Skip to main content
Back to QUADRATIC EQUATIONS

Your Progress

0 / 914 Answered
0
Correct
0
Incorrect
0%
Accuracy
JEE • MATHEMATICS • QUADRATIC EQUATIONS

Quadratic equations practice · Mixed difficulty

Try a question, then open “View answer” to check it. Sign in to submit answers and save progress.

Practice format and chapter quiz

These sets use single-correct-answer MCQs. They do not cover every JEE Main or JEE Advanced question format and are not full-length mock papers.

Take a chapter quiz →
Showing 901-914 of 914 questions
901 Medium
901 of 914
Analyzing +4 | -1
If [  x]2=[x+2],  where  [x]={\left[ {\;x} \right]^2} = \left[ {x + 2} \right],\;\mathrm{where}\;\left[ x \right] = the greatest integer less than or equal to xx,then xx must be such that
View answer and explanation
Correct option: B
[−1,  0]∪[2,  3]\left[ { - 1,\;0} \right] \cup \left[ {2,\;3} \right]
Option B ([−1,  0]∪[2,  3]\left[ { - 1,\;0} \right] \cup \left[ {2,\;3} \right]) is correct because it represents the intervals of x that satisfy the given equation involving the greatest integer function.
902 Easy
902 of 914
Application +4 | -1
If the sum of the roots of the equation λx2+2x+3λ=0\lambda x^2+2 x+3 \lambda=0 be equal to their product, then λ=\lambda= ?
View answer and explanation
Correct option: D
None of these
Option D (None of these) is correct because solving the equation under the given condition yields a value for λ\lambda that is not present in the provided options.
903 Easy
903 of 914
Application +4 | -1
If α  and  β\alpha \;\mathrm{and}\;\beta be the roots of the equation 2x2+2(a+b)x+a2+b2=0,2{x^2} + 2\left( {a + b} \right)x + {a^2} + {b^2} = 0, then the equation whose roots are (α+β)2  and  (α−β)2{\left( {\alpha + \beta } \right)^2}\;\mathrm{and}\;{\left( {\alpha - \beta } \right)^2}, is
View answer and explanation
Correct option: B
x2−4abx−(a2−b2)2=0{x^2} - 4abx - {\left( {{a^2} - {b^2}} \right)^2} = 0
Option B (x2−4abx−(a2−b2)2=0{x^2} - 4abx - {\left( {{a^2} - {b^2}} \right)^2} = 0) is correct because it is the equation formed with roots (α+β)2(\alpha + \beta)^2 and (α−β)2(\alpha - \beta)^2 after using the relationships between roots and coefficients of the given quadratic equation.
904 Hard
904 of 914
Analyzing +4 | -1
If b>a,b > a, then the equation (x−a)(x−b)−1=0\left( {x - a} \right)\left( {x - b} \right) - 1 = 0 has
View answer and explanation
Correct option: C
Roots in (−∞,a)\left( { - \infty ,a} \right) and other in (b,∞)\left( {b,\infty } \right)
Option C (Roots in (−∞,a)\left( { - \infty ,a} \right) and other in (b,∞)\left( {b,\infty } \right)) is correct because the function changes sign between a and b, indicating a root exists in each of the specified intervals.
905 Medium
905 of 914
Application +4 | -1
If the roots of the equation (p2+q2)x2−2q(p+r)x+(q2+r2)=0\left( {{p^2} + {q^2}} \right){x^2} - 2q\left( {p + r} \right)x + \left( {{q^2} + {r^2}} \right) = 0 be real and equal, then p,  q,  rp,\;q,\;r will be in
View answer and explanation
Correct option: B
GP
The correct answer is B (GP) because the condition for real and equal roots leads to the relation q2=prq^2 = pr, which defines a geometric progression.
906 Medium
906 of 914
Analyzing +4 | -1
The minimum value of f(x)=e(x4−x3+x2)f\left( x \right) = {e^{({x^4} - {x^3} + {x^2})}} is
View answer and explanation
Correct option: C
1
Option C (1) is correct because the minimum value of the exponent occurs at x=0, making the minimum value of the function e0 = 1.
907 Easy
907 of 914
Application +4 | -1
The real value of a for which the sum of the squares of the roots of the equation x2−(a−2)x−a−1=0x^2-(a-2) x-a-1=0 assume the least value is
View answer and explanation
Correct option: A
1
Option A (1) is correct because the sum of the squares of the roots is minimized when a = 1.
908 Hard
908 of 914
Analyzing +4 | -1
The number of values of a for which the system of equation 2∣x∣+∣x∣=y+x2+a{2^{\left| x \right|}} + \left| x \right| = y + {x^2} + a and x2+y2=1{x^2} + {y^2} = 1 has only one solution where a,x,ya,x,y are real, is
View answer and explanation
Correct option: A
1
Option A (1) is correct because by analyzing the symmetry of the equations, we find that there is only one value of 'a' for which the system has a unique solution.
909 Easy
909 of 914
Analyzing +4 | -1
If the ratio of the roots of the equation ax2+bx+c=0a x^2+b x+c=0 be p:qp: q, then:
View answer and explanation
Correct option: B
pqb2−(p+q)2ac=0p q b^2-(p+q)^2 a c=0
Option B (pqb2−(p+q)2ac=0p q b^2-(p+q)^2 a c=0) is correct because it represents the relationship between the coefficients and the ratio of the roots of the quadratic equation.
910 Medium
910 of 914
Analyzing +4 | -1
If for x>0,f(x)=(2−xn)1/nx > 0, f(x)=\left(2-x^n\right)^{1 / n} and g(x)=x2+rx+sg(x)=x^2+r x+s; r,s∈Rr, s \in R. It is given that g(x)−x=0g(x)-x=0 has imaginary roots, then the number of real roots of the equation g(g(x))−f(f(x))=0g(g(x))-f(f(x))=0 is
View answer and explanation
Correct option: D
Zero
Option D (Zero) is correct because g(g(x)) - f(f(x)) is always greater than zero, implying no real roots exist for the equation g(g(x)) - f(f(x)) = 0.
911 Easy
911 of 914
Application +4 | -1
If x2+2ax+10−3a>0x^2+2 a x+10-3 a>0 for each x∈Rx \in R then
View answer and explanation
Correct option: B
−5<a<2-5<\mathrm{a}<2
Option D (−1≤x≤1-1 \leq x \leq 1) is correct because the given equation simplifies to 0 for all x within the domain of the inverse trigonometric functions.
912 Medium
912 of 914
Analyzing +4 | -1
The number of real roots of the equation x2−4x+3+x2−9=4x2−14x+6\sqrt{x^{2}-4 x+3}+\sqrt{x^{2}-9}=\sqrt{4 x^{2}-14 x+6}, is
View answer and explanation
Correct option: A
1
Option A (1) is the correct answer because after simplifying and solving the equation, only one real root satisfies the original equation's domain.
913 Medium
913 of 914
Analyzing +4 | -1
The number of real roots of the equation 5+∣2x−1∣=2x(2x−2)5 + \left| {{2^x} - 1} \right| = {2^x}({2^x} - 2) is
View answer and explanation
Correct option: A
1
Option A (1) is correct because solving the equation with absolute value requires considering two cases, and only one case yields a valid real root.
914 Medium
914 of 914
Analyzing +4 | -1
Product of real roots of the equation

