NEW
New Website Launch
Experience the best way to solve previous year questions with mock tests (very detailed analysis), bookmark your favourite questions, practice etc...
1

### IIT-JEE 2000

Subjective
If $$\alpha ,\,\beta$$ are the roots of $$a{x^2} + bx + c = 0$$, $$\,\left( {a \ne 0} \right)$$ and $$\alpha + \delta ,\,\,\beta + \delta$$ are the roots of $$A{x^2} + Bx + c = 0,$$ $$\left( {A \ne 0\,} \right)\,$$ for some contant $$\delta$$, then prove that $${{{b^2} - 4ac} \over {{a^2}}} = {{{B^2} - 4Ac} \over {{A^2}}}$$.

Solve it.
2

### IIT-JEE 1997

Subjective
Let $$S$$ be a square of unit area. Consider any quadrilateral which has one vertex on each side of $$S$$. If $$a,\,b,\,c$$ and $$d$$ denote the lengths of the sides of the quadrilateral, prove that $$2 \le {a^2} + {b^2} + {c^2} + {d^2} \le 4.$$

Solve it.
3

### IIT-JEE 1995

Subjective
Let $$a,\,b,\,c$$ be real. If $$a{x^2} + bx + c = 0$$ has two real roots $$\alpha$$ and $$\beta ,$$ where $$\alpha < - 1$$ and $$\beta > 1,$$ then show that $$1 + {c \over a} + \left| {{b \over a}} \right| < 0.$$

Solve it.
4

### IIT-JEE 1988

Subjective
Solve $$\left| {{x^2} + 4x + 3} \right| + 2x + 5 = 0$$

$$- 4,\,\left( { - 1\, - \sqrt 3 } \right)$$

### Joint Entrance Examination

JEE Main JEE Advanced WB JEE

### Graduate Aptitude Test in Engineering

GATE CSE GATE ECE GATE EE GATE ME GATE CE GATE PI GATE IN

NEET

Class 12