Find the values of x for which | ll 3 & x x & 1 |= | ll 3 & 2 4 & 1 |.

(d) : We have, | ll 3 & x x & 1 |= | ll 3 & 2 4 & 1 | 3-x^2=3-8 x^2=8 . Hence, x= 2 2

Find the values of x for which | ll 3 & x x & 1 |=

If $\text{f(x)}=|\log_{10}\text{x}|\text{fx}=\log_{10}\text{x},$ then at x = 1:

f(x) is continuous and $\text{f}'(1^+)=\log_{10}\text{e}$
f(x) is continuous and $\text{f}'(1^+)=\log_{10}\text{e}$
f(x) is continuous and $\text{f}'(1^-)=-\log_{10}\text{e}$
f(x) is continuous and $\text{f}'(1^-)=-\log_{10}\text{e}$

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The derivative of $\cos ^{-1}\left(2 x^2-1\right)$ w.r.t. $\cos ^{-1} x$ is

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The value of $\int e^{5 x-3} d x$ is

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If $|\vec{a}|=4$ and $-3 \leq \lambda \leq 2$, then the range of $|\lambda \vec{a}|$ is

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The slope of the tangent to the curve $x = t^2 + 3t - 8, y = 2t^2 - 2t - 5$ at the point $(2, -1)$ is:

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Choose the correct answer from the given four options.
A and B are events such that P(A) = 0.4, P(B) = 0.3 and $\text{P}(\text{A}\cup\text{B})=0.5,$ Then $\text{P}(\text{B}'\cap\text{A})$ equals:

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The system of equations:
x + y + z = 5
x + 2y + 3z = 9
x + 3y + λz = µ
has a unique solution, if

λ = 5, µ = 13
λ ≠ 5
λ = 5, µ ≠ 13
µ ≠ 13

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Let a, b and c be vectors with magnitudes 3, 4 and 5 respectively and a + b + c = 0, then the values of a.b + b.c + c.a is:

47
25
50
-25

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If $\text{A}=\begin{bmatrix} \text{a} & 0 & 0 \\ 0 & \text{a} & 0 \\ 0 & 0 &\text{a} \end{bmatrix},$ then the value of $|$adj $A|$ is$:$

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If the line $\frac{x-2}{2 k}=\frac{y-3}{3}=\frac{z+2}{-1}$ and $\frac{x-2}{8}=\frac{y-3}{6}=\frac{z+2}{-2}$ are parallel, value of k is

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