Two vertices of a triangle | Straight Lines | JEE Main 2024

Competishun Header

JEE Main 2024

09-04-2024 S2

Question

Two vertices of a triangle ABC are $\mathrm{A}(3,-1)$ and $\mathrm{B}(-2,3)$, and its orthocentre is $\mathrm{P}(1,1)$. If the coordinates of the point C are $(\alpha, \beta)$ and the centre of the circle circumscribing the triangle PAB is $(h, k)$, then the value of $(\alpha+\beta)+2(h+k)$ equals :

Select the correct option:

A

51

B

81

C

5

D

15

✓ Correct! Well done.

✗ Incorrect. Try again or view the solution.

Solution

Question Tags

JEE Main

Mathematics

Easy

Start Preparing for JEE with Competishun

Filters 0

Showing 18 questions

QJEE Main 20242024

Let $\alpha, \beta ; \alpha>\beta$, be the roots of the equation $x^2-\sqrt{2} x-\sqrt{3}=0$. Let $P_n=\alpha^n-\beta^n, n \in N$. Then $...

JEE MainMathematicsEasy

View Solution→

QJEE-Main 20242024

For the electro chemical cell

JEE MainChemistryEasy

View Solution→

QJEE-Main 20242024

Consider the given chemical reaction :

JEE MainChemistryEasy

View Solution→

QJEE-Main 20242024

consider-the-above-reaction-sequence-and-identify-the-major-product-p

JEE MainChemistryEasy

View Solution→

QJEE-Main 20242024

Given below are two statements :

JEE MainChemistryEasy

View Solution→

QJEE-Main 20242024

Which one of the following reactions is NOT possible?

JEE MainChemistryEasy

View Solution→

QJEE-Main 20242024

The quantity of silver deposited when one coulomb charge is passed through $\mathrm{AgNO}_3$ solution:

JEE MainChemistryEasy

View Solution→

QJEE Main 20242024

The sum of the coefficient of $x^{2 / 3}$ and $x^{-2 / 5}$ in the binomial expansion of $...

JEE MainMathematicsEasy

View Solution→

QJEE Main 20242024

The value of the integral $\int_{-1}^2 \log _e\left(x+\sqrt{x^2+1}\right) d x$ is :

JEE MainMathematicsEasy

View Solution→

QJEE-Main 20242024

Match List - I with List - II.

JEE MainChemistryEasy

View Solution→

QJEE Main 20242024

If an unbiased dice is rolled thrice, then the probability of getting a greater number in the $i^{\text {th }}$...

JEE MainMathematicsEasy

View Solution→

QJEE Main 20242024

Let a, ar, $a r^{2^2} \ldots \ldots .$. be an infinite G.P. If $\sum_{n=0}^{\infty} a^n=57$ and $\sum_{n=0}^{\infty} a^3 r^{3 n}=9747$,...

JEE MainMathematicsEasy

View Solution→

QJEE-Main 20242024

The metal atom present in the complex MABXL (where $\mathrm{A}, \mathrm{B}, \mathrm{X}$ and L are unidentate ligands and M is...

JEE MainChemistryEasy

View Solution→

QJEE Main 20242024

The integral $\int_{1 / 4}^{3 / 4} \cos \left(2 \cot ^{-1} \sqrt{\frac{1-\mathrm{x}}{1+\mathrm{x}}}\right) \mathrm{dx}$ is equal to:

JEE MainMathematicsEasy

View Solution→

QJEE-Main 20242024

Given below are two statements:

JEE MainChemistryEasy

View Solution→

QJEE Main 20242024

If $\log _e y=3 \sin ^{-1} x$, then $(1-x)^2 y^{\prime \prime}-x y^{\prime}$ at $x=\frac{1}{2}$ is equal to :

JEE MainMathematicsEasy

View Solution→

QJEE Main 20242024

Let $B=\left[\begin{array}{ll}1 & 3 \\ 1 & 5\end{array}\right]$ and $A$ be a $2 \times 2$ matrix such that $\mathrm{AB}^{-1}=\mathrm{A}^{-1}$. If...

JEE MainMathematicsEasy

View Solution→

QJEE-Main 20242024

Given below are two statements : one is labelled as Assertion (A) and the other is labelled as Reason (R).

JEE MainChemistryEasy

View Solution→