List of top Mathematics Questions asked in MHT CET

If the vectors \( \hat{i} + 2\hat{j} + \hat{k} \) and \( \hat{i} + 6\hat{j} + 4\hat{k} \) are collinear, then the values of \( x \) and \( y \) are respectively

The micro-organisms double themselves in 3 hours. Assuming that the quantity increases at a rate proportional to itself, then the number of times it multiplies itself in 18 years is

If \( f(x)=\dfrac{4x+7}{7x-4} \), then the value of \[ f\{f[f(2)]\} \] is

If \[ A = \begin{bmatrix} 2 & 3 \\ 1 & 2 \end{bmatrix}, \quad B = \begin{bmatrix} 1 & 0 \\ 3 & 1 \end{bmatrix}, \] then find \((AB)^{-1}\).

The equation of a plane containing the lines \( \vec{r} = (i + 2j - 4k) + \lambda (2i + 3j + 6k) \) and \( \vec{r} = (i + 3j + 4k) + \mu (i + j - k) \) is

For \( f(x) = [x] \), where \( [x] \) is the greatest integer function, which of the following is true, for every \( x \in \mathbb{R} \)?

If \( ax^2 + 2hxy + by^2 + 2gx + 2fy + c = 0 \) represents a joint equation of directrices of the hyperbola \( 16x^2 - 9y^2 = 144 \), then \( g + f - c = \)

The joint equation of two lines through the origin, each of which makes an angle of \(30^\circ\) with the line \(x + y = 0\), is

If \( \vec{a} = \hat{i} + 5\hat{k}, \, \vec{b} = 2\hat{i} + 3\hat{k}, \, \vec{c} = 4\hat{i} - \hat{j} + 2\hat{k}, \, \vec{d} = \hat{i} - \hat{j} \), then \( (\vec{c} - \vec{a}) \cdot (\vec{b} \times \vec{d}) = \)

The polar co-ordinates of the point whose cartesian co-ordinates are \( (-2, -2) \), are given by

Which of the following statement patterns is a tautology?
\[ \begin{aligned} S_1 &: (\sim q \land p) \land q
S_2 &: [p \land (p \rightarrow q)] \rightarrow q
S_3 &: (p \land q) \land (\sim p \lor \sim q)
S_4 &: (p \land q) \rightarrow r \end{aligned} \]

For every value of \( x \), the function \( f(x) = \frac{1}{a^x}, a>0 \) is

The eccentricity of the hyperbola \( 16x^2 - 3y^2 - 32x - 12y - 44 = 0 \) is

If \[ 2 + 4 + 6 + \cdots \text{ up to } n \text{ terms} = \frac{37}{36}, \] then \( n = \)

The rate of growth of bacteria is proportional to the bacteria present. If it is found that the number doubles in 3 hours, then the number of times the bacteria are increased in 6 hours is

Evaluate the integral \( \int_0^5 \frac{dx}{x^2 + 2x + 10} \)

The perimeter of the triangle whose vertices have the position vectors \( \hat{i} + \hat{j} + \hat{k} \), \( 5\hat{i} + 3\hat{j} - 3\hat{k} \), and \( 2\hat{i} + 5\hat{j} + 9\hat{k} \) is

If \(A(3,2,-1)\) and \(B(1,4,3)\), then the equation of the plane which bisects the segment \(AB\) perpendicularly is

The equation of the line passing through the point $(1,2,3)$ and perpendicular to the lines $\dfrac{x-1}{1} = \dfrac{y-2}{2} = \dfrac{z-3}{3}$ and $\vec r = \lambda(-3\hat i + 2\hat j + 5\hat k)$ is

The derivative of $\cot^{-1}x$ with respect to $\log(1+x^2)$ is

In \( \triangle ABC \), if \( \frac{\cos A}{a} = \frac{\cos B}{b} = \frac{\cos C}{c} \) with usual notations, then the triangle is:

$\cosec 2\theta-\cot 2\theta=$

Evaluate: \[ \frac{\cos 12^\circ - \sin 12^\circ}{\cos 12^\circ + \sin 12^\circ} + \frac{\sin 147^\circ}{\cos 147^\circ} \]

Two dice are thrown together. The probability that the sum of the numbers is divisible by 2 or 3 is

If the symbolic form of the switching circuit is \( \sim p \vee ( p \wedge \sim q) \vee q \), then the current flows through the circuit only if: