Arithmetic
1. Express a speed of 36 kmph in meters per second?

A. 10 mps B. 12 mps C. 14 mps D. 17 mps

Answer: Option (A) 36 * 5/18 = 10 mps
2. The speed of a train is 90 kmph. What is the distance covered by it in 10 minutes?

A. 15 kmph B. 12 kmph C. 10 kmph D. 5 kmph

Answer: Option (A)
Explanation: 90 * 10/60 = 15 kmph
3. A train 240 m in length crosses a telegraph post in 16 seconds. The speed of the train is?

A. 50 kmph B. 52 kmph C. 54 kmph D. 56 kmph

Answer: Option (C)
Explanation: S = 240/16 * 18/5 = 54 kmph
4. The speed of a car is 90 km in the first hour and 60 km in the second hour. What is the average speed of the car?

A. 72 kmph B. 75 kmph C. 30 kmph D. 80 kmph

Answer: Option (B)
Explanation: S = (90 + 60)/2 = 75 kmph
5. Two cars cover the same distance at the speed of 60 and 64 kmps respectively. Find the distance traveled by them if the slower car takes 1 hour more than the faster car.

A. 906 km B. 960 m C. 960 km D. 966 km

Answer: Option (C)
Explanation: 60(x + 1) = 64x X = 15 60 * 16 = 960 km
Algebra
1. The sum and the product of the roots of the quadratic equation x2 + 20x + 3 = 0 are?

A. 10, 3 B. -10, 3 C. 20, -3 D. -10, -3 E. None of these

Answer: Option (E)
Explanation: Some of the roots and the product of the roots are -20 and 3 respectively.
2. A man could buy a certain number of notebooks for Rs.300. If each notebook cost is Rs.5 more, he could have bought 10 notebooks less for the same amount. Find the price of each notebook?

A. 10 B. 8 C. 15 D. 7.50 E. None of these

Answer: Option (A)
Explanation: Let the price of each notebook be Rs.x. Let the number of notebooks which can be brought for Rs.300 each at a price of Rs.x be y. Hence xy = 300 => y = 300/x (x + 5)(y - 10) = 300 => xy + 5y - 10x - 50 = xy =>5(300/x) - 10x - 50 = 0 => -150 + x[latex]^{2}[/latex] + 5x = 0 multiplying both sides by -1/10x => x[latex]^{2}[/latex] + 15x - 10x - 150 = 0 => x(x + 15) - 10(x + 15) = 0 => x = 10 or -15 As x>0, x = 10.
3. Find the roots of quadratic equation: 3x[latex]^{2}[/latex] - 7x - 6 = 0?

A. -6, 3 B. 3, -2/3 C. -5, 2 D. -9, 2 E. None of these

Answer: Option (B)
Explanation: 3x[latex]^{2}[/latex] - 9x + 2x - 6 = 0 3x(x - 3) + 2(x - 3) = 0 (x - 3)(3x + 2) = 0 => x = 3, -2/3.
4. Find the roots of quadratic equation: x[latex]^{2}[/latex] + x - 42 = 0?

A. -6, 7 B. -8, 7 C. 14, -3 D. -7, 6 E. 3, -14

Answer: Option (D)
Explanation: x[latex]^{2}[/latex] + 7x - 6x + 42 = 0 x(x + 7) - 6(x + 7) = 0 (x + 7)(x - 6) = 0 => x = -7, 6.
5. If the roots of the equation 2x[latex]^{2}[/latex] - 5x + b = 0 are in the ratio of 2:3, then find the value of b?

A. 3 B. 4 C. 5 D. 6 E. None of these

Answer: Option (A)
Explanation: Let the roots of the equation 2a and 3a respectively. 2a + 3a = 5a = -(- 5/2) = 5/2 => a = 1/2 Product of the roots: 6a[latex]^{2}[/latex] = b/2 => b = 12a[latex]^{2}[/latex] a = 1/2, b = 3.
Trigonometry
1. If circumference of a circle is divided into 360 congruent parts, angle subtended by one part at center of circle is called

A. angle B. radian C. degree D. minute

Answer: Option (C)
2. Cosecθ =

A. 1/cosθ B. cosθ/sinθ C. sinθ/cosθ D. 1/sinθ

Answer: Option (D)
3. The vertex of an angle in standard form is at

A. (1,0) B. (0,1) C. (1,1) D. (0,0)

Answer: Option (D)
4. In one hour, minutes hand of a clock turns through

A. 5π/6 radians B. 4π/9 radians C. π/4 radians D. 180π radians

Answer: Option (D)
5. The system of measurement in which angle is measured in radians called the

A. Circular system B. Sexagesimal system C. MKS system D. CGS system

Answer: Option (A)
Geometry
1. Coordinates of midpoint of line joining two points (16, 4) and (36, 6) are:

