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How many 3-digit numbers can be formed from the digits 1, 2, 3, 4 and 5 assuming that repetition of the digits is allowed?
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How many 3-digit numbers can be formed from the digits 1, 2, 3, 4 and 5 assuming that repetition of the digits is not allowed?
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How many 3-digit even numbers can be formed from the digits 1, 2, 3, 4, 5, 6 if the digits can be repeated?
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How many 4-letter code can be formed using the first 10 letters of the English alphabet, if no letter can be repeated?
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A coin is tossed 3 times and the outcomes are recorded. How many possible outcomes are there?
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Given 5 flags of different colours, how many different signals can be generated if each signal requires the use of 2 flags, one below the other?
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Draw a quadrilateral in the Cartesian plane, whose vertices are (–4, 5), (0, 7), (5, –5) and (–4, –2). Also, find its area.
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The base of an equilateral triangle with side 2a lies along they y-axis such that the mid point of the base is at the origin. Find vertices of the triangle.
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Find the distance between P (x1, y1) and Q (x2, y2) when :
- PQ is parallel to the y-axis,
- PQ is parallel to the x-axis
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Find a point on the x-axis, which is equidistant from the points (7, 6) and (3, 4).
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Find the slope of a line, which passes through the origin, and the mid-point of the line segment joining the points P (0, –4) and B (8, 0).
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Without using the Pythagoras theorem, show that the points (4, 4), (3, 5) and (–1, –1) are the vertices of a right angled triangle.
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Find the slope of the line, which makes an angle of 30° with the positive direction of y-axis measured anticlockwise.
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Find the value of x for which the points (x, –1), (2, 1) and (4, 5) are collinear.
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Without using distance formula, show that points (–2, –1), (4, 0), (3, 3) and (–3, 2) are vertices of a parallelogram.
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Find the angle between the x-axis and the line joining the points (3, –1) and (4, –2).
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The slope of a line is double of the slope of another line. If tangent of the angle between them is `1/3`, find the slopes of the lines.
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A line passes through (x1, y1) and (h, k). If slope of the line is m, show that k – y1 = m (h – x1).
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If three point (h, 0), (a, b) and (0, k) lie on a line, show that `q/h + b/k = 1`
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Consider the given population and year graph. Find the slope of the line AB and using it, find what will be the population in the year 2010?
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