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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The number of ways to arrange the letters of the English alphabet, so that there are exactly 5 letters between a and b,…
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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…
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The value of tan 1° tan 2° tan 3° ... tan 89° is:
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If (x0, y0) is the solution of the equations (2x)ln2 = (3y)ln3 and 3lnx = 2lny, then x0 is:
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The mean deviation from the mean of the AP a, a + d, a + 2d, ..., a + 2nd, is:
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If the matrix $ \begin{bmatrix}
-1 & 3 & 2 \\
1& k &-3 \\
1 & 4 & 5\\
\end{bmatrix}$ has an …
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In a group of 200 students, the mean and the standard deviation of scores were found to be 40 and 15,
respectively. Lat…
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If [x] represents the greatest integer not exceeding x, then $\int_{0}^{9} [x] dx $ is
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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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The value of $\int_{0}^{\pi/4} log(1+tanx)dx$ is equal to:
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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…
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The value of $\int \frac{(x+1)}{x(xe^{x}+1)} dx$ is equal to
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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,…
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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…
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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…
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If $x = 1$ is the directrix of the parabola $y^{2} = kx - 8$, then k is:
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If $sin x + a cos x = b$, then $|a sin x - cos x|$ is:
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A condition that $x^{3} + ax^{2} + bx + c$ may have no extremum is
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If n and r are integers such that 1 ≤ r ≤ n, then the value of n n-1Cr-1is
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If the foci of the ellipse $b^{2}x^{2}+16y^{2}=16b^{2}$ and the hyperbola $81x^{2}-144y^{2}=\frac{81 \times 144}{25}$ c…
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