A. (26, 5) B. (5, 26) C. (10, 1) D. (1, 10)

Answer: Option (A)
2. Consider a line passing through (1, 2) and (4, 8), the gradient of this line is equal to:

A. 1 ⁄ 2 B. -1 ⁄ 2 C. 2 D. -2

Answer: Option (C)
3. Factorise -20x[latex]^{2}[/latex] - 9x + 20

A. (5 + 4x)(4 - 5x) B. (5 - 4x)(4 - 5x) C. (5 - 4x)(4 + 5x) D. (5 + 4x)(4 + 5x)

Answer: Option (A)
4. Simplify (2 ⁄ tanA) + (4 ⁄ tanB)

A. (2tanB + 4tanA) ⁄ tanAtanB B. (2tanA + 4tanB) ⁄ tanAtanB C. 6 ⁄ (tanA + tanB) D. None of the above

Answer: Option (A)
5. Logarithm to base 10 of 1000 is:

A. 1 B. 2 C. 3 D. 4

Answer: Option (C)
Mensuration
1. What will be the cost of building a fence around a square plot with area equal to 289 sq ft, if the price per foot of building the fence is Rs. 58?

A. Rs. 3944 B. Rs. 3828 C. Rs. 4176 D. Cannot be determined E. None of these

Answer: Option (A)
Explanation: Let the side of the square plot be an ft. a[latex]^{2}[/latex] = 289 => a = 17 Length of the fence = Perimeter of the plot = 4a = 68 ft. Cost of building the fence = 68 * 58 = Rs. 3944.
2. The area of a square is equal to five times the area of a rectangle of dimensions 125 cm * 64 cm. What is the perimeter of the square?

A. 600 cm B. 800 cm C. 400 cm D. 1000 cm E. None of these

Answer: Option (B)
Explanation: Area of the square = s * s = 5(125 * 64) => s = 25 * 8 = 200 cm Perimeter of the square = 4 * 200 = 800 cm.
3. The parameter of a square is double the perimeter of a rectangle. The area of the rectangle is 480 sq cm. Find the area of the square.

A. 200 sq cm B. 72 sq cm C. 162 sq cm D. Cannot be determined E. None of these

Answer: Option (D)
Explanation: Let the side of the square be a cm. Let the length and the breadth of the rectangle be l cm and b cm respectively. 4a = 2(l + b) 2a = l + b l . b = 480 We cannot find ( l + b) only with the help of l. b. Therefore a cannot be found. Area of the square cannot be found.
4. A cube of side one-meter length is cut into small cubes of side 10 cm each. How many such small cubes can be obtained?

A. 10 B. 100 C. 1000 D. 10000 E. None of these

Answer: Option (C)
Explanation: Along one edge, the number of small cubes that can be cut = 100/10 = 10 Along each edge, 10 cubes can be cut. (Along length, breadth, and height). Total number of small cubes that can be cut = 10 * 10 * 10 = 1000
5. The radius of a wheel is 22.4 cm. What is the distance covered by the wheel in making 500 resolutions?

A. 252 m B. 704 m C. 352 m D. 808 m E. None of these

Answer: Option (B)
Explanation: In one resolution, the distance covered by the wheel is its own circumference. Distance covered in 500 resolutions. = 500 * 2 * 22/7 * 22.4 = 70400 cm = 704 m.
Statistics
1. Which of the following is the explanatory variable in this study?

A. Exercise B. Lung capacity C. Smoking or not D. Occupation

Answer: Option (D)
2. The two treatments in this study were:

A. Walking for half an hour three times a week and reading a book for half an hour three times a week. B. Having blood pressure measured at the beginning of the study and having blood pressure measured at the end of the study. C. Walking or reading a book for half an hour three times a week and having blood pressure measured. D. Walking or reading a book for half an hour three times a week and doing nothing.

Answer: Option (A)
3. A magazine printed a survey in its monthly issue and asked readers to fill it out and send it in. Over 1000 readers did so. This type of sample is called

A. a cluster sample. B. a self-selected sample. C. a stratified sample. D. a simple random sample.

Answer: Option (B)
4. A polling agency conducted a survey of 100 doctors on the question “Are you willing to treat women patients with the recently approved pill RU-486”? The conservative margin of error associated with the 95% confidence interval for the percent who say 'yes' is

A. 50% B. 10% C. 5% D. 2%

Answer: Option (B)
5. The value of a correlation is reported by a researcher to be r = −0.5. Which of the following statements is correct?

A. The x-variable explains 25% of the variability in the y-variable. B. The x-variable explains −25% of the variability in the y-variable. C. The x-variable explains 50% of the variability in the y-variable. D. The x-variable explains −50% of the variability in the y-variable.

Answer: Option (A)