Major Competitive Exams

Civil Services Defence Exams Engineering & Architecture Admissions Government Jobs Management Admissions Undergraduate

Q. Calculate the range of the data set: 4, 8, 15, 16, 23, 42.

A. 38
B. 36
C. 34
D. 32

Solution

Range = Maximum - Minimum = 42 - 4 = 38.

Correct Answer: A — 38

Learn More →

Q. Calculate the range of the data set: 8, 12, 15, 20, 22.

A. 10
B. 12
C. 14
D. 15

Solution

Range = Max - Min = 22 - 8 = 14.

Correct Answer: A — 10

Learn More →

Q. Calculate the range of the following data set: 12, 15, 20, 22, 30.

A. 10
B. 12
C. 18
D. 20

Solution

Range = Maximum - Minimum = 30 - 12 = 18.

Correct Answer: C — 18

Learn More →

Q. Calculate the range of the following data set: 15, 22, 8, 19, 30.

A. 7
B. 15
C. 22
D. 30

Solution

Range = max - min = 30 - 8 = 22.

Correct Answer: D — 30

Learn More →

Q. Calculate the range of the following data set: 4, 8, 15, 16, 23, 42.

A. 38
B. 36
C. 34
D. 32

Solution

Range = Maximum - Minimum = 42 - 4 = 38.

Correct Answer: A — 38

Learn More →

Q. Calculate the range of the following data set: 8, 12, 15, 7, 10.

A. 5
B. 8
C. 10
D. 12

Solution

Range = Maximum - Minimum = 15 - 7 = 8.

Correct Answer: A — 5

Learn More →

Q. Calculate the RMS speed of a gas with molar mass 0.028 kg/mol at 300 K. (R = 8.314 J/(mol K))

A. 500 m/s
B. 600 m/s
C. 700 m/s
D. 800 m/s

Solution

Using v_rms = sqrt(3RT/M), we find v_rms = sqrt(3 * 8.314 * 300 / 0.028) = 600 m/s.

Correct Answer: B — 600 m/s

Learn More →

Q. Calculate the scalar product of A = (1, 1, 1) and B = (2, 2, 2).

A. 3
B. 4
C. 5
D. 6

Solution

A · B = 1*2 + 1*2 + 1*2 = 2 + 2 + 2 = 6.

Correct Answer: D — 6

Learn More →

Q. Calculate the scalar product of the vectors (1, 0, 0) and (0, 1, 0).

A. 0
B. 1
C. 2
D. 3

Solution

Scalar product = 1*0 + 0*1 + 0*0 = 0.

Correct Answer: A — 0

Learn More →

Q. Calculate the scalar product of the vectors (1, 2, 3) and (4, 5, 6).

A. 32
B. 33
C. 34
D. 35

Solution

Scalar product = 1*4 + 2*5 + 3*6 = 4 + 10 + 18 = 32.

Correct Answer: A — 32

Learn More →

Q. Calculate the scalar product of the vectors (2, 3, 4) and (4, 3, 2).

A. 28
B. 29
C. 30
D. 31

Solution

Scalar product = 2*4 + 3*3 + 4*2 = 8 + 9 + 8 = 25.

Correct Answer: A — 28

Learn More →

Q. Calculate the scalar product of the vectors (3, 0, -3) and (1, 2, 1).

A. 0
B. 1
C. 2
D. 3

Solution

Scalar product = 3*1 + 0*2 + (-3)*1 = 3 + 0 - 3 = 0.

Correct Answer: A — 0

Learn More →

Q. Calculate the scalar product of the vectors A = (1, 2, 3) and B = (4, 5, 6).

A. 32
B. 30
C. 28
D. 26

Solution

A · B = 1*4 + 2*5 + 3*6 = 4 + 10 + 18 = 32.

Correct Answer: B — 30

Learn More →

Q. Calculate the scalar product of the vectors A = (4, -1, 2) and B = (2, 3, 1).

A. 10
B. 8
C. 6
D. 12

Solution

A · B = 4*2 + (-1)*3 + 2*1 = 8 - 3 + 2 = 7.

Correct Answer: A — 10

Learn More →

Q. Calculate the scalar product of the vectors K = (0, 1, 2) and L = (3, 4, 5).

A. 10
B. 11
C. 12
D. 13

Solution

K · L = 0*3 + 1*4 + 2*5 = 0 + 4 + 10 = 14.

Correct Answer: A — 10

Learn More →

Q. Calculate the term containing x^3 in the expansion of (2x + 5)^6. (2000)

A. 1500
B. 1800
C. 2000
D. 2500

Solution

The term containing x^3 is C(6,3) * (2)^3 * (5)^(6-3) = 20 * 8 * 125 = 20000.

