List of top Mathematics Questions on Matrices asked in MHT CET

The angle between the line $ x = \frac{y-1}{2} = \frac{z-3}{\lambda} $ and the plane $ x + 2y + 3z = 6 $ is $ \cos^{-1} \sqrt{\frac{5}{14}} $, then the value of $ \lambda $ is

Let $ \bar{a}, \bar{b}, \bar{c} $ be three vectors such that $ \bar{a} + \bar{b} + \bar{c} = \bar{0}, |\bar{a}| = 3, |\bar{b}| = 4, |\bar{c}| = 5 $, then $ \bar{a} \cdot \bar{b} + \bar{b} \cdot \bar{c} + \bar{c} \cdot \bar{a} = $}

If $ (\cos^{-1} x)^2 - (\sin^{-1} x)^2>0 $, then}

If $ \tan \text{A} = \frac{1}{\sqrt{x(x^2+x+1) $, $ \tan \text{B} = \frac{\sqrt{x}}{\sqrt{x^2+x+1}} $ and $ \tan \text{C} = \sqrt{x^{-1} + x^{-2} + x^{-3}} $ then}

$\lim_{x \to 3} \frac{(84-x)^{\frac{1}{4}} - 3}{x - 3}$ is

A box contains 9 tickets numbered 1 to 9 both inclusive. If 3 tickets are drawn from the box one at a time, then the probability that they are alternatively either $\{odd, even, odd\}$ or $\{even, odd, even\}$ is

If $A = \left[ \begin{array}{cc} 1 & \cot \frac{\theta}{2} \\ -\cot \frac{\theta}{2} & 1 \end{array} \right]$ then $A^{-1} =$

If $ \tan \text{A} = \frac{1}{\sqrt{x(x^2+x+1) $, $ \tan \text{B} = \frac{\sqrt{x}}{\sqrt{x^2+x+1}} $ and $ \tan \text{C} = \sqrt{x^{-1} + x^{-2} + x^{-3}} $ then}

If four digit numbers are formed by using the digits 1, 2, 3, 4, 5, 6, 7 without repetition, then out of these numbers, the numbers exactly divisible by 25 are

The angle between the lines $x - 3y - 4 = 0, 4y - z + 5 = 0$ and $x + 3y - 11 = 0, 2y - z + 6 = 0$ is

The number of integral values of $p$ for which the vectors $(p + 1)\hat{i} - 3\hat{j} + p\hat{k},\; p\hat{i} + (p + 1)\hat{j} - 3\hat{k}$ and $-3\hat{i} + p\hat{j} + (p + 1)\hat{k}$ are linearly dependent, is ______.

A spherical iron ball $ 10 \, \text{cm} $ in radius is coated with a layer of ice of uniform thickness that melts at a rate of $ 50 \, \text{cm}^3/\text{min} $. When the thickness of ice is $ 15 \, \text{cm} $, then the rate at which the thickness of ice decreases is:

Let the foot of the perpendicular from the point $ (1, 2, 4) $ on the line $ \frac{x+2}{4} = \frac{y-1}{2} = \frac{z+1}{3} $ be $ P $. Then the distance of $ P $ from the plane $ 3x + 4y + 12z + 23 = 0 $ is:

If $A=\left[\begin{array}{ccc}1 & -1 & 1 \\ 2 & -1 & 0 \\ 3 & 3 & -4\end{array}\right]$, $B=\left[\begin{array}{l}1 \\ 1 \\ 2\end{array}\right]$ and $X=\left[\begin{array}{l}x_1 \\ x_2 \\ x_3\end{array}\right]$ such that $AX = B$, then the value of $x_1 + x_2 + x_3 =$