If \[a=\frac{1}{\sqrt{10}}(3\hat{i}+\hat{k})\] and \[b=\frac{1}{7}(2\hat{i}+3\hat{j}-6\hat{k}),\] then the value of\[(2a-b)\].\[\{(a\times b)\times (a+2b)\}\]is ______.
Find the values of x for which the angle between the vectors \[\overrightarrow{a}=2{{x}^{2}}\,\hat{i}+4\,x\hat{j}+\hat{k}\] and \[\overrightarrow{b}=7\,\hat{i}-2\hat{j}+x\hat{k}\] is Obtuse.
If \[\overrightarrow{a}=\hat{i}+\hat{j}+\hat{k},\] \[\overrightarrow{c}=\hat{j}-\hat{k}\] are given vectors, then find a vector \[\overrightarrow{b}\] satisfying the equations \[\overrightarrow{a}\times \overrightarrow{b}=\overrightarrow{c}\]and \[\overrightarrow{a}\times \overrightarrow{b}=3\].
If \[\overrightarrow{p},\] \[\overrightarrow{q}\] and \[\overrightarrow{r}\] are perpendicular to \[\overrightarrow{q}+\overrightarrow{r},\] \[\overrightarrow{r}+\overrightarrow{p}\] and \[\overrightarrow{p}+\overrightarrow{q},\] respectively and if \[|\overrightarrow{p}+\overrightarrow{q}|\,\,=6,\] \[|\overrightarrow{q}+\overrightarrow{r}|\,\,=4\sqrt{3}\,\]and \[|\overrightarrow{r}+\overrightarrow{p}|\,\,=4\] then \[|\overrightarrow{p}+\overrightarrow{q}+\overrightarrow{r}|\]is _________.
If the angle \[\theta \] between the line \[\frac{x+1}{1}=\frac{y-1}{2}=\frac{z-2}{2}\] and the plane \[2x-y+\sqrt{\lambda }\,z+4=0\] is such that\[\sin \theta =\frac{1}{3}\]. Then, value of \[\lambda \] is_______.
If\[\int{{{\sin }^{5/2}}x{{\cos }^{3}}x\,\,dx=2{{\sin }^{A/2}}x\left[ \frac{1}{B}-\frac{1}{C}{{\sin }^{2}}x \right]}+c,\]then the value of \[\left( A+B \right)-C\] is equal to
Given that the sum of two non-negative quantities is 200, the probability that their product is not less than \[\frac{3}{4}\] times their greatest product value is ______.
A clerk was asked to mail three report cards to three students. He addresses three envelopes but unfortunately paid no attention to which report card should be put in which envelope. What is the probability that exactly one of the students received his or her own card?
A card from a pack of 52 cards is lost. From the remaining cards of the pack, two cards are drawn and are found to be diamonds. The probability of the lost card being a diamond is _______.
Consider the linear programming problem. Maximise \[Z=4x+y,\] Subject of the constraints \[x+y\le 50,\] \[x+y\ge 100\]and\[x,\]\[y\ge 0\]. Then find the maximum value of Z.
Direction: Each of the questions below consists of, a question and three statements numbered I, II and III underneath. You have to decide the data provided in which of the statements are sufficient to answer the question.
Choose your answer accordingly.
Among A, B, C, D and E who scored the lowest?
I. B scored lower than only E.
II. A scored higher than D and C.
III. A scored lower than B.
A)
Only I and II
doneclear
B)
Only II and III
doneclear
C)
Only I and III
doneclear
D)
All I, II and III
doneclear
E)
The question cannot be answered even with all the three statements together
Direction: Each of the questions below consists of, a question and three statements numbered I, II and III underneath. You have to decide the data provided in which of the statements are sufficient to answer the question.
Choose your answer accordingly.
How many sons does P have?
I. F is sister of B.
II. B is brother of D and E.
III. P's wife K is mother of D.
A)
All I, II and III
doneclear
B)
Only I and II
doneclear
C)
Only II and III
doneclear
D)
Only I and III
doneclear
E)
The question cannot be answered even with all the three statements together
Direction: Each of the questions below consists of, a question and three statements numbered I, II and III underneath. You have to decide the data provided in which of the statements are sufficient to answer the question.
Choose your answer accordingly.
How is D related to R?
I. D's brother is the only son of R's father.
II. D's sister is daughter of J.
III. D and B are siblings.
A)
Only I
doneclear
B)
Only I and II
doneclear
C)
Only II
doneclear
D)
Only II and III
doneclear
E)
The question cannot be answered even with all the three statements together
Direction: Each of the questions below consists of, a question and three statements numbered I, II and III underneath. You have to decide the data provided in which of the statements are sufficient to answer the question.
Choose your answer accordingly.
Village F is in which direction of village M?
I. Village H is to the West of village D which is to the South of village F.
Direction: Each of the questions below consists of, a question and three statements numbered I, II and III underneath. You have to decide the data provided in which of the statements are sufficient to answer the question.
Choose your answer accordingly.
How is 'gone' written in a code language?
I. 'gone are the days' is written as 'da na ta pi' in that code language.
II. 'few days are there' is written as 'ka ta ha da' in that code language.
III. 'the new book is good' is written as 'ja sa pi ra ni' in that code language.
In a certain code 'hua pih uf pu' means 'he is very intelligent', 'pih hua kup kit' means 'she is very fair', 'luck uf hua' means 'Jai is intelligent' and 'uf kit pod' means 'fair and intelligent'. What code stands for Jai?
Direction: In each of the questions below are given three statements followed by three conclusions numbered I, II and III. You have to take the given statements to be true even if they seem to be at variance from commonly known facts. Read all the conclusions and then decide which of the given conclusions logically follows from the given statements disregarding commonly known facts.
Direction: In each of the questions below are given three statements followed by three conclusions numbered I, II and III. You have to take the given statements to be true even if they seem to be at variance from commonly known facts. Read all the conclusions and then decide which of the given conclusions logically follows from the given statements disregarding commonly known facts.
In the following diagram, parallelogram represents women, triangle represents sub-inspectors of police and circle represents graduate. Which numbered area represents women who are graduates and sub-inspectors of police?
A and B are two students. Their chances of solving a problem correctly are \[\frac{1}{3}and\frac{1}{4},\] respectively. If the probability of their making a common error is \[\frac{1}{20}\] and they obtain the same answer, then the probability of there answer to be correct is ________.
If \[f(x)=\left| \begin{matrix} \cos x & x & 1 \\ 2\sin x & {{x}^{2}} & 2x \\ \tan x & x & 1 \\ \end{matrix} \right|\] then \[\underset{x\to 0}{\mathop{\lim }}\,\,\,\left[ \frac{f'(x)}{x} \right]\] is ________.
If \[2\,\,f\,\,(x)=f\,\,(xy)+f\,\,\left( \frac{x}{y} \right)\] for all positive values of x and y, \[f(1)=0\] and\[f'\left( 1 \right)=1\], then f(e) is _______.
If \[f(x)=(\cos x+i\,\,\sin \,x)\,\,(\cos 2x+i\,\,\sin 2\,x)\]\[(\cos 3x+i\,\,\sin 3\,x)..........(cos\,\,nx+i\,\,sin\,nx)\]and f(1) = 1, then f "(1) is equal to _______.
In \[\Delta ABC\], the mid-points of the sides AB, BC and CA are respectively (I, 0, 0), (0, m, 0) and (0, 0, n). Then, \[\frac{A{{B}^{2}}+B{{C}^{2}}+C{{A}^{2}}}{{{I}^{2}}+{{m}^{2}}+{{n}^{2}}}\] is equal to ______.