MCQ Answers

 1. (REF=25847) : MN is a mid-segment of triangle ABC. If MN is 48 cm, what is the length of BC? Answer: 96 cm Solution: As MN is mid-segment, BC = 2*MN = 2*48 = 96 cm 2. (REF=25846) : Find the largest angle in the triangle given below. Answer: MAR Solution: The angle opposite to the largest side is the largest angle in a triangle. The largest side is MR (or RM) which is 62 m. Hence the angle opposite to it MAR (or RAM) is the largest angle 3. (REF=25853) : ABC is a right triangle. AM is perpendicular to BC. The size of angle ABC is equal to 55 degrees. Find the size of angle MAC. Answer: 55 degrees Solution: As ABC=55 degree, MCA = 180 - (90+55) = 35 degrees. MAC = 180 - (AMC+MCA) = 180 - (90+35) = 55 degrees 4. (REF=25862) : The vertices of the inscribed (inside) square bisect the sides of the second (outside) square. Find the ratio of the area of the outside square to the area of the inscribed square. Answer: 2:1 Solution: Let the side of the outside square be a. Area of the outside

 1. (REF=10499) : The length of the longest chord that can be inscribed in a circle of radius 12cm is Answer: 24 cms Solution: The longest chord the diameter and hence reqd length = 2r = 24 cms. 2. (REF=10492) : If each interior angle of a regular polygon is 150 degrees, find the number of sides in the polygon. Answer: 12 Solution: Interior angle = (n-2)180/n = 150, Solving n=12 3. (REF=9214) : In a decagon, how many triangles can be formed using the vertices of the decagon such that only one side of the triangle is same as one side of the decagon? Answer: 60 Solution: The shortcut formula is N (N-4). Here as it is a decagon N=10. Hence num of triangles = 10 * 6 = 60 4. (REF=10497) : In the below figure, x:y:z = 3:4:5, then find w. Answer: 60 degrees Solution: x+y+z = 180, 3x+4x+5x = 180, x=15, So x=45, y = 60, z=75. w is alternatively opposite to y and hence is 60 degrees 5. (REF=10494) : If a parallelogram can be circumscribed by a circle, then it must be a Answer: Rectangle Solution

 1. Find the area of a regular hexagon inscribed in a circle of radius 18 cms. Answer: 841.75 sq.cms approx Sollution: In a regular hexagon the radius of the circle is equal to it's side as the center of the circle forms an equilateral triangle with the end points of a side. Area of the desired regular hexagon = 6 * Area of equilateral triangles formed = 6 * 1/4 * SQRT(3) * side^2 = 6/4 * SQRT(3) * 18 * 18 = 841.75 sq.cms approx 2. A rectangle of length 11 meters and width 8 meters is rolled about its length. The volume of the resulting cylinder is Answer: 77 cu.m Solution: L = 11 m Height of the cylinder = h = 8m Let the radius of cylinder be r. 2*pi*r = L, so r = L/(2*pi) Volume = pi* r^2 * h = (11 * 11 * 8) /(4 * 22/7) = 77 cu.m 3. The radii of top and bottom of a bucket are 25cms and 20cms respectively. If the volume of the bucket is 67100 cubic cms, find the height of the bucket. Answer: 42 cms Solution: The volume of a tapered bucket is given by the formula, v= pi/3 * height

1. Grass in lawn grows equally thick and in a uniform rate. It takes 24 days for 70 cows and 60 days for 30 cows to eat the whole of the grass. How many cows are needed to eat the grass in 96 days? Answer: 20 Solution: Let the initial amount of grass be g and growth rate per day be r. The amount which a cow eats in one day = c. g + 24r = 24*70*c - Eqn1 g + 60r = 30*60*c - Eqn2 Using the above two equations, 36r=120c - Eqn3, Now for 96 days, let the days required be n. g + 96r = 96 * n * c - Eqn4, Subtracting Eqn2 from Eqn4, 36r = c(96n-1800), Now from Eqn3, 36r=120c. Hence 120c=c(96n-1800), solving n= 1920/96 = 20 2. If the list price of a book is reduced by Rs.5, then a person can buy 5 more books for Rs. 300. The list price of the book is Answer: Rs.20 Solution: Let the list price be x. Number of books that can be bought = 300/x Now when reduced by Rs.5, number of books that can be bought = 300/(x-5). Hence 300/(x-5)  - 300/x = 5, 300x - 300x + 1500 = 5 * x * (x-5), x^2 -5x -300 = 0,

 1. Choose the option to fill the blanks Rajesh was talking to his girlfriend __ 3 a.m. Answer: until 2. Choose the option to fill the blanks      The man __ Uganda had many interesting stories to tell about his home country Answer: from 3. Choose the option to fill the blanks Although no one buys bikes of XYZ company these days, XYZ company still has a show room __ Mount Road. Answer: on 4. Choose the option to fill the blanks     The students voiced their anger against the government's despotic policies __ holding a protest rally Answer: by 5. Choose the correct article to fill in the blanks. __ sun shines brightly. Answer: the 6. Choose the correct article to fill in the blanks. Life is not __ bed of roses. Answer: a 7. Choose the option to fill the blanks The food will be ready  ___  about ten minutes Answer: in 8. Choose the correct article to fill in the blanks. He became ___  good doctor. Answer: a 9. Choose the option to fill the blanks The parcel will be delivered ___ half

