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

Solve for x : ` (log 64)/(log 8)` = log x

If log₁₀2 = a and log₁₀3 = b; express each of the following in terms of 'a' and 'b' : log 60

If log₁₀2 = a and log₁₀3 = b; express each of the following in terms of 'a' and 'b' :  log `3 1/8`

State, true or false : log 1 x log 1000 = 0

State, true or false : 
`log x/log y` = log x - log y

State, true or false : 
If `log 25/log 5 = log x`, then x = 2.

State, true or false : 
log x x log y = log x + log y

Given that log x = m + n and log y = m - n, express the value of log ` ( 10x  ) / ( y ^ 2  )`  in terms of m and n.

If log₁₀ 8 = 0.90, find the value of:

log₁₀ 4

If the following pair of the triangle is congruent? state the condition of congruency : 
In Δ ABC and Δ DEF, AB = DE, BC = EF and ∠ B = ∠ E.

Use the information in the given figure to prove:

1. AB = FE
2. BD = CF 

If the following pair of the triangle is congruent? state the condition of congruency: 

In ΔABC and ΔQRP, AB = QR, ∠B = ∠R and ∠C = P.

If the following pair of the triangle is congruent? state the condition of congruency: 

In ΔABC and ΔPQR, AB = PQ, AC = PR, and BC = QR.

The given figure shows a circle with center O. P is mid-point of chord AB.

Show that OP is perpendicular to AB.

The following figure shows a circle with center O.

If OP is perpendicular to AB, prove that AP = BP.

In a triangle ABC, D is mid-point of BC; AD is produced up to E so that DE = AD.
Prove that :
(i) ΔABD and ΔECD are congruent. 
(ii) AB = CE.
(iii) AB is parallel to EC

In a triangle ABC, D is mid-point of BC; AD is produced up to E so that DE = AD. Prove that:

 AB = CE.

In a triangle ABC, D is mid-point of BC; AD is produced up to E so that DE = AD. Prove that:

AB is parallel to EC.

A triangle ABC has ∠B = ∠C.
Prove that: The perpendiculars from the mid-point of BC to AB and AC are equal.

A triangle ABC has ∠B = ∠C.

Prove that: The perpendiculars from B and C to the opposite sides are equal.