# Which of the following pairs of numbers can be the number of adults and childrens?

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1 Certain number of persons comprising adults and children went to an exhibition. Entry ticket for the children is Rs 1.50 and Rs 4.50 for the adults. Total cost of the tickets come out to be Rs 600. Which of the following pairs of numbers can be the number of adults and childrens? A. 90, 70 B. 100, 60 C. 110, 50 D. 120, 40 Mean of five observations is 7, on excluding two observations, the mean reduces to 6. On adding, the difference of the two excluded observations, the mean of the four observations becomes. What are the two excluded observations? A. 2, 9 B. 6, 13 C. 5, 12 D. 8, 15 Which of the following graph correctly represents the line 4x 3y = 24? A. B. C. D.

2 The sum of squares of 100 observations was calculated as Later, it was found that two values, 53 and 42, were wrongly read as 35 and 24, at the time of calculation. The corrected sum of squares is A B C D If a cone and a cylinder of same radii have the same volume, then what is the ratio of the heights of the cone and the cylinder? A. 1:1 B. 1:2 C. 2:1 D. 3:1 The given figure shows a circle with centre O. What is the measure of OCA? A. 10 B. 15 C. 20 D. 25 A survey is conducted to know the number of mobile phones used in each family of a certain locality of 1000 families. The given data shows the results of the survey. Number of mobile phones Number of families What is the probability that a randomly chosen family has 4 mobile phones?

3 A. B. C. D. What is the length of the line segment joining the mid points of the diagonals of a trapezium that is parallel to each of the parallel sides having lengths 12 cm and 4 cm. A. 2 cm B. 3 cm C. 4 cm D. 6 cm The given figure shows a triangle ABC in which medians AD, BE, and CF intersect at point G. If the area of ABC is 30 cm 2, then what is the area of the shaded region? A. 7.5 cm 2 B. 10 cm 2 C cm 2 D. 15 cm 2 Which of the following graphs correctly represents the line 3x + 4y = 12?

4 A. B. C. D. The arithmetic mean of a series of 20 items was calculated as 20. While calculating it, an item 13 was measured as 30. The correct arithmetic mean is A B

5 C D A hemispherical bowl of thickness 0.7 cm is made up of a metal such that the inner radius of the bowl is 2.1 cm. The cost of the metal used is Rs 1.5 per cm 3. What is the approximate cost of the metal used to make such a bowl? A. Rs 30 B. Rs 35 C. Rs 40 D. Rs 45 The given figure shows a circle with centre O. What is the measure of BOC? A. 45 B. 55 C. 70 D. 80 A die is thrown 400 times and the outcome of each throw is noted down. The given table shows the frequencies of the outcomes. Number on the top face of the die Frequency What is the probability of getting the number 5 in the next throw? A

6 B C D The given figure shows a quadrilateral ABCD in which the diagonals AC and BD intersect each other at O. AB = BC, CAD = 25 and Area ( AOB) = Area ( COD). What is the measure of ABC? A. 130 B. 140 C. 145 D. 155 If a variable takes discrete values like x + 4, median is, then the A. B. C. D. f a cone of height 24 cm is surmounted on a cylinder of radius 7 cm and height 30 cm, then what is the ratio of the curved surface area of the cone to that of the cylinder? A. 5:12 B. 5:21 C. 12:13 D. 25:26 The mean income of a group of workers is and that of another group of workers is. If the number of workers in the second group is 10 times the number of workers in the first group, then the mean income of the combined group of workers is

7 A. B. C. D. A cone and a cylinder have the same base area. The height and radius of these two solids are the same. If a sphere has the same radius as that of the cone, then what is the ratio of the volumes of the cone, the sphere and the cylinder? A. 1: 4: 1 B. 1: 2: 1 C. 1: 4: 3 D. 1: 2: 3 The straight line 2x 5y = 5 meets the negative y-axis at a point whose coordinates are A. (0, 3) B. (1, 2) C. (1, 2) D. (0, 1) The mean of a set of numbers is. If each number is divided by 3, then the new mean is A. B. C. D. The total surface areas of the two hemispheres are in the ratio 25: 16. If the sum of their radii is 9 cm, then what are the respective radii of the two hemispheres? A. 8 cm and 1 cm B. 7 cm and 2 cm C. 6 cm and 3 cm D. 5 cm and 4 cm The arithmetic mean of n numbers is. If the sum of the first (n 1) numbers is k, then the n th number is A.

8 B. C. D. If a cone and a cylinder have the same base area and the same volume, then what is the ratio of their respective heights? A. 1: 1 B. 3: 1 C. 4: 9 D. 9: 1 The mean weight of a group of 6 students and a teacher is 41 kg. If the teacher is excluded from the group, then the mean weight gets reduced by 2.5 kg. What is the weight of the teacher? A. 42 kg B. 45 kg C. 56 kg D. 57 kg If the radius of a sphere is increased by 10%, then what is the percentage increase in the surface area of the sphere? A. 10% B. 21% C. 100% D. 121% The given figure shows a circle with centre O.

