गणित (भाग-IV)

⏱️ --:--
Question 1 / 60
If (x² + y² + z² - 64) = -2 and x + y = 3z, then value of z is:
A
2
B
3
C
4
D
5
The value of √10.0000 + √100.000 - √1000.0000 is:
A
0.30644
B
0.3244
C
1.03644
D
0.3644
The value of 99 × 98 × 99 is:
A
9899
B
98999
C
99899
D
99998
The value of (2.75)³ - (2.25)³ / (2.75)² + 2.75 × 2.25 + (2.25)² is:
A
0.3
B
0.5
C
3
D
5
Arrange the following fractions in ascending order: 4/5, 7/8, 6/7, 5/6
A
4/5, 7/8, 6/7, 5/6
B
5/6, 6/7, 7/8, 4/5
C
4/5, 5/6, 6/7, 7/8
D
7/8, 6/7, 5/6, 4/5
The diagonal of a rectangle is 8 cm. The angle between side and diagonal of a rectangle is 30°, then the area of rectangle is:
A
16 cm²
B
16√3 cm²
C
8√3 cm²
D
16√3 cm²
The ratio of length and perimeter of any rectangle is 5 : 16, then the ratio of its length and breadth is:
A
5 : 11
B
5 : 8
C
5 : 4
D
5 : 3
Which of the following is the largest number? 0.9, 0.9, 0.09, 0.09
A
0.9
B
0.9
C
0.09
D
0.09
The value of √20+√20+√20+......∞ is:
A
2
B
4
C
5
D
10
If x + y = a + b, ax - by = a² - b², then the value of 'x' and 'y' is:
A
x = a, y = b
B
x = -a, y = b
C
x = a, y = -b
D
x = -a, y = -b
The roots of the quadratic equation 2x² + kx + 3 = 0 are equal, then value of 'k' is:
A
±2√6
B
±3√8
C
±5√6
D
±4√3
If the average of a, b, c is 'm' and (ab + bc + ca) = 0, then the average value of a² + b² + c² is:
A
m²
B
3m²
C
6m²
D
9m²
-5 + (-8) + (-11) + ……… + (-230) is:
A
-8930
B
8930
C
8989
D
8900
The length of the sides of a triangle is p, q, r respectively. If p² + q² + r² = pq + qr + pr, then triangle is:
A
Isosceles triangle
B
Equilateral triangle
C
Right angle triangle
D
Obtuse angle triangle
Sum of all the prime numbers between 50 to 90 is:
A
485
B
572
C
722
D
635
What is the unit place number in (2137)⁷⁵³?
A
1
B
3
C
7
D
9
If (x+1)/(x-1) + (x+2)/(x-2) = (22x+30)/(11x-18), then the value of 'x' is:
A
6
B
-6
C
5
D
-5
Find the sum of first 24 terms of the list of numbers whose nth term is a_n = 3 + 2n:
A
680
B
670
C
672
D
675
The value of √(0.081×0.484) / √(0.0064×6.25) is:
A
9
B
0.9
C
99
D
0.99
A lot of 20 bulbs contains 4 defective pieces. One bulb is drawn at random from the lot. What is the probability that this bulb is defective?
A
1/2
B
1/4
C
1/5
D
2/5
Express 135° in radians:
A
2π/3
B
3π/4
C
2π/5
D
3π/5
If sin θ = a/b, θ is in first quadrant, then cos θ is equal to:
A
a/√(b² - a²)
B
b/√(b² - a²)
C
b/a
D
√(b² - a²)/b
Find the value of 'b' for which (2x + 3) is a factor of 2x³ + 9x² - x - b:
A
-25
B
15
C
20
D
51
The ratio of incomes of two persons is 9 : 7 and the ratio of their expenditures is 4 : 3. If each of them manages to save Rs. 2,000 per month, then one person monthly income is:
A
18,000
B
16,000
C
9,000
D
20,000
The value of (1 - 1/3)(1 - 3/5)(1 - 5/7).........(1 - 997/999) is:
A
5/999
B
1001/999
C
1001/3
D
1001/333
If mean of the following data is 18. Then the missing frequency 'a' is: x: 12, 14, 16, 18, 20, 22, 24; f: 7, 6, 9, 13, a, 5, 4
A
22
B
20
C
19
D
18
In ΔABC, if 3∠A = 4∠B = 6∠C, then ∠A is equal to:
A
60°
B
80°
C
30°
D
40°
Express 0.23535 …….. in the form of p/q:
A
233/990
B
235/99
C
2.35/9.9
D
235/999
The radius of a circle is 13 cm and a chord's distance from center is 12 cm, then the length of the chord is equal to:
A
15 cm
B
12 cm
C
10 cm
D
20 cm
The solution of following system of linear equation is: √7x + √11y = 0, √3x - √5y = 0
A
x = -√11/7, y = -√11/7
B
x = √11/7, y = √11/7
C
x = 0, y = 1
D
x = 0, y = 0
The difference between compound interest and simple interest is Rs. 620 for 3 years at 10% per year, then what would be principal amount?
