Previous Year Papers

Download Solved Question Papers Free for Offline Practice and view Solutions Online.

Test Series

Take Zigya Full and Sectional Test Series. Time it out for real assessment and get your results instantly.

Test Yourself

Practice and master your preparation for a specific topic or chapter. Check you scores at the end of the test.

Algebra

Multiple Choice Questions

31.

If $straight a greater than straight b greater than 0 comma space space AB space equals space straight a minus straight b space cm comma space space space BC space equals space 2 square root of ab space cm comma space space then space angle ABC$ is

$45 degree$
$60 degree$
$90 degree$
$90 degree$

130 Views

32.

If ab = 21 and $fraction numerator left parenthesis straight a plus straight b right parenthesis squared over denominator left parenthesis straight a minus straight b right parenthesis end fraction space equals space 25 over 4$ then value of $straight a squared plus straight b squared plus 3 ab$ is

155 Views

33.
Given, $straight a minus straight b space equals space 2$ and $straight a cubed minus straight b cubed space equals space 26$ then $left parenthesis straight a plus straight b right parenthesis squared$ is

9

4

16

16

As we all know that,
$straight a cubed minus straight b cubed space equals space left parenthesis straight a minus straight b right parenthesis thin space left parenthesis straight a squared plus ab plus straight b squared right parenthesis$
or we can write
$left parenthesis straight a cubed minus straight b cubed right parenthesis space equals space left parenthesis straight a minus straight b right parenthesis left parenthesis straight a squared plus ab plus straight b squared minus 2 ab plus 2 ab right parenthesis$
$rightwards double arrow$ 26 = 2 x $open parentheses left parenthesis straight a minus straight b right parenthesis squared plus 3 ab close parentheses$
$rightwards double arrow space left parenthesis straight a minus straight b right parenthesis squared plus 3 ab space equals space 13$
$rightwards double arrow space space space 3 ab space equals space left parenthesis 13 right parenthesis minus left parenthesis 2 right parenthesis squared rightwards double arrow space space space 3 ab space equals space 13 minus 4 rightwards double arrow space space ab space equals space 3$
$therefore space space space space space space left parenthesis straight a plus straight b right parenthesis squared space equals space left parenthesis straight a minus straight b right parenthesis squared plus 4 ab space space space space space space space space space space space space space space space space space space space space space space space equals space left parenthesis 2 right parenthesis squared plus 4 cross times 3 space equals space 4 plus 12 space equals space 16$

130 Views

34.

If x + y + z = 9 then value of $left parenthesis straight x minus 4 right parenthesis cubed plus left parenthesis straight y minus 2 right parenthesis cubed plus left parenthesis straight z minus 3 right parenthesis cubed minus 3 left parenthesis straight x minus straight y right parenthesis left parenthesis straight y minus straight z right parenthesis left parenthesis straight z minus 3 right parenthesis$ is

131 Views

35.

If $straight a over straight b plus straight b over straight a equals negative 1$ , then the value of $straight a squared over straight b squared minus straight b squared over straight a squared$ is

1
-1
0
0

112 Views

36.

Among below expressions which one can be expressed as the difference of two cubic expressions?

$straight x cubed plus straight y cubed plus 3 straight x plus 3 straight y$
$straight x cubed plus 2 straight x squared plus 3 straight x plus straight x squared$
$straight x cubed plus 3 straight x squared plus 3 straight x minus 2$
$straight x cubed plus 3 straight x squared plus 3 straight x minus 2$

105 Views

37.

If $straight a squared plus 1 over straight a squared space equals space 7$ and V₁ and V₂ are the minimum and the maximum values of $straight a cubed plus 1 over straight a cubed comma space$ then $straight V subscript 2 minus straight V subscript 1$ is equal to

107 Views

38.

If $straight x plus fraction numerator 1 over denominator 9 straight x end fraction space equals space 4 comma$ then $9 straight x squared plus fraction numerator 1 over denominator 9 straight x squared end fraction$ is

117 Views

39.

If a = 2, b = -3 then the value of $27 straight a cubed minus 54 straight a squared straight b space plus space 36 ab squared minus 8 straight b cubed$ is

1562
1616
1676
1676

95 Views

40.

If $straight a cubed plus 1 over straight a cubed space equals space 2 comma space$ then value of $fraction numerator straight a squared plus 1 over denominator straight a end fraction$ is (a is a positive number):