Test Details

Quadratic Equations

Test is compulsory for all.

Jan 23, 1:00 PM

40 minutes

Jan 23, 1:40 PM

40.0 marks

MCQ

20 questions

Akash dubey

{I provide classes for the subjects class- 9, 10, 11, 12 = Maths class- 9, 10, 11, 12 = Science class- 11, 12 = Physics}

Class Details

Maths

Class-10th 2023

Maths

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Question Text

Question 1 :
A train travels at a certain average speed for a distance of 63 km and then travels a distance of 72 km at an average speed of 6 km/h more than its original speed. If it takes 3 hours to complete the total journey, original average speed of the train is?

Question 3 :
If $\frac{1}{2}$ is a root of the equation $x^2+kx-\frac{5}{4}=0$, then the value of k is?

Question 4 :
Values of $k$ for which the quadratic equation $2x^2–kx+k=0$ has equal roots is

Question 5 :
State True or False: If the coefficient of $x^2$ and the constant term of a quadratic equation have opposite signs, then the quadratic equation has real roots.

Question 6 :
Justify why the following quadratic equation has two distinct real roots: $\left(x-1\right)\left(x+2\right)+2=0$

Question 7 :
The altitude of a right triangle is 7 cm less than its base. If the hypotenuse is 13 cm, find the other two sides.

Question 9 :
Is the following situation possible? If so, determine their present ages.The sum of the ages of two friends is 20 years. Four years ago, the product of their ages in years was 48.

Question 11 :
State True or False: Every quadratic equation has at most two roots.

Question 12 :
State True or False: Every quadratic equation has exactly one root.

Question 13 :
Find the roots of the quadratic equations, if they exist, by the method of completing the square: $2x^2 + x – 4 = 0$

Question 14 :
Does the following equation has the sum of its roots as 3? $2x^2-3x+6=0$

Question 15 :
Find the roots of the following quadratic equation (by the factorisation method): $\frac{2}{5}x^2-x-\frac{3}{5}=0$

Question 16 :
Check whether the following is quadratic equation : $x^2 - 2x = (-2)(3-x)$

Question 17 :
At present Asha’s age (in years) is 2 more than the square of her daughter Nisha’s age. When Nisha grows to her mother’s present age, Asha’s age would be one year less than 10 times the present age of Nisha. Find the present age of Asha.

Question 19 :
A quadratic equation $ax^2 + bx + c =0$ has two distinct real roots when :

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