If the volume of the parallelepiped whose adjacent edges are ả = 2î + 3ĵ + 4k, b = î + aĵ + 2k, and ĉ = î + 2ĵ + ak is15, then a is equal to

Correct Answer: Option C - 9/2.

Let a be the distance between the lines -2x + y = 2 and 2x - y = 2, and b be the distance between the lines 4x – 3y= 5 and 6y - 8x = 1, then

Correct Answer: Option D - 11√2a = 40b.

If cosec θ - cotθ = 2, then the value of cosec θ is

Correct Answer: Option C - 4/5.

The solution of the equation 4 cos² x + 6 sin² x = 5 are

Correct Answer: Option A - x = nπ ± π/4.

The function f(x) = { ((1 + 2x)^(1/x), x ≠ 0), (e², x = 0) is

Correct Answer: Option A - Differentiable at x = 0.

Let a = 2î + 2ĵ + k and b be another vector such that ả. b = 14 and ả × b = 3î + ĵ − 8k the vector b =

Correct Answer: Option C - 5î + ĵ – 2k.

The first three moments of a distribution about 2 are 1, 16, -40 respectively. The mean and variance of the distribution are

Correct Answer: Option C - (3,15).

A survey is done among a population of 200 people who like either tea or coffee. It is found that 60% of the population like tea and 72% of the population like coffee. Let x be the number of people who like both tea & coffee. Let m ≤ x ≤ n, then choose the correct option.

Correct Answer: Option B - n - m = 28.

The value of cot(cosec⁻¹(5/3) + tan⁻¹(2/3)) is

Correct Answer: Option A - 6/17.

If 0 < P(A) < 1 and 0 < P(B) < 1 and P(A ∩ B) = P(A)P(B), then

Correct Answer: Option A - P(B|A) = P(B) – P(A).

Which of the following is NOT true?

Correct Answer: Option B - lim (1 / (x*e^(1/x))) = 0 as x→0+.

f(x) = x + |x| is continuous for

Correct Answer: Option B - x ∈ (-∞, ∞) − {0}.

If a1, a2,..., an are any real numbers and n is any positive integer, then

Correct Answer: Option D - None of the above.

If D = | 1 1 1 | | 1 2+x 1 | | 1 1 2+y | for x ≠ 0, y ≠ 0, then D is

Correct Answer: Option C - Divisible by (1 + x) and (1 + y).

Area of the parallelogram formed by the lines y = 4x, y = 4x + 1, x + y = 0 and x + y = 1

Correct Answer: Option A - 1/5.

A four-digit number is formed using the digits 1, 2, 3, 4, 5 without repetition. The probability that is divisible by 3 is

Correct Answer: Option B - 1/4.

For a ∈ R (the set of al real numbers), a ≠ 1. lim n→∞ ( (1ª+2ª+...+nª) / ((n+1)ᵃ⁻¹[(na+1)(na+2)...(na+n)]) ) = 1/60. Then one of the value of a is

Correct Answer: Option C - -15/2.

If ἄ = λî + j − 2k, b = î + λĵ − 2k, ĉ = î + ĵ + k and [a b c] = 7, then the values of λ are

Correct Answer: Option B - 6, -2.

The function f (x) = log(x + √x² + 1) is

Correct Answer: Option A - an even function.

The area enclosed within the curve |x| + |y|= 2 is

Correct Answer: Option A - 16 sq.unit.

If (x/a)² + (y/b)² = 1, (a > b) and x² - y² = c² cut at right angles, then

Correct Answer: Option A - a² + b² = 2c².

If α, β are the roots of x² − x − 1 = 0 and An = αⁿ + βⁿ, the Arithmetic mean of An-1 and An is

Correct Answer: Option B - An+1 / 2.

If a1, a2... an, are in Arithmetic Progression with common difference d, then the sum (sind) (coseca₁. cosec a₂ + cosec a₂.cosec a₃ + … + cosec an−₁. cosec an) is equal to

Correct Answer: Option A - cot a₁ - cot an.

Solutions of the equation tan⁻¹ √x² + x + sin⁻¹ √x² + x + 1 = π/2 are

Correct Answer: Option D - 0, -2.

A straight line through the point (4, 5) is such that its intercept between the axes is bisected at A, then its equation is

Correct Answer: Option B - 3x – 4y + 7=0.

The value of ∫ (x²-1)dx / (x³√2x⁴-2x²+1) is

Correct Answer: Option B - (1/2)√(2 + 1/x² + 1/x⁴) + C.

Coordinate of the focus of the parabola 4y² + 12x - 20y + 67 = 0 is

Correct Answer: Option B - (17/4, -5/2).

