Test Details

Quadratic Equations

Mar 28, 8:30 PM

90 minutes

Mar 28, 10:00 PM

50.0 marks

MCQ

24 questions

Manish Anand

I am B.Tech and M.Tech in mechanical engineering from NIT Patna. From past 20 years I am teaching for 11th, 12th ,IIT-JEE, MCA ENTRANCE EXAM, NET, GATE etc. Expertise in PURE AND APPLIED HIGHER ENGINEERING MATHEMATICS, DISCRETE MATHS, NUMERICAL METHODS, OPERATION RESEARCH, TOC,CO etc. I have worked with FIITJEE DELHI, BRILLIANT TUTORIAL, PATNA SUPER 30 etc as Senior Faculty of Maths. Presently I am running my own institute named VASISTHA MATHEMATICS in Patna and also working with RPSIT, NIT PAT

Class Details

Mathematics

10th Pre Foundation 4 JEE

Mathematics

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Question Text

Question 1 :
Find the quadratic equation in $x$, whose solutions are $3$ and $2$.

Question 2 :
The discriminant of $x^2 - 3x + k = 0$ is 1 then the value of $k = .............$

Question 3 :
The length of a rectangular verandah is $3\:m$ more than its breadth. The numerical value of its area is equal to the numerical value of its perimeter. Taking $x$ as the breadth of the verandah, write an equation in $x$ that represents the above statement.

Question 4 :
State the following statement is True or False The sum of a natural number $x$ and its reciprocal is $\displaystyle \frac{37}{6}$, then the equation is $x\, +\, \displaystyle \frac{1}{x}\, =\, \displaystyle \frac{37}{6}$.

Question 8 :
The following equation is a qudratic equation. $16x^2 \, - \, 3 \, = \, (2x \, + \, 5)(5x \, - \, 3)$

Question 9 :
If the roots of the equation $ax^2+bx+c=0$ are all real equal then which one of the following is true?

Question 11 :
The roots of $a{ x }^{ 2 }+bx+c=0$, where $a\neq 0,b,c\epsilon R$ are non real complex and $a+c<b$. Then

Question 12 :
If $x=1+i$ is a root of the equation $x^3-ix+1-i=0$, then the other real root is

Question 13 :
If the equation $\displaystyle \lambda x^{2}-2x+3= 0$has positive roots for some real$\displaystyle \lambda $, then

Question 14 :
If the absolute value of the difference of roots of the equation $\displaystyle x^{2}+px+1=0$ exceeds $\sqrt{3p}$

Question 15 :
If the graph of $f\left(x\right)=x^{2}+\left(3-k\right)x+k,\left(where\ k\in\ R\right)$ lies above and below $x-axis$, then $k$ cannot be

Question 16 :
The value of $a$ for which one root of the quadratic equation $(a^2-5a+3) x^2+(3a-1)x+2=0 $ is twice as large as the other, is :

Question 17 :
The given equation has real roots. State true or false: $8x^2 + 2x -3 = 0$

Question 18 :
If $\displaystyle px^{2}+qx+r=0$ has no real roots and $p,q,r$ are real such that $p+r> 0$, then

Question 20 :
$\alpha ,\beta $ are roots of the equation $2{x^2} - 5x - 6 = 0$ then

Question 21 :
Divide 15 into 2 parts such that the product of 2 numbers is 56.

Question 22 :
Find the values of $K$ so that the quadratic equations $x^2+2(K-1)x+K+5=0$ has atleast one positive root.

Question 23 :
If one of the roots of $x^2-bx+c=0,\:(b,c)\:\epsilon\:Q$ is $\sqrt{7-4\sqrt 3}$ then:

Question 24 :
The equation $\displaystyle 9y^{2}(m+3)+6(m-3)y+(m+3)=0 $, where $m$ is real has real roots then 

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