List of top Mathematics Questions on Straight lines asked in MHT CET

The separate equations of the lines represented by the equation \( 3x^2 - 2\sqrt{3} xy - 3y^2 = 0 \) are
If the line \[ \vec{r} = (i - 2j + 3k) + \lambda(2i + j + 2k) \quad \text{is parallel to the plane} \quad \vec{r} \cdot (3i - 2j + mk) = 10, \] then the value of \( m \) is
If \( \mathbf{a} = 2\hat{i} - \hat{j} + \hat{k} \), \( \mathbf{b} = \hat{i} + 2\hat{j} - 3\hat{k} \), and \( \mathbf{c} = 2\hat{i} + 3\hat{j} + 5\hat{k} \) are coplanar, then \( \lambda \) is the root of the equation
The joint equation of a pair of lines passing through \((2,3)\) and parallel to the lines \[ x^2 - y^2 = 0 \] is
The approximate value of the function \( f(x) = x^3 + 5x^2 - 7x + 10 \) at \( x = 1 \) is
The measure of the acute angle between the lines given by the equation \( 3x^2 - 4\sqrt{3}xy + 3y^2 = 0 \) is
If \( f(x) = \log(\sec x + \tan x) \), then \[ f'\left( \frac{\pi}{4} \right) = \]
The acute angle included between the lines \[ x\sin\theta - y\cos\theta = 5 \] and \[ x\sin\alpha - y\cos\alpha + 11 = 0 \] is
The line cuts the \(X\)-axis and \(Y\)-axis at the points \(A\) and \(B\) respectively. The point \((5,6)\) divides the line segment \(AB\) internally in the ratio \(3:1\). Then the equation of the line is
The auxiliary equation of the lines passing through the origin and having slopes \[ \sqrt{3} + 1 \quad \text{and} \quad \sqrt{3} - 1 \quad \text{is} \]
The equations of the lines which make intercepts on the axes whose sum is 8 and product is 15 are
The area included between the parabolas \( y^2 = 5x \) and \( x^2 = 5y \) is
If \[ y = \tan^{-1}\left( \frac{\sqrt{1 + \cos \frac{x}{2}}}{\sqrt{1 - \cos \frac{x}{2}}} \right) \] then \( \frac{dy}{dx} \) is
The line $5x + y - 1 = 0$ coincides with one of the lines given by $5x^2 + xy - kx - 2y + 2 = 0 $ then the value of k is
The joint equation of lines passing through the origin and trisecting the first quadrant is ________
The perpendiculars are drawn to lines $L_1$ and $L_2$ from the origin making an angle $\frac{\pi}{4}$ and $\frac{3\pi}{4}$ respectively with the positive direction of X-axis. If both the lines are at unit distance from the origin, then their joint equation is
If $p$ is the length of perpendicular from the origin to the line whose intercepts on the axes are $a$ and $b$ respectively, then $\frac{1}{a^2} + \frac{1}{b^2}$ equals
Joint equation of pair of lines through $ (3, - 2) $ and parallel to $ x^2 - 4xy + 3y^2 = 0 $ is
If limx→∞(x2+x+1x+1−px−q)=−3, then p and q is:
If OA→=a→ and OB→=b→, then BA→ is:
A circle with center (4,−5) is tangent to the y -axis in the standard (x,y) coordinate plane. What is the radius of this circle?
The solution of differential equation dy=(4+y2)dx is:
What is the area of the region bounded by the curve f(x)=1−x24,x∈[−2,2] and the x-axis?
Find the angle between two vectors (a→=2i^+j^−3k^) and (b→=3i^−2j^−k^).
Find the maximum value of 15sin θ + 20cos θ.