Welcome to your Geometry(Senior Class Maths Study by Topics) NAME EMAIL PHONE NUMBER 1. Find the measure of angle A in the figure below. 51° 87° 103° 98° None 2. The parallelogram shown in the figure below has a perimeter of 44 cm and an area of 64 cm^{2}. Find angle T in degrees. 55.2° 64° 34.8° 12.3° None 3. When two straight lines intersect I. adjacent angles are equal II. adjacent angles are supplementary III. vertically opposite angles are equalIV. vertically opposite angles are supplementary Which of the above statements are true? II and IV only II and III only I and IV only I and III only None 4. The figure below shows two concentric circles with centre O. PQRS is a square inscribed in the outer circle. It also circumscribes the inner circle, touching it at points B, C, D and A. What is the ratio of the perimeter of the outer circle to that of polygon ABCD? π/2 π/4 π 3π/2 None 5. A city has two perfectly circular and concentric ring roads, the outer ring road (OR) being twice as long as the inner ring road (IR). There are also four (straight line) chord roads from E1, the east end point of OR to N2, the north end point of IR; from N1, the north end point of OR to W2, the west end point of IR; from W1, the west end point of OR, to S2, the south end point of IR; and from S1 the south end point of OR to E2, the east end point of IR. Traffic moves at a constant speed of 30π km/hr on the OR road, 20π km/hr on the IR road, and 15 5 km/hr on all the chord roads. Amit wants to reach N2 from S1. It would take him 90 minutes if he goes on minor arc S1 – E1 on OR, and then on the chord road E1 – N2. What is the radius of the outer ring road in kms? 60 30 20 40 None 6. In the above figure, ACB is a right-angled triangle. CD is the altitude. Circles are inscribed within the <span id="MathJax-Element-39-Frame" class="mjx-chtml MathJax_CHTML" style="line-height: 0;text-indent: 0px;text-align: left;text-transform: none;font-style: normal;font-weight: 400;font-size: 18.72px;letter-spacing: normal;float: none;direction: ltr;max-width: none;max-height: none;min-width: 0px;min-height: 0px;border: 0px;margin: 0px;padding: 1px 0px;color: #4c4c4c;font-family: 'Open Sans', sans-serif;background-color: #ffffff" role="presentation" data-mathml="ΔACD">ΔACDΔACD and <span id="MathJax-Element-40-Frame" class="mjx-chtml MathJax_CHTML" style="line-height: 0;text-indent: 0px;text-align: left;text-transform: none;font-style: normal;font-weight: 400;font-size: 18.72px;letter-spacing: normal;float: none;direction: ltr;max-width: none;max-height: none;min-width: 0px;min-height: 0px;border: 0px;margin: 0px;padding: 1px 0px;color: #4c4c4c;font-family: 'Open Sans', sans-serif;background-color: #ffffff" role="presentation" data-mathml="ΔBCD">ΔBCDΔBCD. P and Q are the centres of the circles. The distance PQ is √50 5 7 8 None 7. In a regular pentagon ABCDE, /AC/ intersects /BD/ at F. Calculate <CBD. 36 degrees 60 degrees 72 degrees 108 degrees None 8. Which of the following statements is false? An equiangular triangle is also equilateral If two triangles are similar, then they are also congruent An equilateral triangle is also equiangular If two triangles are congruent, then they are also similar None 9. Euclid has a triangle in mind. Its longest side has length 20 and another of its sides has length 10.Its area is 80. What is the exact length of its third side √250 √260 √290 √270 None 10. Find the total surface area of a closed conical container with radius 5 cm and a height of 15 cm. 124 sq. cm 327 sq. cm 209 sq. cm 420 sq. cm None 11. A point P moves such that it is always equidistant from two fixed points X and Y. When /XY/ is 12 cm and P is 8 cm from /XY/, the distance of P from Y is 10 cm 20 cm 8 cm 12 cm None 12. A city has two perfectly circular and concentric ring roads, the outer ring road (OR) being twice as long as the inner ring road (IR). There are also four (straight line) chord roads from E1, the east end point of OR to N2, the north end point of IR; from N1, the north end point of OR to W2, the west end point of IR; from W1, the west end point of OR, to S2, the south end point of IR; and from S1 the south end point of OR to E2, the east end point of IR. Traffic moves at a constant speed of 30π km/hr on the OR road, 20π km/hr on the IR road, and 15 5 km/hr on all the chord roads. Amit wants to reach E2 from N1 using first the chord N1 – W2 and then the inner ring road. What will be his travel time in minutes on the basis of information given in the above question? 105 60 45 90 None 13. A regular polygon with (2m + 1) sides has each interior angle equal to 144°. The value of m is 8 10 5 9/2 None 14. Each side of the square pyramid shown below measures 10 inches. The slant height, H, of this pyramid measures 12 inches.What is the total surface area, in square inches, of the pyramid? 40sq. inches 340 sq. inches 140 sq. inches 240 sq. inches None 15. Which two angles are not supplementary? 