Yukti Vault

JEE Mathematics / Practice

Question Bank

Showing 16-20 of 408 questions.

Page 4 of 82

IIT-JEE 1979Question 16

The harmonic mean of two numbers is $4$. Their arithmetic mean $A$ and the geometric mean $G$ satisfy the relation $2A+G^{2}=27$. Find the two numbers.

Sequence and Series · Means and Inequalities (AM, GM, HM)

Write your solution on paper, then reveal the worked solution to compare.

IIT-JEE 1979Question 17

If $\alpha,\beta$ are the roots of $x^{2}+px+q=0$ and $\gamma,\delta$ are the roots of $x^{2}+rx+s=0$, evaluate $(\alpha-\gamma)(\alpha-\delta)(\beta-\gamma)(\beta-\delta)$ in terms of $p,q,r$ and $s$. Deduce the condition that the equations have a common root.

Quadratic Equation · Common Roots

Write your solution on paper, then reveal the worked solution to compare.

IIT-JEE 1983Question 18

Find all real values of $x$ which satisfy $x^{2}-3x+2>0$ and $x^{2}-2x-4\le0$.

Quadratic Equation · Sign, Range and Inequalities of Quadratic Expressions

Write your solution on paper, then reveal the worked solution to compare.

IIT-JEE 1978Question 19

One side of a rectangle lies along the line $4x+7y+5=0$. Two of its vertices are $(-3,1)$ and $(1,1)$. Find the equations of the other three sides.

Points and Straight Lines

Write your solution on paper, then reveal the worked solution to compare.

IIT-JEE 1978Question 20

A triangle $ABC$ has sides $AB=AC=5$ cm and $BC=6$ cm. Triangle $A'B'C'$ is the reflection of the triangle $ABC$ in a line parallel to $AB$ placed at a distance $2$ cm from $AB$, outside the triangle $ABC$. Triangle $A''B''C''$ is the reflection of the triangle $A'B'C'$ in a line parallel to $B'C'$ placed at a distance of $2$ cm from $B'C'$ outside the triangle $A'B'C'$. Find the distance between $A$ and $A''$.

Points and Straight Lines

Write your solution on paper, then reveal the worked solution to compare.