Mathematics Subject(Part-IV)

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Question 1 / 60
The least common multiple of 18, 24, 60 will be:
A
120
B
240
C
360
D
480
1/2 × 1/5 × 1/6 × 1/7 × 1/100 is equal to:
A
0
B
1/125
C
1/25
D
1/50
If the mean of 6, 4, 7, P and 10 is 8, what is the value of P?
A
11
B
12
C
13
D
14
What is the median of following data? 25, 34, 31, 23, 22, 26, 35, 28, 20, 32
A
22
B
27
C
25
D
20
(x - y)(x + y)(x² + y²)(x⁴ + y⁴) is equal to:
A
x¹⁶ - y¹⁶
B
x⁸ + y⁸
C
x⁸ - y⁸
D
x¹⁶ + y¹⁶
The area of the base of a right circular cylinder is 154 cm² and its height is 15 cm. What is the volume of cylinder?
A
2310 cm³
B
5720 cm³
C
1780 cm³
D
3803 cm³
If sec θ – cosec θ = 0, then the value of (sec θ + cosec θ) will be:
A
3/2
B
2/3
C
0
D
2√2
How many spherical bullets can be made out of solid cube of lead whose edge measures 44 cm, each bullet being 4 cm in diameter?
A
1500
B
2541
C
1161
D
2270
In a cricket match, a batsman hits a boundary 8 times out of 40 balls he plays. What is the probability that he didn't hit a boundary?
A
0.2
B
0.3
C
0.6
D
0.8
For numbers 2, 2, 4, 5 and 12. Which of the following statement is true?
A
Mean = Median
B
Mean < Mode
C
Mean > Mode
D
Mode = Median
The value of (√5+√3)/(√5-√3) + (√5+√3) is:
A
4
B
8
C
9
D
10
The radius and slant height of a cone are in the ratio of 4 : 7. If its curved surface area is 792 cm². What is its radius?
A
2 cm
B
5 cm
C
11 cm
D
12 cm
√2 is:
A
Rational Number
B
Natural Number
C
Irrational Number
D
Integer Number
P, Q and R together can complete a work in 30 days. If the ratio of efficiency of P, Q and R is 20 : 15 : 12 respectively, then in how many days R can alone complete the same work?
A
195/2
B
235/2
C
225/2
D
215/2
If a = 4 and b = 6, then the value of a√(4b² - a²) will be:
A
8√2
B
28
C
12
D
3
The volume of a solid cylinder is 448π cm³ and height 7 cm. What is its lateral surface area?
A
754 cm²
B
866 cm²
C
539 cm²
D
352 cm²
The sum of consecutive numbers from 1 to 50 is:
A
1250
B
1275
C
1225
D
1255
A shopkeeper marks a product at ₹3750. He sells it at a 20% discount and still makes a profit of ₹250. What is the difference between the marked price and the cost price of the product?
A
750
B
500
C
1000
D
1050
In a circle of radius 21 cm, an arc subtends an angle of 60° at the centre. The length of the arc is:
A
20 cm
B
21 cm
C
22 cm
D
25 cm
The Highest Common Factor (HCF) of 24, 30, 54 will be:
A
2
B
3
C
5
D
6
The diameter of a right circular cone is 8 cm and its volume is 48π cm³. What is its height?
A
25 cm
B
21 cm
C
9 cm
D
15 cm
The value of √2 upto 3 decimal places is:
A
1.410
B
1.412
C
1.414
D
1.413
The measure of the angle between the coordinate axes is:
A
0°
B
90°
C
180°
D
360°
Two numbers are chosen from the first 50 natural numbers. What is the probability of both the numbers being prime?
A
17/245
B
19/245
C
21/245
D
23/245
If θ is an acute angle and tan θ + cot θ = 2, then the value of tan⁵θ + cot¹⁰θ is:
A
1
B
2
C
4
D
1/2
The factors of x³ - 7x + 6 are:
A
x(x-6)(x-1)
B
(x²-6)(x-1)
C
(x+1)(x+2)(x-3)
D
(x-1)(x+3)(x-2)
Neha's father bought 3 dozen pencils for ₹360. What is the cost of 7 pencils?
A
₹70
B
₹80
C
₹75
D
₹60
If (x - 3) is a factor of x² - ax - 15, then a = ?
A
-2
B
5
C
-5
D
3
A village having a population of 4000 requires 150 liters of water per day. It has a tank measuring 20 m × 15 m × 6 m. For how many days will the water of this tank last?
A
10 days
B
7 days
C
3 days
D
1 day
If 1³ + 2³ + 3³ + 4³ + 5³ + 6³ = 441, then the value of 2³ + 4³ + 6³ + 8³ + 10³ + 12³ is:
A
3528
B
3529
C
3600
D
3728
If (x + 1) and (x - 2) are factors of x³ + ax² - bx - 6, then find the values of a and b respectively:
A
2, 3
B
3, 5
C
5, 3
D
2, 5
The radius of the top and bottom of a bucket of slant height 35 cm are 25 cm and 8 cm. The curved surface of the bucket is:
A
3630 cm²
B
3500 cm²
C
3750 cm²
D
4000 cm²
A solid cube is cut into two cuboids of equal volumes. What is the ratio of total surface area of the given cube and that of one of the cuboids?
