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How many equilateral triangles can be formed by joining any three vertices of a cube?


A) 0

B) 4

C) 8

D) None of these

Correct Answer:
C) 8


Part of solved CDS Maths(1) questions and answers : Exams >> CDSE >> CDS Maths(1)




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Similar Questions
1). For the next two (2) items that follow :
ABCD is a trapezium in which AB is parallel to CD. Let M be the midpoint of BC.
68. Consider the following statements :
1. 'Area of triangle ADM + Area of triangle DCM' is equal to three-fourth of the area of trapezium ABCD, if AB = CD.
2. 'Area of triangle DCM + Area of triangle ABM' is always greater than half of the area of trapezium ABCD.
Which of the above statements is/are correct?
A). 1 only
B). 2 only
C). Both 1 and 2
D). Neither 1 nor 2
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2). Consider the following statements :
1. 'Area of triangle ADM Area of triangle ABM' is always equal to area of triangle DCM, if AB = CD.
2. Half of area of triangle ABM is equal to one-eighth of area of trapezium ABCD. if AB = CD
Which of the above statements is/are correct?
A). 1 only
B). 2 only
C). Both 1 and 2
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3). ABCD is a parallelogram. P and R are the midpoints of DC and BC respectively. The line PR intersects the diagonal AC at Q. The distance CQ will be equal to
A). \( \Large \frac{AC}{4} \)
B). \( \Large \frac{BD}{3} \)
C). \( \Large \frac{BD}{4} \)
D). \( \Large \frac{AC}{3} \)
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4). Consider the following statements in respect of an equilateral triangle :
1. The altitudes are congruent.
2. The three medians are congruent.
3. The centroid bisects the altitude.
Which of the above statements are correct?
A). 1 and 2 only
B). 2 and 3 only
C). 1 and 3 only
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5). Consider the following : ABC and DEF are triangles in a plane such that AB is parallel to DE, BC is parallel to EF and CA is parallel to FD.
Statement I : If angle ABC is a right angle, then angle DEF is also a right angle. ,
Statement II : Triangles of the type ABC and DEF are always congruent.
Which one of the following is correct in respect of the above statements ?
A). Statement-I and Statement-II are correct and Statement-II is the correct explanation of Statement-I
B). Statement-I and Statement-II are correct and Statement-II in not the correct explanation of Statement-l
C). Statement-l is correct and Statement-II is incorrect
D). Statement I is incorrect and Statement-II is correct
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6). Let the incircle to a triangle ABC touch BC, AC and AB respectively at the points X, Y and Z.
Statement I: If AB > BC, then AB + AZ < BC + XC
Statement H : AZ = AY
Which one of the following is correct in respect of the above statements?
A). Statement-I and Statement-II are correct and Statement-II is the correct explanation of Statement-I
B). Statement-I and Statement-II are correct and Statement-II in not the correct explanation of Statement-l
C). Statement-l is correct and Statement-II is incorrect
D). Statement I is incorrect and Statement-II is correct
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7). Let ABC be a triangle in which \( \angle ACB = 60^{\circ}\) and AC = x < BC. Let the circle with centre at C and radius x meet BC at D. Let CF be the perpendicular drawn from C meeting AD at F.
Statement I : Triangle ACD is isosceles but not equilateral.
Statement II : DF = x/2
Which one of the following is correct in respect of the above statements?
A). Statement I and Statement II are correct and Statement II is the correct explanation of Statement I
B). Statement I and Statement II are correct and Statement II is not the correct explanation of Statement I
C). Statement I is correct and Statement II is incorrect
D). Statement I is incorrect and Statement II is correct
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8). Bisectors of two adjacent angles A and B of a quadrilateral ABCD intersect each other at a point P. Which one of the following is correct?
A). \(2 \angle APB = \angle C + \angle D \)
B). \(\angle APB = \angle C + \angle D \)
C). \(\angle APB = 180^{\circ}( \angle A + \angle B) \)
D). \(\angle APB = 180^{\circ}( \angle C + \angle D) \)
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9). In a triangle ABC, AD is the median through A and E is the midpoint of AD, and BE produced meets AC at F. Then AF is equal to
A). \( \Large \frac{AC}{5} \)
B). \( \Large \frac{AC}{4} \)
C). \( \Large \frac{AC}{3} \)
D). \( \Large \frac{AC}{2} \)
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10). Three straight lines are drawn through the three vertices of a triangle ABC, the line through each vertex being parallel to the opposite side. The triangle DEF is bounded by these parallel lines. Consider the following statements in respect of the triangle DEF:
1. Each side of triangle DEF is double the side of triangle ABC to which it is parallel.
2. Area of triangle DEF is four times the area of triangle ABC.
Which of the above statements is/are correct?
A). 1 only
B). 2 only
C). Both 1 and 2
D). Neither 1 nor 2
-- View Answer
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