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A train is moving along a straight line with a constant acceleration a. A boy standing in the train throws a ball forward at an angle of 60° to the horizontal. The boy has to move forward by 1.15m inside the train to catch t ...

\hspace{-16}$If $\bf{\mathbb{I} = \int_{0}^{\pi}\frac{\pi}{\pi^2-\cos^2 (x)}dx}$, Then $\bf{[\;\mathbb{I}\; ]=}$ ...

Although some you might have seen this question before give it a try. If p,q are positive integers such that- 1- 1/2 + 1/3 - 1/4 +.........- 1/1318 + - 1/1319 = p/q Show that 1979 divides p. ...

If a line lies on a plane can we say that the line is parallel to that plane? ...

If the area enclosed between x2+y2≤9(pi)2 and sin(x-y)≥0 is m(pi)3/n sq units,then find [m]-[n]+[ m+n/m-n ]? ...

2nCn/(n+1) is an integer. ...

Prove that (a1+a2+...+an)!/a1!a2!...an! is an integer ...

An inverted “V” is made up of two uniform boards each weighing 200 N. Each side has the same length and makes an angle 30° with the vertical as shown in figure. The magnitude of the static frictional force that acts o ...

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If f(x)=3x3-13x2+14x-2 and p,q,r are roots of f(x)=0 such that p<q<r,then 1),[q],[r] where [.] denotes greatest integer function,are in A)A.P B)G.P C)H.P D)A.G.P 2) \fn_jvn \lim_{n\rightarrow \infty }(p)^{n!}(q)^{1/n} = ...

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Why do we see the characteristic colour of a metal ion when a salt of that metal ion is introduced in the flame? Why is it that all metal ions do not give the flame test? ...

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The distance between 2 parallel lines is one unit.A point 'A' is chosen to lie between the lines at a distance d from one of them.Triangle ABC is equilateral with B on one line and C on the other parallel line.The length of t ...

For S≡9x2-24xy+16y2-20x-15y-60=0,find the equation of the axis,directrix and length of latus rectum of the parabola? ...

Q1:The teacher of a class having a large number of students decides to take a test.After the test ended the teacher took the papers from the students and randomly distributed them among the students to check. Prove that the p ...

1)If \dpi{100} \fn_jvn \int_{a}^{b}(2+x-x^{2}) is maximum find a+b? 2)For f(x)= 6/1+31ex the possible number of different integral values which f(x) can take is? 3)if \dpi{100} \fn_jvn \lim_{x\rightarrow \infty }\sqrt[3]{8x^{ ...

Four fair dice D1, D2, D3 and D4, each having six faces numbered 1, 2, 3, 4, 5, and 6, are rolled simultaneously. The probability that D4 shows a number appearing on one of D1, D2 and D3 is (A) 91/216 (B) 108/216 (C) 125/216 ...

Determine all such integers a and b for which one of the roots of 3x3+ax2+bx+12=0 is equal to 1 + Ö3. ...

If A=\begin{bmatrix} 4 & 6 & 6\\ 1& 3 & 2\\ -1& -4 &-3 \end{bmatrix} and A^{-1}=\alpha A^{2}+\beta A+\gamma I,then \alpha +\beta +\gamma is ...

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x,y belong to R,x2+y2+xy=1,then the minimum value of x3y+y3x+4 is? ...

\hspace{-16}$Calculate The Remainder When $\bf{2^{2009}}$ is divided by $100$ ...

\hspace{-16}$Solve for real $\bf{(x,y,z)}$ in \\\\\\ $\bf{x[x]+z\{z\}-y\{y\}=0.16}$\\\\ $\bf{y[y]+x\{x\}-z\{z\}=0.25}$\\\\ $\bf{z[z]+y\{y\}-x\{x\}=0.49}$ ...

Can you cut a hale into a cube so that a slightly larger cube can pass through the hole? ...

6 apples and 6 mangoes are to be distributed among 10 boys so that each boy gets atleast 1 fruit.Find the number of ways in which the fruits can be distributed. ...

If a six digit number abcdef is multiplied with 6,the resulting number is defabc.Find c+f? ...

Large number of capacitors of rating 10 microfarad/200 V are available. The minimum number of capacitors required to design a 10 microfarad/700V capacitor is: (a)16 (b)4 (c)8 (d)7 ...

If the line 2x-y+1=0 touches a circle at the point (2,5) and the centre of the circle lies on the line x+y-9=0, find the equation of the circle. ...

1.922 g of MeOH was burnt in a constant-volume bomb calorimeter. The temperature of water rose by 4.2oC. If the heat capacity of the calorimeter and its contents is 10.4kJoC-1, calculate the molar heat of combustion of MeOH. ...