Test Details

Quadratic Equations - NCERT

Revision test

Jan 28, 7:15 PM

60 minutes

Jan 28, 8:20 PM

60.0 marks

MCQ

30 questions

sudhir kumar

PGT

Class Details

S. St

Std. 10 Gyan Varika

S. St

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Question Text

Question 1 :
The product of Sunita’s age (in years) two years ago and her age four years from now is one more than twice her present age. What is her present age?

Question 2 :
Find the roots of the quadratic equations, if they exist, by applying quadratic formula: $2x^2 + x + 4 = 0$

Question 4 :
What are the roots of the quadratic equation $2x^2-\sqrt{5}x-2=0$ using the quadratic formula.

Question 5 :
Sum of the areas of two squares is $468 m^2$. If the difference of their perimeters is 24 m, find the sides of the two squares.

Question 6 :
Represent the following situation in the form of a quadratic equation : The product of two consecutive positive integers is 306. We need to find the integers.

Question 7 :
Find the values of k for each of the following quadratic equations, so that they have two equal roots: $kx (x – 2) + 6 = 0$

Question 8 :
State True or False whether the following quadratic equation has two distinct real roots: $\left(x-1\right)\left(x+2\right)+2=0$

Question 10 :
Check whether the following is a quadratic equation: $(2x – 1)(x – 3) = (x + 5)(x – 1)$

Question 11 :
State True or False: Every quadratic equation has at least one real root.

Question 12 :
Find two numbers whose sum is 27 and product is 182.

Question 13 :
Find the discriminant of the equation $3x^2 – 2x +\frac{1}{3} = 0$.

Question 15 :
Represent the following situation in the form of a quadratic equation : The area of a rectangular plof is 528 $m^2$. The length of the plof (in metres) is one more than twice its breadth. We need to find the length and breadth of the plof.

Question 17 :
State True or False: Every quadratic equation has exactly one root.

Question 18 :
Represent the following situation in the form of quadratic equations: Rohan’s mother is 26 years older than him. The product of their ages (in years) 3 years from now will be 360. We would like to find Rohan’s present age.

Question 19 :
At $t$ minutes past 2 pm, the time needed by the minutes hand of a clock to show 3 pm was found to be 3 minutes less than $\frac{t^2}{4}$ minutes. Find $t$.

Question 20 :
The sum of the reciprocals of Rehman’s ages, (in years) 3 years ago and 5 years from now is $\frac{1}{3}$. Find his present age.

Question 21 :
Justify why the following quadratic equation has no two distinct real roots: $x\left(1-x\right)-2=0$

Question 22 :
State True or False whether the following quadratic equation has two distinct real roots: $x\left(1-x\right)-2=0$

Question 23 :
What is the general expression (standard form) for quadratic equations ?

Question 24 :
The diagonal of a rectangular field is 60 metres more than the shorter side. If the longer side is 30 metres more than the shorter side, find the sides of the field.

Question 25 :
Check whether the following is a quadratic equation: $(x + 1)^2 = 2(x – 3)$

Question 26 :
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 Nisha.

Question 27 :
State True or False: If in a quadratic equation, the coefficient of x is zero, then the quadratic equation has no real roots.

Question 28 :
State True or False whether the following quadratic equation has two distinct real roots: $x^2-3x+4=0$

Question 29 :
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 30 :
A cottage industry produces a certain number of pottery articles in a day. It was observed on a particular day that the cost of production of each article (in rupees) was 3 more than twice the number of articles produced on that day. If the total cost of production on that day was Rs. 90, find the number of articles produced.

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