Important Questions on Algebra for MAH MBA CET

0
1076
Important Questions On Algebra For MAH MBA CET Exam
Important Questions On Algebra For MAH MBA CET Exam

Algebra Questions for MAH MBA CET Exam

Download MAH MBA CET Algebra Questions and Answers PDF covering the important questions. Most expected Algebra questions with explanations for MAH MBA CET / MMS CET 2021 exam.

Download Important Questions on Algebra for MHCET Exam

Enroll to MAH MBA CET Crash Course

Take a MAH MBA CET Free Mock Test

Get 10 MAH MBA CET mocks for just Rs. 499

Question 1: $\sqrt{8 + \sqrt{57 + \sqrt{38 + \sqrt{108 + \sqrt{169}}}}}$

a) 4

b) 6

c) 8

d) 10

Question 2: If a * b = 2a + 3b – ab, then the value of (3 * 5 + 5 * 3) is

a) 10

b) 6

c) 4

d) 2

Question 3: If a * b = $a^{b}$, then the value of 5 * 3 is

a) 125

b) 243

c) 53

d) 15

Question 4: If $x = 1 + \sqrt{2} + \sqrt{3}$ , then the value of $(2x^4 – 8x^3 – 5x^2 + 26x- 28)$ is __?

a) $6\sqrt{6}$

b) $0$

c) $3\sqrt{6}$

d) $2\sqrt{6}$

Question 5: If $a^2+b^2+c^2=2(a-2b-c-3)$ then the value of a+b+c is

a) 3

b) 0

c) 2

d) 4

Take a MAH MBA CET Free Mock Test

Get 10 MAH MBA CET mocks for just Rs. 499

Question 6: Find the simplest value of $2\sqrt{50} + \sqrt{18} – \sqrt{72}$ is __? $(\sqrt{2} = 1.414)$.

a) 9.898

b) 10.312

c) 8.484

d) 4.242

Question 7: If $a^{3}-b^{3}-c^{3}=0$ then the value of $a^{9}-b^{9}-c^{9}-3a^{3} b^{3} c^{3}$ is

a) 1

b) 2

c) 0

d) -1

Question 8: If $\frac{p^2}{q^2}+\frac{q^2}{p^2}$=1 then the value of $(p^{6}+q^{6})$ is

a) 0

b) 1

c) 2

d) 3

Question 9: If $(m+1) = \sqrt{n}+3$ the value of $\frac{1}{2}(\frac{m^{3}-6m^{2}+12m-8}{\sqrt{n}}-n)$

a) 0

b) 1

c) 2

d) 3

Question 10: If $x=\frac{a-b}{a+b},y=\frac{b-c}{b+c},z=\frac{c-a}{c+a}$ then $\frac{(1-x)(1-y)(1-z)}{(1+x)(1+y)(1+z)}$ is equal to

a) 1

b) 0

c) 2

d) $\frac{1}{2}$

Enroll to MAH MBA CET Crash Course

Join MAH MBA CET Telegram Group

Question 11: If $\frac{\sqrt{7}-1}{\sqrt{7}+1}-\frac{\sqrt{7}+1}{\sqrt{7}-1}=a+\sqrt{7} b$ the values of a and b are respectively

a) $\sqrt{7},-1$

b) $\sqrt{7}, 1$

c) $0, -\frac{2}{3}$

d) $-\frac{2}{3}, 0$

Question 12: If m = – 4, n = – 2, then the value of $m^3 – 3m^2 + 3m + 3n + 3n^2 + n^3$ is

