Elementary Mathematics
The rabbit population in community A increases at 25% per year
The rabbit population in community A increases at 25% per year while that in community B increases at 50% per year. If the present populations of A and B are equal, what will he the ratio of the number of rabbits in community B to that in community A after 2 years?
- 1.44
- 1.72
- 1.90
- 1.26
In a certain year, a school had 60% boys and 40% girls as students
In a certain year, a school had 60% boys and 40% girls as students. In the next five years the number of boys decreased by 10% and the number of girls increased by 10%. What is the change in total roll strength of the school in the five years?
- 3% increase
- 2% decrease
- No change
- 5% decrease
What is the number whose 20% is 30% of 40
What is the number whose 20% is 30% of 40?
- 50
- 60
- 80
- 90
The radius of the base of a right circular cone is increased by 15%
The radius of the base of a right circular cone is increased by 15% keeping the height fixed. The volume of the cone will be increased by
- 34.75%
- 32.25%
- 31%
- 30%
The price of an article is ₹ 25. After two successive cuts
The price of an article is ₹ 25. After two successive cuts by the same percentage, the price becomes ₹ 20.25. If each time the cut was x%, then
- x = 9
- x = 10
- x = 11
- x = 11.5
If m% of m + n% of n = 2% of (m × n)
If m% of m + n% of n = 2% of (m × n), then what percentage of m is n?
- 25%
- 50%
- 75%
- 100%
A man loses 20% of his money. After spending 25% of the remainder
A man loses 20% of his money. After spending 25% of the remainder, he has ₹ 480 left. What is the amount of money he originally had?
- ₹ 600
- ₹ 720
- ₹ 800
- ₹ 840
An employee is required to contribute 10% of his pay
An employee is required to contribute 10% of his pay to General Provident Fund. If he gets ₹13,500 as net pay in a month, then what is the monthly General Provident Fund contribution (assuming no other deductions)?
- ₹ 1215
- ₹ 1350
- ₹ 1500
- ₹ 1650
The tank-full petrol in Arun's motor-cycle lasts for 10 days
The tank-full petrol in Arun's motor-cycle lasts for 10 days. If he starts using 25% more everyday, how many days will the tank-full petrol last?
- 5
- 6
- 7
- 8
In a group of persons, 70% of the persons are male
In a group of persons, 70% of the persons are male and 30% of the persons are married. If two sevenths of males are married, what fraction of the females is single?
- 2/7
- 3/7
- 2/3
- 1/3
In a garrison, there was food for 1000 soldiers for one month
In a garrison, there was food for 1000 soldiers for one month. After 10 days, 1000 more soldiers joined the garrison. How long would the soldiers be able to carry on with the remaining food?
- 10 days
- 25 days
- 20 days
- 15 days
In a class of 45 students, a boy is ranked 20th
In a class of 45 students, a boy is ranked 20th. When two boys joined, his rank was dropped by one. What is his new rank from the end?
- 25th
- 26th
- 28th
- 27th
A student on her first 3 tests receive an average score of N points
A student on her first 3 tests receive an average score of N points. If she exceeds her previous average score by 20 points on her fourth test, then what is the average score for the first 4 tests?
- N + 10
- N + 4
- N + 5
- N + 20
with 0 < θ < 90°, then what is θ equal to?If 3 sin x + 5 cos x = 5, then what is the value of (3 cos x – 5 sin x)
If 3 sin x + 5 cos x = 5, then what is the value of (3 cos x – 5 sin x)?
- 0
- 2
- 3
- 5
If tan (A + B) = √3 and tan A = 1, then tan (A - B) is equal to
If tan (A + B) = √3 and tan A = 1, then tan (A - B) is equal to
- 0
- 1
- 1/√3
- √2
The angles of elevation of the top of a tower from two points
The angles of elevation of the top of a tower from two points situated at distance 36 m and 64 m from its base and in the same straight line with it are complementary. What is the height of the tower?
- 48 m
- 30 m
- 25 m
- 24 m
If 2 cot θ = 3, then what is the value of
If 2 cot θ = 3, then what is the value of (2 cos θ - sin θ) / (2 cos θ + sin θ)?
- 1/3
- 1/2
- 3/4
- 2/3
The value of cosec^2 67 + sec^2 57 - cot^2 33 - tan^2 23
The value of cosec2 67 + sec2 57 - cot2 33 - tan2 23 is
- 2√2
- 2
- √2
- 0
If tan A + cot A = 4, then tan^4 A + cot^4 A
If tan A + cot A = 4, then tan4 A + cot4 A is equal to
- 194
- 191
- 110
- 80
The angle of elevation of the tip of a tower from a point
The angle of elevation of the tip of a tower from a point on the ground is 45°. Moving 21 m directly towards the base of the tower, the angle of elevation changes to 60°. What is the height of the tower, to the nearest meter?
- 48 m
- 49 m
- 50 m
- 51 m
If sin x + cos x = c, then sin^6 x + cos^6 x is equal to
If sin x + cos x = c, then sin6 x + cos6 x is equal to
- (1 + 6c2 - 3c4)/16
- (1 + 6c2 - 3c4)/4
- (1 + 6c2 + 3c4)/16
- (1 + 6c2 + 3c4)/4
What is the angle of elevation of the sun when the shadow
What is the angle of elevation of the sun when the shadow of a pole is √3 times the length of the pole?
- 30°
- 45°
- 60°
- 75°
From an aeroplane vertically above a straight horizontal road
From an aeroplane vertically above a straight horizontal road, the angle of depression of two consecutive kilometer stones on the opposite sides of the aeroplane are found to be α and β. The height of the aeroplane above the road is
- (tan α + tan β) / (tan α tan β)
- (tan α tan β) / (tan α + tan β)
- (cot α cot β) / (cot α + cot β)
- (cot α + cot β) / (cot α cot β)
From the top of a building 90 m high, the angles of depression
From the top of a building 90 m high, the angles of depression of the top and the bottom of a tree are 30° and 45° respectively. What is the height of the tree?
