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the larger of two supplementary angles exceeds the smaller by 180 find them ans990810ans x y 1800 x - y
students are made to stand in rows if one student is extra in a row there would be 2 rows less if one student is less in a row there would be 3 rows
find the value of p and q for which the system of equations represent coincident lines 2x 3y 7 pq1x p2q2y 4pq1ans a1 2 b1 3 c1 7a2 p q
41x 53y 135 53x 41y 147ans 41x 53 y 135 53 x 41 y 147add the two equations solve it to get x y 3 -------1 subtract solve it to
a2bx 2a- by 2 a - 2bx 2a by 3ans 5b - 2a10ab a 10b10ab ans2ax 4ay y we get 4bx - 2by -12ax 4ay 5 4bx- 2by - 1solve this to
7y 3 - 2x 2 14 4 y - 2 3x - 3 2ans 7y 3 - 2 x 2 14 --------- 14y- 2 3x - 3 2 ----------2from
solve for x yx y - 82 x 2 y - 143 3x y - 1211 ans x2 y6ans x y - 82 x 2y - 14 3
pair of linear equations in two variables like the crest of a peacock so is mathematics at the head of all
if the ratios of the polynomial ax33bx23cxd are in ap prove that 2b3-3abca2d0ans let px ax3 3bx2 3cx
if alpha amp szlig are the zeroes of the polynomial 2x2 - 4x 5 then find the value of aalpha2 szlig2 b 1 alpha 1 szlig c alpha - szlig2 d
if alphabeta are the zeros of a quadratic polynomial such that alpha beta 24 alpha - beta 8 find a quadratic polynomial having alpha and beta as
if the squared difference of the zeros of the quadratic polynomial x2 px 45 is equal to 144 find the value of
on dividing the polynomial 4x4 - 5x3 - 39x2 - 46x - 2 by the polynomial gx the quotient is x2 - 3x - 5 and the remainder is -5x 8find the polynomial
if alpha beta are the zeros of the polynomial x2 8x 6 frame a quadratic polynomial whose zeros are a 1alpha and 1beta b 1 betaalpha 1
if alphabeta are the zeros of the polynomial 2x2 - 4x 5 find the value of a alpha2 beta2 b alpha - beta2ans p x 2 x2 - 4 x
find the quadratic polynomial whose sum and product of zeros are radic2 1 1 radic2 1ans sum 2 radic2product 1qp x2 - sum x
find the greatest number of 6 digits exactly divisible by 24 15 and 36 ans999720ans lcm of 24 15 36lcm 3 times 2 times 2 times 2 times 3 times 5
show that for odd positive integer to be a perfect square it should be of the form8k 1 let a2m1ans squaring both sides we get a2 4m m 1 1there4
show that the product of 3 consecutive positive integers is divisible by 6ansnn1n2 be three consecutive positive integerswe know that n is of the
if d is the hcf of 30 72 find the value of x amp y satisfying d 30x 72yans5 -2 not uniqueans using euclids algorithm the hcf 30 7272
show that 571 is a prime numberans let x571rarrradicxradic571now 571 lies between the perfect squares of 232 and 242prime numbers
find the least number that is divisible by all numbers between 1 and 10 both inclusiveans the required number is the
find the largest possible positive integer that will divide 398 436 and 542 leaving remainder 7 11 15 respectivelyans 17ans the required number is
prove that one of every three consecutive integers is divisible by 3ansnn1n2 be three consecutive positive integerswe know that n is of the form 3q
express the gcd of 48 and 18 as a linear combination ans not uniqueabqr where o le r lt