Gunjo Pachauri

Solution Let the number be x.Hence, the two consecutive numbers are x and x+1.According to the given statement, the equation becomes⇒ x + x + 1 = 11⇒ 2x + 1 = 11⇒ 2x = 10⇒ x = 10/2 = 5If x = 5, then x + 1 = 5 + 1 = 6Hence, the […]

Solution (x² + 2y) × (x³ – 2xy + y³)= x²(x³ – 2xy + y³) + 2y(x³ – 2xy + y³)= x⁵ – 2x³y + x²y³ + 2x³y – 4xy² + 2y⁴= x⁵ + x²y³ – 4xy²+ 2y⁴Put x = 1 and y = -1= (1)⁵ + (1)² (-1)³ – 4(1)(-1)2 + 2(-1)4= 1 +

Solution L = 20cm , B = 15cm , H = 10cmSurface area of cuboid = 2(lb + bh + hl)= 2(20×15+15×10+10×20)cm²= 2(300 + 150 + 200)cm²= 2(650)cm² = 1300cm²

Solution Given,x(x + 1) + 8 = (x + 2) (x – 2)x²+x+8 = x²-2² [By algebraic identities]Cancel x² both the sides.x+8=-4x+12=0Since, this expression is not in the form of ax²+bx+c, hence it is not a quadratic equation.

Solution For any polyhedron,F + V – E = 2Given here, F = 7, V = 10, E = ?Substituting the values, we get;7 + 10 – E = 217 – E = 2E = 17 – 2E = 15

Solution Given: scale of map = 1 : 80000000Thus, 1 unit on map shows 80000000 units in the real world.If A and B are 3 cm apart on map,Actual distance = 3cm × 80000000= 240000000= 2400 kmIf C and D are at a distance of 32km apart, then3200km = 3200 × 1000 × 100cm= 320000000

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= 2Hence, the team played 25 matches.

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

Solution Surface Area = 2 × (Length × Width + Width × Height + Height × Length)Surface Area = 2 × (10 units × 6 units + 6 units × 8 units + 8 units × 10 units)Surface Area = 2 × (60 + 48 + 80) square unitsSurface Area = 376 square units.

Solution (98)² can be further written as (100 – 2)²By comparing the above equation with the identity, we geta = 100 and b = 2(98)²=(100)²−2(100)(2)+(2)²=10000−400+4=9604