MCA NIMCET 2014 Previous Year Question Paper and Solution with PDF

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MCA NIMCET Previous Year Questions (PYQs)

MCA NIMCET 2014 PYQ

Qus : 1MCA NIMCET PYQ 2014

A password consists of two alphabets from English followed by three numbers chosen from 0 to 3. If repetitions are allowed, the number of different passwords is

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MCA NIMCET Previous Year PYQMCA NIMCET NIMCET 2014 PYQ

Solution

Qus : 2MCA NIMCET PYQ 2014

An equilateral triangle is inscribed in the parabola $y^{2} = 4ax$, such that one of the vertices of the triangle coincides with the vertex of the parabola. The length of the side of the triangle is:

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MCA NIMCET Previous Year PYQMCA NIMCET NIMCET 2014 PYQ

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Qus : 3MCA NIMCET PYQ 2014

A chain of video stores sells three different brands of DVD players. Of its DVD player sales, 50% are brand 1, 30% are brand 2 and 20% are brand 3. Each manufacturer offers one year warranty on parts and labor. It is known that 25% of brand 1 DVD players require warranty repair work whereas the corresponding percentage for brands 2 and 3 are 20% and 10% respectively. The probability that a randomly selected purchaser has a DVD player that will need repair while under warranty, is:

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Qus : 4MCA NIMCET PYQ 2014

The locus of the intersection of the two lines $\sqrt{3} x-y=4k\sqrt{3}$ and $k(\sqrt{3}x+y)=4\sqrt{3}$, for different values of k, is a hyperbola. The eccentricity of the hyperbola is:

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MCA NIMCET Previous Year PYQMCA NIMCET NIMCET 2014 PYQ

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Qus : 5MCA NIMCET PYQ 2014

Constant forces $\vec{P}= 2\hat{i} - 5\hat{j} + 6\hat{k} $ and $\vec{Q}= -\hat{i} + 2\hat{j}- \hat{k}$ act on a particle. The work done when the particle is displaced from A whose position vector is $4\hat{i} - 3\hat{j} - 2\hat{k} $, to B whose position vector is $6\hat{i} + \hat{j} - 3k\hat{k}$ , is:

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MCA NIMCET Previous Year PYQMCA NIMCET NIMCET 2014 PYQ

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Qus : 6MCA NIMCET PYQ 2014

The value of $\int \sqrt{x} e^{\sqrt{x}} dx$ is equal to:

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MCA NIMCET Previous Year PYQMCA NIMCET NIMCET 2014 PYQ

Solution

Qus : 7MCA NIMCET PYQ 2014

For the vectors $\vec{a}=-4\hat{i}+2\hat{j}, \vec{b}=2\hat{i}+\hat{j}$ and $\vec{c}=2\hat{i}+3\hat{j}$, if $\vec{c}=m\vec{a}+n\vec{b}$ then the value of m + n is

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MCA NIMCET Previous Year PYQMCA NIMCET NIMCET 2014 PYQ

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Qus : 8MCA NIMCET PYQ 2014

The value of $\int_{0}^{\pi/4} log(1+tanx)dx$ is equal to:

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MCA NIMCET Previous Year PYQMCA NIMCET NIMCET 2014 PYQ

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Qus : 9MCA NIMCET PYQ 2014

The number of ways in which 5 days can be chosen in each of the 12 months of a non-leap year, is:

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MCA NIMCET Previous Year PYQMCA NIMCET NIMCET 2014 PYQ

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Qus : 10MCA NIMCET PYQ 2014

If [x] represents the greatest integer not exceeding x, then $\int_{0}^{9} [x] dx $ is

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Qus : 11MCA NIMCET PYQ 2014

In a group of 200 students, the mean and the standard deviation of scores were found to be 40 and 15, respectively. Later on it was found that the two scores 43 and 35 were misread as 34 and 53, respectively. The corrected mean of scores is:

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MCA NIMCET Previous Year PYQMCA NIMCET NIMCET 2014 PYQ

Solution

Given: $n=200$, reported mean $=40$ ⇒ reported total $$S_{\text{reported}}=200\times 40=8000.$$

Two scores were misread: true $(43,35)$ but used as $(34,53)$.

Correct the total: $$S_{\text{correct}}=S_{\text{reported}}-\big(34+53\big)+\big(43+35\big) =8000-87+78=7991.$$

Corrected mean: $$\bar{x}_{\text{correct}}=\frac{S_{\text{correct}}}{n} =\frac{7991}{200}=39.955\;\approx\;39.96.$$

Answer: $39.955$ (≈ $39.96$).

