Let $T:\mathbb{R}^4 \rightarrow \mathbb{R}^3$ be a linear transformation defined by $T(x_1,x_2,x_3,x_4)=C(x_1-x_2,;x_2-x_3,;x_3-x_4)$ Then which of the following is true?(i) $\dim(\ker T)=1$ if $C \ne 0$ (ii) $\dim(\ker T)=0$ if $C=0$ (iii) $\dim(\ker T)=1$ if $T$ is onto
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An integrating factor of
$\frac{dy}{dx} = \frac{1}{3x + y^2 + 2}$ is:
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The sampling scheme in which only first unit is selected randomly is known as:
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The solution of
$3\frac{\partial^2 z}{\partial x,\partial y} - 2\frac{\partial^2 z}{\partial y^2} - \frac{\partial z}{\…
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The solution of the differential equation
$y\sin 2x,dx - (y^2 + \cos^2 x),dy = 0$ is:
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The Laplace transform of $\sin \sqrt{x}$ is:
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Max $z = 6x_1 - x_2$Subject to$2x_1 - x_2 \le 2$$x_1 \le 3$$x_1, x_2 \ge 0$The above LPP has:
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A discrete random variable $X$ taking non-negative values has the following moment generating function
$M_X(t) = e^{2(…
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Let $X$ be a continuous random variable such that $E|X| < \infty$ and
$P\left(X \ge \frac12 + x\right) = P\left(X \le …
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Which of the following statements is not true?
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Let $X$ be a random variable having distribution function $F(x)$. Then which of the following statements may not be tru…
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Which of the following is a 2-dimensional subspace of $\mathbb{R}^3$?
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Let $X_1, X_2, … , X_n$ be i.i.d. random variables having pdf
$f(x) = (1/θ) e^{-x/θ},; 0 < x < ∞,; θ > 0$
The cdf of …
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$ \lim_{x→0} (cosec x)^{1/log x} $
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The ring $Z[\sqrt{3}] = {a + b\sqrt{3} ; a,b \in Z}$
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Which of the following is true?
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A box contains tickets numbered $1$ to $N$.
Let $X$ be the largest number drawn in $n$ random drawings with replacement…
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At point ‘A’ on a roller-coaster as shown in figure, a 150 kg car is traveling at 13 m/s and is 3 m above the ground. T…
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A particle of rest mass $m_0$ moves initially with velocity $0.6c$ and finally with $0.8c$. The product of initial and …
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A circular hole of radius 1 m is cut from a disc of radius 6 m. The centre of the hole is 3 m from the disc’s centre. T…
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In a series LCR circuit with $R=2.5,k\Omega$, $C=4,\mu F$, voltage across $R$ is 250 V at resonance. Find voltage acros…
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