a) – 126

b) 124

c) – 124

d) 126

Question 13: If $x+\frac{1}{x}=1$ then the value of $\frac{x^2+3x+1}{x^2+7x+1}$

a) $1$

b) $\frac{3}{7}$

c) $\frac{1}{2}$

d) 2

Question 14: If $x=\sqrt{a^3\sqrt{b}\sqrt{a^3}\sqrt{b}}$ then the value of x is

a) $\sqrt[5]{ab^3}$

b) $\sqrt[3]{a^3b}$

c) $\sqrt[3]{a^5b}$

d)  $a^2\sqrt b\sqrt[4]{a}$

Question 15: If the cube root of 79507 is 43, then the value of $\sqrt[3]{79.507}+\sqrt[3]{0.079507}+\sqrt[3]{0.000079507}$
is

a) 0.4773

b) 477.3

c) 47.73

d) 4.773

Free MAH MBA CET Preparation Videos

Take a MAH MBA CET Free Mock Tests

Question 16: If $\frac{x}{y}$=$\frac{3}{4}$ the ratio of $(2x+3y)$ and $(3y-2x)$ is

a) 2 : 1

b) 3 : 2

c) 1 : 1

d) 3 : 1

Question 17: If m – 5n = 2, then the vlaue of $(m^{3} – 125n^{3}$ – 30 mn) is

a) 6

b) 7

c) 8

d) 9

Question 18: If $x+\frac{1}{x}=2$ then the value of $x^{12}+\frac{1}{x^{12}}$ is

a) 2

b) -4

c) 0

d) 4

Question 19: If 5x + 9y = 5 and $125x^{3}$ + $729y^{3}$ = 120 then the value of the product of x and y is

a) $\frac{1}{9}$

b) $\frac{1}{135}$

c) $45$

d) $135$

Question 20: What is the value of $\frac{(941+149)^{2}+(941-149)^{2}}{(941\times941+149\times149)}?$

a) 10

b) 2

c) 1

d) 100

Enroll to MAH MBA CET Crash Course

Get 10 MAH MBA CET mocks for just Rs. 499

Answers & Solutions:

1) Answer (A)

Start from the root of 169 then second root will reduce to 11, thrid root will reduce to 7, fourth root will reduce to 8, and finally it reduce to value 4

2) Answer (A)

For 3*5 put a=3 and b=5 in given equation
and for 5*3 put a=5 and b=3 in equation
now add both values

3) Answer (A)

Put a=5 and b=3 in given equation
hence it will be $5^{3}$ = 125

4) Answer (A)

x = 1+ $\sqrt {2} + \sqrt {3} $
$(x-1)^{2}$ = $(\sqrt {2} + \sqrt {3}) ^ {2} $
$x^{2} +1 – 2x = 5 + 2 \sqrt {6}$
$x^{2} – 2x = 4 + 2 \sqrt {6}$ ( eq. (1) )
$(x^{2} – 2x)^{2} = x^{4} + 4x^{2} – 4x^{3} = 40 + 16\sqrt{6} $ eq (2)
Now in $2x^{4} – 8x^{3} – 5x^{2} + 26x – 28 $
or $2(x^{4} – 4x^{3}) – 5x^{2} + 26x – 28 $ ( putting values from eq (1) and eq (2) )
After solving we will get it reduced to $6\sqrt{6}$

5) Answer (B)

Given $a^2+b^2+ c^2=2(a-2b-c-3)$,

So, $(a-1)^2+(b+2)^2+(c-1)^2=0$

Hence, a=1, b=-2 and c=1

So, the sum of the equation is

6) Answer (A)

Given equation can be reduced in the form of $10\sqrt2 + 3\sqrt2 – 6\sqrt2 = 7\sqrt2$
Hence  $7\sqrt2$ will be around 9.898

7) Answer (C)

shortcut :

put c = 0 in  $a^{3}-b^{3}-c^{3}=0$ $\Rightarrow$ $a^{3}=b^{3}$

$a^{9}-b^{9}-(0)^{9}-3a^{3} b^{3} (0)^{3}$ = $a^{9}-b^{9}$ = $(a^{3})^{3}-(b^{3})^{3}$ =  $(a)^{3}-(a)^{3}$ = 0  ( $\because$ $a^{3}=b^{3}$ )

so the answer is option C.

