Mock Test: गणित (भाग-IV)

QUESTION 91

If (x² + y² + z² - 64) = -2 and x + y = 3z, then value of z is:

A

2

B

3

C

4

D

5

QUESTION 92

The value of √10.0000 + √100.000 - √1000.0000 is:

A

0.30644

B

0.3244

C

1.03644

D

0.3644

QUESTION 93

The value of 99 × 98 × 99 is:

A

9899

B

98999

C

99899

D

99998

QUESTION 94

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

QUESTION 95

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

QUESTION 96

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

QUESTION 97

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

QUESTION 98

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

QUESTION 99

The value of √20+√20+√20+......∞ is:

A

2

B

4

C

5

D

10

QUESTION 100

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

QUESTION 101

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

QUESTION 102

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

QUESTION 103

-5 + (-8) + (-11) + ……… + (-230) is:

A

-8930

B

8930

C

8989

D

8900

QUESTION 104

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

QUESTION 105

Sum of all the prime numbers between 50 to 90 is:

A

485

B

572

C

722

D

635

QUESTION 106

What is the unit place number in (2137)⁷⁵³?

A

1

B

3

C

7

D

9

QUESTION 107

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

QUESTION 108

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

QUESTION 109

The value of √(0.081×0.484) / √(0.0064×6.25) is:

A

9

B

0.9

C

99

D

0.99

QUESTION 110

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

QUESTION 111

Express 135° in radians:

A

2π/3

B

3π/4

C

2π/5

D

3π/5

QUESTION 112

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

QUESTION 113

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

QUESTION 114

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

QUESTION 115

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

QUESTION 116

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

QUESTION 117

In ΔABC, if 3∠A = 4∠B = 6∠C, then ∠A is equal to:

A

60°

B

80°

C

30°

D

40°

QUESTION 118

Express 0.23535 …….. in the form of p/q:

A

233/990

B

235/99

C

2.35/9.9

D

235/999

QUESTION 119

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

QUESTION 120

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

QUESTION 121

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

QUESTION 122

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

QUESTION 123

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

QUESTION 124

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

QUESTION 125

Which mathematician wrote 'Lilavati', a book on mathematical principles?

A

Bhaskaracharya - II

B

Aryabhatta

C

Shridharacharya

D

Brahmagupta

QUESTION 126

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

QUESTION 127

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

QUESTION 128

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%

QUESTION 129

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

QUESTION 130

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

QUESTION 131

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

QUESTION 132

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

QUESTION 133

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

QUESTION 134

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

QUESTION 135

If a + b + c = 0, then the value of (a²/bc + b²/ca + c²/ab) is:

A

0

B

1

C

-1

D

3

QUESTION 136

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

QUESTION 137

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

QUESTION 138

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°

QUESTION 139

If √1.96 = 400, then the value of 'x' is:

A

532.4

B

560

C

440

D

480

QUESTION 140

'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

QUESTION 141

Square root of (14-6√5) is:

A

±(3+√5)

B

±(3-√5)

C

±(√3-3)

D

±(√3+3)

QUESTION 142

For which students promotive programs are required in mathematics teaching method?

A

Weak students

B

Mentally retarded students

C

Backward students

D

Intelligent students

QUESTION 143

How many two digit natural numbers are divisible by 3?

A

60

B

30

C

50

D

20

QUESTION 144

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

QUESTION 145

The value of ³√(3√(3√3)) is:

A

3¹/³

B

3¹/⁹

C

3⁷/⁹

D

3¹³/²⁷

QUESTION 146

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

QUESTION 147

If 3(x-5)/4 = 3 - (x-3)/2, then value of x is:

A

-5

B

3

C

5

D

-3

QUESTION 148

'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

QUESTION 149

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)

QUESTION 150

If √3 = 1.732, then 1/√3 is equal to:

A

0.866

B

0.433

C

0.277

D

0.5773