What is the solution of the equation

x log_{10} (10/3) + log_{10} 3 = log_{10} (2 + 3^{x}) + x?

- 10
- 3
- 1
- 0

If α and β are the roots of the equation x^{2} + px + q = 0, then what is α^{2} + β^{2} equal to?

- p
^{2}– 2q - q
^{2}– 2p - p
^{2}+ 2q - q
^{2}– q

The pair of linear equations kx + 3y + 1 = 0 and 2x + y + 3 = 0 intersect each other, if

- k = 6
- k ≠ 6
- k = 0
- k ≠ 0

The cost of a diamond varies directly as the square of its weight. A diamond broke into four pieces with their weights in the ratio of 1:2:3:4. If the loss in total value of the diamond was the ₹ 70,000, what was the price of the original diamond?

- ₹ 1,00,000
- ₹ 1,40,000
- ₹ 1,50,000
- ₹ 1,75,000

In a 100 m race, A runs at a speed of 5/3 m/s. If A gives a start of 4 m to B and still beats him by 12 seconds, what is the speed of B?

- 5/4 m/s
- 7/5 m/s
- 4/3 m/s
- 6/5 m/s

If 15 men take 21 days of 8 hours each to do a piece of work, then what is the number of days of 6 hours each that 21 women would take, if 3 women would do as much work as 2 men?

- 18
- 20
- 25
- 30

Leela got married 6 years ago. Today her age is 1¼ times her age at the time of her marriage. Her son’s age is 1/10 times her age. What is the present age of her son?

- 1 year
- 2 years
- 3 years
- 4 years

A and B working together can finish a piece of work in 12 days while B alone can finish it in 30 days. In how many days can A alone finish the work?

- 18 days
- 20 days
- 24 days
- 25 days

The values of x which satisfy the equation 5^{1+x} + 5^{1–x} = 26 are

- –1, 1
- 0, 1
- 1, 2
- –1, 0

If 5 men can do a piece of work in 10 days and 12 women can do the same work in 15 days, the number of days required to complete the work by 5 men and 6 women is

- 7½ days
- 8 days
- 9½ days
- 12 days

A passenger train departs from Delhi at 6 pm for Mumbai. At 9 pm, an express train, whose average speed exceeds that of the passenger train by 15 km/hour leaves Mumbai for Delhi. Two trains meet each other mid-route. At what time do they meet, given that the distance between the cities is 1080 km?

- 4 p.m.
- 2 a.m
- 12 midnight
- 6 a.m.

In a class of 49 students, the ratio of girls to boys is 4:3. If 4 girls leave the class, the ratio of girls to boys would be

- 11:7
- 8:7
- 6:5
- 9:8

What is the LCM of x^{3} + 8, x^{2} + 5x + 6 and x^{3} + 4x^{2} + 4x?

- x (x + 2)
^{2}(x + 3) (x^{2}- 2x + 4) - x (x - 2)
^{2}(x - 3) (x^{2}+ 2x + 4) - (x + 2)
^{2}(x + 3) (x^{2}- 2x + 4) - (x - 2)
^{2}(x - 3) (x^{2}- 2x + 4)

Rajendra bought a mobile with 25% discount on the selling price. If the mobile cost him Rs. 4,875, what is the original selling price of the mobile?

- Rs. 6,300
- Rs. 6,400
- Rs. 6,500
- Rs. 6,600

A 225 m long train is running at a speed of 30 km/hour. How much time does it take to cross a man running at 3 km/hour in the same direction?

- 40 seconds
- 30 seconds
- 25 seconds
- 15 seconds

The difference between the simple and the compound interest on a certain sum of money at 4% per annum in 2 years is Rs. 10. What is the sum?

- Rs. 5,500
- Rs. 6,000
- Rs. 6,250
- Rs. 7,500

If a% of a + b% of b = 2% of ab, then what percent of a is b?

- 50%
- 75%
- 100%
- Cannot be determined

5/9 ^{th} part of the population in a village are males. If 30% of the males are married, the percentage of unmarried females in the total population is

- 20
^{2}/_{9} - 27
^{2}/_{9} - 27
^{7}/_{9} - 29
^{2}/_{9}

Sunil wants to spend Rs.200 on two types of sweets, costing Rs.7 and Rs.10 respectively. What is the maximum number of sweets he can get so that no money is left over?