Qus : 12MCA NIMCET PYQ 2014

If the matrix $ \begin{bmatrix} -1 & 3 & 2 \\ 1& k &-3 \\ 1 & 4 & 5\\ \end{bmatrix}$ has an inverse matrix, then the value of K is:

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Solution

Qus : 13MCA NIMCET PYQ 2014

The mean deviation from the mean of the AP a, a + d, a + 2d, ..., a + 2nd, is:

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MCA NIMCET Previous Year PYQMCA NIMCET NIMCET 2014 PYQ

Solution

AP: $a,\,a+d,\,a+2d,\,\dots,\,a+2nd$ has $2n+1$ terms. The mean is the middle term $a+nd$.

Mean deviation from the mean (MD): average of absolute deviations from $a+nd$.

Symmetry gives pairs at distances $kd$ for $k=1,\dots,n$. Hence

$$\text{MD}=\frac{1}{2n+1}\Big[2\sum_{k=1}^{n} kd\Big] =\frac{2d}{2n+1}\cdot\frac{n(n+1)}{2} =\frac{d\,n(n+1)}{2n+1}.$$

Answer: $\displaystyle \boxed{\frac{d\,n(n+1)}{2n+1}}$.

Qus : 14MCA NIMCET PYQ 2014

If (x₀, y₀) is the solution of the equations (2x)^ln2 = (3y)^ln3 and 3^lnx = 2^lny, then x₀ is:

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Solution

Qus : 15MCA NIMCET PYQ 2014

The value of tan 1° tan 2° tan 3° ... tan 89° is:

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MCA NIMCET Previous Year PYQMCA NIMCET NIMCET 2014 PYQ

Solution

Qus : 16MCA NIMCET PYQ 2014

If $\alpha$ and $\beta$ are the roots of the equation $2x^{2}+ 2px + p^{2} = 0$, where $p$ is a non-zero real number, and $\alpha^{4}$ and $\beta^{4}$ are the roots of $x^{2} - rx + s = 0$, then the roots of $2x^{2} - 4p^{2}x + 4p^{4} - 2r = 0$ are:

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MCA NIMCET Previous Year PYQMCA NIMCET NIMCET 2014 PYQ

Solution

Qus : 17MCA NIMCET PYQ 2014

The number of ways to arrange the letters of the English alphabet, so that there are exactly 5 letters between a and b, is:

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MCA NIMCET Previous Year PYQMCA NIMCET NIMCET 2014 PYQ

Solution

Qus : 18MCA NIMCET PYQ 2014

Suppose, the system of linear equations

-2x + y + z = l

x - 2y + z = m

x + y - 2z = n

is such that l + m + n = 0, then the system has:

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MCA NIMCET Previous Year PYQMCA NIMCET NIMCET 2014 PYQ

Solution

Qus : 19MCA NIMCET PYQ 2014

If $\vec{A}=4\hat{i}+3\hat{j}+\hat{k}$ and $\vec{B}=2\hat{i}-\hat{j}+2\hat{k}$ , then the unit vector $\hat{N}$ perpendicular to the vectors $\vec{A}$ and $\vec{B}$ ,such that $\vec{A}, \vec{B}$ , and $\hat{N}$ form a right handed system, is:

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Solution

Qus : 20MCA NIMCET PYQ 2014

The value of $\int \frac{(x+1)}{x(xe^{x}+1)} dx$ is equal to

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MCA NIMCET Previous Year PYQMCA NIMCET NIMCET 2014 PYQ

Solution

Qus : 21MCA NIMCET PYQ 2014

The sum of two vectors $\vec{a}$ and $\vec{b}$ is a vector $\vec{c}$ such that $|\vec{a}|=|\vec{b}|=|\vec{c}|=2$. Then, the magnitude of $\vec{a}-\vec{b}$ is equal to:

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Solution

Qus : 22MCA NIMCET PYQ 2014

If x and y are positive real numbers satisfying the system of equations $x^{2}+y\sqrt{xy}=336$ and $y^{2}+x\sqrt{xy}=112$, then x + y is:

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MCA NIMCET Previous Year PYQMCA NIMCET NIMCET 2014 PYQ

Solution

Qus : 23MCA NIMCET PYQ 2014

From three collinear points A, B and C on a level ground, which are on the same side of a tower, the angles of elevation of the top of the tower are 30°, 45° and 60° respectively. If BC = 60 m, then AB is:

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MCA NIMCET Previous Year PYQMCA NIMCET NIMCET 2014 PYQ

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Qus : 24MCA NIMCET PYQ 2014

If $x = 1$ is the directrix of the parabola $y^{2} = kx - 8$, then k is:

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MCA NIMCET Previous Year PYQMCA NIMCET NIMCET 2014 PYQ

Solution

Qus : 25MCA NIMCET PYQ 2014

If $sin x + a cos x = b$, then $|a sin x - cos x|$ is:

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MCA NIMCET Previous Year PYQMCA NIMCET NIMCET 2014 PYQ