9 What is the measure of APD? A. 20 B. 25 C. 30 D. 35 The given figure shows a circle with centre O, where XY is the tangent to the circle at point A. AB is the angle bisector of XAC. What is the measure of CAY? A. 65 B. 50 C. 45 D. 30 The given figure shows a parallelogram ABCD in which X and Y are the mid-points of sides AB and AD respectively. If the area of CXY = 24 cm 2, then what is the area of parallelogram ABCD? A. 32 cm 2 B. 48 cm 2 C. 64 cm 2 D. 96 cm 2

10 In the given figure, XY is the tangent at point C of the semi-circle with centre O. What is the measure of BCY? A. 20 B. 30 C. 40 D. 50 In the given figure, XY is the tangent at point C of the semi-circle with centre O. What is the measure of BCY? A. 20 B. 30 C. 40 D. 50 The given figure shows a quadrilateral ABCD. A line drawn from A parallel to BD intersects CD produced at Q. BP is a line parallel to CQ such that QP BP. If CQ = 22 cm and PQ = 5 cm, then what is the area of quadrilateral ABCD? A. 55 cm 2 B. 65 cm 2

11 C. 165cm 2 D. 220 cm 2 The given figure shows a circle with centre O. What is the measure of DAC? A. 25 B. 45 C. 65 D. 75 In the given figure, ABCD is a rhombus and PQCB is a rectangle. If AC = 12 cm and BD = 16 cm, then what is the measure of PB? A. 8 cm B. 9.6 cm C. 10 cm D cm Ashu hired a cab in the night to go to a party. The cab provider told him that he will charge Rs 1000 for the cab and an extra charge of Rs 100 will be applicable for each hour after 12:00 a.m.

12 Ashu used the cab for x hours more after 12:00 a.m. If y is the total amount paid by Ashu, then which equation represents the given situation? A. y + 100x = 1000 B. y = 100x C. y = x D. y + 100x = 0 What is the measure of ABC in the given figure? A. 21 B. 31 C D The given figure shows a parallelogram PQRS in which A and B are any two points in the interior region. AS and BP intersect each other at C, while AR and QB intersect each other at D. If area (ASBR) = 35 cm 2 and area (ACBD) = 20 cm 2, then what is the area of the shaded portion? A. 35 cm 2 B. 50 cm 2 C. 55 cm 2 D. 70 cm 2 What is the area of the region enclosed by the lines x = 0, y = 0 and x + y = 2?

13 A. square units B. square units C. 2 square units D. 4 square units The ratio of radii of a cylinder and cone is 1: 3 and the ratio of their heights is 3: 4. What is the ratio of the volumes of the cylinder and the cone? A. 1: 4 B. 3: 4 C. 1: 9 D. 4: 9 What are the respective values of x and y in the given figure? A. 40 and 45 B. 45 and 40 C. 135 and 165 D. 160 and 135 If (1, k) is a solution of the equation 2x + 5y = 12, then what is the value of k? A. 1 B. C. 2 D.

14 What is the measure of EFC in the given figure? A. 59 B. 76 C. 104 D. 121 If the line ax + by + c = 0 is parallel to x-axis, then which of the following relations is correct? A. a = 0 B. b = 0 C. c = 0 D. a = b A hemispherical tub is full of water. The water is to be emptied in cylindrical bottles. The radius of the cylindrical bottles is the same as that of the hemisphere. The height of the bottles is one-sixth of their radius. How many cylindrical bottles can be filled from the water in the hemispherical tub? A. 2 B. 4 C. 6 D. 8 In the given figure, ABC is an isosceles triangle with AB = BC.

15 What are the respective measures of EDC and DEC? A. 64 and 18 B. 108 and 18 C. 116 and 64 D. 134 and 108 A metallic cylinder of radius 8 cm and height 20 cm is melted and recasted into 15 equal small spheres. What is the diameter of each sphere? A. 2 cm B. 4 cm C. 8 cm D. 16 cm A circle with centre O is shown in the given figure. What is the measure of BDC? A. 60 B. 80 C. 100 D. 120 The slant height and the curved surface area of a cone are 13 cm and 65π cm 2 respectively. What is the volume of the cone? A. 49π cm 3 B. 95π cm 3 C. 100π cm 3 D. 169π cm 3

