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Algebra
1.If a * b = 2a - 3b + ab, then 3 * 5 + 5 * 3 is equal to?

Answer:Option 1

Explanation:

Solution:
35+5335=2×33×5+3×535=615+1535=653=2×53×3+3×553=109+1553=1635+536+1622

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2.If
p×q=p+q+pq,
   then the value of 8 × 2 is?

Answer:Option 1

Explanation:

Solution:
8×2=8+2+82=10+4=14

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3.The value of
(1 + 1x)(1 + 1x+1)
   
(1 + 1x+2)(1 + 1x+3)
    is?

Answer:Option 1

Explanation:

Solution:
(1 + 1x)(1 + 1x+1)(1 + 1x+2)(1 + 1x+3)Taking L.C.M of each term.(x+1x)(x+1+1x+1)(x+2+1x+2)(x+3+1x+3)1x×(x+4)x+4x

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4.If
2a+ba+4b=3,
  then find the value of
a+ba+2b=?

Answer:Option 1

Explanation:

Solution:
2a+ba+4b=3 (Given)2a+b=3(a+4b)2a+b=3a+12ba=11ba=11ba+ba+2b11b+b11b+2b10b9b109

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5.If a * b = a + b + ab, then 3 * 4 - 2 * 3 is equal to?

Answer:Option 1

Explanation:

Solution:
ab=a+b+ab34=3+4+3×4=1923=2+3+2×3=113423 =1911=8

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6.If a : b = 2 : 3 and b : c = 4 : 5, find a2 : b2 : bc = ?

Answer:Option 1

Explanation:

Solution:
a:b=2:3 and b:c=4:5a  b  c2×(4) 3×(4)4×(3) 5×(3)8  12  15  _¯a2:b2:bc(8)2:(12)2:(12×15)64:144:180

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7.If
A:B=12:38,
  
B:C=13:59
  and
C:D=56:34,
    then find the ratio of A : B : C : D = ?

Answer:Option 1

Explanation:

Solution:
A:B=12:38A:B=8:6A:B=4:3B:C=13:59B:C=9:15B:C=3:5C:D=56:34C:D=20:18C:D=10:9A: B ::D4 : 33 : 510 : 9 8 :6 :10 : 9 _¯

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8.If
1440.144=14.4x,
   then the value of x is?

Answer:Option 1

Explanation:

Solution:
1440.144=14.4x144×1000144=144x×101000=14410xx=1441000×10x=14410000x=0.0144

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9.If 1 < x < 2, then the value of
(x1)2 + (x3)2 is?

Answer:Option 1

Explanation:

Solution:
1<x<2(x1)2 + (x3)2(Square root cancel with square)x1+3x=2

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10.If a ⊕ b = (a × b) + b, then 5 ⊕ 7 equals to?

Answer:Option 1

Explanation:

Solution:
ab=(a×b)+b57=(5×7)+7=35+7=42

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