(English Medium) ICSE Class 10 - CISCE Question Bank Solutions for Mathematics

Find the mean proportion of the following :

`28/3` and `175/27`

If x, 12 and 16 are in continued proportion! find x. 

If `1/12` , x and `1/75` are in continued proportion , find x.

If y is the mean proportional between x and z, show that :

xyz (x+y+z)³ =(xy+yz+xz)³  

If y is the mean proportional between x and y; show that y(x+z) is the mean p roporti ona I between x²+ y² and y²+ z² 

If three quantities are in continued proportion, show that the ratio of the first to the third is the duplicate ratio of the first to the second. 

Given four quantities p, q, r and s are in proportion, show that 
q²(p - r) : rs (q - s) =(p²- q²- pq): ( r²-s²-rs). 

If a : b = c : d; then show that (ax+ by) : b = (cx+ dy) : d 

If ( a+c) : b = 5 : 1 and (bc + cd) : bd = 5 : 1, then prove that a : b = c : d 

Find the smallest number that must be subtracted from each of the numbers 20, 29, 84 and 129 so that they are in proportion.

Find two nurnbers whose mean proportional is 12 and the third proportional is 324.

Find two numbers whose mean proportional is 18 and the third proportional is 486. 

If a : b : : c : d, then prove that 

 2a+7b : 2a-7b = 2c+7d : 2c-7d 

If u, v, w, and x are in continued proportion, then prove that (2u+3x) : (3u+4x) : : (2u³+3v³) : (3u³+4v³) 

If p, q and r in continued proportion, then prove the following: 

(p² - q²)(q² + r²) = (q² - r²)(p² + q²)

If p, q and r in continued proportion, then prove the following: 

(p + q + r )(p - q + r) = p² + q² + r² 

If u, v, w, and x are in continued proportion, then prove that (2u+3x) : (3u+4x) : : (2u³+3v³) : (3u³+4v³)  

`("pqr")^2 (1/"p"^4 + 1/"q"^4 + 1/"r"^4) = ("p"^4 + "q"^4 + "r"^4)/"q"^2`

If p, q and r in continued proportion, then prove the following :

`"p"^2 - "q"^2 + "r"^2 = "q"^4 (1/"p"^2 - 1/"q"^2 - 1/"r"^2)`

If a, b, c and dare in continued proportion, then prove that 

ad (c² + d²) = c³ (b + d)

If a, b, c and dare in continued proportion, then prove that 

`sqrt (("a + b + c")("b + c + d")) = sqrt "ab" + sqrt "bc" + sqrt "cd"`