-
question_answer1)
Identify the expression equivalent to \[\left( \frac{1}{3y}+\frac{1}{4x} \right)\left( \frac{1}{3y}-\frac{1}{4x} \right).\]
A)
\[\frac{1}{3{{y}^{2}}}-\frac{1}{4{{x}^{2}}}\] done
clear
B)
\[\frac{1}{3{{y}^{2}}}+\frac{1}{4{{x}^{2}}}\] done
clear
C)
\[\frac{1}{4{{x}^{2}}}-\frac{1}{3{{y}^{2}}}\] done
clear
D)
\[\frac{1}{9{{y}^{2}}}-\frac{1}{16{{x}^{2}}}\] done
clear
View Solution play_arrow
-
question_answer2)
Which of the following is the expansion of \[{{\left( \frac{3}{7}x-\frac{1}{2}y \right)}^{2}}?\]
A)
\[\frac{3}{7}{{x}^{2}}-\frac{1}{2}{{y}^{2}}+\frac{3}{7}xy\] done
clear
B)
\[\frac{3}{7}{{x}^{2}}+\frac{3}{7}xy+\frac{1}{4}{{y}^{2}}\] done
clear
C)
\[\frac{9}{49}{{x}^{2}}-\frac{3}{7}xy+\frac{1}{4}{{y}^{2}}\] done
clear
D)
\[\frac{9}{49}{{x}^{2}}+\frac{3}{7}xy+\frac{1}{4}{{y}^{2}}\] done
clear
View Solution play_arrow
-
question_answer3)
Which of the following identities is applicable to find the value of \[{{(99)}^{2}}.\]
A)
\[{{a}^{2}}-{{b}^{2}}=(a+b)(a-b)\] done
clear
B)
\[{{(a-b)}^{2}}={{a}^{2}}-2ab+{{b}^{2}}\] done
clear
C)
\[{{(a+b)}^{3}}={{a}^{3}}+3{{a}^{2}}b+3a{{b}^{2}}+{{b}^{3}}\] done
clear
D)
\[{{(a-b)}^{3}}={{a}^{3}}-3{{a}^{2}}b+3a{{b}^{2}}-{{b}^{3}}\] done
clear
View Solution play_arrow
-
question_answer4)
If a + b = 7 and \[{{a}^{2}}+{{b}^{2}}=25,\]find the value of ab.
A)
26 done
clear
B)
24 done
clear
C)
13 done
clear
D)
12 done
clear
View Solution play_arrow
-
question_answer5)
If\[x=0.1,\]find the value of\[~100-10x.\]
A)
100 done
clear
B)
99 done
clear
C)
90 done
clear
D)
110 done
clear
View Solution play_arrow
-
question_answer6)
Find the value of \[100\frac{1}{2}\times 99\frac{1}{2}.\]
A)
\[9999\frac{1}{4}\] done
clear
B)
\[9999\frac{7}{4}\] done
clear
C)
\[9999\frac{3}{4}\] done
clear
D)
\[9999\frac{5}{4}\] done
clear
View Solution play_arrow
-
question_answer7)
Which of the following is the simplest form of \[\frac{{{(4x+2m)}^{2}}(-4{{m}^{2}}+16{{x}^{2}})}{(4{{m}^{2}}+16{{x}^{2}}+16mx)(-2m+4x)}\]
A)
\[~4m+2x\] done
clear
B)
\[~4x-2m\] done
clear
C)
\[~4m+16x\] done
clear
D)
\[4x+2m\] done
clear
View Solution play_arrow
-
question_answer8)
Identify the expression equivalent to the expansion of \[{{(2a+b-c)}^{2}}.\]
A)
\[2{{a}^{2}}+{{b}^{2}}+{{c}^{2}}-2ab-2bc-2ca\] done
clear
B)
\[4{{a}^{2}}+{{b}^{2}}+{{c}^{2}}-4ab+4bc+4ca\] done
clear
C)
\[4{{a}^{2}}-{{b}^{2}}+{{c}^{2}}-4ab-4bc-4ca\] done
clear
D)
\[4{{a}^{2}}+{{b}^{2}}+{{c}^{2}}+4ab-2bc-4ac\] done
clear
View Solution play_arrow
-
question_answer9)
Which of the following products is equal to\[25{{x}^{2}}-30xy+9{{y}^{2}}?\]
A)
\[\text{(}5x+3y\text{)(}5x+3y\text{)}\] done
clear
B)
\[\text{(}5x-3y\text{)(}5x-3y\text{)}\] done
clear
C)
