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

1

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

Topic: NIMCET 2014

2

If the matrix $ \begin{bmatrix} -1 & 3 & 2 \\ 1& k &-3 \\ 1 & 4 & 5\\ \end{bmatrix}$ has an …

Topic: NIMCET 2014

3

In a group of 200 students, the mean and the standard deviation of scores were found to be 40 and 15, respectively. Lat…

Topic: NIMCET 2014

4

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

Topic: NIMCET 2014

5

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

Topic: NIMCET 2014

6

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

Topic: NIMCET 2014

7

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\v…

Topic: NIMCET 2014

8

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

Topic: NIMCET 2014

9

Constant forces $\vec{P}= 2\hat{i} - 5\hat{j} + 6\hat{k} $ and $\vec{Q}= -\hat{i} + 2\hat{j}- \hat{k}$&n…

Topic: NIMCET 2014

10

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 …

Topic: NIMCET 2014

1

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

Topic: NIMCET 2014

2

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

Topic: NIMCET 2014

3

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

Topic: NIMCET 2014

4

Suppose, the system of linear equations -2x + y + z = l x - 2y + z = m x + y - 2z = n is such that …

Topic: NIMCET 2014

5

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 $\hat{N}$ perpend…

Topic: NIMCET 2014

6

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

Topic: NIMCET 2014

7

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,…

Topic: NIMCET 2014

8

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}=11…

Topic: NIMCET 2014

9

From three collinear points A, B and C on a level ground, which are on the same side of a tower, the angles of elevatio…

Topic: NIMCET 2014

10

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

Topic: NIMCET 2014