Logical Reasoning — Chapter Test | Class 10 IMO

Q1

1 − sin²θ is equal to:

From sin²θ + cos²θ = 1, 1 − sin²θ = cos²θ.

Q2

Multiplying every observation by 3 multiplies the mean by:

Scaling all data by 3 scales the mean by 3.

Q3

If c = 0 in ax² + bx + c = 0 (a ≠ 0), then one root is:

ax² + bx = x(ax + b) = 0 gives x = 0 as one root.

Q4

A frustum can be seen as a large cone with a smaller similar cone removed from its:

A frustum is the cone with the top (a smaller similar cone) cut off.

Q5

An ogive is the graph of:

An ogive plots cumulative frequencies.

Q6

A circle and a square have equal perimeters. The figure with the larger area is the:

For a fixed perimeter, the circle encloses the maximum area.

Q7

If two lines in a plane are parallel, the system is:

Parallel lines never meet, so there is no solution — the system is inconsistent.

Q8

If the product of the zeroes of a quadratic is negative, the zeroes:

A negative product means one zero is positive and the other negative.

Q9

A tangent and a radius drawn to the point of contact are always:

The radius is perpendicular to the tangent at the contact point.

Q10

The measure most affected by an extreme value is the:

The mean uses every value, so an outlier shifts it the most.

Q11

If two solids have equal volumes but different shapes, then their surface areas are:

Equal volume does not force equal surface area.

Q12

A standard deck contains how many cards?

A standard deck has 52 cards.

Q13

The point (−3, 5) lies in which quadrant?

Negative x with positive y places it in Quadrant II.

Q14

A number is divisible by 10 if and only if it is divisible by:

Since 10 = 2 × 5, divisibility by 10 needs both factors 2 and 5.

Q15

sin 30° compared with sin 60° is:

sin increases on 0°–90°, so sin 30° < sin 60°.