**5.
QUADRATIC EQUATIONS**

Hi
friends and my dear students! In this post, I have covered **Important questions for 10**^{th}** class
maths chapter-5 ****Quadratic-equations****, Chapter wise previous
year Questions. **After Reading Please do share it with your friends. **Learn maths for All classes here**

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**PRIORITY-I
**

**1 MARK QUESTIONS: **

1. Raju and
Rajendar together have 45 marbles. Both of them lost 5 marbles each and the
product of the number of marbles now they have is 124. Represent the situation
in the form of quadratic equation to find out how many marbles they have
previously?

2. The sum of the
reciprocals of Rehman’s ages (in years) 3 year ago and 5 years from now is 1/3
find his present age.

3. Verify the following equations are quadratic or
not? Explain?

^{2} =3.(x+1/x)+4;

ii.
(2x+1)(3x+2)=6 (x-1)(x-2);

iii. x^{2}+2
x+3=0

4. Determine the
nature of roots ofi) x^{2}+x+1=0,ii.
2x^{2}+x-1=0 iii. 4x^{2}-4x+1=0

5. The hypotenuse of a right triangle is 25cm. we know that the difference in the lengths of the other two sides is 5cm. Represent the situation in the form of quadratic equation to find out the lengths of two sides?

6. The product of two consecutive positive integers is 306. Represent the situation in the form of quadratic equation to find the integers?

7. Verify that 1 and 3/2 are roots of 2x^{2}-5x+3=0?

8. Find the roots of 2x^{2}-5x+3=0 by
factorization method?

9. Find the discriminant of 2x^{2}-4x+3=0√and hence find the nature of the
roots?

10. Find the value of k for 2x^{2}-kx+3=0,so
that it has two equal roots ?

Also Check

**Important questions for 10th class maths chapter-1 Real numbers**

**Important questions for 10th class maths chapter-4**** **LINEAR EQUATIONS

Important questions for 10th class maths chapter-3 polynomial

**2
MARKS QUESTIONS **

11. Find two
numbers whose sum is 27 and the product is 182?

12. The root of
the following equations has real and equal roots, find the value k.

i. x^{2}-2x(1+3k)+7(3+2k)=0

ii.(k+1)x^{2}-2(k-1)x+1=0

13. Solve 2/x2-5/x
+2=0 by factorization method.

14. Find the quadratic equation whose roots are 2+√3 and 2-√3

15. Check (x-2) is
a factor of x^{3}-4x^{2}-x+1=0

16. Explain the
benefits of evaluating the discriminant of a quadratic equation before
attempting to solve it. What does it value signifies?

17. Find two
consecutive positive integers, sum of whose square is 613?

18. Find the roots
of i) = 1/x +4,1/x-7 =11/30x≠-4,7ii) 1/x-1/x-2=3 ≠0,2

19. find the roots
of the equation i. 5x^{2}-6x-2=0 by the method of completing the square
ii.x^{2}+7x-6=0, iii. x^{2}-10x+9=0

20. the difference of squares of two numbers is 180
the square of the smaller number is 8 times the larger number find the two
numbers

21. Sum of the
area of two squares is 468m2 if the difference of their perimeters is 24m then
find the sides of the two squares.

22. Write any two
uses of quadratic equations?

23. Find roots of √2x^{2}+7x+5√2=0

24. Find two
consecutive odd positive integers, sum of whose square is 290?

25. Find the roots√2x^{2}-2√2x+1=0 if they
exist, using quadratic formula?

26. Find the roots
of x+1/x=3

27. Find the
discriminant of3x^{2}-2x+1/3=0 and find the nature of its roots find
them if they are real?

**4
MARKS QUESTIONS: **

1. Find the
dimensions of the rectangle whose perimeter is 28m, and whose area is 40m^{2}

2. The base of a
triangle is 4cm longer than its altitude. If the area of triangle is 48cm^{2},
then find its base and altitude?

3. It is possible
to design a rectangular park of perimeter 80m and area 400m^{2}? If so
find its length and breadth

4. If a polygon of
‘n’ sides has 1/2n(n-3) diagonals. How many sides will a polygon having 65
diagonals? Is there a polygon with 50 diagonals?.