Correct Answer: B — 1800

Learn More →

Q. Calculate the term containing x^3 in the expansion of (x + 2)^7.

A. 56
B. 84
C. 112
D. 128

Solution

The term containing x^3 is C(7,3) * (2)^4 = 35 * 16 = 560.

Correct Answer: B — 84

Learn More →

Q. Calculate the term independent of x in the expansion of (2x - 3)^5.

A. -243
B. 0
C. 243
D. 81

Solution

The term independent of x is C(5,5) * (2x)^0 * (-3)^5 = 1 * 1 * (-243) = -243.

Correct Answer: A — -243

Learn More →

Q. Calculate the term independent of x in the expansion of (2x^2 - 3x + 4)^3.

A. 12
B. 24
C. 36
D. 48

Solution

The term independent of x occurs when the powers of x cancel out. The term is C(3,0)(4)^3 + C(3,1)(-3x)(4)^2 + C(3,2)(-3x)^2(4) + C(3,3)(-3x)^3 = 64 - 36 + 0 + 0 = 28.

Correct Answer: B — 24

Learn More →

Q. Calculate the term independent of x in the expansion of (2x^2 - 3x + 4)^5.

A. 80
B. 120
C. 160
D. 200

Solution

The term independent of x occurs when the powers of x cancel out. This can be calculated using the binomial expansion.

Correct Answer: C — 160

Learn More →

Q. Calculate the term independent of x in the expansion of (2x^2 - 3x)^4.

A. -81
B. 108
C. -108
D. 81

Solution

The term independent of x occurs when 2k = 4, k = 2. The term is C(4,2) * (2x^2)^2 * (-3x)^2 = 6 * 4 * 9 = -216.

Correct Answer: C — -108

Learn More →

Q. Calculate the term independent of x in the expansion of (x/2 - 3)^6.

A. 729
B. 729/64
C. 729/32
D. 729/16

Solution

The term independent of x occurs when k = 3, which gives C(6,3) * (x/2)^3 * (-3)^3 = 20 * (1/8) * (-27) = -67.5.

Correct Answer: B — 729/64

Learn More →

Q. Calculate the term independent of x in the expansion of (x/2 - 3)^8.

A. -3
B. -8
C. 0
D. 256

Solution

The term independent of x occurs when k = 4. Thus, the term is C(8,4) * (x/2)^4 * (-3)^4 = 70 * (1/16) * 81 = 256.

Correct Answer: D — 256

Learn More →

Q. Calculate the term independent of x in the expansion of (x^2 - 3x + 2)^4.

A. 8
B. 12
C. 16
D. 20

Solution

The term independent of x occurs when the powers of x cancel out. The term is C(4,2) * (2)^2 * (-3)^2 = 6 * 4 * 9 = 216.

Correct Answer: B — 12

Learn More →

Q. Calculate the value of (1 + 3)^5 using the binomial theorem.

A. 81
B. 243
C. 125
D. 256

Solution

(1 + 3)^5 = 4^5 = 1024.

Correct Answer: B — 243

Learn More →

Q. Calculate the value of 100 - (25 × 3). (2015)

A. 25
B. 75
C. 50
D. 70

Solution

25 × 3 = 75, then 100 - 75 = 25.

Correct Answer: B — 75

Learn More →

Q. Calculate the value of 12 × 3 - 4 × 2. (2023) 2023

A. 28
B. 32
C. 34
D. 30

Solution

12 × 3 = 36 and 4 × 2 = 8, so 36 - 8 = 28.

Correct Answer: A — 28

Learn More →

Q. Calculate the value of 12 × 3 - 4. (2021)

A. 32
B. 28
C. 36
D. 24

Solution

12 × 3 = 36, then 36 - 4 = 32.

Correct Answer: B — 28

Learn More →

Q. Calculate the value of 12 × 5 - 8. (2021)

A. 52
B. 60
C. 56
D. 48

Solution

12 × 5 = 60, then 60 - 8 = 52.

Correct Answer: C — 56

Learn More →

Q. Calculate the value of 12 × 8 - 10. (2021)

A. 86
B. 82
C. 78
D. 80

Solution

12 × 8 = 96, then 96 - 10 = 86.

Correct Answer: B — 82

Learn More →

Showing 3481 to 3510 of 27896 (930 Pages)

Major Competitive Exams

On a scale of 0–10, how likely are you to recommend The Soulshift Academy?