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Solution The AP can be expressed as a, (a + d), —, (a +10d).The sum of the first 3 terms is (3a + 3d) = 51 and that of the last 3 is (3a + 27d) = 99.Solving these equations, we get a = 15 and d = 2.The arithmetic mean of the 3 terms […]

Solution: Two angles of triangle= 4x and 5x (let)According to the question.2(4x+ 5x) = 180∘⇒ 18x= 180∘⇒ x = 180∘/18 = 10∘:. The smallest angle= 4x = 4*10 = 40∘Then the answer is 40∘.

Solution x²-45x+324=0Solving this quadratic equation-x²−36x−9x+324=0⇒x(x−36)−9(x−36)=0(x−9)(x−36)=0So, x = 9 and 36.

Solution: First number * second number  = LCM * HCF Let the second number be x. :. lOx = 30 * 5 ⇒x= 30*5/10 = 15 Then the option is (3) 15

Solution Consider the equation 3x + 2y = 12Now, square both sides:(3x + 2y)² = 12²=> 9x² + 12xy + 4y² = 144=>9x² + 4y² = 144 – 12xyFrom the questions, xy = 6So,9x² + 4y² = 144 – 72Thus, the value of 9x² + 4y² = 72

Solution: According to the question, Total marks = 71* 14= 994 Correct total marks = 994+(56-42) + (32-74) = 994+14-42 = 966 Required average = 966/14 = 69 Then the option is (3) 69

Solution Let the number be x.Then the other number = x + 9Sum of two numbers = 45According to the question, x + (x + 9) = 45⇒ 2x + 9 = 45⇒ 2x = 45 – 9 (transposing 9 to the R.H.S changes to -9)⇒ 2x = 36⇒ 2x/2 = 36/2 (divide by 2

Solution Assume the natural number = xIf the number increased by 12 = x + 12Then,Reciprocal of the number = 1/xAs per the question, we get,x + 12 = 160 times of reciprocal for xx + 12 = 160/ xx( x + 12 ) = 160×2 + 12x – 160 = 0x2 + 20x –

Solution: Distance = Speed * Time = (40*6 1/4) km = (40*25/4) km = 250km New speed= 50 kmph :. Required time = Distance/Speed = 250/50 = 5 hours Then the answer is 5 hours.

(1) yz (2) xz/y (3) xy/z (4) xyz Solution: Product of two numbers= HCF * LCM⇒ Number = zx and zy:. zx*zy = z*LCM⇒ LCM =xyz Then the option is (4) xyz