Dakshana Mock Test Season XIV Solutions

1] A big cube of side 8 cm is formed by rearranging together 64 small but identical cubes each of side 2 cm. Further, if the corner cubes in the topmost layer of the big cube are removed, what is the change in total surface area of the big cube?

Answer: Remains the same as previously

2] Three equal circles of unit radius touch each other. Then, the area of the circle circumscribing the three circles is

Answer: π(2+√3)²/3

3] ABCD is a square. A circle is inscribed in the square. Also, taking A, B, C, D the vertices of square as the centres of four quadrants, drawn inside the circle, which are touching each other on the mid-points of the sides of square. Area of square is 4cm². What is the area of the shaded region?

Image not to scale

Answer: (2π-4)cm²

4] A, B and C shoot to hit a target. A hits the target 4 times in 5 trials. B hits it 3 times in 4 trials and C hits it 2 times in 3 trials. What is the probability that the target is hit by atleast 2 persons?

Answer: 5/6

5] In the given figure, CD is a direct common tangent to two circles, intersecting each other at A and B, then ∠CAD + ∠CBD = ?

Answer: 180°

6] A tank 4 m long, 2.5 m wide and 6 m deep is dug in a field, 10 m long and 9 m wide. Then, the earth dugout is evenly spread over the remaining field. Then, the rise in the level of the field will be:

Answer: 75cm

7] A medicine capsule is in the shape of a cylinder of diameter 0.5 cm with two hemispheres stuck to each of its ends. The length of the entire capsule is 2 cm. The capacity of the capsule is
(Take π = 3.14)

Answer: 0.36 cm³

8] 125 identical cubes are cut from a big cube and all the smaller cubes are arranged in a town to form a long cuboid. What is the percentage increase in the total surface area of the cuboid over the total surface area of the cube?

Answer: (234+2/3)%

9] The radius of a circle is 20 cm. The radii (in cm) of three concentric circles drawn in such a manner that the whole area is divided into four equal parts, are:

Answer: 10√3, 10√2, 10

10] In the adjoining figure, the chords XY and SR are produced to meet outside the circle at P. The chords XR and YS meet inside the circle at T. If, ∠TXY=x and ∠XTS=y, then ∠P is equal to

Answer: y - 2x

11] A cow is tied to a corner (vertex) of a regular hexagonal fenced area of side 'a' meters by rope of length 5a/2 meters in a grass field. (The cow cannot graze inside the fenced area). What is the maximum possible area of the grass field to which the cow has access to graze?

Answer: 5πa²

12] The circumference of the front wheel of a cart is 30 feet long and that of the back wheel is 36 feet long. What is the distance traveled by the cart, when the front wheel has done five more revolutions than the rear wheel?

Answer: 900 ft

13] A number x is chosen at random from the numbers, -3, -2, -1, 0, 1, 2, 3. The probability that [x] < 2 is

Answer: 3/7

14] A bag contains 4 red and 3 black balls. A second bag contains 2 red and 4 black balls. One bag is selected at random, then, from the selected bag one ball is drawn from it. Find the probability that the ball drawn is red.

Answer: 19 / 42

15] ABCD is a square, in which a circle is inscribed touching all the sides of square. In the four corners of the square, 4 smaller circles of equal radii are drawn, containing maximum possible area. What is the ratio of the area of larger circle to that of sum of the areas of four smaller circles?

Answer: 1 : 68 - 48√2

16] An open box (face with largest area is open, such that, the face's slab was earlier resting on other four sides) is made of wood 2 cm thick. Its internal, length is 86 cm, breadth is 46 cm and height is 38 cm. The cost of painting the outer surface of the box at Rs.10 per m² is:

Answer: Rs. 15.70

17] In the adjoining figure, ∠ACE is a right angle, there are three circles which just touch each other and AC and EC are the tangents to all the three circles. What is the ratio of radii of the largest circle to that of the smallest circle?

Answer: 1 : (17-12√2)

18] The mean of following data is 18.75 then, the value of p is

x	10	15	p	25	30
f	5	10	7	8	2

Answer: 20

19] Which of the following is a measure of central tendency?

Answer: Mean

20] Median of a given frequency distribution is found graphically with the help of

Answer: Ogive

21] The measure of central tendency which is given by the x-coordinate of the point of intersection of the more than ogive and less than ogive is

Answer: Median

22] Find the probability that a leap year selected at random will contain 53 Sundays.

Answer: 2/7

23] From a well shuffled pack of 52 cards, three cards are drawn at random. Find the probability of drawing an ace, a king and a jack.

Answer: 16/5525

24] If the curved surface area of a right circular cone is 12320 cm² and the radius of its base is 56 cm then, its height is ___. (Take π = 22/7)

Answer: 42 cm

25] A solid metal cone with base-radius 12 cm and height 24 cm is melted to form solid spherical balls each of diameter 6 cm. The number of such balls made is

Answer: 32

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