A
1 : 2
B
3 : 2
C
3 : 5
D
4 : 1
If √2 = 1.414, then the value of √3 ÷ √6 upto three places of decimal is:
A
0.414
B
0.702
C
0.413
D
0.707
If (2K - 1, K) is a solution of the equation 10x - 9y = 12, then K = ?
A
1
B
2
C
3
D
4
If expression x + (1/4)√x + a² is a perfect square, then what is the value of 'a'?
A
± 1/18
B
± 1/8
C
- 1/5
D
1/4
The value of (38×38×38+34×34×34)/(38×38+34×34-38×34) + (28×28×28-38×34×84)/(-38×34-34×28-38×28) is:
A
200
B
100
C
150
D
110
If (x-3)² + (y-5)² + (z-4)² = 0, then the value of (x²/9 + y²/25 + z²/16) will be:
A
12
B
9
C
3
D
1
A bag contain 1 rupee coins, 50 paise coins and 10 paise coins. The number of coins are in the ratio of 3 : 4 : 5. If the total amount is ₹187, the number of 50 paise coins is:
A
136
B
170
C
180
D
200
If 2x = 3y = -6z, then the value of (1/x + 1/y + 1/z) will be:
A
0
B
1
C
3/2
D
-1/2
The value of (125)^(-2/3) will be:
A
1/25
B
1/125
C
1/625
D
1/3125
Solve: 9 – 8.5 × 0.6 ÷ 5 + 1 = ?
A
9.99
B
8.89
C
9.88
D
8.98
The value of (5^(5/3) × 5^(2/3)) ÷ 5^(-1) will be:
A
0
B
1
C
5
D
10
Which term of the Arithmetic Progression 3, 8, 13, 18, .... is 78?
A
16th
B
13th
C
12th
D
10th
If a - b = a where a ≠ 0, b ≠ 0, then the value of a³ + b³ is:
A
-2
B
-1
C
1
D
0
The value of √(2√(2√(2√(2.....)))) is:
A
1
B
3
C
2
D
5
What will be the area of a triangle, two sides of which are 8 cm and 11 cm and the perimeter is 32 cm?
A
84 cm²
B
9√15 cm²
C
8√30 cm²
D
(√3/4) cm²
A boy travels 24 km towards east from his house, then he turned his left and covers another 10 km. What is his total displacement?
A
22 km
B
23 km
C
25 km
D
26 km
The angles of quadrilateral ABCD, taken in order, are in the ratio 3 : 7 : 6 : 4, then ABCD is a:
A
Isosceles triangle
B
Rhombus
C
Parallelogram
D
Trapezium
Which of the following fractions are in ascending order?
A
7/9, 8/11, 11/14, 13/15
B
9/11, 7/8, 14/15, 13/13
C
8/7, 9/11, 13/11, 14/15
D
7/8, 11/9, 11/13, 15/14
What will be the exterior angles of a hexagon?
A
7.2°
B
60°
C
54°
D
108°
A, B & C are the three angles of a triangle. If A – B = 15°, B – C = 30°, then ∠A, ∠B and ∠C = ?
A
∠A = 80°, ∠B = 65°, ∠C = 35°
B
∠A = 30°, ∠B = 60°, ∠C = 90°
C
∠A = 40°, ∠B = 60°, ∠C = 80°
D
∠A = 90°, ∠B = 40°, ∠C = 50°
What will be the compound proportion of (2 : 3), (5 : 6) and (8 : 9)?
A
1 : 2
B
20 : 27
C
15 : 9
D
40 : 81
If x is a real number, then the minimum value of x² - x + 1 will be:
A
0
B
3/4
C
1
D
1/4
If (x + y) : (x - y) = 7 : 3, then ratio of (x² + y²) : (x² - y²) will be:
A
19 : 20
B
29 : 21
C
39 : 29
D
40 : 21
The dimensions of a cuboid are in the ratio of 1 : 2 : 3 and its total surface area is 88 m². What are the dimensions?
A
2 m, 4 m, and 6 m
B
3 m, 6 m and 9 m
C
2 m, 3 m and 6 m
D
6 m, 8 m and 10 m
If (x + 1/x)² = 3, then the value of (x⁷² + x⁶⁶ + x⁵⁴ + x³⁶ + x²⁴ + x⁶ + 1) is:
A
1
B
0
C
2
D
3
Given ∠POR = 3x and ∠QOR = 2x + 10°. If POQ is a straight line, then the value of x is:
A
30°
B
36°
C
17°
D
34°
If O(p/3, 4) is the midpoint of the line segment joining the points P(-6, 5) and Q(-2, 3), then the value of p is:
A
7/2
B
-12
C
4
D
-4
△ABC is a right-angled triangle, right angled at B. If AB = 5 cm and BC = 5 cm, then AC will be:
A
6.171 cm
B
7.171 cm
C
6.071 cm
D
7.071 cm