Question – 1
1. Area of a right triangle is 504 sq.cm. The length of the hypotenuse is 65 cm.?
| Column-A | Column-B |
|---|---|
| Sum of the sides containing the right angle | Length of the hypotenuse |
- A. If the quantity on the left is greater
- B. If the quantity on the right is greater
- C. If both are equal
- D. If the relationship cannot be determined without further information
- Answer:A
- Answer Explanation:The sum of any two sides of a triangle is always greater than the third side. Hence, option A is correct.
Question – 2
2. Consider the sequence -9, -5, -1, 3,….?
| Column-A | Column-B |
|---|---|
| The 50th term | 191 |
- A. If the quantity on the left is greater
- B. If the quantity on the right is greater
- C. If both are equal
- D. If the relationship cannot be determined without further information
- Answer:B
- Answer Explanation:Let the first term of the sequence be a and the common difference be d.a= -9d = -1-(-5) = 5-1=4The nth term of the sequence is given byTn=a+(n-1)d=-9+(50-1)4=-9+49*4=-9+196=187The 50th term is 187Option B is correct
Question – 3
3.
| Column-A | Column-B |
|---|---|
| Number of ways in which one person can be selected from a group of 10 | Number of ways in which two persons can be chosen from a group of 20 |
- A. If the quantity on the left is greater
- B. If the quantity on the right is greater
- C. If both are equal
- D. If the relationship cannot be determined without further information
- Answer:B
- Answer Explanation:One person can be selected from a group of 10 in C(10,1) waysC(10,1)=10!/[1!9!] =10Two persons can be selected from a group of 20 in C(20,2) waysC(20,2)=20!/[2!18!]=20*19/2=10*19=190Option B is correct.
Question – 4
4. logx/2=logy/3=logz/5.?
| Column-A | Column-B |
|---|---|
| xy | yz |
- A. If the quantity on the left is greater
- B. If the quantity on the right is greater
- C. If both are equal
- D. If the relationship cannot be determined without further information
- Answer:B
- Answer Explanation:Let logx/2=logy/3=logz/5=klogx=2k, logy=3k and logz=5klogx+logy = 2k+3k=5klog(xy) = 5klogy+logz = 3k+5k=8klog(yz) = 8klog(xy)
Question – 5
5. The average of the marks obtained by 30 students of a class is 50. If the score of one student is removed, the average reduces by 1.?
| Column-A | Column-B |
|---|---|
| Average score of the remaining students | The score that was removed |
- A. If the quantity on the left is greater
- B. If the quantity on the right is greater
- C. If both are equal
- D. If the relationship cannot be determined without further information
- Answer:B
- Answer Explanation:Average = Total marks/number of studentsTotal marks = Average*number of students= 50*30 = 1500New average = 50-1=49Number of students = 30-1=29Total marks = 49*29= 1421Marks of the student = 1500-1421= 79The score that was removed = 79Average score of the remaining students = 49Option B is correct.
Question – 6
6. A square is constructed taking a side of a rectangle as a side of the square.?
| Column-A | Column-B |
|---|---|
| Perimeter of the square | Perimeter of the rectangle |
- A. If the quantity on the left is greater
- B. If the quantity on the right is greater
- C. If both are equal
- D. If the relationship cannot be determined without further information
- Answer:D
- Answer Explanation:We do not know whether the square is along the length or along the breath of the rectangle.Hence, we cannot compare the perimeters.Option D is correct.
Question – 7
7. A point divides the line joining (-1,-5) and (6,5) in the ratio 1:6.?
| Column-A | Column-B |
|---|---|
| Ordinate of the point | Abscissa of the point |
- A. If the quantity on the left is greater
- B. If the quantity on the right is greater
- C. If both are equal
- D. If the relationship cannot be determined without further information
- Answer:B
- Answer Explanation:The coordinates of the point are given by((-1*6+6*1)/(6+1), (-5*6+5*1)/(6+1))= ((-6+6)/7, (-30+5)/7)= (0, -25/7)Abscissa is the x co-ordinate and hence it is greater than the ordinate, which is the y co-ordinate.Option B is correct.
Question – 8
8.
| Column-A | Column-B |
|---|---|
| Number of two-digit numbers | Number of three-digit numbers less than 250 |
- A. If the quantity on the left is greater
- B. If the quantity on the right is greater
- C. If both are equal
- D. If the relationship cannot be determined without further information
- Answer:B
- Answer Explanation:Number of two-digit numbers = 99-9=90Number of three-digit numbers less than 250=250-99=15190<151Option B is correct.