normal method :

$a^{3}-b^{3}-c^{3}=0$

$a^{3}=b^{3}+c^{3}$

cubing on both sides,

$(a^{3})^{3}=(b^{3}+c^{3})^{3}$

$a^{9}=b^{9}+c^{9}+3b^{3} c^{3}(b^{3}+c^{3})$

$a^{9}=b^{9}+c^{9}+3b^{3} c^{3}(a^{3})$

$a^{9}-b^{9}-c^{9}-3a^{3}b^{3} c^{3}=0$

so the answer is option C.

8) Answer (A)

Expression : $\frac{p^2}{q^2}+\frac{q^2}{p^2}$ = 1

=> $\frac{p^{4}+q^{4}}{p^2q^2}$ = 1

=> $p^4+q^4 = p^2q^2$ ————–Eqn(1)

Now, to find : $(p^{6}+q^{6})$

=> $(p^2)^3 + (q^2)^3$

Using the formula, $a^3 + b^3 = (a+b)(a^2+b^2-ab)$

=> $(p^2+q^2)(p^4+q^4-p^2q^2)$

From eqn (1), we get :

=> $(p^2+q^2)(p^2q^2-p^2q^2)$

=> $(p^2+q^2)*0$

= 0

9) Answer (A)

If $(m+1) = \sqrt{n}+3$

=> $m-2 = \sqrt{n}$ ————–Eqn(1)

to find : $\frac{1}{2}(\frac{m^{3}-6m^{2}+12m-8}{\sqrt{n}}-n)$

$\because (m-2)^3 = m^{3}-6m^{2}+12m-8$

=> $\frac{1}{2}(\frac{(m-2)^3}{\sqrt{n}}-n)$

Using eqn(1), we get :

=> $\frac{1}{2}(\frac{(\sqrt{n})^3}{\sqrt{n}}-n)$

=> $\frac{1}{2}(n-n)$

= 0

10) Answer (A)

If $x=\frac{a-b}{a+b}$

=> $(1-x) = 1- (\frac{a-b}{a+b})$

=> $(1-x) = \frac{2b}{a+b}$

Similarly, $(1+x) = \frac{2a}{a+b}$

Applying the same method, we get :

=> $(1-y) = \frac{2c}{b+c}$ and => $(1+y) = \frac{2b}{b+c}$

=> $(1-z) = \frac{2a}{c+a}$ and => $(1+z) = \frac{2c}{c+a}$

Putting above values in the equation : $\frac{(1-x)(1-y)(1-z)}{(1+x)(1+y)(1+z)}$

=> $\frac{(\frac{2b}{a+b})(\frac{2c}{b+c})(\frac{2a}{c+a})}{(\frac{2a}{a+b})(\frac{2b}{b+c})(\frac{2c}{c+a})}$

=> $\frac{2a*2b*2c}{2a*2b*2c}$

= 1

Free MAH MBA CET Preparation Videos

Take a MAH MBA CET Free Mock Tests

11) Answer (C)

$\frac{\sqrt{7}-1}{\sqrt{7}+1}-\frac{\sqrt{7}+1}{\sqrt{7}-1}=a+\sqrt{7} b$

L.H.S. = $\frac{\sqrt{7}-1}{\sqrt{7}+1}-\frac{\sqrt{7}+1}{\sqrt{7}-1}$

= $\frac{(\sqrt{7}-1)^2 – (\sqrt{7}+1)^2}{(\sqrt{7}-1)(\sqrt{7}+1)}$

= $\frac{(7+1-2\sqrt{7})-(7+1+2\sqrt{7})}{7-1}$

= $\frac{-4\sqrt{7}}{6}$

= $\frac{-2\sqrt{7}}{3}$

Now, comparing with R.H.S. $a+\sqrt{7} b$

we get,

$a=0$ and $b=\frac{-2}{3}$

12) Answer (A)

