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

KCET KCET 2019Relations and Functions

Solution:

## $a^{ ∗}e=a$ $a^{∗ }e=a \Rightarrow\, \frac{2 ae}{5}=a \Rightarrow e=\frac{5}{2}$ $a^{ ∗}a^{-1}=e\Rightarrow \frac{2a a^{-1}}{5}=\frac{5}{2} \Rightarrow a^{-1}=\frac{25}{4a}$ $2^{ ∗}x=3^{-1}\Rightarrow\frac{2\left(2x\right)}{5}=\frac{25}{4\left(3\right)}$ $\Rightarrow\, x=\frac{125}{48}$

You must select option to get answer and solution

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

KCET 2019 Binomial Theorem

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

KCET 2018 Three Dimensional Geometry

## 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

KCET 2019 Application of Integrals

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

KCET 2019 Three Dimensional Geometry

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

KCET 2005 Permutations and Combinations

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

KCET 2019 Matrices

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

KCET 2019 Application of Integrals

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

KCET 2019 Integrals

## 9. 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 $B =$

KCET 2019 Matrices

## 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

KCET 2019 Differential Equations