List of top Mathematics Questions asked in NATA

Triangle ABC has angles A = 60° and B = 70°. The in-center of this triangle is at I. Find angle BIC. (Provide answer in degrees)

A glass of cylindrical shape has radius of 3.5cm and height equal to 8cm. A water jug has a volume equal to 1540cm³. How many times the water has to be poured from glass to fill the jug completely? (Take π = \(\frac{22}{7}\)) 

Find the number of angles in the following figure. 40° 20° 30°

A regular octahedron has 12 edges, how many vertices does it have?

A box contains 5 red marbles, 8 white marbles and 4 green marbles. One marble is taken out of the box at random. What is the probability that the marble taken out will be not green?

The sum of the measures of the angles of regular polygon is 2160°. How many sides does the polygon have?

A metallic sphere of radius 4.2 cm is melted and recast into the shape of a cylinder of radius 6 cm. Find the height of the cylinder.

Seven cubes of same volume having side 5 cm are joined end to end. Find the Surface area of the resulting cuboid. (Answer to be provided in cm²).

Find the area of a square, one of whose diagonals is 9.2 m long. (Provide answer up to the second decimal in sq m)

A small village, having a population of 5,000 requires 75 litres of water per head per day. The village has got an overhead tank of measurement 40 m x 25m x 15 m. For how many days will the water in the tank last?

The difference between two positive numbers is 5 and the sum of their squares is 73. Find the product of these numbers.

NAT A cube is coloured red on all faces. It is cut into 64 smaller cubes of equal size. How many cubes have one red painted face?

A tank is 25 m long, 12 m wide and 6 m deep. What is the cost of plastering its walls and bottom if the cost per square meter is Rs 75 per sq. m? (Answer to be provided in Rupees)

Two ships are sailing in the sea on the two sides of a lighthouse. The angle of elevation of the top of the lighthouse is observed from the ships are 30° and 45° respectively. If the lighthouse is 100 m high, then what is the distance between the two ships?(Answer to be provided in meters)

The average of 15 numbers is 18. The average of first 8 is 19 and the last 8 is 17, then what is the \(8^{th}\) number?

If (2,0) is a solution of linear equation 2x+3y=k, then what is the value of k?

A lady grows cabbage in her garden that is in the shape of a square. Each cabbage takes 1 square foot of area in her garden. This year, she has increased her output by 211 cabbages when compared to last year. The shape of the area used for growing the cabbage has remained a square in both these years. How many cabbages did she produce this year?

What is the radius of the incircle of the triangle whose sides measure 5,12 and 13 units?
(Answer to be provided only in units)

How many diagonals does a 63-sided convex polygon have?

What is the measure of the radius of the circle that circumscribes a triangle whose sides measure 9, 40 and 41?

40 men took a dip in a water tank 50 m long and 20 m broad on a religious day. If the average displacement of water by a man is 5 m3, what will the rise in the water level in the tank be?
(Answer to be provided in cm)

A hollow iron pipe is 20 cm long and its external diameter is 10 cm. If the thickness of the pipe is 1 cm and iron weighs 8 g/cm3, then what is the weight of the pipe?
(Answer to be provided in kg to the third decimal).

The product of two numbers is 120 and the sum of their squares is 289. The sum of the number is:

A card board sheet is of rectangular shape with dimensions 50cm×30cm. From each of its corners, a square is cut off so as to make an open box. If the side of the square is 10 cm, then what is the volume of the box?
(Answer to be provided in cm³)

The figure below shows an unfolded pattern of a die. If four such identical dice are stacked one on top of another, as shown on the right, what is the sum of the numbers appearing on the faces which are parallel to the ground ?