Mathematics Tes...

What is the seventh term of sequence 0, 3, 8, 15, 24, _____?

If \(\omega\) is the cube root of unity, then what is the value of:

\(\left|\begin{array}{ccc}1 & \omega & \omega^{2} \\ \omega & \omega^{2} & 1 \\ \omega^{2} & 1 & \omega\end{array}\right|\)

If the roots of the quadratic equation \(x^{2}-4 x-\log _{10} N=0\) are real, then what is the minimum value of \(\mathrm{N}\) ?

A card is drawn from a well shuffled deck of \(52\) cards. Find the probability of getting a king of red suit.

The equations x = a cos θ - b sin θ , and y = a sin θ + b cos θ, 0 ≤ θ ≤ 2π represent:

If \(\int \frac{(x-1)^{2}}{\left(x^{2}+1\right)^{2}} d x=\tan ^{-1} x+g(x)+\mathrm{k}\), then \(g(x):\)

If \(x^{m} y^{n}=a^{m+n},\) then what is \(\frac{d y}{d x}\) equal to?

What is the number of ways that a cricket team of 11 players can be made out of 15 players?

Direction: In the given question, two equations numbered l and II are given. Solve both the equations and mark the appropriate answer.

I. x² = 841

II. y² – 15y – 76 = 0

\(PA\) and \(PB\) are two tangents from a point \(P\) outside the circle with center \(O\) at the point \(A\) and \(B\) on it. If \(\angle APB =130^{\circ}\), then \(\angle OAB\) is equal to: