The relationship among the three words in the question can best be represented by one of the four diagrams. Select the correct diagram. Professor, Researcher, Scientist
Sanjeev walks 10 metres towards the South. Turning to the left, he walks 20 metres and then moves to his right. After moving a distance of 20 metres, he turns to the right and walks 20 metres. Finally, he turns to the right and moves a distance of 10 metres. How far and in which direction is he from the starting point?
The sum of the incomes of A and B is more than that of C and D taken together. The sum of the incomes of A and C is the same as that B and D taken together. Morever, A earns half as much as the sum of the incomes of B and D. Whose income is the highest?
If the positions of the first and the sixth letters in the word "DISTRIBUTE9 are interchanged; similarly the positions of the second and the seventh, the third and the eighth and so on. Which of the following letters will be the fifth from left after interchanging the positions?
A square transparent sheet with a pattern is given. Select the best answer, to how the pattern would appear when the transparent sheet is folded along the dotted line.
Let \[\vec{p}\] and \[\vec{q}\] be the position vectors of P and Q respectively, with respect to O and \[|\vec{p}|\,\,=p,\,|\vec{q}|\,=q\] The points R and S divide PQ internally and externally in the ratio 2 : 3 respectively. If OR and OS are perpendicular, then
Let a relation R? in the set R of real number be defined as \[(a,b)\in R'\] if and only if \[1+ab>0\] for all\[a,\,b\in R\text{ }\]. Which of the following options is correct for relation R
If \[f:R\to R\text{ }\] and \[g:R\to R\text{ }\] are defined by \[f(x)=2x+3\]and \[g\,(x)={{x}^{2}}+7\], then the values of x such that g{f{x)) = 8 are
AOB is the positive quadrant of the ellipse \[\frac{{{x}^{2}}}{{{a}^{2}}}+\frac{{{y}^{2}}}{{{b}^{2}}}=1\] in which OA = a, OS = b. The area between the arc AB and the chord AB of the ellipse is
If \[si{{n}^{-1}}\,a+si{{n}^{-\,1}}b+si{{n}^{-1}}c=\pi \], then the value of \[a\sqrt{(1-{{a}^{2}})}+b\sqrt{(1-{{b}^{2}})}+c\sqrt{(1-{{c}^{2}})}\]will be
Let \[A\,({{x}_{1}},{{y}_{1}})\]and \[B\,({{x}_{2}},{{y}_{2}})\] be any two points on the parabola \[y=a\,{{x}^{2}}+bx+c\] and let \[C\,({{x}_{3}},{{y}_{3}})\] be the point on the arc AB where the tangent is parallel to the chord AB. What is the value of \[{{x}_{3}}\] in terms of \[{{x}_{1}}\] and\[{{x}_{2}}\]?
The curve \[{{\left( \frac{x}{a} \right)}^{n}}+{{\left( \frac{y}{b} \right)}^{n}}=2\] touches the straight line \[\frac{x}{a}+\frac{y}{b}=2\] at the point (a, b)
In a survey among S-school students, 68% of those surveyed were in favour of at least one of the three magazines-A, S and C. 38% of those surveyed favoured magazine A, 26% favoured magazine B and 36% favoured magazine C. If 11% of those surveyed favoured all three magazines. What percent of those surveyed favoured more than one of the three magazines?
Farhan invested certain amount in three different schemes A, B and C with the rate of interest 10% p.a., 12% p.a. and 15% p.a. respectively. If the total interest occurred in one year was T 200 and the amount invested in Scheme C was 50% of the amount invested in Scheme A and 240% of the amount invested in Scheme S, what was the amount invested in Scheme S ?
Mr. Martin is holding a trivia contest. The 13 students who are participating randomly draw cards that are numbered with consecutive integers from 1 to 13.
The student who draws number 1 will be the host.
The students who draw the other odd numbers will be on the Red team.
The students who draw the even numbers will be on the Blue team.
One student has already drawn a card and is on the Blue team. If Kevin is the next student to draw a card, what is the probability that he will be on the Red team?
Arjit being a party animal wants to hold as many parties as possible among his 20 friends. However, his father has warned him that he will be financing his parties under the following conditions only :
The invitees have to be among his 20 best friends.
He cannot call the same set of friends to a party more than once.
The number of invitees to every party have to be the same.
Given these constraints, Arjit wants to hold the maximum number of parties. How many friends should he invite to each party?
Dev and Tukku can do a piece of work in 45 and 40 days respectively. They began the work together, but Dev leaves after some days and Tukku finished the remaining work in 23 days. After how many days did Dev leave?
Three Englishmen and three Frenchmen work for the same company. Each of them knows a secret not known to others. They need to exchange these secrets over person-to-person phone calls so that eventually each person knows all six secrets.
None of the Frenchmen knows English and only one Englishman knows French. What is the minimum number of phone calls needed for the above purpose?
The following system of equations represents the profit margin of two major companies where x represents sales and y represents discounts to clients. \[\left\{ \begin{align} & 3x-4y=12 \\ & x-2y=2 \\ \end{align} \right.\] Which of the following is the best approach to solving this system of equations?
A)
Multiply the expression x-2y by 3 and add the first equation to the second equation
doneclear
B)
Substitute the expression 2 + 2y for x in the first equation of the system
doneclear
C)
Add the first equation to the second equation
doneclear
D)
Substitute the expression x-2y for x in the first equation of the system
The Lucknow Indore Express without its rake can go 24 km an hour, and the speed is diminished by a quantity that varies as the square root of the number of wagons attached. If it is known that with four wagons its speed is 20 km/h, the greatest number of wagons with which the engine can just move is
The value of \[(x+y)(x-y)+\frac{1}{2!}(x+y)(x-y)\]\[({{x}^{2}}+{{y}^{2}})+\frac{1}{3!}(x+y)(x-y)({{x}^{4}}+{{y}^{4}}+{{x}^{2}}{{y}^{2}})+......+\] \[\infty \]is___________.
The number of positive integral solutions of the equation \[{{\tan }^{-1}}x+co{{x}^{-1}}\frac{y}{\sqrt{1+{{y}^{2}}}}={{\sin }^{-1}}\frac{3}{\sqrt{10}}\]is_.
Let \[\vec{a},\text{ }\vec{b}\] and \[\vec{c}\] be three vectors having magnitudes 1, 1 and 2 respectively. If \[\vec{a}\times (\vec{a}\times \vec{c})+\vec{b}=\vec{0}\], then the acute angle between \[\vec{a}\] and\[\vec{c}\]is______.
Observe the following statements : \[A:\int{\left( \frac{{{x}^{2}}-1}{{{x}^{2}}} \right)}\,e\frac{{{x}^{2}}+1}{x}dx=e\frac{{{x}^{2}}+1}{x}+C\]and \[R:f'(x){{e}^{f(x)\,}}dx=f(x)+c\] Then which of the following statements is true?
A)
Both A and R are true and R is not the correct reason for A.
doneclear
B)
Both A and R are true and R is the correct reason for A.