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#### Algebra Important Questions

10th Standard EM

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Maths

Time : 01:00:00 Hrs
Total Marks : 50
5 x 1 = 5
1. A system of three linear equations in three variables is inconsistent if their planes

(a)

intersect only at a point

(b)

intersect in a line

(c)

coincides with each other

(d)

do not intersect

2. The solution of the system x + y − 3x = −6, −7y + 7z = 7 , 3z = 9 is

(a)

x = 1, y = 2, z = 3

(b)

x = −1, y = 2, z = 3

(c)

x = −1, y = −2, z = 3

(d)

x = 1, y = 2, z = 3

3. If (x - 6) is the HCF of x2 - 2x - 24 and x2 - kx - 6 then the value of k is

(a)

3

(b)

5

(c)

6

(d)

8

4. $\frac {3y - 3}{y} \div \frac {7y - 7}{3y^{2}}$ is

(a)

$\frac {9y}{7}$

(b)

$\frac {9y^{2}}{(21y - 21)}$

(c)

$\frac {21y^2 - 42y + 21}{3y^{2}}$

(d)

$\frac {7(y^{2} - 2y + 1)}{y^{2}}$

5. y2 + $\frac {1}{y^{2}}$ is not equal to

(a)

$\frac {y^{2} + 1}{y^{2}}$

(b)

${ \left( y+\frac { 1 }{ y } \right) }^{ 2 }$

(c)

${ \left( y-\frac { 1 }{ y } \right) }^{ 2 }+2$

(d)

${ \left( y+\frac { 1 }{ y } \right) }^{ 2 }-2$

6. 7 x 2 = 14
7. In an interschool atheletic meet, with 24 individual events, securing a total of 56 points, a first place secures 5 points, a second place secures 3 points, and a third place secures 1 point. Having as many third place finishers as first and second place finishers, find how many athletes finished in each place.

8. Solve x + 2y - z = 5; x - y + z = -2; -5x - 4y + z = -11

9. Solve 3x + y -3z = 1; -2x - y + 2z = 1; -x - y + z = 2.

10. Solve $\frac { x }{ 2 } -1=\frac { y }{ 6 } +1=\frac { z }{ 7 } +2$$\frac { y }{ 3 } +\frac { z }{ 2 } =13$

11. Solve: $\frac { 1 }{ 2x } +\frac { 1 }{ 4y } -\frac { 1 }{ 3z } =\frac { 1 }{ 4 }$;  $\frac { 1 }{ x } =\frac { 1 }{ 3y }$$\frac { 1 }{ x } -\frac { 1 }{ 5y } +\frac { 4 }{ z } =2\frac { 2 }{ 15 }$

12. Find the values of k for which the following equation has equal roots.
(k - 12)r + 2(k - 12)x + 2 = 0

13. Prove that the equation x2(a2+b2)+2x(ac+bd)+(c2+ d2) = 0 has no real root if ad≠bc.

14. 7 x 3 = 21
15. Find the square root of the following expressions
256(x - a)2 (x - b)4 (x - c)16 (x - d)20

16. Find the square root of the following expressions
16x2 + 9y2 - 24xy + 24x - 18y + 9

17. Find the square root of the following expressions
(16x2 + x - 1)(3x2 + 2x - 1)(2x2 + 3x + 1)

18. Find the square root of the following expressions
$\left[ \sqrt { 15 } { x }^{ 2 }+\left( \sqrt { 3 } +\sqrt { 10 } \right) x+\sqrt { 2 } \right] \left[ \sqrt { 5 } { x }^{ 2 }+\left( 2\sqrt { 5 } +1 \right) x+2 \right] \left[ \sqrt { 3 } { x }^{ 2 }+\left( \sqrt { 2 } +2\sqrt { 3 } \right) x+2\sqrt { 2 } \right]$

19. The sum of two numbers is 15. If the sum of their reciprocals is $\frac{3}{10}$, find the numbers.

20. A two digit number is such that the product of its digits is 12. When 36 is added to the number the digits interchange their places. Find the number.

21. Seven years ago, Varun's age was five times the square of swati's age. Three years hence Swati's age will be two fifth of Varun's age. Find their present ages.

22. 2 x 5 = 10
23. Find the GCD of the following by division algorithm 2x4 + 13x3 + 27x + 7, x3 + 3x2 + 3x + 1, x2 + 2x + 1

24. Find two consecutive natural numbers whose product is 20.