How many minimum number of colours will be required to paint all the sides of a cube without the adjacent sides having the same colours?
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NIMCET 2017 #1202
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NIMCET 2017 #1234
A and B are independent witness in a case. The chance that A speaks truth is x and B speaks
truth is y. If A and B agree on certain statement, the probability that the statement is true is
NIMCET 2017 #1235
The harmonic mean of two numbers is 4. Their arithmetic mean A and the geometric mean G satisfy the relation 2A+G2 = 27, then the two numbers are
NIMCET 2017 #1236
In an entrance test there are multiple choice questions, with four possible answer to each question of which one is correct. The probability that a student knows the answer to a question is 90%. If the student gets the correct answer to a question, then the probability that he as guessing is
NIMCET 2017 #1237
A man is known to speak the truth 2 out of 3 times. He threw a dice cube with 1 to 6 on its faces and reports that it is 1. Then the probability that it is actually 1 is
NIMCET 2017 #1238
Let A and B be two events such that , 
and
and 
where 
stands for the complement of event A. Then the events A and B areNIMCET 2017 #1239
The mean and variance of a random variable X having binomial distribution are 4 and 2 respectively. The P(X = 1) is
NIMCET 2017 #1240
isNIMCET 2017 #1241
If E1 and E2 are two events associated with a random experiment such that P (E2) = 0.35, P (E1 or E2) = 0.85 and P (E1 & E2) = 0.15 then P(E1) is
NIMCET 2017 #1242
NIMCET 2017 #1243
If in a triangle ABC, the altitudes from the vertices A, B, C on opposite sides are in HP, then sin A, sin B, sin C are in
NIMCET 2017 #1244
α, β are the roots of the an equation $x^2- 2x cosθ + 1 = 0$, then the equation having roots αn and βn is
NIMCET 2017 #1245
NIMCET 2017 #1246
Three positive number whose sum is 21 are in arithmetic progression. If 2, 2, 14 are added to them respectively then resulting numbers are in geometric progression. Then which of the following is not among the three numbers?
NIMCET 2017 #1247
= 
, then NIMCET 2017 #1248
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NIMCET 2017 #1251
If cosθ = 4/5 and cosϕ = 12/13, θ and ϕ both in the fourth quadrant, the value of cos( θ + ϕ )is
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NIMCET 2017 #1254
If non-zero numbers a, b, c are in A.P., then the straight line ax + by + c = 0 always passes
through a fixed point, then the point is
NIMCET 2017 #1255
If the lines x + (a – 1)y + 1 = 0 and 2x + a2y – 1 = 0 are perpendicular, then the condition satisfies by a is
NIMCET 2017 #1256
In a triangle ABC, let angle C = π/2. If R is the inradius and R is circumradius of the triangle ABC,
then 2(r + R) equals
NIMCET 2017 #1257
If x2 + 3xy + 2y2 – x – 4y – 6 = 0 represents a pair of straight lines, their point of intersection is
NIMCET 2017 #1258
NIMCET 2017 #1259
If the graph of y = (x – 2)2 – 3 is shifted by 5 units up along y-axis and 2 units to the right along
the x-axis, then the equation of the resultant graph is
NIMCET 2017 #1260
NIMCET 2017 #1261
The equation of the hyperbola with centre at the region, length of the transverse axis is 6 and
one focus (0, 4) is
NIMCET 2017 #1262
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 $\vec{c}$
NIMCET 2017 #1263
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
NIMCET 2017 #1264
and 
be three vector such that |
| = 2, |NIMCET 2017 #1265
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NIMCET 2017 #1268
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
NIMCET 2017 #1269
Let A and B two sets containing four and two elements respectively. The number of subsets of
the A × B, each having at least three elements is
NIMCET 2017 #1270
The slope of the function \[
f(x) =
\begin{cases}
x^2 \sin\!\left(\dfrac{1}{x}\right), & \text{if } x \ne 0, \\[8pt]
0, & \text{if } x = 0
\end{cases}
\]
NIMCET 2017 #1271
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NIMCET 2017 #1273
Let f(x) be a polynomial of degree four, having extreme value at x = 1 and x = 2. If $\lim _{{x}\rightarrow0}[1+\frac{f(x)}{{x}^2}]=3$, then f(2) is
NIMCET 2017 #1274
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NIMCET 2017 #1284
What is the largest number of positive integers to be picked up randomly so that the sum of
difference of any two of the chosen numbers is divisible by 10?