\[\text{(}3x-5y\text{)(}3x-5y\text{)}\] done
clear
D)
\[\text{(}3x+5y\text{)(}3x+5y\text{)}\] done
clear
View Solution play_arrow
-
question_answer10)
Find the value of the expression\[\frac{{{(a-c)}^{2}}-{{(a+c)}^{2}}}{{{({{a}^{2}}+{{c}^{2}})}^{2}}-({{a}^{2}}-{{c}^{2}})},\]when \[a=\frac{1}{3}\]and \[c=\frac{1}{17}.\]
A)
-51 done
clear
B)
92 done
clear
C)
68 done
clear
D)
85 done
clear
View Solution play_arrow
-
question_answer11)
If \[a+b=8\]and \[ab=12,\]find the value of \[{{a}^{4}}+{{b}^{4}}.\]
A)
1680 done
clear
B)
1312 done
clear
C)
1424 done
clear
D)
2030 done
clear
View Solution play_arrow
-
question_answer12)
Find the value of the algebraic expression \[{{x}^{2}}y-3xy+5\]when \[x=4\]and \[y=1.\]
A)
6 done
clear
B)
7 done
clear
C)
8 done
clear
D)
9 done
clear
View Solution play_arrow
-
question_answer13)
Identify the product of \[({{x}^{3}}+15)\] and \[(2{{x}^{3}}-3).\]
A)
\[2{{x}^{6}}+{{x}^{3}}-54\] done
clear
B)
\[2{{x}^{6}}+27{{x}^{3}}-45\] done
clear
C)
\[~2{{x}^{9}}-\text{ }{{x}^{6}}-45\] done
clear
D)
\[~2{{x}^{9}}+{{x}^{6}}-45\] done
clear
View Solution play_arrow
-
question_answer14)
Find the value of \[1.8\times 1.8-2\text{ }\times \text{ }1.8\text{ }\times \text{ }1.2+\text{ }\]\[1.2\text{ }\times \text{ }1.2.\]
A)
0.60 done
clear
B)
0.26 done
clear
C)
0.16 done
clear
D)
0.36 done
clear
View Solution play_arrow
-
question_answer15)
What must be added to \[{{x}^{2}}+10x\]to make it a perfect square?
A)
49 done
clear
B)
25 done
clear
C)
100 done
clear
D)
36 done
clear
View Solution play_arrow
-
question_answer16)
Find the product of\[(12{{m}^{2}}n-3m{{n}^{2}}-1)\] and \[6{{m}^{2}}{{n}^{2}}.\]
A)
\[72{{m}^{4}}{{n}^{3}}-18{{m}^{3}}{{n}^{4}}-6{{m}^{2}}{{n}^{2}}\] done
clear
B)
\[24{{m}^{4}}{{n}^{3}}-15{{m}^{3}}{{n}^{4}}-5{{m}^{2}}{{n}^{2}}\] done
clear
C)
\[60{{m}^{4}}{{n}^{3}}-16{{m}^{3}}{{n}^{4}}-4{{m}^{2}}{{n}^{2}}\] done
clear
D)
\[48{{m}^{4}}{{n}^{3}}-12{{m}^{3}}{{n}^{4}}-8{{m}^{2}}{{n}^{2}}\] done
clear
View Solution play_arrow
-
question_answer17)
If \[{{\left( 2a-\frac{1}{a} \right)}^{2}}=4{{a}^{2}}-x+\frac{1}{a},\]find the value of \['x'\]
A)
2 done
clear
B)
1 done
clear
C)
4 done
clear
D)
-2 done
clear
View Solution play_arrow
-
question_answer18)
Find the value of \[{{\left( 19\frac{1}{2} \right)}^{2}}.\]
A)
\[340\frac{1}{4}\] done
clear
B)
\[360\frac{1}{4}\] done
clear
C)
\[370\frac{1}{4}\] done
clear
D)
\[380\frac{1}{4}\] done
clear
View Solution play_arrow
-
question_answer19)
If \[3y-\frac{1}{2y}=8,\] find the value of \[9{{y}^{2}}+\frac{1}{4{{y}^{2}}}.\]
A)
63 done
clear
B)
65 done
clear
C)
67 done
clear
D)
69 done
clear
View Solution play_arrow
-
question_answer20)
Which of the following expressions are perfect squares?
