Mathematics Tes...

A relation R is defined on the set N of natural numbers as xRy ⇒ x² – 4xy + 3y² = 0. Then which one of the following is correct?

The probability that in a random arrangement of the letters of the word INSTITUTION the three T are together is:

If the line \(2{x}+\sqrt{6} {y}=2\) touches the hyperbola \({x}^{2}-2{y}^{2}=4\), then the point of contact is:

The centre of the circle passing through the point \((0,1)\) and touching the parabola \(y=x^2\) at the point \((2,4)\) is:

If \(\cot \left[\tan ^{-1} \mathrm{a}-\tan ^{-1}\left(\frac{{x}-{y}}{{x}+{y}}\right)\right]=1\), then:

Suppose X = {1, 2, 3, 4} and R is a relation on X. If R = {(1, 1), (2, 2), (3, 3), (1, 2), (2, 1), (2, 3), (3, 2), (1, 3), (3, 1)}, then which one of the following is correct?

If \(5\left(\tan ^2 x-\cos ^2 x\right)=2 \cos 2 x+9\), then the value of \(\cos 4 x\) is:

Prove that \(1+3+5+\ldots . .+(2 \mathrm{n}-1)=\mathrm{n}^{2}\).

If \(a\) denotes the number of permutations of \(x+2\) things taken all at a time, \(b\) the number of permutations of \(x\) things being taken 11 at a time and \(c\) the number of permutations of \(x-11\) things taken all at a time such that \(a=182 b c\), then the value of \(x\) is:

The function \(f(x)=\frac{4 x^{3}-3 x^{2}}{6} -2 \sin x+(2 x-1) \cos x\):