The equation of the tangent at any point of curve x = a cos³2t, y = 2√2 a sin t with m as its slope is

Correct Answer: Option B - y = mx - a(m + 1/m).

If Π[i=1 to n] tan(αᵢ) = 1 ∀ αᵢ ∈ [0, π/2] where i = 1,2,3, ... n. Then maximum of value of Π[i=1 to n] sin αᵢ

Correct Answer: Option B - 1/2^(n/2).

A speaks truth in 60% and B speaks the truth in 50% cases. In what percentage of cases, they are likely in contradict each other while narrating some incident is

Correct Answer: Option A - 1/2.

Let A and B be sets. A ∩ X = B ∩ X = φ and A U X = B U X for some set X, relation between A & B.

Correct Answer: Option A - A=B.

Find foci of the equation x² + 2x – 4y² + 8y - 7 = 0

Correct Answer: Option B - (−1 ± √5, 1).

The locus of the mid-point of all chords of the parabola y² = 4x which are drawn through its vertex is

Correct Answer: Option B - y² = 2x.

If a = î − k̂ and b = xî + ĵ + (1 − x)k̂ and c = yî + xĵ + (1 + x - y)k̂, then [a b c] depends on

Correct Answer: Option A - Neither x nor y.

If a, b are unit vectors such that |2a + b| = 3 then which of the following statement is true?

Correct Answer: Option A - a is parallel to b.

If ∫f(x)dx = g(x) then ∫ x⁵ f(x³) dx

Correct Answer: Option B - (1/3)x³g(x³) − ∫ x²g(x³)dx + C.

lim (x⁴-1)/(x-1) as x->1 = lim (x³-k³)/(x²-k²) as x->k, then find k

Correct Answer: Option A - 8/3.

The graph of function f(x) = logₑ(x³ + √(x⁶ + 1)) is symmetric about:

Correct Answer: Option C - origin.

If the equation |x²- 6x + 8| = a has four real solution then find the value of a?

Correct Answer: Option C - a ∈ (0,1).

Largest value of cos² θ – 6 sin θ cos θ + 3 sin² θ + 2

Correct Answer: Option C - 4 + √10.

Given to events A and B such that odd in favour A are 2: 1 and odd in favour of A U B are 3: 1. Consistent with this information the smallest and largest value for the probability of event B are given by

Correct Answer: Option A - 1/12 ≤ P(B) ≤ 3/4.

If A and B are square matrices such that B = - A⁻¹ BA, then (A + B)² is

Correct Answer: Option B - A² + B².

A bag contain different kind of balls in which 5 yellow, 4 black & 3 green balls. If 3 balls are drawn at random then find the probability that no black ball is chosen

Correct Answer: Option A - 14/55.

Between any two real roots of the equation eˣ sinx = 1, the equation eˣ cosx = -1 has

Correct Answer: Option A - Atleast one root.

The maximum value of f(x) = (x − 1)²(x + 1)³ is equal to 2ᴾ3 /3125 then the ordered pair of (p, q) will be

Correct Answer: Option B - (7,3).

The coefficient of x⁵⁰ in the expression of (1 + x)¹⁰⁰⁰ + 2x(1 + x)⁹⁹⁹ + 3x²(1 + x)⁹⁹⁸ + ...... + 1001x¹⁰⁰⁰

Correct Answer: Option C - ¹⁰⁰²C₅₀.

Let a, b, c, d be no zero numbers. If the point of intersection of the line 4ax + 2ay + c = 0 & 5bx + 2by + d=0 lies in the fourth quadrant and is equidistance from the two are then

Correct Answer: Option C - 3bc - 2ad = 0.

The negation of ~S v (~R ∧ S) is equivalent to

Correct Answer: Option C - S ∧ R.

A point P in the first quadrant, lies on y² = 4ax, a > 0, and keeps a distance of 5a units from its focus. Which of the following points lies on the locus of P?

Correct Answer: Option B - (1,1).

If ∫ x sin x sec³ x dx = (1/2)[f(x) sec² x + g(x) (tanx)] + C, then which of the following is true?

Correct Answer: Option C - f(x) + g(x) = 0.

θ = cos⁻¹(3/√20) is the angle between a = î - 2xĵ + 2yk̂ & b = xî + ĵ + yk̂ then possible values at (x, y) that lie on the locus

Correct Answer: Option A - (0,1).

Let R be reflexive relation on the finite set a having 10 elements and if m is the number of ordered pair in R, then

Correct Answer: Option A - m ≥ 10.

If |x - 6| = |x² - 4x| - |x² - 5x + 6|, where x is a real variable

Correct Answer: Option B - x ∈ [2,3] U [6, ∞).

The range of values of θ in the interval (0, π) such that the points (3, 2) and (cos θ, sin θ) lie on the same sides of the line x + y − 1 = 0, is

Correct Answer: Option B - (0, π/2).

Which of the following number is the coefficient of x¹⁰⁰ in the expansion of logₑ((1+x)/(1+x²)), |x| < 1?

Correct Answer: Option A - 0.01.

A real valued function f is defined as f(x) = { x-1, if -1 ≤ x ≤ 0; |x-1|, if 0 ≤ x ≤ 2 }. Which of the following statement is FALSE?

Correct Answer: Option C - f(|x|) + |f(x)| = 1, if 0 ≤ x ≤ 1.

A line segment AB of length 10 meters is passing through the foot of the perpendicular of a pillar, which is standing at right angle to the ground. Tip of the pillar subtends angles tan⁻¹ 3 and tan⁻¹ 2 at A and B respectively. Which of the following choice represents the height of the pillar?

Correct Answer: Option C - 12 meter.

If a vector having magnitude of 5 units, makes equal angle with each of the three mutually perpendicular axes, then the sum of the magnitude of the projections on each of the axis is

Correct Answer: Option B - 5√3 unit.

Bag I contains 3 red, 4 black and 3 white balls and Bag II contains 2 red, 5 black and 2 white balls. One balls is transferred from Bag I to Bag II and then a ball is drawn from Bag II. The ball so drawn is found to be black in colour. Then the probability, that the transferred is red, is:

Correct Answer: Option B - 5/18.

Complete the series: 3, 10, 24, 45, 73, ......

Correct Answer: Option C - 108.

NIMCETNITs Consortium (rotating NIT each year)Postgraduate EntranceComputer Based Test

NIMCET 2023 Practice Questions & Answers

120 Questions·Free Practice·MCQ with Explanations

NIMCET 2023 Examination

Conducting Body: NIT Jamshedpur

The official 2023 entrance paper for MCA admissions across National Institutes of Technology (NITs) in India. This paper tests the candidate's aptitude in higher mathematics and logical reasoning.

Key Syllabus Coverage:

Math: Calculus, Vectors, Probability, and Algebra.
Computer: Binary arithmetic, Data representation, and Boolean algebra.
Reasoning: Puzzles, Blood relations, and Series completion.

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A circle touches the x-axis and also touches the circle with centre (0, 3) and radius 2. The locus of the centre of the circle is

a circle
an ellipse
a parabola
a hyperbola

View Answer & Explanation

Correct Answer: Option C -

a parabola

A computer producing factory has only two plants T₁ and T₂. Plant T₁ produces 20% and plant T₂ produces 80% of total computers produced. 7% of computers produced in the factory turn out to be defective. It is known that P (computer turns out to be defective given that it is produced in plant T₁) = 10P (computer turns out to be defective given that it is produced in plant T₂). where P(E) denotes the probability of an event E. A computer produced in the factory is randomly selected and it does not turn out to be defective. Then the probability that it is produced in plant T₂ is

36/73
47/75
78/93
79/83

View Answer & Explanation

Correct Answer: Option C -

78/93

The mean of 5 observation is 5 and their variance is 124. If three of the observations are 1,2 and 6; then the mean deviation from the mean of the data is:

View Answer & Explanation

Correct Answer: Option C -

2.8

The perimeter of a ∆ABC is 6 times the arithmetic mean of the sines of its angles. If the side a is 1, then the angle A is

π/6
π/3
π/2
π

View Answer & Explanation

Correct Answer: Option A -

π/6

In an examination of nine papers, a candidate has to pass in more papers than the number of papers in which he fails in order to be successful. The number of ways in which he can be unsuccessful is

255
256
128
9 × 8!

View Answer & Explanation

Correct Answer: Option B -

256

For a group of 100 candidates, the mean and standard deviation of scores were found to be 40 and 15 respectively. Later on, it was found that the scores 25 and 35 were misread as 52 and 53 respectively. Then the corrected mean and standard deviation corresponding to the corrected figures are

39.9, 14.79
39.5, 14
39.55, 14.97
40.19, 15.1

View Answer & Explanation

Correct Answer: Option C -

39.55, 14.97

Consider the following frequency distribution table. Class Interval: 10-20, 20-30, 30-40, 40-50, 50-60, 60-70, 70-80 Frequency: 180, f1, 34, 180, 136, f2, 50 If the total frequency is 685 & median is 42.6 then the values of f₁ and f₂ are

80, 25
83, 22
79, 26
82, 23

View Answer & Explanation

Correct Answer: Option D -

82, 23

If f(x) = lim (6^x - 3^x - 2^x + 1) / (loge 9(1-cos x)) as x->0 is a real number the lim f(x) as x->0 is

2
3
loge 2
loge 3

View Answer & Explanation

Correct Answer: Option C -

loge 2

The sum of infinite terms of decreasing GP is equal to the greatest value of the function f(x) = x³ + 3x – 9 in the interval [−2, 3] and difference between the first two terms is f'(0). Then the common ratio of the GP is

-2/3
2/3
+1/3
-1/3

View Answer & Explanation

Correct Answer: Option C -

+1/3

The value of ∫[from -π/3 to π/3] (x sinx) / cos²x dx is

(1/3)(4π + 1)
(4π/3) - 2 log tan(5π/12)
(π/3) + log tan(5π/12)
(4π/3) - log tan(5π/12)

View Answer & Explanation

Correct Answer: Option B -

(4π/3) - 2 log tan(5π/12)

NIMCET 2023 Practice Questions & Answers

NIMCET 2023 Examination

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