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Integrate \(\int_{-1} ^{2} (2x^2 + x) \mathrm {d} x\)
The nth term of a sequence is given by 2\(^{2n - 1}\). Find the sum of the first four terms.
Solve the inequality: -7 \(\leq\) 9 - 8x < 16 - x
Solve for x in \(\frac{4x - 6}{3} \leq \frac{3 + 2x}{2}\)
If \(f(x) = 3x^3 + 4x^2 + x - 8\), what is the value of f(-2)?
\(\frac{d}{dx} [\log (4x^3 - 2x)]\) is equal to
If \(y = 6x^3 + 2x^{-2} - x^{-3}\), find \(\frac{\mathrm d y}{\mathrm d x}\).
If \(\begin{vmatrix} 2 & -4 \\ x & 9 \end{vmatrix} = 58\), find the value of x.
If P(2, m) is the midpoint of the line joining Q(m, n) and R(n, -4), find the values of m and n.
If given two points A(3, 12) and B(5, 22) on a x-y plane. Find the equation of the straight line with intercept at 2.
The marks scored by 30 students in a Mathematics test are recorded in the table below:
| Scores (Mark) | 0 | 1 | 2 | 3 | 4 | 5 |
| No of students | 4 | 3 | 7 | 8 | 6 | 2 |
What is the total number of marks scored by the children?
In the figure above, |CD| is the base of the triangle CDE. Find the area of the figure to the nearest whole number.
If \(4\sin^2 x - 3 = 0\), find the value of x, when 0° \(\leq\) x \(\leq\) 90°
From the cyclic quadrilateral MNOP above, find the value of x.
The locus of a point which moves so that it is equidistant from two intersecting straight lines is the
| Score (x) | 0 | 1 | 2 | 3 | 4 | 5 | 6 |
| Freq (f) | 5 | 7 | 3 | 7 | 11 | 6 | 7 |
Find the variance
| Score (x) | 0 | 1 | 2 | 3 | 4 | 5 | 6 |
| Freq (f) | 5 | 7 | 3 | 7 | 11 | 6 | 7 |
Find the mean of the data.
Given matrix M = \(\begin{vmatrix} -2 & 0 & 4 \\ 0 & -1 & 6 \\ 5 & 6 & 3 \end{vmatrix}\), find \(M^{T} + 2M\)
In how many ways can the word MATHEMATICIAN be arranged?
If a fair coin is tossed 3 times, what is the probability of getting at least two heads?