Solution

Qus : 26MCA NIMCET PYQ 2014

A condition that $x^{3} + ax^{2} + bx + c$ may have no extremum is

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MCA NIMCET Previous Year PYQMCA NIMCET NIMCET 2014 PYQ

Solution

Qus : 27MCA NIMCET PYQ 2014

If n and r are integers such that 1 ≤ r ≤ n, then the value of n ^n-1C_r-1is

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MCA NIMCET Previous Year PYQMCA NIMCET NIMCET 2014 PYQ

Solution

Qus : 28MCA NIMCET PYQ 2014

If the foci of the ellipse $b^{2}x^{2}+16y^{2}=16b^{2}$ and the hyperbola $81x^{2}-144y^{2}=\frac{81 \times 144}{25}$ coincide, then the value of $b$, is

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Solution

Qus : 29MCA NIMCET PYQ 2014

There are 8 students appearing in an examination of which 3 have to appear in Mathematics paper and the remaining 5 in different subjects. Then, the number of ways they can be made to sit in a row, if the candidates in Mathematics cannot sit next to each other is

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Solution

Qus : 30MCA NIMCET PYQ 2014

If $x$ is so small that $x^{2}$ and higher powers of $x$ can be neglected, then $\frac{(9+2x)^{1/2}(3+4x)}{(1-x)^{1/5}}$ is approximately equal to

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MCA NIMCET Previous Year PYQMCA NIMCET NIMCET 2014 PYQ

Solution

Qus : 31MCA NIMCET PYQ 2014

If the sets A and B are defined as A = {(x, y) | y = 1 / x, 0 ≠ x ∈ R}, B = {(x, y)|y = -x ∈ R} then

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MCA NIMCET Previous Year PYQMCA NIMCET NIMCET 2014 PYQ

Solution

Sets: $A=\{(x,y)\mid y=\tfrac{1}{x},\ x\in\mathbb{R}\setminus\{0\}\}$, $B=\{(x,y)\mid y=-x,\ x\in\mathbb{R}\}$.

Intersection: Solve $ \frac{1}{x} = -x $ with $x\neq 0$. \[ \frac{1}{x} = -x \;\Longrightarrow\; 1 = -x^2 \;\Longrightarrow\; x^2 = -1, \] which has no real solution.

Conclusion: $A \cap B = \varnothing$ (they are disjoint in $\mathbb{R}^2$).

Note: Over complex numbers, the intersection would be at $x=\pm i$, but for real $x$, there is none.

Qus : 32MCA NIMCET PYQ 2014

If A, B and C is three angles of a ΔABC, whose area is Δ. Let a, b and c be the sides opposite to the angles A, B and C respectively. Is $s=\frac{a+b+c}{2}=6$, then the product $\frac{1}{3} s^{2} (s-a)(s-b)(s-c)$ is equal to

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MCA NIMCET Previous Year PYQMCA NIMCET NIMCET 2014 PYQ

Solution

Qus : 33MCA NIMCET PYQ 2014

A normal to the curve $x^{2} = 4y$ passes through the point (1, 2). The distance of the origin from the normal is

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Qus : 34MCA NIMCET PYQ 2014

Suppose r integers, 0 < r < 10, are chosen from (0, 1, 2, ...,9) at random and with replacement. The probability that no two are equal, is

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Qus : 35MCA NIMCET PYQ 2014

If $x^{2} + 2ax + 10 - 3a > 0$ for all x ∈ R, then

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MCA NIMCET Previous Year PYQMCA NIMCET NIMCET 2014 PYQ

Solution

Qus : 36MCA NIMCET PYQ 2014

A box contains 3 coins, one coin is fair, one coin is two headed and one coin is weighted, so that the probability of heads appearing is $\frac{1}{3}$ . A coin is selected at random and tossed, then the probability that head appears is

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MCA NIMCET Previous Year PYQMCA NIMCET NIMCET 2014 PYQ

Solution

Qus : 37MCA NIMCET PYQ 2014

If a vector $\vec{a}$ makes an equal angle with the coordinate axes and has magnitude 3, then the angle between $\vec{a}$ and each of the three coordinate axes is

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MCA NIMCET Previous Year PYQMCA NIMCET NIMCET 2014 PYQ

Solution

Qus : 38MCA NIMCET PYQ 2014

If $f(x)=\left\{\begin{matrix} \frac{sin[x]}{[x]} &, [x]\ne0 \\ 0 &, [x]=0 \end{matrix}\right.$ , where [x] is the largest integer but not larger than x, then $\lim_{x\to0}f(x)$ is

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MCA NIMCET Previous Year PYQMCA NIMCET NIMCET 2014 PYQ

Solution

Qus : 39MCA NIMCET PYQ 2014

If tan A - tan B = x and cot B - cot A = y, then cot (A - B) is equal to

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MCA NIMCET Previous Year PYQMCA NIMCET NIMCET 2014 PYQ

