Loci and concurrency Questions and answers

  1. Elementary Mathematics
    1. Area and perimeter
    2. Circles
    3. Clocks
    4. Factorisation
    5. Geometry
    6. Height and Distance
    7. Indices and Surd
    8. LCM and HCF
    9. Loci and concurrency
    10. Logarithms
    11. Polynomials
    12. Quadratic Equations
    13. Quadrilateral and parallelogram
    14. Rational expression
    15. Real Analysis
    16. Rectangular and Cartesian products
    17. Set theory
    18. Simple and Decimal fraction
    19. Simplification
    20. Statistics
    21. Straight lines
    22. Triangle
    23. Trigonometric ratio
    24. Trigonometry
    25. Volume and surface area
1). The maximum number of tangents which can be drawn from an external point to a circle is
A). two
B). one
C). zero
D). none of these
2). A circular running track is 10 m wide. The difference in the length of the outer boundary and the inner boundary
I. depends on the length of the track
II. depends on the radius of the inner boundary
III. depends on the area of the track
IV is \( \Large 20 \pi m \).
Select the correct answer using the codes below:
Codes :

A). I, II and III
B). I and III
C). II and III
D). IV alone
3). The boundary of the shaded region in the given diagram consists of five semicircular areas. If AB=7cm, BC=3.5cm, CD=7cm and DE=7 cm, then area of the shaded region is

A). \( \Large \frac{17.5}{2} \times \frac{3.5}{2}\ \pi\ cm^{2} \)
B). \( \Large \frac{17.5 \times 21}{2}\ \pi\ cm^{2} \)
C). \( \Large \frac{35 \times 21}{16}\ \pi\ cm^{2} \)
D). \( \Large \frac{35 \times 21 \pi }{8}\ cm^{2} \)
4). If C is a circle passing through three non-collinear points D,E, F such that DE = EF = DF = 3 cms, then radius of the circle C is
A). \( \Large \frac{\sqrt{3}}{2}\ cm \)
B). \( \Large \sqrt{3}\ cm \)
C). \( \Large \frac{1}{\sqrt{3}}\ cm \)
D). \( \Large \frac{2}{\sqrt{3}}\ cm \)
5). In a circle of radius 7 cm, an arc subtends an angle of \( \Large 108 ^{\circ} \) at the centre. The area of the sector is
A). \( \Large 43.2\ cm^{2} \)
B). \( \Large 44.2\ cm^{2} \)
C). \( \Large 45.2\ cm^{2} \)
D). \( \Large 46.2\ cm^{2} \)


6). Area of the shaded portion in the given figure, where the arcs are quadrants of a circle, is
A). \( \Large 42\ m^{2} \)
B). \( \Large 56\ m^{2} \)
C). \( \Large 64\ m^{2} \)
D). \( \Large 144\ m^{2} \)
7). In the given figure, PQ is tangent at A; BC is the diameter. If \( \Large \angle ABC = 42 ^{\circ}.\ then\ \angle PAB \) is equal to
A). \( \Large 21 ^{\circ} \)
B). \( \Large 42 ^{\circ} \)
C). \( \Large 48 ^{\circ} \)
D). \( \Large 84 ^{\circ} \)
8). If length of the tangent from origin to the circle \( \Large x^{2}+y^{2}-26x+K=0\ is\ 5 \), then K is equal to
A). \( \Large \sqrt{5} \)
B). 5
C). 10
D). 25
9). If area of the given circle is \( \Large 100 \pi \) square cm, then side of the square inscribed in the circle is
A). 10 cm
B). \( \Large 10\sqrt{2}\ cm \)
C). 20 cm
D). \( \Large 20\sqrt{2}\ cm \)
10). The middle points of all chords (each having the same length) of a circle lie on a
A). rectangle
B). square
C). circle
D). parallelogram
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Total Pages : 4