# Q. If $^nC_{12}= ^nC_{6}$ then $^nC_{2}$=.........

KCET KCET 2005Permutations and Combinations

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## 1. The number of terms in the expansion of $(x^2 +y^2 )^{25} - (x^2 - y^2)^{25}$ after simplification is

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## 2. The locus represented by $xy + yz = 0$ is

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## 3. The area of the region above X-axis included between the parabola $y^2 = x$ and the circle $x^2 + y^2 = 2x$ in square units is

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## 4. Foot of the perpendicular drawn from the point (1, 3, 4) to the plane 2x - y + z + 3 = 0 is

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## 5. If $P$ and $Q$ are symmetric matrices of the same order then $PQ - QP$ is

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## 6. The area of the region bounded by Y-axis, y = cos x and y = sin x 0 $\le$ x $\le \frac{\pi}{2}$ is

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## 7. $\int x^{3} \sin 3x dx =$

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## 8. If $3A + 4B' =$$\begin{bmatrix}7&-10&17\\ 0&6&31\end{bmatrix}$ and $2B - 3A'$ $\begin{bmatrix}-1&18\\ 4&0\\ -5&-7\end{bmatrix}$ then $B =$

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## 9. On the set of positive rationals, a binary operation * is defined by a * b = $\frac{2ab}{5}$ . If 2 * x = $3^{-1}$ then x =

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## 10. The equation of the curve passing through the point (1, 1) such that the slope of the tangent at any point (x, y) is equal to the product of its co-ordinates is

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