\[9{{x}^{2}}-6x+9\] \[{{x}^{2}}-7x+10\] |
\[49{{x}^{2}}+9{{y}^{2}}-42xy\] \[16{{x}^{2}}+24x+9\] |
A)
Only (i) and (ii) done
clear
B)
Only (ii) and (iii) done
clear
C)
Only (i) and (iv) done
clear
D)
Only (iii) and (iv) done
clear
View Solution play_arrow
-
question_answer21)
Find the value of\[\frac{0.75\times 0.75-0.25\times 0.25}{0.5}\]
A)
0.50 done
clear
B)
0.75 done
clear
C)
0.25 done
clear
D)
1.0 done
clear
View Solution play_arrow
-
question_answer22)
Find the value of \[25{{x}^{2}}+10xy-{{y}^{2}},\] when \[x=4\]and \[y=1.\]
A)
400 done
clear
B)
440 done
clear
C)
439 done
clear
D)
441 done
clear
View Solution play_arrow
-
question_answer23)
If \[\left( a-\frac{1}{a} \right)=4,\]find the value of \[{{a}^{2}}+\frac{1}{{{a}^{2}}}.\]
A)
16 done
clear
B)
18 done
clear
C)
14 done
clear
D)
20 done
clear
View Solution play_arrow
-
question_answer24)
Find the value of \[10.01\times 9.99.\]
A)
90.0099 done
clear
B)
90.0099 done
clear
C)
90.9900 done
clear
D)
99.9999 done
clear
View Solution play_arrow
-
question_answer25)
Find the product of \[\text{(}p+1\text{)(}p+2\text{)}\] and \[(p+3).\]
A)
\[{{p}^{3}}+4{{p}^{2}}+11p+8\] done
clear
B)
\[{{p}^{3}}+6{{p}^{2}}+11p+6\] done
clear
C)
\[{{p}^{3}}+6{{p}^{2}}+12p+14\] done
clear
D)
\[~{{p}^{3}}+6{{p}^{2}}+12p+12\] done
clear
View Solution play_arrow
-
question_answer26)
Find the value of \[52\text{ }\times \text{ }52\text{ }+\text{ }2\text{ }\times \text{ }52\text{ }\times \text{ }48\text{ }+\text{ }48\text{ }\times \text{ }48.\]
A)
12148 done
clear
B)
10000 done
clear
C)
11234 done
clear
D)
14136 done
clear
View Solution play_arrow
-
question_answer27)
Identify the middle term in the product of \[(2{{x}^{3}}-4)\] and \[(5{{x}^{3}}-3).\]
A)
\[-14{{x}^{3}}\] done
clear
B)
\[-26{{x}^{3}}\] done
clear
C)
\[10{{x}^{6}}\] done
clear
D)
12 done
clear
View Solution play_arrow
-
question_answer28)
Find the product of \[(a+\sqrt{2})(a-\sqrt{2})\] and \[({{a}^{2}}+2).\]
A)
\[{{a}^{4}}+4\] done
clear
B)
\[~{{a}^{4}}+8\] done
clear
C)
\[~{{a}^{4}}-4\] done
clear
D)
\[{{a}^{4}}-8\] done
clear
View Solution play_arrow
-
question_answer29)
Given \[v+\frac{1}{v}=7,\]find the value of \[{{v}^{4}}+\frac{1}{{{v}^{4}}}.\]
A)
2209 done
clear
B)
2207 done
clear
C)
2227 done
clear
D)
2272 done
clear
View Solution play_arrow
-
question_answer30)
The perimeter of a triangle is\[10{{p}^{2}}-6p+9\] and two of its sides are \[2{{p}^{2}}-3p+1\] and \[5{{p}^{2}}-4p+4.\] Find third side of the triangle.
