Practice NAT Mathematics questions with answers and explanations.
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The complement contains universal-set elements not in A.
Removing 2 and 4 leaves 1, 3, and 5.
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Selection without order uses combinations.
5C2 = 5 × 4 ÷ 2 = 10.
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A set with n elements has 2ⁿ subsets.
For n = 5, this is 2⁵ = 32.
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There are 4 choices for the first digit, then 3, then 2.
Thus, 4 × 3 × 2 = 24.
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Use n(M ∪ E) = n(M) + n(E) - n(M ∩ E).
Thus, 22 + 18 - 8 = 32.
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There are 5 letters with L repeated twice and E repeated twice.
Distinct arrangements = 5!/(2!2!) = 30.
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Thirty-two students study at least one subject.
Out of 40 students, 40 - 32 = 8 study neither.
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Average the x-coordinates and the y-coordinates separately.
The midpoint is ((2 + 8)/2, (3 + 7)/2) = (5, 5).
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Curved surface area is 2πrh.
Thus, 2π × 4 × 7 = 56π cm².
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Cone volume is one-third πr²h.
Thus, 1/3 × π × 9 × 12 = 36π cm³.
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Sphere volume is 4/3 πr³.
Thus, 4/3 × π × 27 = 36π cm³.
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The edge length is the cube root of the volume.
Since 6³ = 216, the edge is 6 cm.