There are two circles in xy -plane whose equations are x² + y² - 2y = 0 and x² + y² – 2y -3 = 0. A point (x,y) is chosen at random inside the larger circle. Then the probability that the point has been taken from smaller circle is

Correct Answer: Option C - 1/2.

If x^m * y^n = (x + y)^(m+n), then dy/dx is

Correct Answer: Option D - x/y.

The value of 3^(3-log₃5) is

Correct Answer: Option D - 5/9.

There are two sets A and B with |A| = m and |B| = n. If |P(A)| - |P(B)| = 112 then choose the wrong option (where |A| denotes the cardinality of A, and P(A) denotes the power set of A)

Correct Answer: Option A - m + n = 11.

The eccentricity of an ellipse, with its center at the origin is 1/3. If one of the directrices is x = 9, then the equation of ellipse is:

Correct Answer: Option B - 8x² + 9y² = 72.

If the angle of elevation of the top of a hill from each of the vertices A, B and C of a horizontal triangle is α, then the height of the hill is

Correct Answer: Option A - 1/2 * b tan α sec B.

If (ả × b) x ĉ = ả × (b × ĉ), then

Correct Answer: Option C - a and ĉ are collinear.

Today is Wednesday. What would be the day after 61 days?

Correct Answer: Option B - Monday.

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

NIMCET 2022 Practice Questions & Answers

120 Questions·Free Practice·MCQ with Explanations

National Institute of Technology MCA Common Entrance Test (2022)

Conducting Body: NIT Jamshedpur

This exam serves as the gateway for admission into the Master of Computer Applications (MCA) program at participating NITs.

Paper Pattern:

Mathematics: 50 Questions (Highest Weightage)
Analytical Ability & Logical Reasoning: 40 Questions
Computer Awareness: 10 Questions
General English: 20 Questions

Note: This paper follows the standard marking scheme of +4 for correct answers and -1 for incorrect answers.

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Inverse of the function f(x) = (10X-10-x)/(10x+10-x) is

log10(2-x)
1/2 log10 ((1+x)/(1-x))
1/2log10(2x-1)
1/2log10 ((2x)/(2-x))

View Answer & Explanation

Correct Answer: Option B -

1/2 log10 ((1+x)/(1-x))

Let a, b, c be distinct non-negative numbers. If the vectors aî + aĵ + ck , î + k and cî + cĵ + bk lie in a plane, then c is

The Arithmetic Mean of a and b
The Geometric Mean of a and b
The Harmonic Mean of a and b
Equal to zero

View Answer & Explanation

Correct Answer: Option B -

The Geometric Mean of a and b

The correct expression for cos¯¹(−x) is

π/2 - cos-1 x
π − cos−1 x
π + cos−1 x
π/2 + cos-1 x

View Answer & Explanation

Correct Answer: Option B -

π − cos−1 x

Suppose that the temperature at a point (x, y), on a metal plate is T(x, y) = 4x² - 4xy + y². An ant, walking on the plate, traverses a circle of radius 5 centered at the origin. What is the highest temperature encountered by the ant?

View Answer & Explanation

Correct Answer: Option A -

125

The 10th and 50th percentiles of the observation 32, 49, 23, 29, 118 respectively are

21, 32
23, 32
23, 33
22, 31

View Answer & Explanation

Correct Answer: Option A -

21, 32

Angles of elevation of the top of a tower from three points (collinear) A, B and C on a road leading to the foot of the tower are 30°, 45° and 60° respectively. The ratio of AB and BC is

√3: 1
√3:2
1:2
2:3

View Answer & Explanation

Correct Answer: Option B -

√3:2

If the foci of the ellipse x²/25 + y²/b² = 1 and the hyperbola x²/144 - y²/81 = 1/25 are coincide, then the value of b² is

View Answer & Explanation

Correct Answer: Option B -

A particle is at rest at the origin. It moves along the x -axis with an acceleration x - x², where x is the distance of the particle at time t. The particle next comes to rest after it has covered a distance

1
1/2
2
None of these

View Answer & Explanation

Correct Answer: Option D -

None of these

If a < b then ∫[a to b] (|x - a| + |x - b|) dx is equal to

(b-a)² / 2
(b²-a²) / 2
(a³-b³) / 2
(b − a)²

View Answer & Explanation

Correct Answer: Option A -

(b-a)² / 2

The domain of the function f(x) = cos⁻¹(x) / [x] is

[-1,0)U{1}
[-1,1]
[-1,1)
None of the above

View Answer & Explanation

Correct Answer: Option C -

[-1,1)

NIMCET 2022 Practice Questions & Answers

National Institute of Technology MCA Common Entrance Test (2022)

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