If the area of a triangle whose vertices are \((-2,4),(2,-6)\) and \((k, 4), k>0\), is 35 sq.units, then the value of \(k\) is

If a 99% confidence interval states that the population mean is greater than 100 and less than 400, then the sample mean and margin of error respectively are:

If \(A^2-A+I=0\), then \(A^{-1}\) is equal to :

A plane meets the coordinates axes at A, B and C such that centroid of \(\triangle A B C\) is at the point (2, 3, 1). If the equation of the plane is 3x + 2y + 6z = k, then k is:

Which of the following statements are correct?
(A) The method of least squares determines the position of the trend line of the given time series.
(B) The trend line is called the line of best fit.
(C) The line of best fit is a line in which the sum of deviations of the actual values of the variable from their corresponding trend value is always positive.
(D) The normal equations of the trend line \(y=a+b x\) are \(\sum y=n a+b \sum x\) and \(\sum x y=a \sum x+b \sum x^2\), where \(n\) is the numbers of observations.
Choose the correct answer from the options given below:

For any 2 × 2 matrix, if \(A(\operatorname{adj} A)=\left[\begin{array}{cc}100 & 0 \\ 0 & 100\end{array}\right]\), then |A| is equal to:

Let \(\vec{a}=2 \hat{i}-\hat{j}, \vec{b}=-4 \hat{j}+\hat{k}\) and \(\vec{c}=\hat{i}+2 \hat{k}\). If \(\vec{d}\) is a vector perpendicular to both \(\vec{a}\) and \(\vec{b}\) such that \(\vec{c} \cdot \vec{d}=34\), then \(|\vec{d}|\) is equal to

If \(A\) is a \(3 \times 3\) matrix such that \(|\operatorname{adj} A|=9\) and \(\left|k A^{-1}\right|=9\), then the value of \(k\) are :

Read the following paragraph and answer the given questions.
Cancer detection is based on biopsy and histopathological studies. Techniques like radiography (use of X-rays), CT (computed tomography) and MRI (magnetic resonance imaging) are very useful to detect cancers of the internal organs. Do you know why mother's milk is considered very essential for the new-born infant? The yellowish fluid colostrum secreted by mother during the initial days of lactation has abundant antibodies (IgA) to protect the infant. Different species of Plasmodium (P. vivax, P. malaria and P. falciparum) are responsible for different types of malaria. Of these, malignant malaria caused by Plasmodium falciparum is the most serious one and can even be fatal. The exaggerated response of the immune system to certain antigens present in the environment is called allergy. The use of drugs like anti-histamine, adrenalin and steroids quickly reduce the symptoms of allergy. Drugs like barbiturates, amphetamines, benzodiazepines, and other similar drugs, that are normally used as medicines to help patients cope with mental illnesses like depression and insomnia, are often abused. Morphine is a very effective sedative and painkiller, and is very useful in patients who have undergone surgery.
Malignant malaria is caused by -

If the matrix \(\left[\begin{array}{ccc}x-y & 1 & -2 \\ 2 x-y & 0 & 3 \\ 2 & -3 & 0\end{array}\right]\) is skew-symmetric, then the values of \(x\) and \(y\) are respectively:

If the matrix \(\left[\begin{array}{ccc}3 & 2 a & -5 \\ 4 & 0 & b \\ -5 & 3 & 10\end{array}\right]\) is symmetric, then the value of \(5 a+2 b\) is :

The integral \(I=\int e^x\left(\frac{x-1}{3 x^2}\right) d x\) is equal to:

A point charge is placed at any point on the axis of an electric dipole at some large distance, experiences a force F. The force acting on the point charge when it's distance from the dipole is halved will be