- 30√3 m
- 90 - 30√3 m
- 90 + 30√3 m
- 60 + 30√3 m
If x = a cos θ + b sin θ and y = a sin θ – b cos θ
If x = a cos θ + b sin θ and y = a sin θ – b cos θ, then what is x2 + y2 equal to?
- 2ab
- a + b
- a2 + b2
- a2 – b2
An aeroplane flying at a height of 300 m above the ground passes
An aeroplane flying at a height of 300 m above the ground passes vertically above another plane at an instant when the angles of elevation of the two planes from the same point on the ground are 60° and 45° respectively. What is the height of the lower plane from the ground?
- 100√3 m
- 100/√3 m
- 50√3 m
- 150(√3 + 1) m
If 7 sin^2 x + 3 cos^2 x = 4, then what is the value of tan x
If 7 sin2 x + 3 cos2 x = 4, 0 < x < 90°, then what is the value of tan x?
- √2
- 1
- √3/2
- 1/√3
What is the value of (Quant Trigo #01)
What is 
equal to?
- cos2 A - sin2 A
- cos A - sin A
- 1
- 2
What is the value of which satisfies the equation cos θ + tan θ = 1
What is the value of which satisfies the equation cos θ + tan θ = 1?
- 0°
- 30°
- 45°
- 60°
If cos θ1 + cos θ2 + cos θ3 = 3, then what is sin θ1 + sin θ2 + sin θ3
If cos θ1 + cos θ2 + cos θ3 = 3, then what is sin θ1 + sin θ2 + sin θ3 equal to?
- 0
- 1
- 2
- 3
What is the minimum value of 9 tan^2 θ + 4 cot^2 θ
What is the minimum value of 9 tan2 θ + 4 cot2 θ
- 6
- 9
- 12
- 13
If D is the number of degrees and R is the number of radians in an angle θ
If D is the number of degrees and R is the number of radians in an angle θ, then which one of the following is correct?
- πD = 180R
- πD = 90R
- πR = 180D
- πR = 90D
The geometric mean of 32, 4, 8, X, 2 is 8. What is the value of X
The geometric mean of 32, 4, 8, X, 2 is 8. What is the value of X?
- 2
- 4
- 8
- 16
The mean of 100 values is 45. If 15 is added to each of the first forty
The mean of 100 values is 45. If 15 is added to each of the first forty values and 5 is subtracted from each of the remaining sixty values, the new mean becomes
- 45
- 48
- 51
- 55
The arithmetic mean and geometric mean of two numbers
The arithmetic mean and geometric mean of two numbers are 14 and 12 respectively. What is the harmonic mean of the numbers?
- 32/3
- 10
- 72/7
- 13
Ten observations are written in ascending order
Ten observations 6, 14, 15, 17, x + 1, 2x - 13, 30, 32, 34 and 43 are written in ascending order. The median of the data is 24. What is x?
- 15
- 18
- 20
- 24
Which relations for the numbers 10, 7, 8, 5, 6, 8, 5, 8, 6 is correct
Which one of the following relations for the numbers 10, 7, 8, 5, 6, 8, 5, 8, 6 is correct?
- Mean = Mode
- Mean = Median
- Mean > Median
- Mean > Mode
In histogram the width of the bars is proportional to
In histogram the width of the bars is proportional to
- number of classes
- class interval
- cumulative frequency
- frequency
What are the values of f1 and f2 respectively
Consider the following frequency distribution:
What are the values of f1 and f2 respectively?
- 10 and 17
- 17 and 10
- 11 and 16
- 16 and 11
An individual purchases three qualities of pencils
An individual purchases three qualities of pencils. The relevant data is given below:
It is known that the average price per pencil is ₹1.25. What is the value of x?
- ₹10
- ₹30
- ₹40
- ₹60
In an asymmetrical-distribution, if the mean and median of the distribution
In an asymmetrical-distribution, if the mean and median of the distribution are 270 and 220 respectively, then the mode of the data is
- 120
- 220
- 280
- 370
In a pie diagram, there are four slices with angles 150°, 90°, 60° and 60°
In a pie diagram, there are four slices with angles 150°, 90°, 60° and 60°. A new pie diagram is formed by deleting one of the slices having angle 60° in the given pie diagram. In the new pie diagram
- The largest slice has angle 150°
- The smallest slice has angle 70°
- The largest slice has angle 180°
- The smallest slice has angle 90°
If the mean of the above distribution is 50, what is the value of f
Consider the following distribution:
If the mean of the above distribution is 50, what is the value of f?
- 24
- 34
- 56
- 96
The mean marks obtained by 300 students in a subject are 60
The mean marks obtained by 300 students in a subject are 60. The mean of top 100 students was found to be 80 and the mean of last 100 students was found to be 50. The mean marks of the remaining 100 students are
- 70
- 65
- 60
- 50
The mean of 5 numbers is 15. If one more number is included
The mean of 5 numbers is 15. If one more number is included, the mean of the 6 numbers becomes 17. What is the included number?
- 24
- 25
- 26
- 27
If a + b = 5 and ab = 6, then what is the value of a^3+ b^3
If a + b = 5 and ab = 6, then what is the value of a3+ b3?
- 35
- 40
- 90
- 125
Log (40^2-20^2) is equal to
Log (402 - 202) is equal to
- log 3
- log 60 + log 20
- log 40 – log 20
- log 20
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