Question – 9
9.
| Column-A | Column-B |
|---|---|
| Number of vertices of a rectangle | Number of triangles that can be formed from the vertices of a rectangle |
- A. If the quantity on the left is greater
- B. If the quantity on the right is greater
- C. If both are equal
- D. If the relationship cannot be determined without further information
- Answer:C
- Answer Explanation:Number of vertices of a rectangle = 4Number of triangles that can be formed from the vertices of a rectangle = C(4,3)= 4!/(3!1!)= 4Hence, option C is correct.
Question – 10
10.
| Column-A | Column-B |
|---|---|
| Perimeter of a square with each side 29 cm long. | Perimeter of a rhombus whose diagonals are 40cm and 42cm long |
- A. If the quantity on the left is greater
- B. If the quantity on the right is greater
- C. If both are equal
- D. If the relationship cannot be determined without further information
- Answer:C
- Answer Explanation:Perimeter of the square = 29*4=116 cmThe diagonals of a rhombus bisect each other at right angles.Thus, the rhombus is divided into 4 congruent right triangles.The hypotenuse of any triangle is a side of the rhombus.Applying Pythagoras theorem, we getHypotenuse = Sqrt[(40/2)^2+(42/2)^2]= sqrt(20^2+21^2)= sqrt(400+441)= sqrt(841)= 29cmPerimeter of the rhombus = 4*29= 116 cmOption C is correct.[20^2=20*20]
Question – 11
11. The radius of a circle is 49cm. Each side of a square is equal to the diameter of the circle.?
| Column-A | Column-B |
|---|---|
| Area of the square | Area of the circle |
- A. If the quantity on the left is greater
- B. If the quantity on the right is greater
- C. If both are equal
- D. If the relationship cannot be determined without further information
- Answer:A
- Answer Explanation:Area of the circle = pi*r^2, where r is the radius of the circleArea = 22/7*49*49=7546 sq.cm.Each side of the square = 2*radius= 2*49 = 98cmArea of square = side*side= 98*98=9604 sq.cm.Option A is correct.[pi=22/7, r^2=r*r]
Question – 12
12. A chord of length 112 cm is at a distance of 33 cm from the centre. ?
| Column-A | Column-B |
|---|---|
| Length of the chord. | Radius of the circle |
- A. If the quantity on the left is greater
- B. If the quantity on the right is greater
- C. If both are equal
- D. If the relationship cannot be determined without further information
- Answer:A
- Answer Explanation:A line drawn from the center of the circle perpendicular to the chord will bisect the chord.This line, the radius of the circle and the chord form a right triangle.Applying the Pythagoras theorem to the triangle, we getHypotenuse = sqrt[base^2+perpendicular^2]= sqrt[(112/2)^2+33^2]= sqrt[56^2+1089]= sqrt[3136+1089]= sqrt(4225) = 65cmRadius of the circle is 65 cm.Length of the chord is 112 cm.Option A is correct.[x^2=x*x]
Question – 13
13. The population of a town is 140000. It increases by 5% in the first year. In the second year, it decreases by 10%.?
| Column-A | Column-B |
|---|---|
| Population after the first year | Population after the second year |
- A. If the quantity on the left is greater
- B. If the quantity on the right is greater
- C. If both are equal
- D. If the relationship cannot be determined without further information
- Answer:A
- Answer Explanation:This problem is similar to a problem of compound interest.Population after 1 year = 140000(1+5/100) = 147000Population after 2 years = 147000(1-10/100) = 132300Option A is correct.
Question – 14
14.
| Column-A | Column-B |
|---|---|
| Number of factors of 20 that are smaller than 40 | Number of multiples of 20 that are smaller than 45 |
- A. If the quantity on the left is greater
- B. If the quantity on the right is greater
- C. If both are equal
- D. If the relationship cannot be determined without further information
- Answer:A
- Answer Explanation:Factors of 20 = 1, 2, 4, 5, 10, 20Multiples of 20 that are smaller than 45 = 20, 40Option A is correct.
Question – 15
15. A teacher prepares a test having 5 objective-type questions. Each question has an incorrect and a correct option.?
| Column-A | Column-B |
|---|---|
| The number of correct ways in which the test can be answered | The number of incorrect ways in which the test can be answered |
- A. If the quantity on the left is greater
- B. If the quantity on the right is greater
- C. If both are equal
- D. If the relationship cannot be determined without further information
- Answer:B
- Answer Explanation:Each question can be answered in 2 waysThere are in all 5 questions.Number of ways in which the test can be answered = 2*2*2*2*2 = 32Number of correct ways of answering the test = 1Number of incorrect ways of answering the test = 32-1=31Option B is correct.