1
MHT CET 2024 3rd May Morning Shift
MCQ (Single Correct Answer)
+2
-0

The line L given by $\frac{x}{5}+\frac{y}{b}=1$ passes through the point $(13,32)$. The line K is parallel to L and has the equation $\frac{x}{c}+\frac{y}{3}=1$. Then the distance between $L$ and $K$ is

A
$\frac{23}{\sqrt{15}}$
B
$\sqrt{17}$
C
$\frac{17}{\sqrt{15}}$
D
$\frac{23}{\sqrt{17}}$
2
MHT CET 2024 2nd May Evening Shift
MCQ (Single Correct Answer)
+2
-0

The diagonals of a parallelogram $A B C D$ are along the lines $x+3 y=4$ and $6 x-2 y=7$. Then ABCD must be a

A
rectangle
B
square
C
rhombus
D
cyclic quadrilateral
3
MHT CET 2024 2nd May Evening Shift
MCQ (Single Correct Answer)
+2
-0

If the equation $7 x^2-14 x y+p y^2-12 x+q y-4=0$ represents a pair of parallel lines then the value of $\sqrt{p^2+q^2-p q}$ is

A
$\sqrt{119}$
B
$\sqrt{107}$
C
$\sqrt{109}$
D
$\sqrt{108}$
4
MHT CET 2024 2nd May Morning Shift
MCQ (Single Correct Answer)
+2
-0

The slopes of the lines given by $x^2+2 h x y+2 y^2=0$ are in the ratio $1: 2$, then $h$ is

A
$\frac{1}{2}$
B
$\frac{3}{2}$
C
$3$
D
$1$
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