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Which of the following statements is incorrect?

A For natural numbers a and b, if a divides b² then a divides b.
B For any natural number is irrational.
C Product of distinct prime numbers is always equal to their L.C.M.
D For any natural number n, 6ⁿ never ends with digit zero.

Let ABC be a right angled triangle in which AB = 3 cm, BC = 4 cm and ∠B = 90°. BD is the perpendicular from B on AC. The circle through B, C, D is drawn.
Given below are steps of construction of tangents from A to this circle. Identify the wrong step. Steps of construction :
Step I : Draw ΔABC and perpendicular BD from B on AC.
Step II : Draw a circle with BC as a diameter. This circle will pass through D.
Step III : Let O be the mid point of BC. Join AO.
Step IV : Draw a circle with AO as radius. This circle cuts the circle drawn in step II at B and P.
Step V : Join AP. AP and AB are desired tangents drawn from A to the circle passing through B, C and D.

AOnly I
BOnly IV
COnly III
DOnly V

In the given figure, the line segment XY is parallel to side AC of ΔABC and it divides the triangle into two parts of equal area. Then, find

(i) AX : AB
(ii) .

	(i)	(ii)
A
B
C		, 3
D

If sinθ + sin²θ + sin³θ = 1, then the value of cos⁶θ - 4cos⁴θ + 8cos²θ is ______.

A6
B8
C4
D3

Solve for x and y :

Ax = - a, y = b
Bx = b², y = a²
Cx = a², y = b²
Dx = b, y = - a

Find the number of rectangles formed in the given figure.


A24
B28
C36
DNone of these

Fill in the blanks.
In 'Less Than' Ogive, the cumulative frequencies are written corresponding to the __P__ limits of the classes of the given data.
In 'More Than' Ogive, the cumulative frequencies are written corresponding to the __Q__ limit of the classes.
On an ogive, point P whose y - coordinate = n/2 (i.e., half of the total number of the entries), has its x - coordinate equal to the __R__ of the data. Two ogives, one 'less than' type and the other 'more than' type for the same data when drawn simultaneously on the same graph, intersect each other at the point P whose __S__ = n/2 and __T__ = median of the data where n is the total number of the entries of the data.

---------- P--------Q---------R-----------S--------------T
AUpper - Lower - Mediany - coordinatex - coordinate
BLower - Upper - Mediany - coordinatex - coordinate
CUpper - Lower - Median x - coordinatey - coordinate
DUpper - Lower - Upper limity - coordinatex - coordinate

A real number will have ________.
A Terminating decimal expansion
B Non-terminating decimal expansion
C Repeating decimal expansion
D Both (B) and (C)

A boy was asked to multiply a given number by (8/17). Instead, he divided the given number by (8/17) and got the result 225 more than what he should have got if he had multiplied the number by (8/17). The given number was ________.

A 8
B 17
C 64
D 136

There is a set of three figures X, Y and Z showing a sequence of folding a piece of paper. Fig. (Z) shows the manner in which the folded paper has been cut. Select a figure from the options which would most closely resembles the unfolded form of Fig. (Z).


A
B
C
D