- 25
- 26
- 27
- 28

The HCF of two expressions p and q is 1. What is the reciprocal of their LCM?

- p + q
- p – q
- pq
- (pq)
^{-1}

A thief is spotted by a policeman from a distance of 100 m. When the policeman starts the chase, the thief also starts running. If the speed of the thief is 8 km/hour and that of the policeman is 10 km/hour, then how far will the thief have to run before he is overtaken?

- 200 m
- 300 m
- 400 m
- 500 m

Aman and Alok attempted to solve a quadratic equation. Aman made a mistake in writing down the constant term and ended up in roots (4, 3). Alok made a mistake in writing down the coefficient of x to get roots (3, 2). The correct roots of the equation are

- –4, –3
- 6, 1
- 4, 3
- –6, –1

The system of equations 2x + 4y = 6 and 4x + 8y = 8 is

- Consistent with a unique solution
- Consistent with infinitely many solutions
- Inconsistent
- None of the above

The ratio of two numbers is 1:5 and their product is 320. What is the difference between the squares of these two numbers?

- 1024
- 1256
- 1536
- 1640

25 kg of alloy X is mixed with 125 kg of alloy Y. If the amount of lead and tin in the alloy X is in the ratio 1:2 and the amount of lead and tin in the alloy Y is in the ratio 2:3, then what is the ratio of lead to tin in the mixture?

- 1:2
- 2:3
- 3:5
- 7:11

The mean of 5 numbers is 15. If one more number is included, the mean of the 6 numbers becomes 17. What is the included number?

- 24
- 25
- 26
- 27

The mean marks obtained by 300 students in a subject are 60. The mean of top 100 students was found to be 80 and the mean of last 100 students was found to be 50. The mean marks of the remaining 100 students are

- 70
- 65
- 60
- 50

Consider the following distribution:

If the mean of the above distribution is 50, what is the value of f?

- 24
- 34
- 56
- 96

In a pie diagram, there are four slices with angles 150°, 90°, 60° and 60°. A new pie diagram is formed by deleting one of the slices having angle 60° in the given pie diagram. In the new pie diagram

- The largest slice has angle 150°
- The smallest slice has angle 70°
- The largest slice has angle 180°
- The smallest slice has angle 90°

In an asymmetrical-distribution, if the mean and median of the distribution are 270 and 220 respectively, then the mode of the data is

- 120
- 220
- 280
- 370

An individual purchases three qualities of pencils. The relevant data is given below:

It is known that the average price per pencil is ₹1.25. What is the value of x?

- ₹10
- ₹30
- ₹40
- ₹60

Consider the following frequency distribution:

What are the values of f_{1} and f_{2} respectively?

- 10 and 17
- 17 and 10
- 11 and 16
- 16 and 11

The Kashmir region receives additional amount of precipitation during the winter brought by

- South-west Monsoon
- Western Disturbances
- Retreating Monsoon
- Temperate Cyclone

Which part of India has the Kalakot tertiary coal field?

- Brahmaputra river basin of Assam
- Damodar river basin of Jharkhand and West Bengal
- Himalayan mountain region
- Cardamom hills in Kerala

Which one of the following is the scientific name of the causal organism of elephantiasis?

- Ascaris lumbricoides
- Culex pipiens
- Wuchereria bancrofti
- Fasciola hepatica

Golden rice is a genetically-modified crop plant where the incorporated gene is meant for biosynthesis of

- Omega-3 fatty acids
- Vitamin A
- Vitamin B
- Vitamin C

An object moves in a circular path with a constant speed. Which one of the following statements is correct?

- The centripetal acceleration of the object is smaller for a gentle curve (i.e., curve of larger radius) than that for a sharp curve (i.e., curve of smaller radius).
- The centripetal acceleration is greater for a gentle curve than that for a sharp curve.
- The centripetal acceleration is the same for both, the gentle and sharp curves.
- The centripetal acceleration causes the object to slow down.