List of top Mathematics Questions asked in NATA

A hall is 15 m long and 12 m broad. If the sum of the areas of the floor and the ceiling is equal to the sum of the areas of four walls, the volume of the hall is:

Area and perimeter of a rectangular field are 2000 sq.m. and 180 m respectively. What is the length and breadth?

Find the value of log_y(x⁴) if log_x(y³) = 2

If \(tan ^{-1}(sinx)=\frac{\pi}{4}\),then the value of \(x\) is:

How many terms are in the Arithmetic Progression 20, 25, 30,..., 135, 140?

If \(cos2\theta+sin\theta= \sqrt{2}cos \theta,Then \ cos\theta-sin \theta=? \)

A and B together can do a piece of work in 30 days. A having worked for 16 days, B finishes the remaining work alone in 44 days. In how many days shall B finish the whole workalone?

A is two years older than B who is twice as old as C. If the total of the ages of A, B and C be 27, then how old is B?

If log₁₀10=1, log₁₀100=2, what is the value of log₅125?

f \(\int_0 ^a3x^2dx=8\) then find the value of a

If \(log_8 x+log_4 x+log_2 x=11,x=?\)

Sarthak bought 7 new trading cards to add to his collection. The next day his dog ate half of his collection. There are now only 31 cards left. How many cards did Sarthak start with ?

Given an A.P. whose terms are all positive integers. The sum of its first nine terms is greater than 200 and less than 220. If the second term in it is 12, then its 4th term is :

A salesman has a 70% chance to sell a product to any customer. The behavior of successive customers is independent. If two customers A and B enter, what is the probability that the salesman will sell the product to customer A or B?

If \( \log 2 + \log(x+3) - \log(3x-5) = \log 3 \). The value of \( x = ? \) 

If \( x = t \) and \( y = \frac{1}{t} \), then \(\frac{dy}{dx}\) is equal to:

\[\log(\sin 1^\circ) \times \log(\sin 2^\circ) \times \ldots \times \log(\sin 90^\circ) \text{ is}\]

Everybody in a room shakes hands with everybody else. The total number of handshakes is 66. Then the total number of persons in the room is:

A complete cycle of a traffic light takes 60 seconds. During each cycle the light is green for 25 sec, yellow for 5 sec and red for 30 sec. At a randomly chosen time, the probability that the light will not be green is

The probability that a leap year will have 53 Fridays or 53 Saturday is

A supporting element on a curved opening is called as

A regular hexagonal pyramid is sliced by a plane such that it passes through the centre of its axis. How many additional edges shall be created.