NIMCET 2017 Previous Year Questions (PYQs) – Page 7 of 12
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The direction cosines of the vector a = (- 2i + j – 5k) are
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4
Solution
The equation of the hyperbola with centre at the region, length of the transverse axis is 6 and
one focus (0, 4) is
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Solution
If $\vec{a}$, $\vec{b}$ and $\vec{c}$ are vectors such that $\vec{a}$+$\vec{b}$+$\vec{c}$ = 0 and |$\vec{a}$| =7, $\vec{b}$=5, |$\vec{c}$| = 3, then the angle between the vectors $\vec{b}$ and $\vec{c}$
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Solution
If 
, 
and
, and 
, (a ≠ b ≠ c ≠ 1) are co-planar, then the value of 
is1
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Solution
Let a, b and c be three vectors having magnitudes 1, 1 and 2 respectively. If a x (a x c) - b = 0, then the acute angle between a and c is
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Solution
Let 
, 
and 
be three vector such that || = 2, || = 3, || = 5 and ++ = 0. The value of .+.+. is
, and be three vector such that || = 2, || = 3, || = 5 and ++ = 0. The value of .+.+. is1
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Solution
If = (i + 2j - 3k) and =(3i -j + 2k), then the angle between ( + ) and ( - )
= (i + 2j - 3k) and =(3i -j + 2k), then the angle between ( + ) and ( - )1
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Solution
The number of elements in the power set P(S) of the set S = {2, (1, 4)} is
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4
Solution
Given: \( S = \{2, (1,4)\} \)
Here, the set \(S\) has two elements:
- The number \(2\)
- The ordered pair \((1,4)\)
Hence, \(|S| = 2\).
Formula: The number of elements in the power set of a set having \(n\) elements is \(2^n\).
\[ |P(S)| = 2^{|S|} = 2^2 = 4 \]
✅ Therefore, the number of elements in \(P(S)\) is 4.
If (1 - x + x2 )n = a + a1x + a2x2 + ... + a2nx2n , then a0 + a2 + a4 + ... + a2n is
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Solution
m distinct animals of a circus have to be placed in m cages, one is each cage. There are n small
cages and p large animal (n < p < m). The large animals are so large that they do not fit in small
cage. However, small animals can be put in any cage. The number of putting the animals into
cage is
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4
Solution
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