage of discount allowed to gain 16%?

A group of students decided to collect as many paise from each member of the group as is the number of members. If the total collection amounts to Rs. 59.29, then the number of members in the group is ________

A water pump pumps out 14 L of water per minute from a reservoir. How many litres of water will be pumped out in 1 of an hour?

Present ages of Trishika and Sanchi are in the ratio of 5 : 4 respectively. Three years hence, the ratio of their ages will become 11 : 9 respectively. What is Sanchi's present age?

The circumference of the base of a circular cylinder is 8 cm. The height of the cylinder is same as the diameter of the base. How much water can the cylinder hold?

A loan was repaid in two annual instalments of Rs. 3630 each. If the rate of interest be 10% per annum compounded annually, then find the sum that was borrowed.

Mr Hooda sets up a business and invests Rs. 80,000. During the first three successive years, his profits were 20%, 30% and 40% respectively. Find his total profit, if each year the profit was on previous year's capital.

State 'T' for true and 'F' for false and select the correct option.

(i) If Sunil bought a laptop for Rs. 44,000 including a tax of 10%, then price of the laptop before the tax was added was Rs. 40,000.

(ii) x % of y is equal to y % of x.
(iii) The compound interest on Rs. 12,000 for 1 years at 10 % per annum compounded half yearly is Rs. 13,891.50.
(iv) lf a retailer sells an alarm clock for Rs. 350 and gains of its cost price, then the cost price is Rs. 250.

Match the following and select the correct option.

Column – I Figure	Column – II a + b
(P)	(i) 205°
(Q)	(ii) 240°
(R)	(iii) 220°
(S)	(iv) 216°

Arrange the following steps in the correct order while constructing a trapezium PQRS in which SR II PQ, PQ = 11 cm, QR = 9 cm, PS = 9.5 cm and Q = 70°.

Step 1: With Q as centre, draw PQY = 70°.
Step 2: With R as centre, draw QRZ = 110°.
Step 3: Draw PQ = 11 cm.
Step 4: With P as centre, draw an arc of radius 9.5 cm which meets RZ at point S.
Step 5: With Q as centre, draw an arc of radius 9 cm on and mark the point as R.
Step 6: Join PS.

If seven slips of paper are labelled as 1, 2, 3, 4, 6, 7, 8 and one is drawn out of it, then

(i) What is the probability that it is 3?
(ii) What is the probability that it is greater than 5?
(iii) What is the probability that it is an even number?

In the given figure (not drawn to scale), find the value of (b + d) - (a + c).