We are given that m = -4 and n = -2

Expression : $m^3 – 3m^2 + 3m + 3n + 3n^2 + n^3$

= $(m^3 – 3m^2 + 3m – 1) + (n^3 + 3n^2 + 3n + 1)$

= $(m-1)^3 + (n+1)^3$

= $(-4-1)^3 + (-2+1)^3$

= $(-5)^3 + (-1)^3$

= $-125 – 1 = -126$

13) Answer (C)

Expression : $x+\frac{1}{x}=1$

=> $x^2 + 1 = x$ ——Eqn(1)

To find : $\frac{x^2+3x+1}{x^2+7x+1}$

= $\frac{(x^2+1) + 3x}{(x^2+1) + 7x}$

Using eqn(1),we get :

= $\frac{x + 3x}{x + 7x} = \frac{4}{8}$

= $\frac{1}{2}$

14) Answer (D)

$x=\sqrt{a^3\sqrt{b}\sqrt{a^3}\sqrt{b}}$.

here we know that $\sqrt{b} \times \sqrt{b}$ = b

and $\sqrt{a^3} = a\sqrt{a}$

hence,$x=\sqrt{a^3\sqrt{b}\sqrt{a^3}\sqrt{b}}$ = $a^2\sqrt b\sqrt[4]{a}$

15) Answer (D)

Since $\sqrt[3]{79507}$ = 43

=> $\sqrt[3]{79.507}$ = 4.3

=> $\sqrt[3]{0.079507}$ = 0.43

=> $\sqrt[3]{0.000079507}$ = 0.043

=> 4.3+0.43+0.043 = 4.773

16) Answer (D)

Let $x = 3k$ and $y = 4k$

=> $\frac{2x + 3y}{3y – 2x}$

= $\frac{6k + 12k}{12k – 6k}$

= $\frac{18}{6}$

= $\frac{3}{1}$ = 3 : 1

17) Answer (C)

Using the formula, $(x-y)^3 = x^3 – y^3 -3xy(x-y)$

=> $(m – 5n)^3 = m^3 – 125n^3 – 15mn(m-5n)$

=> $2^3 = m^3 – 125n^3 – 15mn*2$

=> $m^3 – 125n^3 – 30mn = 8$

18) Answer (A)

Expression : $x+\frac{1}{x}=2$

Squaring both sides

=> $x^2 + \frac{1}{x^2} + 2 = 4$

=> $x^2 + \frac{1}{x^2} = 2$

Cubing both sides

=> $x^6 + \frac{1}{x^6} + 3.x.\frac{1}{x}(x+\frac{1}{x}) = 8$

=> $x^6 + \frac{1}{x^6} = 8-6 = 2$

Again, squaring both sides, we get :

=> $x^{12} + \frac{1}{x^{12}} + 2 = 4$

=> $x^{12} + \frac{1}{x^{12}} = 2$

19) Answer (B)

Expression : $5x + 9y = 5$

Cubing both sides, we get :

=> $(5x + 9y)^3 = 125$

=> $125x^3 + 729y^3 + 135xy(5x+9y) = 125$

=> $125x^3 + 729y^3 + 135xy*5 = 125$

Since, $125x^{3}$ + $729y^{3} = 120$

=> $xy = \frac{5}{5*135} = \frac{1}{135}$

20) Answer (B)

Expression : $\frac{(941+149)^{2}+(941-149)^{2}}{(941\times941+149\times149)}$

= $\frac{(941^2 + 149^2 + 2.941.149) + (941^2 + 149^2 – 2.941.149)}{941^2 + 149^2}$

= $\frac{2 * (941^2 + 149^2)}{941^2 + 149^2}$

= 2

Enroll to MAH MBA CET Crash Course

Download MAH CET Free Mock Test App

LEAVE A REPLY

Please enter your comment!
Please enter your name here