16 In the given figure, a circle with centre O is shown. What is the measure of BAC? A. 60 B. 80 C. 120 D. 160 se the following information to answer the next question. A function table is given as: x y The rule followed by the function table is A. y = x 1 B. y = x 2 C. y = x 3 D. y = x 4 The mean weight of ten students is 35 kg. When two more students were included in the group, the mean increased by 1 kg. If the weight of both the new students is the same, then what is the weight of each of the new students? A. 43 kg B. 41 kg C. 39 kg D. 37 kg

17 In the given figure, XY = 6 cm and YZ = 8 cm. P and Q are the mid-points of XY and XZ respectively. What is the area of XPQ? A. 6 cm 2 B. 8 cm 2 C. 12 cm 2 D. 14 cm 2 In parallelogram ABCD, AB = 20 cm and BC = 10 cm. P is the mid-point of side AB. A line through B parallel to PD meets CD at Q and AD produced at R. What is the measure of AR? A. 15 cm B. 17 cm C. 20 cm D. 30 cm The ages of Bob and his father are related by the expression y = 4x 5 where x is Bob s age and y is his father s age. Which of the following conclusions is true about the given expression? A. Bob s father s age is five less than four times Bob s age B. Bob s father s age is four less than five times Bob s age C. Bob s father s age is four times Bob s age D. Bob s father s age as five times Bob s age

18 The mean of eight numbers is 21. If the mean of the first six numbers is 20 and the mean of the last six numbers is 21.5, then what is the mean of the middle four numbers? A B. 19 C D. 23 In the given figure, AB is the diameter of the circle with centre O and D is a point on the circle. C is a point on AD such that OC AD. What is the perimeter of ABD if the perimeter of AOC is 20 cm? A. 30 cm B. 40 cm C. 50 cm D. 60 cm x i f i What is the mean of the given frequency distribution? A B C D

19 In a class of 80 students, 25 students like to play hockey and 55 students like to play football. What is the probability that a randomly chosen student likes to play hockey? A. B. C. D. The given frequency distribution table shows the marks obtained by a group of students of a particular class. Marks obtained Number of students b 4 If the mean of the marks obtained by the students is 68.5, then what is the value of b? A. 7 B. 6 C. 4 D. 3 The given figure shows a circle with XWY = 70 and WZX = 30. What is the measure of WXY? A. 70 B. 80 C. 100 D. 110

20 The given figure represents a parallelogram PQRS in which PM and RN are perpendiculars drawn to the diagonal QS. If the area of the shaded region is 40 cm 2, then what is the area of the parallelogram PQRS? A. 60 cm 2 B. 80 cm 2 C. 100 cm 2 D. 120 cm 2 Jack s height is x inches and his brother s height is y inches. Jack s brother is one foot shorter than Jack. Which of the following equations correctly represents the given situation? A. x = y + 1 B. y = x + 1 C. x = y + 12 D. y = x + 12 The given figure shows a circle with CAD = 30, ADE = 15, and ACD = 75. What are the respective measures of CBE and DEB? A. 90 and 75

21 B. 90 and 105 C. 105 and 120 D. 115 and 135 In the given figure, O is the centre of the circle. A, B and C are three points on the circle. If OC = 8.5 cm and AC = 8 cm, then what is the perimeter of ABC? A cm B cm C. 40 cm D. 47 cm The given figure shows a trapezium PQRS in which PQ SR. A and B are the mid-points of diagonals QS and PR respectively. What is the length of AB? A. 5 cm B. 6 cm C. 7.5 cm D. 8.1 cm

22 What is the value of ( AOB ACB)? A. 15 B. 20 C. 25 D. 30 The given table shows the frequency distribution of a particular data. x f m If the mean of the given distribution is 4.7, then what is the value of m? A. 5 B. 6 C. 11 D. 14 Two coins are simultaneously tossed 200 times and the following table is obtained. Two head One head No head What is the probability of getting two tails.

23 A B C D The mean of thirty numbers is 25. If 15 is subtracted from each of the first 12 numbers and 15 is added to each of the last 18 numbers, then what will be the mean of the new set of numbers? A. 32 B. 31 C. 28 D. 23 The mean weight of all girls of a class is 36 kg and that of the boys of the class is 42 kg. The mean weight of all the students of the class is 40 kg. What is the ratio of the number of girls and boys in the class? A. 1:2 B. 1:4 C. 2:3 D. 3:4 What is the mean of the first five multiples of both the numbers 10 and 3? A. 90 B. 95 C. 105 D. 120 A die is thrown 3000 times and its outcome is noted each time. The given table lists the number of times each number appeared on the die. Outcome Frequency If the same coin is tossed again, then what is the probability of getting an even number on the die?

24 A. B. C. D. The mean of the numbers 21, 30, 16, x, and 9 is 18. The median of the numbers 23, 30, 31, 3x, 3x + y, 60, 67, and 69 is What is the value of y? A. 11 B. 14 C. 33 D. 42

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