A)
\[3{{p}^{2}}-p+4\] done
clear
B)
\[3{{p}^{2}}+p-4\] done
clear
C)
\[~3{{p}^{2}}+p+4\] done
clear
D)
\[~3{{p}^{2}}-p4\] done
clear
View Solution play_arrow
-
question_answer31)
If \[x-\frac{1}{x}=7,\]What is the value of \[{{x}^{2}}+\frac{1}{{{x}^{2}}}?\]
A)
47 done
clear
B)
49 done
clear
C)
51 done
clear
D)
77 done
clear
View Solution play_arrow
-
question_answer32)
Find the value of \[0.67\times 0.67-0.33\times 0.33.\]
A)
0.34 done
clear
B)
0.034 done
clear
C)
3.4 done
clear
D)
34 done
clear
View Solution play_arrow
-
question_answer33)
If \[t+\frac{1}{t}=2,\]find the value of \[t-\frac{1}{t}.\]
A)
0 done
clear
B)
4 done
clear
C)
-2 done
clear
D)
done
clear
View Solution play_arrow
-
question_answer34)
Find the product of \[(2x-3)\]and \[(x+2).\]
A)
\[2{{x}^{2}}-7x+6\] done
clear
B)
\[2{{x}^{2}}-x-6\] done
clear
C)
\[2{{x}^{2}}+x-6\] done
clear
D)
\[2{{x}^{2}}-7x-6\] done
clear
View Solution play_arrow
-
question_answer35)
What is the value of \[\frac{{{(225+175)}^{2}}+{{(125-175)}^{2}}}{225\times 225+175\times 175}?\]
A)
0 done
clear
B)
400 done
clear
C)
2 done
clear
D)
50 done
clear
View Solution play_arrow
-
question_answer36)
Identify the expansion of \[{{\left( \frac{1}{4}+\frac{3}{4}b \right)}^{2}}.\]
A)
\[\frac{1}{16}+\frac{3}{16}b+\frac{{{b}^{2}}}{16}\] done
clear
B)
\[\frac{1}{16}+\frac{3}{8}b+\frac{9}{16}{{b}^{2}}\] done
clear
C)
\[\frac{3}{16}b+\frac{1}{64}+\frac{9}{16}{{b}^{2}}\] done
clear
D)
\[\frac{1}{4}+\frac{3}{4}b+\frac{9}{16}\] done
clear
View Solution play_arrow
-
question_answer37)
If \[\frac{1}{a}=5\]and \[\frac{1}{b}=3,\]Find the value of \[\left( \frac{1}{a}+\frac{1}{b} \right)\]and \[\left( \frac{1}{a}-\frac{1}{b} \right).\]
A)
40 done
clear
B)
24 done
clear
C)
16 done
clear
D)
32 done
clear
View Solution play_arrow
-
question_answer38)
If \[(-2x+3y)\]is a side of a square, find its area.
A)
\[4{{x}^{2}}+2xy+{{y}^{2}}\] done
clear
B)
\[4{{x}^{2}}+4xy+9{{y}^{2}}\] done
clear
C)
\[4{{x}^{2}}-12xy+9{{y}^{2}}\] done
clear
D)
\[4{{x}^{2}}+12xy+9{{y}^{2}}\] done
clear
View Solution play_arrow