If \(\left[\begin{array}{ccc}x-2 & 3 & -2 \\ y & 0 & -4 \\ 2 & z & 0\end{array}\right]\) is a skew symmetric matrix, then the value of \(x+y+z\) is

The matrix \(A=\left[\begin{array}{lll}0 & 0 & 5 \\ 0 & 5 & 0 \\ 5 & 0 & 0\end{array}\right]\) is a :
(A) Diagonal matrix
(B) Scalar matrix
(C) Square matrix
(D) Symmetric matrix
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If \(A=\left[\begin{array}{ccc}a & 1 & -1 \\ 0 & b & 4 \\ 4 & 4 & c\end{array}\right]\) and \(a b c=12, b=4 a\), find the value of \(|A(\operatorname{adj} A)|\)

The area (in sq. units) of the region bounded by the curve \(y=\sqrt{16-x^2}\) and x-axis is

A shopkeeper has 300 Kg millet, a part of which he sells at \(10 \%\) profit. The remaining quantity of millet was of poor quality, and he sold it at a \(5\%\) loss. In the whole transaction, he made a profit of \(7 \%\). The quantity of the millet sold at \(5\%\) loss is :

For the system \(\left[\begin{array}{cc}2 & -3 \\ -4 & 6\end{array}\right]\left[\begin{array}{l}x \\ y\end{array}\right]=\left[\begin{array}{c}5 \\ -10\end{array}\right]\), which of the following statements are correct?
(A) The system has no solution.
(B) The system is consistent.
(C) It has infinitely many solutions.
(D) It has a unique solution.
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If the feasible region of a system of linear inequalities can be enclosed within a circle then it is called

A needle of length 4.5 cm is placed vertically 12 cm away from a convex mirror of focal length 15 cm. The magnification of the image produced is

Arrange the following electromagnetic waves in the order of their decreasing frequency.
(A) Radio wave
(B) Gamma rays
(C) Ultraviolet ray
(D) Infrared wave
(E) Visible light
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The plates of a parallel plate capacitor are separated by a distance d with air as medium between the plates. In order to increase its capacitance by 60%, a slab of dielectric constant 5 having the same area as that of plates is introduced between the plates. The thickness of the dielectric slab is :

The reduction of cyclohexanone with \(NaBH _4\) produces

The probability distribution function of a normal variate with mean \(\mu\) and variance \(\sigma^2\) is given by :
\(f(x)=\frac{1}{\sigma \sqrt{2 \pi}} e^{-\frac{1}{2}\left(\frac{x-\mu}{\sigma}\right)^2},-\infty< x< \infty,-\infty < \mu < \infty, \sigma>0\)
If \(y=f(x)\) be the normal probability curve, then which of the following is correct?
(A) The normal curve is symmetrical about the line \(x=\mu\).
(B) Mean, median and mode of the distribution coincide.
(C) \(Y\)-axis is an asymptote to the normal curve.
(D) If \(x\) increases numerically, \(f(x)\) decreases rapidly.
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\(\int \frac{(x-1) e^x}{x^2} d x\), \(x > 0\) equals (where C is an arbitrary constant)