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Yukti Vault

JEE Mathematics / Practice

Question Bank

Showing 56-60 of 408 questions.

IIT-JEE 1988Question 56
A sign-post in the form of an isosceles triangle $ABC$ is mounted on a pole of height $h$ fixed to the ground. The base $BC$ of the triangle is parallel to the ground. A man standing on the ground at a distance $d$ from the sign-post finds that the top vertex $A$ of the triangle subtends an angle $\beta$ and either of the other two vertices subtends the same angle $\alpha$ at his feet. Find the area of the triangle.
Trigonometric Ratio & Identities

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IIT-JEE 1985Question 57
In a triangle $ABC$, the median to the side $BC$ is of length $\dfrac{1}{\sqrt{11-6\sqrt3}}$ and it divides the angle $A$ into angles $30^\circ$ and $45^\circ$. Find the length of the side $BC$.
Trigonometric Ratio & Identities

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IIT-JEE 1985Question 58
Find the sum of the series $\displaystyle\sum_{r=0}^{n}(-1)^{r}\,{}^{n}C_r\bigg[\frac{1}{2^{r}}+\frac{3^{r}}{2^{2r}}+$ $\displaystyle\frac{7^{r}}{2^{3r}}+\frac{15^{r}}{2^{4r}}+\cdots\text{ up to }m\text{ terms}\bigg]$
Binomial Theorem · Properties and Sums of Binomial Coefficients

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IIT-JEE 1988Question 59
Solve $|x^{2}+4x+3|+2x+5=0$.
Quadratic Equation · Equations with Modulus and Greatest Integer

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IIT-JEE 1985Question 60
One of the diameters of the circle circumscribing the rectangle $ABCD$ is $4y=x+7$. If $A$ and $B$ are the points $(-3,4)$ and $(5,4)$ respectively, then find the area of the rectangle.
Points and Straight Lines

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