Question
If $|(2 \hat{i}+\hat{j}-\hat{k}) \times(5 \lambda-6 i+j)|=17$ then the value of $\lambda$ is
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The function$\text{f(x)}=1+|\cos\text{x}|$ is:
→- Continuous no where.
- Continuous everywhere.
- Not differentiable at x = 0
- Not differentiable at $\text{x}=\text{n}\pi,\text{n}\in\text{Z}.$
Choose the correct answer from the given four options.
If $\vec{\text{a}},\vec{\text{b}},\vec{\text{c}}$ are unit vectors such that $\vec{\text{a}}+\vec{\text{b}}+\vec{\text{c}}=0,$ then the value of $\vec{\text{a}}\cdot\vec{\text{b}}+\vec{\text{b}}\cdot\vec{\text{c}}+\vec{\text{c}}\cdot\vec{\text{a}}$ is:
→If $\vec{\text{a}},\vec{\text{b}},\vec{\text{c}}$ are unit vectors such that $\vec{\text{a}}+\vec{\text{b}}+\vec{\text{c}}=0,$ then the value of $\vec{\text{a}}\cdot\vec{\text{b}}+\vec{\text{b}}\cdot\vec{\text{c}}+\vec{\text{c}}\cdot\vec{\text{a}}$ is:
- 1.
- 3.
- $-\frac{3}{2}.$
- None of these.
The optimal value of the objective function is attained at the points:
- On X - axis
- On Y - axis
- Corner points of the feasible region
- None of these
Mark the correct alternative in the following question:The probability of guessing correctly at least 8 out of 10 answers of a true false type examination is:
→- $\frac{7}{64}$
- $\frac{7}{128}$
- $\frac{45}{1024}$
- $\frac{7}{41}$
The value of k which makes $\text{f(x)}=\begin{cases}\sin\frac{1}{\text{x}},&\text{x}\neq0\\\text{k},&\text{x}=0\end{cases}$ continuous at x = 0, is:
→- 8
- 1
- -1
- none of these
The points $D, E$ and $F$ are the mid-points of $A B, B C$ and $C A$ respectively.
What is the area of the shaded region?
→What is the area of the shaded region?
Choose the correct option from given four options:
$\frac{\text{dx}}{\sin(\text{x}-\text{a})\sin(\text{x}-\text{b})}$ is equal to:
→$\frac{\text{dx}}{\sin(\text{x}-\text{a})\sin(\text{x}-\text{b})}$ is equal to:
- $\sin(\text{b}-\text{a)}\log\Big|\frac{\sin(\text{x}-\text{b})}{\sin(\text{x}-\text{a})}\Big|+\text{C}$
- $\text{cosec}(\text{b}-\text{a)}\log\Big|\frac{\sin(\text{x}-\text{a})}{\sin(\text{x}-\text{b})}\Big|+\text{C}$
- $\text{cosec}(\text{b}-\text{a)}\log\Big|\frac{\sin(\text{x}-\text{b})}{\sin(\text{x}-\text{a})}\Big|+\text{C}$
- $\sin(\text{b}-\text{a)}\log\Big|\frac{\sin(\text{x}-\text{b})}{\sin(\text{x}-\text{a})}\Big|+\text{C}$
Choose the correct answer from the given four options.
You are given that A and B are two events such that $\text{P}(\text{B})=\frac{3}{5},\text{P}\Big(\frac{\text{A}}{\text{B}}\Big)=\frac{1}{2}$ and $\text{P}(\text{A}\cup\text{B})=\frac{4}{5},$ then P(A) equals:
→You are given that A and B are two events such that $\text{P}(\text{B})=\frac{3}{5},\text{P}\Big(\frac{\text{A}}{\text{B}}\Big)=\frac{1}{2}$ and $\text{P}(\text{A}\cup\text{B})=\frac{4}{5},$ then P(A) equals:
- $\frac{3}{10}$
- $\frac{1}{5}$
- $\frac{1}{2}$
- $\frac{3}{5}$
A ladder, 5 meter long, standing on a horizontal floor, leans against a vertical wall. If the top of the ladder slides downwards at the rate of 10cm/ sec, then the rate at which the angle between the floor and the ladder is decreasing when lower end of ladder is 2 metres from the wall is:
The corner points of the feasible region determined by the system of linear constraints are (0, 10), (5, 5), (15, 15), (0, 20). Let Z = px + qy, where p, q > 0. Condition on p and q so that the maximum of Z occurs at both the points (15, 15) and (0, 20) is Maximum of Z occurs at:
- (5, 0)
- (6, 5)
- (6, 8)
- (4, 10)