Discussion
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- Question
Three consecutive integers form the lengths of a right-angled triangle. How many sets of such three consecutive integers is/are possible?
Options- A. Only one
- B. Only two
- C. Only three
- D. Infinitely many
- Correct Answer
- Only one
Explanationlet n-1, n, n+1 be 3 consecutive integers
So
(n+1)^2= n^2+ (n-1)^2
(n+1)^2-(n-1)^2= n^2
4n = n^2
So n = 0 or n = 4
n can?t be 0 as n-1 will be negative then
So 3,4 and 5 is the only triplet formed.
- 1. The corners of a square of side ?a? are cut away so as to form a regular octagon. What is the side of the octagon?
Options- A. a(?2 ?1)
- B. a(?3 ?1)
- C. a/?2+2
- D. a/3 Discuss
- 2. The sum of length, breadth and height of a cuboid is 22 cm and the length of its diagonal is 14 cm. If S is sum of the cubes of the dimensions of the cuboid and V is its volume, then what is (S-3V) equal to?
Options- A. 572 cub.cm
- B. 728 cub.cm
- C. 1144 cub.cm
- D. None of the above Discuss
- 3. The sum of length, breadth and height of a cuboid is 22 cm and the length of its diagonal is 14 cm. What is the surface area of the cuboid?
Options- A. 288 sq.cm
- B. 216 sq.cm
- C. 144 sq.cm
- D. Cannot be determined due to insufficient data Discuss
- 4. An equilateral triangle ABC is inscribed in a circle of radius 20?3. The centroid of the triangle ABC is at a distance d from the vertex A. What is d equal to ?
Options- A. 15 cm
- B. 20 cm
- C. 20?3 cm
- D. 30?3 cm Discuss
- 5. An equilateral triangle ABC is inscribed in a circle of radius 20?3. What is the length of the side of the triangle?
Options- A. 30 cm
- B. 40 cm
- C. 50 cm
- D. 60 cm Discuss
- 6. Two circles are drawn with the same centre. The circumference of the smaller circle is 44 cm and that of the bigger circle is double the smaller one. What is the area between these two circles?A. 154 square cmB. 308 square cmC. 462 square cmD. 616 square cm
Options- A. 154 square cm
- B. 308 square cm
- C. 462 square cm
- D. 616 square cm Discuss
- 7. A rectangular red carpet of size 6 ft ×12 ft has a dark red border 6 inches wide. What is the area of the dark red border?
Options- A. 9 square feet
- B. 15 square feet
- C. 17 square feet
- D. 18 square feet Discuss
- 8. Consider the following statements: 1) An isosceles trapezium is always cyclic. 2) Any cyclic parallelogram is a rectangle. Which of the above statements is/are correct?
Options- A. 1 only
- B. 2 only
- C. Both 1 and 2
- D. Neither 1 nor 2 Discuss
- 9. Consider the following statements: 1) The number of circles that can be drawn through three non-collinear points is infinity. 2) Angle formed in minor segment of a circle is acute. Which of the above statements is/are correct?
Options- A. 1 only
- B. 2 only
- C. Both 1 and 2
- D. Neither 1 nor 2 Discuss
- 10. Consider the following statements: 1) The number of circles that can be drawn through three non-collinear points is infinity. 2) Angle formed in minor segment of a circle is acute. Which of the above statements is/are correct?
Options- A. 1 only
- B. 2 only
- C. Both 1 and 2
- D. Neither 1 nor 2 Discuss
Volume and Surface Area problems
Search Results
Correct Answer: a(?2 ?1)
Correct Answer: 1144 cub.cm
Correct Answer: 288 sq.cm
Explanation:
Let lengths, breadth and height of cuboid be l, b and h respectively
According to question
l+b+h = 22cm......(i)
and
?(l^2+b^2+h^2) = 14cm .....(ii)
Surface area of cuboid = 2(lb+bh+lh)
Squaring eq (i) gives
+ 2(lb+bh+lh) = 484
Substituting l^2+b^2+h^2 from eq (i)
2(lb+bh+lh) = 484 -196 = 288 sq.cm
Correct Answer: 20?3 cm
Correct Answer: 60 cm
Explanation:
Radius of circumcircle of an equilateral triangle = side /?3
R = a/?3
a = R?3 = 20?3 *?3 = 60cm
Correct Answer: 462 square cm
Correct Answer: 17 square feet
Explanation:
Initially carpet is 6×12 = 72 sq feet
Since red border is 6 inches wide from all 4 side
So area without border = 5× 11 = 55 sq feet
Area of border = total?area without border = 72?55 = 17 sq feet
Correct Answer: Both 1 and 2
Explanation:
Since it is an isosceles trapezium
So angle C = angle D = x
let A = 180 ?D = 180 ?x (since AB is parallel to CD)
B = 180-x
A+C = 180 ?x + x = 180 degrees (Property of cyclic quadrilateral)
ABCD is cyclic parallelogram with AB // CD and AD // BC
Considering angles A = C = y (Property of parallelogram) and B=D = x Also since it is cyclic A+C = B+D = 180 degrees
So x=y=90 degrees And also opposite sides are equal being a parallelogram
Thus ABCD is a rectangle
Correct Answer: Neither 1 nor 2
Explanation:
(1)
Only one circle can be drawn through 3 non collinear points
Angle in the minor segment is always obtuse
Correct Answer: Neither 1 nor 2
Explanation:
(1)
Only one circle can be drawn through 3 non collinear points
Angle in the minor segment is always obtuse
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