GATE Questions

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As parabola is a locus of a point, which moves so that its distance from focus and directrix is always equal.

The latus rectum of a conic section is the chord (line segment) that passes through the focus, is perpendicular to the major axis and has both endpoints on the curve. The length of the latus rectum is determined differently for each conic.

The length of a parabola's latus rectum is 4p, where p is the distance from the focus to the vertex.

Abhinav Bindra is an Indian professional shooter who is the world and Olympic champion in the 10 m air rifle event.

Cp1 = p2 - p1 ,
Cp2 = p3 - p2
..
..
..
Cp23 = p24 - p23
Sum of series = (p2-p1) + (p3-p2) + .....(p23-p22) + (p24-p23)
All terms get cancelled, except p1 = 2 and p24 = 89
So Sum = -p1 + p24
Sum of series = -2 + 89 = 87

Let the speed of the trains be x and y respectively
length of train1 = 47x
length of train2 = 31y
Relative speed= x + y
Time taken to cross each other = 33 s
=> 47x+31yx+y= 33
=> (47x + 31 y) = 33(x + y)
=> 14x = 2y
=> x/y = 2/14 = 1/7

 = 1:7

We know thatThe Difference between Compound Interest and Simple Interest for n years at R rate of interest is given by C.In - S.In = PR100n

Here n = 2 years, R = 20%, C.I - S.I = 56

$$\begin{gathered} 56 = P201002 \\ => P = 56 x 52 \\ => P = 56 x 25 \\ => P = Rs. 1400 \end{gathered}$$

Here to convert 0.125 into %

First convert to fractio

Multiply and divide by 1000

=> 0.125 x 10001000 = 1251000 = 18

=> Now, $$\begin{gathered} in percentage \\ 18 x 100 = 12.5% \end{gathered}$$

Let 'R%' be the rate of interest

From the given data,

$$\begin{gathered} 25202400 = 1 + R10041 + R1003 \\ ⇒1 + R100 = 6360 \\ ⇒R = 5 \end{gathered}$$

Hence, the rate of interest R = 5% per annum.