गणित (भाग-IV)

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Question 1 / 60
The value of √(43-12√7) - 2√(16+6√7) is:
A
1
B
3
C
5
D
6
If the sum of two numbers is 40 and their product is 375, then those numbers are:
A
16, 24
B
20, 20
C
25, 15
D
30, 10
If the area of the base of a cuboid is 80 square cm, the area of the other two adjacent faces are 72 square cm and 40 square cm, then the volume of that cuboid is:
A
480 cm³
B
360 cm³
C
240 cm³
D
80 cm³
If √(3ⁿ) = 729, then the value of n is:
A
6
B
8
C
10
D
12
If the length of the diagonal of a cube is 17.32 cm, then the volume of the cube is:
A
10 cm³
B
100 cm³
C
1000 cm³
D
10000 cm³
The median of the following data is: 25, 34, 31, 23, 22, 26, 35, 29, 18, 32
A
26
B
27
C
27.5
D
28.5
A garden is 84 meters long and 64 meters wide. There is a path all around inside it whose area is 1632 square meters. The width of that path is:
A
5 meters
B
6 meters
C
8 meters
D
10 meters
If the height of an equilateral triangle is 18 cm, then its area is:
A
36√3 cm²
B
72√3 cm²
C
96√3 cm²
D
108√3 cm²
If n is a natural number other than a perfect square, then the number √n is:
A
Rational
B
Irrational
C
Integer
D
Natural
If α and β are the roots of the equation x² - 2x - 1 = 0, then the value of (α²β + αβ²) is:
A
-2
B
3
C
2
D
1
The radius of a wire has been reduced to one-third. If its volume remains the same, then the increase in its length is:
A
2 times
B
3 times
C
6 times
D
9 times
If sin θ + cosec θ = 2, then the value of (sin¹¹ θ + cosec¹¹ θ) is:
A
3
B
1
C
2
D
4
If tan 2θ · tan 4θ = 1, then the value of tan 3θ is:
A
0
B
1
C
√3
D
∞
The mode of the following data is: 4, 6, 5, 7, 9, 8, 10, 4, 7, 6, 6, 8, 8, 7, 7
A
6
B
7
C
8
D
9
The decimal representation of -16/45 is:
A
0.35
B
1.35
C
-1.35
D
-0.35
If the length of the shadow of a vertical tower is 1/√3 times its height, then the angle of elevation of the sun is:
A
30°
B
45°
C
60°
D
90°
The value of √(4+√(4+√(4+......))) is:
A
1
B
(1+√17)/2
C
(1-√17)/2
D
4
Minimum value of (3 sin² θ + 4 cos² θ) is:
A
0
B
1
C
2
D
3
If the sum of two numbers is 352 and their H.C.F. is 32, then the possible pairs of such numbers are:
A
Five
B
Six
C
Four
D
Three
The average of n numbers is m and the average of m numbers is n. Taking all the numbers together the average is:
A
m + n
B
mn
C
mn/(m+n)
D
2mn/(m+n)
The mean of 8 numbers is 22. If one number is excluded, then their mean is 16. The excluded number is:
A
16
B
22
C
32
D
64
The mean of the following distribution is: x: 4,6,9,10,15 and f: 5,10,10,7,8
A
8
B
9
C
10
D
12
The radius of the base of a right circular cone and its height are in the ratio 5 : 12. If the volume of the cone is 2512 cm³, then its slant height is:
A
22 cm
B
24 cm
C
26 cm
D
28 cm
The average of n numbers a₁, a₂, …, aₙ is a. The value of Σ(aᵢ − a) is:
A
0
B
1
C
n
D
a
When seen from the top of a 90 meter high rock, the angles of depression of the top and bottom of a tower are 30° and 60°, respectively, then the height of that tower is:
A
45 meter
B
60 meter
C
75 meter
D
30 meter
A cylindrical tank of diameter 35 cm is completely filled with water. If 11 liters of water is taken out from the tank, then how much will the level of the tank decrease?
A
9.428 cm
B
10.428 cm
C
11.428 cm
D
12.428 cm
For an asymmetrical distribution, if the median is 7 and the mean is 10, then the mode is:
A
11
B
4
C
3
D
1
The value of √(1+√(3/343)) is:
A
1
B
2
C
3
D
7
If 1² + 2² + 3² + …… + x² = x(x+1)(2x+1)/6, then the value of (1² + 3² + 5² + …… + 19²) is:
A
2500
B
2485
C
2100
D
1330
A hollow cylindrical tube of 20 cm long is made of iron. If its outer and inner diameters are 8 cm and 6 cm respectively, then the volume of iron used in making the tube is:
A
440 cm³
B
880 cm³
C
1760 cm³
D
240 cm³
A is twice as good a workman as B and together they complete a work in 26 days. In how much time will A alone complete the same work?