t2x2+∣x∣+9=0t^{2} x^{2}+|x|+9=0
View answer and explanation
Correct option: A
is always positive
Option A (is always positive) is correct because the product of real roots is equal to 9 divided by t squared, which is always positive.
Revision notes and key takeaways

Review QUADRATIC EQUATIONS in your textbook or class notes, then use this set to check your understanding.

Showing 901-914 of 914 questions

Continue Your Practice

📚 More Sets in This Chapter

Try different difficulty levels to master this topic

→ ENGINEERING MATHEMATICS - QUADRATIC EQUATIONS MCQs (Easy) 528 MCQs → ENGINEERING MATHEMATICS - QUADRATIC EQUATIONS MCQs (Hard) 24 MCQs → ENGINEERING MATHEMATICS - QUADRATIC EQUATIONS MCQs (Medium) 362 MCQs
🎯 Next Chapters to Practice

Continue building your subject mastery

→ SEQUENCE OF SERIES 1764 MCQs → DEFINITE INTEGRATION 1443 MCQs → MATRICES 1363 MCQs → INDEFINITE INTEGRATION 1179 MCQs
📚 Switch Set (ALL)
Chapter Sets
ALL 914 MCQs EASY 528 MCQs HARD 24 MCQs MEDIUM 362 MCQs
0 /914
0✓ 0✗
0% Accuracy
Type at least 2 characters or jump directly:
🩺 NEET MCQs 🔬 JEE MCQs 🎯 JEE College Predictor Study guides 📊 Dashboard
🔓

Save your learning progress

Sign in with a free account to save your practice answers and quiz results, then return to them when you revise.

Continue with Free Account →