 1. Choose the one which best expresses the given sentence in Indirect/Direct speech She said that her brother was getting married. Answer: She said, "My brother is getting married." 2. Choose the option which represents the indirect speech of the sentence below. She said, "Please don't go away" Answer: She begged me not to go away 3. Choose the relevant form of the indirect speech for the given sentence. I said to him, "you must learn the test-taking strategies" Answer: I said to him that he had to learn the test-taking strategies. 4. Convert the sentence to Direct / Indirect speech Prem said to his friends, “We can finish the homework now”. Answer: Prem told his friends that they could finish the homework then. 5. Convert the sentence to direct / indirect speech: They said, 'We've played in this ground for a long time.' Answer: They said that they had played in that ground for a long time. 6. The below sentence is either in direct or indi

1. If the operation + is defined by the equation 4a + 5b =  20ab , what is the value of  16 + 20 ? Answer: 320 Solution: 16 + 20 = 4*4 + 5*4 which is similar to 4a + 5b. Thus, 20ab = 20*4*4 = 320 2. If the operation + is defined by the equation a + b = 3a / 2b, what is the value of 2 + 3 ? Answer: 1 Solution: The expression becomes 3(2) / 2(3) = 6/6 = 1 3. If the operation - is defined by the equation x - y = x * y + x , what is the value of 4 - 5 ? Answer: 24 Solution: The expression becomes 4 * 5 + 4 = 20 + 4 = 24 4. If the operation - is defined by the equation a - b = (9a + 12b) % 2, what is the value of 9 - 2 ? Note: % denotes remainder(modulo) operation Answer: 1 Solution: The expression becomes (81 + 24) % 2 = 105 % 2 = 1  5. If the operation * is defined by the equation a * b = 4a + 3b, what is the value of 5 * 9 ? Answer: 47 Solution: The expression becomes 4(5)+3(9) = 20 + 27 = 47 6. If the operation * is defined by the equation c * d = (3c / 2d) + 4d , what is the value of 6

 The number of laptops sold in four consecutive months is as shown in the chart. Please answer the following questions based on the chart. 1. What was the percentage increase in laptops sold in Cochin in March when compared to January? Answer: 0% Solution: Increase is zero % as both in Jan and March only 2000 units were sold in Cochin. 2. How many units were sold more in Chennai in the given four months when compared to Bangalore? Answer: 5000 Solution: Num. sold in Chennai = 22000, Bangalore = 17000. Hence 22000-17000 = 5000 units. 3. Which location(s) did well in the sales of laptops in March when compared to February? Answer: Chennai and Cochin Solution:  % change in chennai = -2000*100/ 6000 = -33.33% Bangalore = -2000*100/ 5000 = -40% Cochin = -1000*100/3000 = -33.33% Hence Chennai and Cochin did well. 4. How many units were sold across locations in the months of January and April? Answer: 27000  Solution: Jan. 11000 sold and April 16000. Hence total = 27000 units. Answer the foll

 1. In the following questions, mark 1, if statement I alone can help determine the conclusion 2, if statement II alone can help determine the conclusion 3, if statement I and II taken together can help determine the conclusion 4, if none of the statements, taken together or separately can help determine the conclusion Conclusion: Sunitha wears an Emerald ring. (I)  Sunitha believes in astrology. (II) People who believe in astrology wear rings Answer: 4 Solution: Option 4. Statement I and II does not help us to conclude if it is Emerald ring. (Though Sunitha believes in astrology and also wears a ring, the ring could be a Topaz or a Diamond ring etc). 2. In the following questions, mark 1, if statement I alone can help determine the answer 2, if statement II alone can help determine the answer 3, if statement I and II taken together can help determine the answer 4, if none of the statements, taken together or separately can help determine the answer What is the value of x? (I) x + y =

 1. What is/are the statement(s) necessary/sufficient to answer the below question. What is the age of Dinesh ? Statements : (1) Ratio between the ages of Arul and Dinesh is 4 : 3                     (2) After 6 years Arul's age will be 26 years.                     (3) Dinesh's father was 28 years when he was born. Answer: Statements 1 and 2 Solution: By statement 1, Let the ages be x. So Arul's age : Dinesh's age = 4x : 3x By statement 2, 4x + 6 = 26                           => 4x = 26 - 6  => 4x = 20      => x = 5 So Dinesh's age = 3x = 15 So statements 1 and 2 are sufficient to answer 2. What is/are the statement(s) necessary/sufficient to answer the below question. Find the value of x and y? Statements: (1) x is three times y.                        (2) y is15 percent of 300. Answer: BOTH statements together are sufficient. Solution: Solving the equations by using both the statements yield the result. Hence, both statements are necessary to answer the

 216 cubes of similar size are arranged in the form of a bigger cube. The six faces of the bigger cube are painted with green, red, blue, violet, white, pink colours. Related Comprehension Questions 1. How many cubes are painted with red or blue? Answer: 66 or 72 Solution: In one face 36 smaller cubes will be present. When red and blue are not adjacent 36*2=72 cubes will be painted with red or blue. When these colours are in adjacent faces, the six common cubes are to be subtracted giving 72-6=66 2. How many cubes are painted with red or blue or green? Answer: 91 or 96 Solution: When all three colours are adjacent to each other, we get 36 + 30 + 25 = 91 (We subtract the common cubes from 36 and hence 30 and 25) When one of the three colours is in between the other two, we get 36+30+30 = 96 3. How many cubes are painted with red or blue but not green? Answer: 55 or 60 Solution: When all three colours are adjacent to each other, we get 30+25 = 55 When green coloured face is in between th