(English Medium) ICSE Class 9 - CISCE Question Bank Solutions for Mathematics

Prove the following:

`root("ab")(x^"a"/x^"b")·root("bc")(x^"b"/x^"c")·root("ca")(x^"c"/x^"a")` = 1

Prove the following:
(x^a)^b-c x (x^b)^c-a x (x^c)^a-b = 1

Prove the following:

`(x^("p"("q"-"r")))/(x^("q"("p"-"r"))) ÷ (x^"q"/x^"p")^"r"` = 1

Express the following in the logarithmic form:
3³ = 27

Express the following in the logarithmic form:
5⁴ = 625

Express the following in the logarithmic form:
9⁰ = 1

Express the following in the logarithmic form:

`(1)/(8)` = 2^-3 

Express the following in the logarithmic form:
11² = 121

Express the following in the logarithmic form:

3^-2 = `(1)/(9)`

Express the following in the logarithmic form:
10^-4 = 0.0001

Express the following in the logarithmic form:
7⁰ = 1

Express the following in the logarithmic form:

`(1/3)^4 = (1)/(81)`

Express the following in the logarithmic form:

9^-4 = `(1)/(6561)`

State true or false in the following:
If 4³ = 64, then log ₃ 64 = 4

State true or false in the following:
If x^y = z, then y = log_xz

Which of the following pairs of triangles are congruent? Give reasons
ΔABC;(BC = 5cm,AC = 6cm,∠C = 80°);
ΔXYZ;(XZ = 6cm,XY = 5cm,∠X = 70°).

Which of the following pairs of triangles are congruent? Give reasons
ΔABC;(AB = 8cm,BC = 6cm,∠B = 100°);
ΔPQR;(PQ = 8cm,RP = 5cm,∠Q = 100°).

Which of the following pairs of triangles are congruent? Give reasons
ΔABC;(AB = 5cm,BC = 7cm,CA = 9cm);
ΔKLM;(KL = 7cm,LM = 5cm,KM = 9cm).

Which of the following pairs of triangles are congruent? Give reasons
ΔABC;(∠B = 70°,BC = 6cm,∠C = 50°);
ΔXYZ;(∠Z = 60°,XY = 6cm,∠X = 70°).

Which of the following pairs of triangles are congruent? Give reasons
ΔABC;(∠B = 90°,BC = 6cm,AB = 8cm);
ΔPQR;(∠Q = 90°,PQ = 6cm,PR = 10cm).