A
40,000
B
12,000
C
10,000
D
20,000
The sides of a triangle are 3 cm, 4 cm and 5 cm, then area of triangle is:
A
6 cm²
B
3 cm²
C
3/2 cm²
D
3/4 cm²
The length of diagonal of a square is 'a' cm, the area of square is:
A
2a cm²
B
a/√2 cm²
C
a²/2 cm²
D
a²/4 cm²
Which statement is true about discriminant of quadratic equation ax² + bx + c = 0?
A
Two distinct real roots, if b² - 4ac > 0
B
Two equal real roots, if b² - 4ac = 0
C
No real roots, if b² - 4ac < 0
D
All of the above
Which mathematician wrote 'Lilavati', a book on mathematical principles?
A
Bhaskaracharya - II
B
Aryabhatta
C
Shridharacharya
D
Brahmagupta
The HCF and LCM of 96 and 404 respectively are:
A
2 and 6969
B
4 and 9696
C
2 and 5446
D
2 and 9696
The sum of three consecutive even positive numbers is 28 more than the average of three numbers, the smallest number is equal to:
A
6
B
12
C
14
D
16
If the ratio of principal amount and simple interest of one year is 25 : 1, then rate of interest is:
A
4%
B
25%
C
5%
D
20%
Which of the following is not a principle of programmed instruction?
A
Principle of small step
B
Principle of self pacing
C
Principle of abstraction
D
Principle of immediate feedback
The ratio of surface area of two spheres is 4 : 9, the ratio of their volumes is:
A
2 : 3
B
4 : 9
C
8 : 27
D
64 : 729
The average of 9 numbers is 30. The average of first 5 numbers is 25 and last 3 numbers is 35, then 6th number is equal to:
A
20
B
30
C
40
D
50
The height of a cone is 16 cm and its base radius is 12 cm, then what is the curved surface area and the total surface area of cone? (π = 3.14)
A
753.6 cm² and 1205.76 cm²
B
1205.76 cm² and 753.6 cm²
C
753.6 cm² and 1210.76 cm²
D
452.16 cm² and 753.6 cm²
Diagnostic test for fundamental process in arithmetic was developed by:
A
G. M. Ruch
B
G. T. Buswell and Lenore John
C
Leo J. Bruckner
D
Fred J. S. Schonell and F. Eleanor Schonell
Which of the following Maxime of Teaching is based on Gestalt Psychology?
A
From known to unknown
B
From concrete to abstract
C
From particular to general
D
From whole to part
If a + b + c = 0, then the value of (a²/bc + b²/ca + c²/ab) is:
A
0
B
1
C
-1
D
3
The interior angle of a regular polygon is:
A
(n - 2)×180°
B
(n/2)×180°
C
((n-2)×180°)/n
D
n(n-3)/2
The area of trapezium shape table top is 0.88 m² and its one parallel side is 1 m and the distance between parallel side is 0.8 m, then its another parallel side is:
A
1.2 m
B
0.1 m
C
2.1 m
D
2.5 m
The ratio of angles of a pentagon is 1 : 2 : 3 : 5 : 9, the value of its smallest angle is:
A
22°
B
34°
C
45°
D
27°
If √1.96 = 400, then the value of 'x' is:
A
532.4
B
560
C
440
D
480
'A' can do a piece of work in 4 hours, 'B' and 'C' can do together this work in 3 hrs and 'A' and 'C' can do together in 2 hrs. In what time could 'B' do it alone?
A
10 hrs
B
12 hrs
C
8 hrs
D
24 hrs
Square root of (14-6√5) is:
A
±(3+√5)
B
±(3-√5)
C
±(√3-3)
D
±(√3+3)
For which students promotive programs are required in mathematics teaching method?
A
Weak students
B
Mentally retarded students
C
Backward students
D
Intelligent students
How many two digit natural numbers are divisible by 3?
A
60
B
30
C
50
D
20
In a frequency distribution, the class marks are 10, 15, 20, 25, 30, then the class size is:
A
3
B
4
C
5
D
6
The value of ³√(3√(3√3)) is:
A
3¹/³
B
3¹/⁹
C
3⁷/⁹
D
3¹³/²⁷
If a:b = 2:3, b:c = 4:5, c:d = 6:7, then a:d is:
A
12:35
B
16:35
C
24:35
D
12:37
If 3(x-5)/4 = 3 - (x-3)/2, then value of x is:
A
-5
B
3
C
5
D
-3
'All science education which does not commence with Mathematics is invariably defective at its foundation.' This statement was stated by whom?
A
Roger Bacon
B
Hoghben
C
Herbert
D
Longback Comte
The expression x³ - 3x² - 9x - 5 has factors:
A
(x - 1)²(x + 5)
B
(x + 1)²(x - 5)
C
(x - 2)²(x + 1)
D
(x + 1)(x + 2)(x + 16)
If √3 = 1.732, then 1/√3 is equal to:
A
0.866
B
0.433
C
0.277
D
0.5773