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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).

(1)16 (2)18 (3) 19 (4) 12 Solution: ⇒When we divide 1000 by 225.quotient = 4⇒When we divide 5000 by 225.quotient = 22:. Required answer = 22 – 4 = 18 ⇒Then the option is (2) 18

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)

(1) 24 km/hr. (2) 36 km/hr. (3) 40 km/hr. (4)45 km/hr. Solution: ⇒Suppose length of train be x  According to question x+50/14= x/10 ⇒ 14x = 10x+500 ⇒ 4x= 500 ⇒ x= 500/4=125m Therefore, speed = 125/10*18/5= 45kmph

Solution Here Given, Length=32cmBreadth=21cmRequired length of wooden strip = Perimeter of photograph=2(length +breadth)=2(32+21)=2×53cm=106cmRequired Length of wooden strip = 106cm

made the mistake of dividing the fraction by 6/7 and so got an answer which exceeded the correct answer by 13/70. Find the fraction- (1) 2/3 (2) 3/5 (3) 4/5 (4) 7/9 Solution: Let the fraction = x According to the question : 6/7 of x = x/6/7 – 13/70 ⇒ 6x/7 = 7x/6-13/70 ⇒7x/6-6x/7

Solution L = 2B – 1, Diagonal = 17. D² = L²+ B²⇒ 289 = (2B –1)²+ B²⇒ B = 8 & L = 15.Also 8, 15, 17 is a Pythagorean triplet.So answer can be reached directly.

(1) 7 (2)19 (3) 82 (4) 84 Solution : If each number is multiplied by a certain number, then the  average is also multiplied by that number. = Requires average = 7*12=84 Then option is (4) 84

Solution L. H. S. = (3x + 2)²= (3x)² + 2² + 2 × 2 × 3x= 9x² + 4 + 12xR.H. S. = 3x² + 6x + 4Therefore, L. H. S. ≠ R. H. S.Hence, correct statement is (3x + 2)² = 9x² + 4 + 12x

Solution Let Sum of zeroes (α + β) = S = -8 …[Given]Product of zeroes (αβ) = P = 12 …[Given]Quadratic polynomial is x² – Sx + P= x² – (-8)x + 12= x²+ 8x + 12= x² + 6x + 2x + 12= x(x + 6) + 2(x + 6)= (x + 2)(x +