A
33 days
B
35 days
C
37 days
D
39 days
If the area of a plot is 212 square yards, then the area in square feet is:
A
636
B
1272
C
1908
D
2120
The value of (1−1/2)(1−1/3)(1−1/4)……(1−1/n) is:
A
1/n
B
2/n
C
2(n−1)/n
D
2/n(n+1)
There are 9 red, 7 white and 4 black balls in a bag. If 2 balls are drawn randomly, then the probability that both balls are of the same colour is:
A
36/190
B
57/190
C
63/190
D
81/190
If the sum of the radius and height of a solid cylinder is 20 cm and its total surface area is 880 square cm, then its volume is:
A
1760 cm³
B
8800 cm³
C
2002 cm³
D
4804 cm³
If a child has a mental age of 6 years and a chronological age of 5 years, then the Intelligent Quotient (IQ) of the child is:
A
80
B
100
C
120
D
140
A watch was sold at a profit of 20%. If it had been sold for ₹ 400 less, there would have been a loss of 20%. The cost price of the watch is:
A
₹ 1000
B
₹ 2000
C
₹ 3000
D
₹ 4000
Two numbers are respectively 30% and 44% less than a third number. By what percent is the second number less than the first number?
A
10%
B
20%
C
30%
D
40%
The branch of philosophy that focuses on the nature of reality is:
A
Connectionism
B
Epistemology
C
Metaphysics
D
Pedagogy
The three sides of a triangle are 10 meter, 12 meter and 14 meter. The area of the incircle of that triangle is:
A
33π/11 square meter
B
22π/11 square meter
C
11π/11 square meter
D
9π/11 square meter
If the cost price of 24 articles is equal to the selling price of 18 articles, then the percentage profit is:
A
25 1/3%
B
31 1/3%
C
16 2/3%
D
33 1/3%
Two equal circles pass through the center of each other. If the radius of each circle is 5 cm, then the length of their common chord is:
A
5
B
5√3
C
10√3
D
5√3/2
According to John Dewey, schools must prepare students for:
A
Research
B
Future life
C
Entrepreneurship
D
Present life
If (x + 1/x) = 2, then the value of (√x + 1/√x) is:
A
√2
B
2
C
1
D
1+√2
If the sum of n terms of an arithmetic progression is (3n² + 5n), then 158 is:
A
26th term
B
27th term
C
28th term
D
29th term
If (x⁴ + 1/x⁴) = 119 and x > 1, then the value of (x³ - 1/x³) is:
A
18
B
36
C
54
D
72
If S is the incentre of triangle ABC and ∠A = 30°, then the value of ∠BSC is:
A
90°
B
100°
C
105°
D
110°
If a = (√5+1)/(√5-1) and b = (√5-1)/(√5+1), then the value of (a² + ab + b²)/(a² - ab + b²) is:
A
1/3
B
2/3
C
1
D
4/3
Which number is to be subtracted from each of the numbers 3, 5, 6, 7 so that the four numbers obtained become proportional?
A
5
B
7
C
9
D
11
The population of a city 3 years ago was 40960. If the present population of that city is 49130, then the percentage annual increase is:
A
2 1/4%
B
5 1/4%
C
6 1/4%
D
7 1/4%
If 12 men do a piece of work in 20 days, then in how many days will 60 men do the same work?
A
4
B
3
C
2
D
6
Progressive education emphasizes learning by:
A
Reading
B
Writing
C
Doing
D
Enjoying
The marked price of a fan is ₹ 1500 and a discount of 20% is given on the marked price. Now, the additional discount given to a customer to keep the net price of that fan at ₹ 1116 is:
A
5%
B
6%
C
7%
D
8%
If 2 letters are chosen from the English alphabet, then the probability of both the letters being vowels is:
A
1/65
B
2/65
C
3/65
D
4/65
If 1/(x+1) + 1/(y+2) + 1/(z+1009) = 1, then the value of x + y + z is:
A
1
B
2
C
3
D
6
If S is the circumcenter of triangle ABC and ∠A = 50°, then the value of ∠BCS is:
A
30°
B
40°
C
50°
D
60°
If (3x - y) : (x + 5y) = 5 : 7, then the value of (x + y) : (x - y) is:
A
1 : 2
B
2 : 1
C
3 : 1
D
1 : 3
Special Education is related to:
A
Talented students
B
Education for disabled
C
Teachers
D
Weak students
If (x + 1/x) = 5, then the value of (x³ + 1/x³) is:
A
125
B
110
C
25
D
5
The sum of all three digit numbers divisible by 5 is:
A
98560
B
98540
C
98520
D
98550