Solution

Qus : 40MCA NIMCET PYQ 2014

If $a = log_{12}^{18}$, $b = log_{24}^{54}$, then $ab + 5(a - b)$ is

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MCA NIMCET Previous Year PYQMCA NIMCET NIMCET 2014 PYQ

Solution

Qus : 41MCA NIMCET PYQ 2014

A student takes a quiz consisting of 5 multiple choice questions. Each question has 4 possible answers. If a student is guessing the answer at random and answer to different are independent, then the probability of atleast one correct answer is

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MCA NIMCET Previous Year PYQMCA NIMCET NIMCET 2014 PYQ

Solution

Qus : 42MCA NIMCET PYQ 2014

The condition that the line lx + my + n = 0 becomes a tangent to the ellipse $\frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}=1$ , is

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MCA NIMCET Previous Year PYQMCA NIMCET NIMCET 2014 PYQ

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Qus : 43MCA NIMCET PYQ 2014

The value of sin 20° sin 40° sin 80° is

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MCA NIMCET Previous Year PYQMCA NIMCET NIMCET 2014 PYQ

Solution

Qus : 44MCA NIMCET PYQ 2014

Two non-negative numbers whose sum is 9 and the product of the one number and square of the other number is maximum, are

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MCA NIMCET Previous Year PYQMCA NIMCET NIMCET 2014 PYQ

Solution

Qus : 45MCA NIMCET PYQ 2014

The median AD of ΔABC is bisected at E and BE is produced to meet the side AC at F. Then, AF ∶ FC is

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Solution

Qus : 46MCA NIMCET PYQ 2014

If PQ is a double ordinate of the hyperbola $\frac{x^{2}}{a^{2}}-\frac{y^{2}}{b^{2}}=1$ such that OPQ is an equilateral triangle, where O is the centre of the hyperbola, then which of the following is true?

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MCA NIMCET Previous Year PYQMCA NIMCET NIMCET 2014 PYQ

Solution

Qus : 47MCA NIMCET PYQ 2014

In ΔABC, if a = 2, b = 4 and ∠C = 60°, then A and B are respectively equal to

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MCA NIMCET Previous Year PYQMCA NIMCET NIMCET 2014 PYQ

Solution

Qus : 48MCA NIMCET PYQ 2014

If $ \int \frac{xe^{x}}{\sqrt{1+e^{x}}}=f(x)\sqrt{1+e^{x}}-2log \frac{\sqrt{1+e^{x}}-1}{\sqrt{1+e^{x}}+1}+C$ then $f(x)$ is

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MCA NIMCET Previous Year PYQMCA NIMCET NIMCET 2014 PYQ

Solution

Qus : 49MCA NIMCET PYQ 2014

The average marks of boys in a class is 52 and that of girls is 42. The average marks of boys and girls combined is 50. The percentage of boys in the class is

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MCA NIMCET Previous Year PYQMCA NIMCET NIMCET 2014 PYQ

Solution

Given averages: Boys = 52, Girls = 42, Combined = 50.

Let the proportion of boys be $p$ (so girls = $1-p$). Weighted mean gives: $$52p + 42(1-p) = 50$$ $$52p + 42 - 42p = 50 \Rightarrow 10p = 8 \Rightarrow p = 0.8.$$

Percentage of boys $= 0.8 \times 100\% = \boxed{80\%}$.

Qus : 50MCA NIMCET PYQ 2014

How many even integers between 4000 and 7000 have four different digits?

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MCA NIMCET Previous Year PYQMCA NIMCET NIMCET 2014 PYQ

Solution

1: Thousands digit

The number is 4-digit and must be between 4000 and 7000.
So the thousands digit can be: 4, 5, or 6.

Step 2: Units digit

The number must be even, so the units digit must be one of {0, 2, 4, 6, 8}.

3: Count cases

Case 1: Thousands digit = 4
Units digit ≠ 4 → possible units = {0, 2, 6, 8} → 4 choices.
Hundreds digit = 8 choices, Tens digit = 7 choices.
Total = 4 × 8 × 7 = 224.

Case 2: Thousands digit = 5
Units digit can be {0, 2, 4, 6, 8} → 5 choices.
Hundreds digit = 8 choices, Tens digit = 7 choices.
Total = 5 × 8 × 7 = 280.

Case 3: Thousands digit = 6
Units digit ≠ 6 → possible units = {0, 2, 4, 8} → 4 choices.
Hundreds digit = 8 choices, Tens digit = 7 choices.
Total = 4 × 8 × 7 = 224.

4: Add results

Total = 224 + 280 + 224 = 728.

Final Answer:

There are 728 such even integers.

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1: Thousands digit

Step 2: Units digit

3: Count cases

4: Add results

Final Answer:

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