Q JEE MAIN 2019

In a triangle, the sum of lengths of two sides is $x$ and the product of the lengths of the...

JEE Main Mathematics Medium

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Q JEE MAIN 2019

The angles $A, B$ and $C$ of a triangle $A B C$ are in A.P. and $a: b=1: \sqrt{3}$. If...

JEE Main Mathematics Easy

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Q JEE Main 2019

If $5,5 r, 5 r^2$ are the lengths of the sides of a triangle, then $r$ cannot be equal to...

JEE Main Mathematics Easy

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Q JEE MAIN 2019

Given $\frac{b+c}{11}=\frac{c+a}{12}=\frac{a+b}{13}$ for $\triangle A B C$ with usual natation. If $\frac{\cos A}{\alpha}=\frac{\cos B}{\beta}=\frac{\cos C}{12}$, then the ordered triplet $(\alpha$,...

JEE Main Mathematics Medium

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Q JEE MAIN 2019

With the usual notation, in $\triangle A B C$, if $\angle A+\angle B=120^{\circ}, a=\sqrt{3}+1$ and $b=\sqrt{3}-1$, then the ratio $...

JEE Main Mathematics Medium

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Q JEE MAIN 2019

If the lengths of the sides of a triangle are in A.P. and the greatest angle is double the smallest,...

JEE Main Mathematics Medium

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Q JEE MAIN 2021

If in a triangle $A B C, A B=5$ units, $\angle B=\cos ^{-1}\left(\frac{3}{5}\right)$ and radius of circumcircle of $...

JEE Main Mathematics Medium

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Q JEE MAIN 2021

A pole stands vertically inside a triangular park $A B C$. Let the angle of elevation of the top of...

JEE Main Mathematics Easy

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Q JEE MAIN 2021

Let the centroid of an equilateral triangle ABC be at the origin. Let one of the sides of the equilateral...

JEE Main Mathematics Easy

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Q JEE MAIN 2021

Let in a right angled triangle, the smallest angle be $\theta$. If a triangle formed by taking the reciprocal of...

JEE Main Mathematics Medium

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Q JEE MAIN 2022

The lengths of the sides of a triangle are $10+x^2, 10+x^2$ and $20-2 x^2$. If for $x=k$, the area of...

JEE Main Mathematics Hard

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Q JEE MAIN 2022

Let $R$ be the point $(3,7)$ and let $P$ and $Q$ be two points on the line $x+y=5$ such that...

JEE Main Mathematics Easy

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Q JEE MAIN 2022

Let $a, b$ and $c$ be the length of sides of a triangle $A B C$ such that $\frac{a+b}{7}=\frac{b+c}{8}=\frac{c+a}{9}$. If...

JEE Main Mathematics Easy

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Q JEE MAIN 2023

In a triangle $A B C$, if $\cos A+2 \cos B+\cos C=2$ and the lengths of the sides opposite to...

JEE Main Mathematics Medium

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Q JEE MAIM 2023

Let $C(\alpha, \beta)$ be the circumcenter of the triangle formed by the lines $$ \begin{aligned} & 4 x+3 y=69 \\...

JEE Main Mathematics Medium

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