Mathematics Tes...

In a town of 10000 families it was found that 40% family buy newspaper A, 20% buy newspaper B and 10% families buy newspaper C, 5% families buy A and B, 3% buy B and C and 4% buy A and C. If 2% families buy all the three newspaper, then the number of families which buy A only is:

If A, B and C are subsets of a given set, then which one of the following relations is not correct?

If \(2 \int_{0}^{1} \tan ^{-1} x\ d x=\int_{0}^{1} \cot ^{-1}\left(1-x+x^{2}\right) d x\), then \(\int_{0}^{1} \tan ^{-1}\left(1-x+x^{2}\right) d x\) is equal to:

If both p and q belong to the set {1, 2, 3, 4}, then how many equations of the form px² + qx + 1 = 0 will have real roots?

At what points on the curve \(x^{2}+y^{2}-2 x-4 y+1=0\), is the tangent parallel to the Y-axis?

If \(\vec{a}=2 \hat{i}+2 \hat{j}+3 \hat{k}, \vec{b}=-\hat{i}+2 \hat{j}+\hat{k}\) and \(\vec{c}=3 \hat{i}+\hat{j}\) are three vectors such that \(\vec{a}+t \vec{b}\) is perpendicular to \(\vec{c},\) then value of t is:

A box contains 3 white and 2 black balls. Two balls are drawn at random one after the other. If the balls are not replaced, what is the probability that both the balls are black?

The value of \(\sin ^{2} 45^{\circ}-\cos ^{2} 15^{\circ}\) is?

\(\left(\begin{array}{ll}2 & 3 \\ 4 & 1\end{array}\right) \times\left(\begin{array}{cc}5 & -2 \\ -3 & 1\end{array}\right)=\left(\begin{array}{cc}1 & -1 \\ 17 & \lambda\end{array}\right)\)then what is λ equal to?

How many combinations are possible while selecting four letters from the word ‘\(SMOKEJACK\)’ with the condition that ‘\(J\)’ must appear in it?