The values of λ, for which the equation x2 – y2 – x + λy – 2 = 0 represents a pair of straight lines, is
1) -3, 1 2) -1, 1 3) 3, – 3 4) 3, 1 Solution: Given x2 – y2 – x... View Article
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The three straight lines ax + by = c, bx + cy = a and cx + ay = b are collinear, if
1) b + c = a 2) c + a = b 3) a + b + c = 0... View Article
The equation of the line passing through the point of intersection of the lines x/a + y/b = 1 and x/b + y/a = 1 and having slope 0 is
1) x = a 2) y = b 3) y = ab/(a + b) 4) none of these Solution: Given... View Article
If (sin θ, cos θ) and (3, 2) lie on the same side of the line x + y = 1, then θ lies between
1) (0, π/2) 2) (0, π) 3) (π/4, π/2) 4) (0, π/4) Solution: Let L be given line x +... View Article
The point of concurrence of the line ax + by + c = 0 and a, b, c satisfy the relation 3a + 2b + 4c = 0 is
1) (3/2, 1/4) 2) (3/4, 1/4) 3) (3/4, 1/2) 4) (3/2, 1/2) Solution: Given relation 3a + 2b + 4c... View Article
If non – zero numbers a, b, c are in HP, then the straight line x/a + y/b + 1/c = 0 always passes through a fixed point. That point is
1) (1, – 1/2) 2) (1, -2) 3) (-1, -2) 4) (-1, 2) Solution: Given a, b, c are in... View Article
If the lines x2 + 2xy – 35y2 – 4x + 44y – 12 = 0 and 5x + λy – 8 = 0 are concurrent, then the value of λ is
1) 0 2) 1 3) – 1 4) 2 Solution: Given x2 + 2xy – 35y2 – 4x + 44y... View Article
The incentre of a triangle with vertices (1, √3), (0, 0), and (2, 0) is
(1) (1, 1/√3) (2) (1, 2/√3) (3) (1, √3/2) (4) none of these Solution: Let A(1, √3), B(0, 0), and... View Article
If the lines 3x + 4y + 1 = 0, 5x + λ y + 3 = 0 and 2x + y – 1= 0 are concurrent, then λ is equal to
1) – 8 2) 8 3) 4 4) – 4 Solution: Given 3x + 4y + 1 = 0 5x... View Article
The equation of the pair of straight lines parallel to X – axis and touching the circle x2 + y2 – 6x – 4y – 12 = 0 is
1) y2 – 4y – 21 = 0 2) y2 + 4y – 21 = 0 3) y2 – 4y... View Article
The equations of the lines through the point (3, 2) which makes an angle of 450 with the line x – 2y = 3 are
1) 3x – y = 7 and x + 3y = 9 2) x – 3y = 7 and 3x... View Article
The equation of the line passing through the point of intersection of the lines x – 3y + 2 = 0 and 2x + 5y – 7 = 0 and perpendicular to the line 3x + 2y+ 5 = 0, is
1) 2x – 3y + 1 = 0 2) 6x – 9y + 11 = 0 3) 2x – 3y... View Article
log4 2 – log16 2 + log 2 – … is equal to
1) e2 2) loge 2 + 1 3) loge 3 – 2 4) 1 – loge 2 Solution: (4) 1... View Article
If (x,y) is the solution of the following equations (2x)log2 = (3y)log3 and 3logx = 2logy, then x is equal to
1) 1/6 2) 1/3 3) 1/2 4) 6 Solution: (3) 1 / 2 (2x)log2 = (3y)log3 and 3logx = 2logy... View Article
Let a > 0, b > 0 and c > 0. Then the roots of the equations ax2 + bx + c = 0
1) are real and negative 2) have negative real parts 3) both (a) and (b) 4) none of these Solution:... View Article
The value of given expression is
\(\begin{array}{l}6+\log _{\frac{3}{2}}\left(\frac{1}{3 \sqrt{2}} \sqrt{4-\frac{1}{3 \sqrt{2}} \sqrt{4-\frac{1}{3 \sqrt{2}} \cdots .}}\right)\end{array} \) 1) 4 2) 5 3) 7 4) None of these... View Article
If 3x = 4x-1, then x is equal to
1) [2 log3 2] / [2 log3 2 – 1] 2) 2 / [2 – log2 3] 3) 1 /... View Article
If x, y and z are real and different and u = x2 + 4y2 + 9z2 – 6yz – 3zx – 2xy, then u is always.
1) non-negative 2) zero 3) non-positive 4) none of these Solution: (1) non-negative f (x, y, z) = x2 +... View Article
The number of digits in 20301 (given, log10 2 = 0.3010) is
1) 602 2) 301 3) 392 4) 391 Solution: (3) 392 Let x = 20301 Number of digits = Integrated... View Article
Solution of the equation 4 . 9x-1 = 3 √(22x+1) is
1) 3 2) 2 3) 3/2 4) 2/3 Solution: (3) 3 / 2 4 . 9x-1 = 3 √(22x+1) [9x-1]... View Article
