If for a real number x, [x] is the greatest integer less than or equal to x, then the value of the integral
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A line 'm' is drawn as reflection of the line 'l' on the x-axis as shown in the figure given below. What will be the slope of line 'm'? (It is given that the reflection is about the x-axis.)
C1 and C2 are circles of unit radii with centres at (0, 0) and (1, 0), respectively. C3 is a circle of unit radius, which passes through the centres of the circles C1 and C2 and has its centre above the x-axis. The equation of the common tangent to C1 and C3, which does not pass through C2, is
The diagonals of a parallelogram PQRS are along the lines x + 3y = 4 and 6x - 2y = 7. Then PQRS must be a
The orthocenter of the triangle formed by the lines xy = 0 and x + y = 1 is
The number of values of k for which the system of equations (k + 1) x + 8y = 4k and kx + (k + 3)y = 3k - 1 has infinitely many solutions is
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