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Given below are the steps of construction of a pair of tangents to a circle of radius 6 cm from a point on the concentric circle of radius 8 cm. Find which of the following steps is INCORRECT?
Steps of Construction
Step I : Take a point O on the plane paper and draw a circle of radius OA = 6 cm. Also, draw a concentric circle of radius OB = 8 cm.
Step II : Find the mid-point A of OB and draw a circle of radius BA = AO. Suppose this circle intersects the circle of radius 6 cm at P and Q.
Step III : Join BP and BQ to get the desired tangents.

A Step I
B Step II
C Step I and Step II
D Step II and Step III

The algebraic sum of the deviations of a frequency distribution from its mean is _____.

A Always positive
B Always negative
C 0
D A non-zero number

Which of the following statements is INCORRECT ?
(i) In order to divide a line segment internally in the ratio m : n, both m and n are real numbers.
(ii) A pair of tangents can be constructed to a circle inclined at an angle of 165°.

AOnly (i)
BOnly (ii)
CBoth (i) and (ii)
DNeither (i) nor (ii)

In each of the following questions, select a figure from amongst the four alternatives, which when placed in the blank space of Fig. (X) would complete the pattern.


A
B
C
D

Which of the following is the mirror image of the given combination, when mirror is kept vertically left?
4Q2PR345Z

A
B
C
D

A transparent sheet (x) with a pattern and a dotted line is given. Select a figure from the option as to how the pattern would appear. When the transparent Sheet (x) is folded along the dotted line.


A
B
C
D

In which of the following options Fig. (X)is exactly embedded as one of its part.


A
B
C
D

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