Mathematics Tes...

The range of the real-valued function \(f(x)=\sqrt{9-x^{2}}\) is:

For \(0

(।) If \(\alpha \in(-1,0)\), then \(b\) cannot be the geometric mean of a and \(\mathrm{c}\)

(II) If \(\alpha \in(0,1)\), then \(b\) may be the geometric mean of \(\mathrm{a}\) and \(\mathrm{c}\)

Find the \(9^{\text {th }}\) term in the expansion of \(\left(\frac{a}{b}-\frac{b}{2 a^{2}}\right)^{12}\).

If the latus rectum of an ellipse is equal to half of its minor axis, then its eccentricity is:

If \(P\) and \(Q\) are two sets, then \((P-Q) \cup(Q-P) \cup(P \cap Q)\) will be:

If (h, k) are the perpendicular distances from (1, 2, 3) to the x-axis, z-axis respectively, then hk is:

A number is called a palindrome if it reads the same backward as well as forward For example 285582 is a six digit palindrome. The number of six digit palindromes, which are divisible by 55 , is

Find the value of \(k\) for which the distance of point \((k+2,2 k+3)\) is \(\frac{4}{ \sqrt{10}}\) from the line \(x+\) \(3 y=7 ?\)

The sum of all three-digit numbers less than or equal to 500, that are formed without using the digit 1 and they all are multiple of 11 , is

Let \(\alpha=\frac{-1+i \sqrt{3}}{2}\). If \(a=(1+\alpha) \sum_{k=0}^{100} \alpha^{2 k}\) and \(b=\sum_{k=0}^{100} \alpha^{3 k}\), then \(a\) and \(b\) are the roots of the quadratic equation: