Arithmetic
1. A train running at the speed of 60 km/hr crosses a pole in 9 seconds. What is the length of the train?

A. 120 metres B. 180 metres C. 324 metres D. 150 metres

Answer: Option (D)
Explanation: Length of the train = (Speed x Time) =50/3 x 9 m = 150 m.
2. A 600m long train is running at 73 Kmph. How much time Train will take to cross an electric pole?

A. 29.58 sec B. 28.58sec C. 29 sec D. 28sec E. None of these

Answer: Option (A)
Explanation: Formula Used: Time = ( Distance / Speed) As all the option given in sec., so convert the train speed (Kmph) in to mps multiply by 5/18 speed (mps) = 73 * 5/18 Time = 600 / (73 * 5/18) = (600 * 18 )/(73 * 5) sec = (10800 / 365) Time take by Train = 29.58Sec
3. A 120 m long train is running at 72 Kmph. How much time will it take to cross a man standing on the platform?

A. 6 sec B. 2.5 sec C. 5 sec D. 12 sec

Answer: Option (A)
Explanation: Formula Used: Time = ( Distance / Speed) As all the option given in sec., so convert the train speed (Kmph) into mps multiply by 5/18 speed (MPs) = 72 * 5/18 = 20 MPs Time = (120 / 20) sec = 6 sec Time take by Train = 6 Sec.
4. A train running at a speed of 126 Kmph. What will be the length of the train if it crosses a tree in 5 sec?

A. 190 meters B. 180 meters C. 143 meters D. 175 meters E. None of these

Answer: Option (D)
Explanation: Formula Used: Distance = (Speed * Time) convert the train speed (Kmph) in to mps multiply by 5/18 speed (mps) = 126 * 5/18 = 35 mps length = ( 35 * 5 ) meter = 175 meter
5. 320m long train is running at 72 Kmph. how much time it will take to cross a platform of 180m long?

A. 20 sec B. 30 sec C. 25 sec D. 27 sec

Answer: Option (C)
Explanation: Total Length = Platform Length + Train Length So Total Length = 500m convert the train speed (Kmph) in to mps multiply by 5/18 speed (mps) = 72 * 5/18 = 20mps Formula Used: Time = Distance/Speed Time = (500 / 20 ) sec = 25 sec.
Algebra
1. If a * b = 2a – 3b + ab, then 3 * 5 + 5 * 3 is equal to :

A. 22 B. 24 C. 26 D. 28

Answer: Option (A)
Explanation: a * b = 2a – 3b + ab Þ 3 * 5 = 2 × 3 – 3 × 5 + 3 × 5 = 6 5 * 3 = 2 × 5 – 3 × 3 + 3 × 5 = 10 – 9 + 15 = 16 Therefore, 3 * 5 + 5 *3 = 6 + 16 = 22
2. For what value of ‘a’, the polynomial 2x3+ ax2+ 11x + a + 3, is exactly divisible by (2x – 1) ?

A. 7 B. –7 C. 5 D. –5

Answer: Option (B)
3. If a + b + c = 15 and a2+ b2+ c2 = 83, then a3 + b3 + c3 – 3abc = ?

A. 160 B. 175 C. 180 D. 100

Answer: Option (C)
4. What will be the value of (x – a)3+ (x – b)3+ (x – c)3 – 3 (x –a) (x – b) (x – c) if a + b+c = 3x ?

A. 1 B. 3 C. 0 D. 5

Answer: Option (C)
5. If 4x2+ 4y2+ 4z2 = 12x + 12y – 18 then x + y + z = ?

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

Answer: Option (A)
Trigonometry
1. Formula for area of a triangle ABC is

A. 2ab sin C = 2bc sin A = 2ac sin B B. 3/2ab sin C = 3/2bc sin A = 3/2ac sin B C. 1/2ab sin C + 1/2bc sin A + 1/2ac sin B D. 1/2ab sin C = 1/2bc sin A = 1/2ac sin B

Answer: Option (D) 1/2ab sin C = 1/2bc sin A = 1/2ac sin B
2. If cos 55° and sin 55° = 0.8 each then answer of cos 125° + 5 sin 55° is

A. 0.8 B. 2.4 C. 2.8 D. 3.2

Answer: Option (B)
3. Number of dimensions a point can have is

A. zero B. one C. infinite D. negative

Answer: Option (D)
4. Solve for G if CSC (11G – 16 degrees) = sec (5G + 26 degrees)

A. 4 degrees B. 5 degrees C. 6 degrees D. 7 degrees

Answer: Option (B)
5. Find the value of sin (arc cos15/17)

A. 8/11 B. 8/15 C. 8/17 D. 8/19

Answer: Option (C)
Geometry
1. ABC is a right angled triangle with a right angle at A. Points D, E are the middle points of AB and AC respectively. Which of the following relations is correct?

A. 3 (BE2 + CD2) = 4 BC2 B. 4(BE2 + CD2) = 5 BC2 C. 4(BE2 + CD2) = 3 BC2 D. None of these

Answer: Option (B)
2. DABC is an isosceles triangle in which AB = AC. Side BA is extended to D such that AB = AD. What will be the value of ÐBCD?

A. 90° B. 60° C. 30° D. 45°

Answer: Option (A)
3. Two circles whose radii are 10 cm and 8 cm, intersect each other and their common chord is 12 cm long. What is the distance between their centers?

A. 11.27 cm B. 12.29 cm C. 12.27 cm D. 13.29 cm

Answer: Option (D)
4. In D ABC, AB = 6 cms, BC = 10 cms, AC = 8cm and AD ^ BC. Find the value of the ratio of BD: DC.

A. 3: 4 B. 9: 16 C. 4: 5 D. 16: 25

Answer: Option (B)
5. In D ABC, a line parallel to BC intersects AB and AC at D and E. If AE = 3 AD, find the ratio BD: EC.

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

Answer: Option (A)
Mensuration
1. The length of a rectangular plot is thrice its breadth. If the area of the rectangular plot is 867 sq m, then what is the breadth of the rectangular plot?

A. 8.5 m B. 17 m C. 34 m D. 51 m E. None of these

Answer: Option (B)
Explanation: Let the breadth of the plot be b. m. Length of the plot = 3 b m (3b)(b) = 867 3b[latex]^{2}[/latex] = 867 b[latex]^{2}[/latex] = 289 = 17[latex]^{2}[/latex] (b > 0) b = 17 m.
2. The length of a rectangular floor is more than its breadth by 200%. If Rs. 324 is required to paint the floor at the rate of Rs. 3 per sq m, then what would be the length of the floor?

A. 27 m B. 24 m C. 18 m D. 21 m E. None of these

Answer: Option (C)
Explanation: Let the length and the breadth of the floor be lm and bm respectively. l = b + 200% of b = l + 2b = 3b Area of the floor = 324/3 = 108 sq m l b = 108 i.e., l * l/3 = 108 l[latex]^{2}[/latex] = 324 => l = 18.
3. What will be the cost of building a fence around a square plot with an 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.
4. The dimensions of a room are 25 feet * 15 feet * 12 feet. What is the cost of whitewashing the four walls of the room at Rs. 5 per square feet if there is one door of dimensions 6 feet * 3 feet and three windows of dimensions 4 feet * 3 feet each?

A. Rs. 4800 B. Rs. 3600 C. Rs. 3560 D. Rs. 4530 E. None of these

Answer: Option (D)
Explanation: Area of the four walls = 2h(l + b) Since there are doors and windows, area of the walls = 2 * 12 (15 + 25) - (6 * 3) - 3(4 * 3) = 906 sq.ft. Total cost = 906 * 5 = Rs. 4530.
5. The sector of a circle has a radius of 21 cm and central angle 135o. Find its perimeter?

A. 91.5 cm B. 93.5 cm C. 94.5 cm D. 92.5 cm E. None of these

Answer: Option (A)
Explanation: The perimeter of the sector = length of the arc + 2(radius) = (135/360 * 2 * 22/7 * 21) + 2(21) = 49.5 + 42 = 91.5 cm
Statistics
1. Marks obtained by an student in 5 subjects are given below 25, 26, 27, 28, 29 in these obtained marks 27 is

A. mode B. median and mode C. mean and median D. both (A) and (C)

Answer: Option (C)
Explanation: 27 is in the middle, so is the median and its the mean too.
2. The median for the data 2, 4, 6, 8, 10, 12, 14 is

A. 6 B. 8 C. 9.5 D. 10

Answer: Option (B)
Explanation: 4th observation i.e., 8 is the median.
3. Action research means

A. A longitudinal research B. An applied research C. Research initiated to solve an immediate problem D. Research with the socio-economic objective

Answer: Option (C)
4. A reasoning where we start with certain particular statements and conclude with a universal statement is called

A. Deductive Reasoning B. Inductive Reasoning C. Abnormal Reasoning D. Transcendental Reasoning

Answer: Option (B)
5. Which of the following variables cannot be expressed in quantitative terms?

A. Socio-economic Status B. Marital Status C. Numerical Aptitude D. Professional Attitude

Answer: Option (C)