5. Two water taps together can fill a tank in 9 3/8hours.
The tap of larger diameter takes 10 hours less than the smaller one to fill the
tank separately find the time in which watch tap can separately fill the tank.

6. If The diagonal of a rectangular field is 60meters more than the shorter side. If the longer side is 30 metre more than the shorter side, find the sides of the field.

7. A ball is
thrown vertically upward from the top of a building 96m tall with an initial
velocity 80m/sec the distance ‘s’ of the ball from the ground after t seconds
is S=96+80t-4.9t2 after how many seconds does the ball strike the ground.

8. A motor boat
whose speed is 18km/h in still water. It takes 1 hour more to go 24km upstream
than to return downstream to the same spot. Find the speed of the stream?

9. The altitude of
a right triangle is 7m less than its base. If the hypotenuse is 13cm. find the
other two sides?

10. A motor boat
heads upstream a distance of 24km on a river whose current is running at 3 km
per hour. The trip up and back takes 6 hours. Assuming that the motor boat maintained a constant speed, what was its speed?

11. Is it possible to design a rectangular mango
grove whose length is twice its breadth, and the area is 800m^{2}? If
so, find its length and breadth?

## Also Check

## IITJEE 7th class Introduction to Algebra Notes

**SSC (10th class) Trigonometry Exercise - 11.1 Solution**

**SSC(10th class) Trigonometry Exercise - 11.1 Solutions**

PRIORITY
– II:

**1
MARK QUESTIONS: **

1.
If the root of the equation x^{2}+7x+k=0 is
-1 then find the value of ‘k’ and other root?

2.
The product of two consecutive odd integers is 63
represent this in the form of a quadratic equation

3.
Give two examples for a quadratic equation which
has no real roots

4.
Find the roots of ? x^{√x =}√x^{x}

5.
Draw the rough sketch of the graph of quadratic
equation touching x-axis at one point?

6.
If b2-4ac≥0, then write the roots of quadratic
equation ax^{2}+bx+c=0?

7.
Find sum and product of the roots of the equation x^{2}-4x+3=0

8.
Why do we take ‘a’ common while making a quadratic
equation ax^{2}+bx+c=0 to complete a square

9.
Find ‘x’ if i. 3+3^{2x}=4^{x}3^{x}
ii. a^{x(x-1)=}1/a^{-6}

10.
Find the value of ‘k’ for which the equation x^{2}-4x+k=0
has distinct real roots.

**2
MARKS QUESTIONS: **

1. Find the roots
of the equation x+1/x+41/4,x≠0?

2. Divide 51 into
two parts such that their product is 378?

3. Find ‘K’ so
that (k-12)x^{2}+2(k-12)x+2=0 has equal roots.

4. Sum of two numbers is 15, if sum of their
reciprocal is 3/10 find the numbers

5. Solve the
equation a^{2}x^{2}+(a^{2}-b^{2})x-b^{2}=0

6. If x=2 and x=3
are roots of the equation 3x^{2}-2k+2m=0 find the value of k and m.

7. Krishna told
“every quadratic equation will have real roots” Raghav told 7x=9x^{2 }is
a quadratic equation who is correct? Justify your answer.

8. Find the value
of ‘k’ if x^{2}+x-k=2 and x^{2}- 10x+(2k-3)=0 have 3 has a
common root.

9. Find the
quadratic equation whose roots are 2+3i and 2-3i

10. Find the value
of k for the quadratic equation 9x^{2}-kx+4=0 so that this has two
equal roots.

11. If the roots
of the quadratic equation kx(x-2)+6=0 are equal then find the value of ‘k’

12. If one root of
the quadratic equation 2x2+kx-6=0 is 2, find the value of k also find the other
root

13. Solve the
quadratic equation x^{2}-2ax+a^{2}- b^{2}=0 by
factorization method.

14. Determine
whether the quadratic equation 3x^{2}+2√5 -5=0 have real roots and if so, find the roots

15. Find the roots
of 9x2+7x-2=0 by using quadratic formula.

16. What are the methods to solve a quadratic equation?

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