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Quadratic Equations Mathematics - Quadratic Equations

ICSE - STD 10 - Mathematics (ICSE - English Medium). 43 questions in this chapter.

Question types

Quadratic Equations question types

43 questions across 4 question groups — pick any mix to generate a Mathematics paper with step-by-step answer keys.

43
Questions
4
Question groups
5
Question types
Sample Questions

Quadratic Equations questions

One sample from each question group in this chapter. Select any group above to see the full set with answer keys.

Q 6[4 marks sum]4 Marks
A fruitseller bought $x$ apples for ₹ $ 1200$.
(a) Write the cost price of each apple in terms of $x$.
(b) If 10 of the apples were rotten and he sold rest at ₹3 more than the cost price of each, write the selling price of $(x-10)$ apples.
(c) If he made a profit of ₹ $ 60$ in this transaction, form an equation in $x$ and solve it to evaluate $x$.
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Q 7[4 marks sum]4 Marks
The hotel bill for a number of people for overnight stay is ₹ $ 14,400$. If there were 4 more people, the bill each person had to pay would have reduced by ₹ $ 600$. Find the number of people staying overnight.
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Q 8[4 marks sum]4 Marks
An aeroplane travelled a distiance of 400 km at an average speed of $x km / h$. On the return journey the speed was increased by $40 km / h$. Write down an expression for the time taken for:
(a) the onward journey
(b) the return journey
If the return journey took 30 minutes less than the onward journey write an equation in $x$ and find the value of $x$.
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Q 9[4 marks sum]4 Marks
The sum of the ages of Vivek and his younger brother Amit is 47 years. The product of their ages in years is 550 . Find their ages.
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Q 10[4 marks sum]4 Marks
The difference of the squares of two natural numbers is 84 . The square of the larger number is 25 times the smaller number. Find the numbers.
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Q 11MCQ1 Mark
The quadratic equation $x^2+m(2 x+m-1)+2=0$ has equal roots. The value of $m$ is :
  • A
    $1$
  • B
    $2$
  • C
    $-2$
  • D
    $0$
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Q 12MCQ1 Mark
The quadratic equation $(m+1) x^2+2(m+3) x+(m+8)=0$ has equal roots. The value of $m$ is :
  • A
    $\frac{1}{3}$
  • B
    $\frac{1}{4}$
  • C
    $3$
  • D
    $-3$
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Q 13MCQ1 Mark
Given the quadratic equation $x^2+2 \sqrt{2} x+1=0$. The roots of the quadratic equation are :
  • A
    $\frac{-\sqrt{2} \pm 1}{2}$
  • B
    $\frac{\sqrt{2} \pm 1}{2}$
  • C
    $\sqrt{2} \pm 1$
  • D
    $-\sqrt{2} \pm 1$
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Q 14MCQ1 Mark
The roots of the quadratic equation $2 x^2-k x+k=0$ are equal. If $k \in N$, then $k$ is equal to :
  • A
    $0$
  • B
    $8$
  • C
    $6$
  • D
    $-6$
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Q 15MCQ1 Mark
For the quadratic equation $3 x^2+7 x+8=0$, the roots are :
  • A
    real and distinct
  • B
    real and equal
  • C
    imaginary
  • D
    both (a) and (b)
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