 ### If f is continuous and integral from $0$ to $9$ $f(x)dx=4$.

The aim of this question is to find the integral of a given expression. Furthermore, the upper and lower limits of the integral are also given, i.e., we have a definite integral in this question. This question is based on the concept of arithmetic. The integral tells us about the area under the curve. Furthermore, […]

### 8 and n as factors, which expression has both of these?

This question aims to find an expression that has both the given factors. Moreover, it is helpful to have a number divisible by the given numbers. This question is based on the concepts of arithmetic, and the factors of a number include all divisors of that specific number. The factors of the number 16, for […]

### A tank of water with depth of $20.0 cm$ and a mirror at its bottom has a small fish floating motionless $7.0 cm$ under the surface of the water. (a) What is the apparent depth of the fish when viewed at normal incidence? (b) What is the apparent depth of the image of the fish when viewed at normal incidence?

This question aims to find the apparent depth of a fish when it is floating motionless in the water and also the apparent depth of its image forming in the mirror at the bottom of the tank. The concepts needed to solve this question are related to refraction in water. Refraction occurs when a light […]

### Given a data set consisting of $33$ unique whole number observations, its five-number summary is: [$12,24,38,51,64$] How many observations are less than $38$?

The aim of this question is to find the number of observations in the set which are less than its median value of $38$. The concept behind this question is the Locator/ Percentile method. We are going to use the Locator/ Percentile method for finding the number of observations in the given five-number summary. The […]

### Find two vectors in opposite directions that are orthogonal to the vector u. $U=\dfrac{-1}{4}i +\dfrac{3}{2}j$

This question aims to find the $2$ vectors which are orthogonal to the given vector $U = dfrac{-1}{4}i+dfrac{3}{2}j$, and these two vectors should be in opposite directions. This question is based on the concept of orthogonal vectors. If two vectors $A$ and $B$ have a dot product equal to zero, then the said two vectors […]