89 degrees and 91 degrees 30 degrees and 150 degrees 23 degrees and 177 degrees 5 degrees and 175 degrees None 16. In the figure (not drawn to scale) given below, if AD = CD = BC and ∠BCE =96^{0} , how much is the value of ∠DBC? 64° 28° 84° 32° None 17. Two identical circles intersect so that their centers, and the points at which they intersect, form a square of side 1 cm. The area in sq. cm of the portion that is common to the two circles is π π/4 π/4 -1 π/5 None 18. Four of five interior angles of a pentagon are equal. If the size of the fifth angle is 80°, then the size of each of the four equal angles is 136 degrees 120 degrees 115 degrees 100 degrees None 19. ABCD is a parallelogram such that AB is parallel to DC and DA parallel to CB. The length of side AB is 20 cm. E is a point between A and B such that the length of AE is 3 cm. F is a point between points D and C. Find the length of DF such that the segment EF divide the parallelogram in two regions with equal areas. 19 cm 17 cm 12 cm 21 cm None 20. In <span id="MathJax-Element-22-Frame" class="mjx-chtml MathJax_CHTML" style="line-height: 0;text-indent: 0px;text-align: left;text-transform: none;font-style: normal;font-weight: 400;font-size: 18.72px;letter-spacing: normal;float: none;direction: ltr;max-width: none;max-height: none;min-width: 0px;min-height: 0px;border: 0px;margin: 0px;padding: 1px 0px;color: #4c4c4c;font-family: 'Open Sans', sans-serif;background-color: #ffffff" role="presentation" data-mathml="ΔABC">ΔABCΔABC, the internal bisector of <span id="MathJax-Element-23-Frame" class="mjx-chtml MathJax_CHTML" style="line-height: 0;text-indent: 0px;text-align: left;text-transform: none;font-style: normal;font-weight: 400;font-size: 18.72px;letter-spacing: normal;float: none;direction: ltr;max-width: none;max-height: none;min-width: 0px;min-height: 0px;border: 0px;margin: 0px;padding: 1px 0px;color: #4c4c4c;font-family: 'Open Sans', sans-serif;background-color: #ffffff" role="presentation" data-mathml="∠A">∠A∠A meets <span id="MathJax-Element-24-Frame" class="mjx-chtml MathJax_CHTML" style="line-height: 0;text-indent: 0px;text-align: left;text-transform: none;font-style: normal;font-weight: 400;font-size: 18.72px;letter-spacing: normal;float: none;direction: ltr;max-width: none;max-height: none;min-width: 0px;min-height: 0px;border: 0px;margin: 0px;padding: 1px 0px;color: #4c4c4c;font-family: 'Open Sans', sans-serif;background-color: #ffffff" role="presentation" data-mathml="BC">BCBC at <span id="MathJax-Element-25-Frame" class="mjx-chtml MathJax_CHTML" style="line-height: 0;text-indent: 0px;text-align: left;text-transform: none;font-style: normal;font-weight: 400;font-size: 18.72px;letter-spacing: normal;float: none;direction: ltr;max-width: none;max-height: none;min-width: 0px;min-height: 0px;border: 0px;margin: 0px;padding: 1px 0px;color: #4c4c4c;font-family: 'Open Sans', sans-serif;background-color: #ffffff" role="presentation" data-mathml="D">DD. If <span id="MathJax-Element-26-Frame" class="mjx-chtml MathJax_CHTML" style="line-height: 0;text-indent: 0px;text-align: left;text-transform: none;font-style: normal;font-weight: 400;font-size: 18.72px;letter-spacing: normal;float: none;direction: ltr;max-width: none;max-height: none;min-width: 0px;min-height: 0px;border: 0px;margin: 0px;padding: 1px 0px;color: #4c4c4c;font-family: 'Open Sans', sans-serif;background-color: #ffffff" role="presentation" data-mathml="AB=4,AC=3and∠A=60∘">AB=4,AC=3 and ∠A=60° AB=4,AC=3 and∠A=60∘, then the length of <span id="MathJax-Element-27-Frame" class="mjx-chtml MathJax_CHTML" style="line-height: 0;text-indent: 0px;text-align: left;text-transform: none;font-style: normal;font-weight: 400;font-size: 18.72px;letter-spacing: normal;float: none;direction: ltr;max-width: none;max-height: none;min-width: 0px;min-height: 0px;border: 0px;margin: 0px;padding: 1px 0px;color: #4c4c4c;font-family: 'Open Sans', sans-serif;background-color: #ffffff" role="presentation" data-mathml="AD">ADAD is 12√3/ 7 15√3/ 8 2√3 6√3/ 7 None 21. In the figure above, AB = BC = CD = DE = EF = FG = GA. Then ∠DAE is approximately 30° 15° 25° 20° None 22. In the following figure, the diameter of the circle is 3 cm. AB and MN are two diameters such that MN is perpendicular to AB. In addition, CG is perpendicular to AB such that AE:EB = 1:2, and DF is perpendicular to MN such that NL:LM = 1:2. The length of DH in cm is (2√2-1)/ 2 (2√2-1)/ 3 (3√2-1)/ 2 2√2-1 None 23. Find the area of the given shape. 270 sq. cm 298 sq. cm 309 sq. cm 183 sq. cm None 24. Four of the interior angles of a pentagon are specified as (80 - y)°, (80 + y)°, (120 - 2y)° and (120 + 2y)°. The size of the fifth interior angle must be 130 degrees 144 degrees 140 degrees 120 degrees None 25. The sides /AB/ and /AC/ of a triangle ABC are produced to D and E respectively such that <DBC = 125° and <BCE = 95°. Find the value of <BAC 85 degrees 40 degrees 90 degrees 55 degrees None 1 out of 25 Time's upTime is Up!