List of practice Questions

In the relation $P =\frac{a}{\beta} e ^{-\frac{a z}{ k \theta}}, p$ is the pressure, $z$ the distance, $k$ is Boltzmann constant and $\theta$ is the temperature, the dimensional formula of $\beta$ will be
The extension in a string obeying Hooke's law $v$ is $x$. The speed of sound in the stretched string is $v$. If the extension in the string is increased to $1.5\, x$, the speed of sound will be
Two springs have their force constant as $k_1$ and $k_2 (k_1 > k_2)$. when they are stretched by the same force
In the following sentence choose the erroneous segment.
A                   B                       C
\(\text{\underline{We took a taxi so we would be on time for the meeting}}\)
When radiation is incident on a photoelectron emitter, the stopping potential is found to be $9V$. If elm for the electron is $1.8 \times 10^{11} \, C \, kg^{-1}$, the maximum velocity of the ejected electron is
The transformation ratio in the step-up transformer is
The equation of progressive wave is $y=0.2 \sin 2 \pi\left[\frac{t}{0.01}-\frac{x}{0.3}\right]$, where $x$ and $y$ are in metre and t is second. The velocity of propagation of the wave is
A ball whose density is $0.4 \times 10^3 \, kg/m^3$ falls into water from a height of $9\,cm$. To what depth does the ball sink?
The table below shows the temperatures in degrees Fahrenheit in a city over one week. If m represents the median temperature, f represents the temperature that occurs most often, and a represents the average (arithmetic mean) of the seven temperatures, which of the following is the correct order of m, f, and a?
          Noontime Temperature
MonTueWedThuFriSatSun
66787569787770
Consider the following piecewise definition of the function f.
\(f(x) =   \begin{cases}   3-x,\,\,\,if & \quad x≤0\\     x^2 +2,\,if & \quad x≥0  \end{cases}\)
Evaluate f(-3).
Inside a triangular park, there is a flower bed forming a similar triangle. Around the flower bed runs a uniform path of such a width that the sides of the park are exactly double the corresponding sides of the flower bed. The ratio of areas of the path to the flower bed is:
The intersection of two cubes cannot be
Area of a square natural lake is 50 sq. kms. A diver wishing to cross the lake diagonally, will have to swim a distance of
In a school drill, a number of children are asked to stand in a circle. They are evenly spaced and the 6th child is diametrically opposite the 16th child. How many children are made to stand in the circle?
A ladder is lying against a wall which is 5 metres high. If the ladder slips 2 metres away from the wall, the top of the ladder touches the foot of the wall. The length of the ladder is
In 4 years, the SI on a certain sum of money is of the principal. What is the annual rate of interest?
A man earns 6% SI on his deposits in Bank A while he earns 8% simple interest on his deposits in Bank B. If the total interest he earns is Rs.1800 in three years on an investment of Rs.9000, what is the amount invested at 6 %?
In a factory, each day the expected number of accidents is related to the number of overtime hour by a linear equation. Suppose that on one day there were 1000 overtime hours logged and 8 accidents reported and on another day there were 400 overtime hours logged and 5 accidents. What is the expected number of accidents when no overtime hours are logged?
Thirty days are in September, April, June and November. Some months are of thirty one days. A month is chosen at random. Then its probability of having exactly three days less than maximum of 31 is
A special lottery is to be held to select a student who will live in the only deluxe room in a hostel. There are 100 Year- Ill, 150 Year-II, and 200 Year-I students who applied. Each Year-III’s name is placed in the lottery 3 times; each Year-II’s name, 2 times; and each Year-I’s name, 1 time. What is the probability that a Year-III’s name will be chosen?
Bags I, II and III together have ten balls. If each bag contains at least one ball, how many balls does each bag have? Decide whether the data given in the statements are sufficient to answer the question.
Statement (1): Bag I contains five balls more than bag III.
Statement (2): Bag II contains half as many balls as bag I
The average of nine numbers is M and the average of three of these is P. If the average of remaining numbers is N, then
The profits of Biscuits India Ltd soared by 32% in the year 2006 - 07 as compared to year 2005 - 06. By what % did Biscuits India’s Sales increase in 2006 - 07 compared to the previous year? ( ssume: Profit = Sales - Expenses) Decide whether the information given in the two statements is sufficient to solve the problem.
Statement (1): Expenses in 2006 - 07 were Rs 1,400 crores, as compared to Rs 1,220 crores in 2005-06
Statement (2): Sales in 2006 - 07 were Rs 4,300 crores
Two persons are climbing up on two moving escalators which have 120 steps. The ratio of 1st person’s speed to that of 1st escalator is 2:3 (steps). The ratio of 2nd person’s speed to that of escalator is 3:5 (steps). Find the total number of steps they both have taken together.
If n=1+x, where x is the product of 4 consecutive positive integers, then which of the following is/are true?
1. n is odd;
2. n is prime
3. n is a perfect square