Gunjo Pachauri

Solution The AP can be expressed as a, (a + d),-, (a + 9d). The sum of the first 3 terms is (3a + 3d) = -36 and the sum of the last 3 terms is (3a + 24d) = 27. Solving these two equations, we get a = -15 and d = 3.

Solution Here,dividend = p(x)Divisor, g(x) = (x – 1 – x2)Quotient, q(x) = (x – 2)Remainder, r(x) = 3∵ Dividend = [Divisor × Quotient] + Remainder∴ P(x) = [g(x) × q(x)] + r(x)= [(x – 1 – x²) (x – 2)] + 3= [x² – x – x³ – 2x + 2 + 2x²] +

Solution To find the mean score, add up all the scores and divide by the number of matches.Total sum of scores = 38 + 45 + 50 + 60 + 65 + 70 + 75 + 80 + 85 + 90 = 658.Number of matches = 10.Mean score = Total sum of scores / Number

Area of a rectangle = length x breadth, hence breadth = area / length.breadth = x² + 12xy + 27y²( x + 9y )= x² + 9xy + 3xy + 27y²( x + 9y )= x ( x + 9y ) + 3y (x + 9y)( x + 9y )breadth = x + 3y

Solution Let no of cars = x and no of motorcycles = yAccording to our conditionx + y = 20X = 20 – y (i)4x + 2y = 56 (ii)Replacing (i) in (ii) we get4(20 – y) + 2y = 5680 – 4y + 2y = 56-2y = -24Thus y = 12Now replacing y =

Solution Given: 5x²−2 , x=3We need to find the value of 5x²−2 at x=3We will put 3 in place of x in the expression 5x²−2Therefore, the value of the expression will be5x²−2=5(3)²−2=5(3)−2=45−2=43

Solution Let the total number of matches played be x.The team won around 10 matches, and the team’s winning percentage was 40%.40/100 × x = 1040x = 10 × 10040x = 1000x = 1000/40= 100/4= 25Hence, the team played 25 matches.

Solution x²+ (x + 1)² = 145⇒2x ²+ 2x + 1 = 145⇒2x ² + 2x – 144 = 0⇒x ² + x – 72 = 0⇒x(x + 9) – 8(x + 9) = 0⇒x = -9,8

Solution p(x) = 2x³+x²–2x–1, g(x) = x+1g(x) = 0⇒ x+1 = 0⇒ x = −1∴Zero of g(x) is -1.Now,p(−1) = 2(−1)³+(−1)²–2(−1)–1= −2+1+2−1= 0∴By the given factor theorem, g(x) is a factor of p(x).

Solution 25x²-4y²+28yz-49z²=25x²-(4y²-28yz+49z²)=25x²- [ (2y)²-2×2y×7z+(7z)²]Using the identity (a−b)²=a²−2ab+b²(5x)²−(2y−7z)²Now using the identity a²−b²=(a+b)(a−b)(5x+2y−7z)(5x−2y+7y)