NMO 2024

Equation of a circle which passes through (3, 6) and

touches the axes is

• None of these

In a group of 6 boys and 4 girls, four children are to be selected. In how many different ways can they be selected such that at least one boy should be there?

• 159

• 194

• 205

• 209

The diagram shows a quadratic curve and a straight

line y = mx + c. They meet at the points P and Q on

the x-axis and y-axis respectively.
(a) Find the equation of the quadratic curve.
(b) Find the values of m and c respectively

Consider the following statements.

Statement 1 : A tangent parallel to x-axis can be drawn

for f(x) = (x – 1)(x – 2)(x – 3) in the interval [1, 3].

Statement 2 : A horizontal tangent can be drawn in

Rolle’s theorem.
Which of the following options is correct?

• Both Statement 1 and Statement 2 are true.

• Both Statement 1 and Statement 2 are false.

• Statement 1 is true but Statement 2 is false.

• Statement 1 is false but Statement 2 is true.

A can lay railway track between two given stations in 16 days and B can do the same job in 12 days. With the help of C, they did the job in 4 days only. Then C alone can do the job in

A toothed wheel of diameter 50 cm is attached to a smaller wheel of diameter 30 cm. How many revolutions will the smaller wheel make when the larger one makes 15 revolutions?

• 18

• 20

• 25

• 30

For a positively skewed distribution, mean is always

• Less than the median

• Less than the mode

• Greater than the mode

• Difficult to tell

There is a definite relationship between figures P and Q. Establish a similar relationship between figures R and S by selecting a figure from the options that would replace the (?) in figure R.

• 
• 
• 
• 

• 4

• 7

• 3

• 1