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The sum of series ∑_x=1ⁿ log [2^x] / [3^x-1] is

1) log [2n-1 / 3n+1]n/2 2) log [2n+1 / 3n-1]n/2 3) log [3n-1 / 2n+1]n/2 4) log [3n+1 / 2n-1]n/2 Solution: (2) log [2n+1 / 3n-1]n/2 ∑x=1n log... View Article

The sequence log a, log (a² / b), log (a³ / b²) …. is

1) a GP 2) an AP 3) a HP 4) both a GP and a HP Solution: (2) an AP log a, log (a2 / b), log (a3 / b2) …. T2 - T1 = log (a2 / b) - log 1 =... View Article

If [log x / (b – c)] = [log y / (c – a)] = [log z / (a – b)], then the value of x^b+c . y^c+a . z^a+b is

1) 1 2) 2 3) 0 4) - 1 Solution: (1) 1 [log x / (b - c)] = [log y / (c - a)] = [log z / (a - b)] [log x / (b - c)] = [log y / (c - a)] =... View Article

The equation of the perpendicular bisector of the line segment joining A ( 2, 3) and B (6, – 5) is

1) x - y = - 1 2) x - 2y = 3 3) x + y = 3 4) x - 2y = 6 Solution: Given points are A (2, 3) and B (6, - 5) Slope of AB = (y2 - y1)/(x2 -... View Article

If any point P is at the equal distances from points A (a + b, a – b) and B (a – b, a + b), then locus of point P is

1) x - y = 0 2) ax + by = 0 3) bx + ay = 0 4) x + y = 0 Solution: Let P(x,y) be the point that is equidistant from A (a + b, a - b) and B (a... View Article

If p is the length of the perpendicular from the origin to the line, whose intercepts with the coordinate axes are 1/3 and 1/4 then the value of p is

1) 3/4 2) 1/12 3) 1/5 4) 5 Solution: Given the intercepts with the coordinate axes are 1/3 and ¼. So the line pass through (⅓, 0) and (0, ¼)... View Article

A straight line passes through the points (5, 0) and (0, 3). The length of the perpendicular from the point (4, 4) on the line is

1) 15/√34 2) √17/2 3) 17/2 4) √(17/2) Solution: The equation of lines passing through two points (x1, y1) and (x2, y2) is y - y1 = ((y2 -... View Article

The points (1, 1), (- 5, 5) and (13, λ) lie on the same straight line if λ is equal to

1) 7 2) - 7 3) ± 7 4) 0 Solution: If the points lie on the same straight line, the slopes will be equal. Let A(1,1), B(-5, 5) and C(13, λ)... View Article

If the slopes of one of the lines given by ax² + 2hxy + by² = 0 is 5 times the other, then

1) 5h2 = 9ab 2) 5h2 = ab 3) h2 = ab 4) 9h2 = 5ab Solution: Given ax2 + 2hxy + by2 = 0 Let m1 and m2 be the slopes of the lines. Given m1 =... View Article

If PM is the perpendicular from P(2, 3) onto the line x + y = 3, then the coordinates of M are

1) (2, 1) 2) (-1, 4) 3) (1, 2) 4) (4, - 1) Solution: Let M(h, k) be the point on the line x + y = 3 So h+k = 3 …(i) Slope of line x + y =... View Article

The equation of the straight line perpendicular to 5x – 2y = 7 and passing through the point of intersection of the lines 2x + 3y = 1 and 3x + 4y = 6, is

1) 2x + 5y + 17 = 0 2) 2x + 5y - 17 = 0 3) 2x - 5y + 17 = 0 4) 2x - 5y = 17 Solution: Given lines 2x + 3y = 1 ..(i) 3x + 4y = 6 …(ii) By... View Article

If the point (a, a) falls between the line |x + y|= 4, then

1) |a|= 2 2) |a|= 3 3) |a| < 2 4) |a| < 3 Solution: Given |x + y| = 4 => x + y = 4 and x + y = -4 Since (a,a) lies between these... View Article

The equation of a line passing through (-2, -4) and perpendicular to line 3x – y + 5 = 0 is

1) 3y + x - 8 = 0 2) 3x + y + 6 = 0 3) x + 3y + 14 = 0 4) None of the above Solution: Given line is 3x - y + 5 = 0 => y = 3x + 5 Here... View Article

If the equations kx² – 2xy – y² – 2x + 2y = 0 represents a pair of lines, then k is equal to

1) 2 2) - 2 3) - 5 4) 3 Solution: Given kx2 - 2xy - y2 - 2x + 2y = 0 Comparing given equation with the general equation ax2 + 2hxy + by2 +... View Article

The straight line whose sum of the intercepts on the axes is equal to half of the product of the intercepts passes through the point

1) (1, 1) 2) (2, 2) 3) (3, 3) 4) (4, 4) Solution: Equation of the line in intercept form is x/a +y/b = 1 => bx + ay = ab …(i) Where a is... View Article

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