### Straight Line Questions (Mathematics):

**Ques. **A straight line through P(1, 2) is such that its intercept between the axes is bisected at P. Its equation is

(a) x + 2y = 5

(b) x – y + 1 = 0

(c) x + y – 3 = 0

(d) 2x + y – 4 = 0

Ans. (d)

**Ques. **The equations to a pair of opposite sides of a parallelogram are x^{2} – 5x + 6 = 0 and

y^{2} – 6y + 5 = 0. The equations to its diagonals are

(a) x + 4y = 13 and y = 4x – 7

(b) 4x + y = 13 and 4y = x – 7

(c) 4x + y = 13 and y = 4x – 7

(d) y – 4x = 13 and y + 4x = 7

Ans. (c)

**Ques. **If P = (1, 0), Q = (-1, 0), R = (2, 0) are 3 given points, then the locus of the point S satisfying the relation SQ^{2} + SR^{2} = 2SP^{2} is

(a) a straight line parallel to the x-axis

(b) circle through the origin

(c) circle with centre at theorigin

(d) a straight line parallel to the y-axis.

Ans. (d)

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**Ques. **The points A(–4, –1), B(–2, –4), C(4, 0) and D(2, 3) are the vertices of a

(a) square

(b) rectangle

(c) rhombus

(d) none of these

Ans. (b)

**Ques. **The area enclosed by |x| + |y| = 1 is

(a) 1

(b) 2

(c) 3

(d) 4

Ans. (b)

**Ques. **If the lines ax + by + c = 0;, bx + cy + a = 0 and cx + ay + b = 0 be concurrent, then

(a) a^{3} + b^{3} + c^{3} + 3abc = 0

(b) a^{3} + b^{3} + c^{3} – abc = 0

(c) a^{3} + b^{3} + c^{3} – 3abc = 0

(d) None of these

Ans. (c)

**Ques. **If (–6, -4) and (3, 5) are the extremities of the diagonals of a parallelogram and (-2, 1) is its third vertex, then its fourth vertex is

(a) (-1, 0)

(b) (0, -1)

(c) (-1, 1)

(d) none of these

Ans. (a)

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**Ques.** The straight line passing through the point of intersection of the straight lines x – 3y+1 = 0 and 2x +5y – 9 = 0 and having infinite slope and at a distance 2 units from the origin has the equation(a) x = 2

(b) 3x + y – 1 = 0

(c) y = 1

(d) None of these

Ans. (a)

**Ques.** In the equation y – y_{1} = m(x – x_{1}) if *m* and *x*_{1} are fixed and different lines are drawn for different values of *y*_{1}, then

(a) The lines will pass through a single point

(b) There will be a set of parallel lines

(c) There will be one line only

(d) None of these

Ans. (b)

**Ques. **Which of the following lines is concurrent with the lines 3x + 4y + 6 = 0and 6x + 5y + 9 = 0

(a) 2x + 3y + 5 = 0

(b) 3x + 3y + 5 = 0

(c) 7x + 9y + 3 = 0

(d) None of these

Ans. (b)

**Ques. **The coordinates of the middle points of the sides of a triangle are (3, 2) (4, 3) and (2, 2). Then the coordinates of its centroid are

(a) (3, 7/3)

(b) (3, 3)

(c) (4, 3)

(d) none of these

Ans. (a)

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**Ques. **The points A(2a, 4a), B(2a, 6a), C(2a + Ö3 a, 5a), a > 0 are the vertices of

(a) a right angled triangle

(b) an equilateral triangle

(c) an isosceles triangle

(d) none of these

Ans. (b)

**Ques. **The value of *k* for which the lines 7x – 8y + 5 = 0, 3x – 4y + 5 = 0 and 4x + 5y + 5 = 0 are concurrent is given by

(a) – 45

(b) 44

(c) 54

(d) – 54

Ans. (a)

**Ques. **The medians AD and BE of a triangle ABC with vertices A(0, b) B(0, 0) and C(a, 0) are perpendicular to each other if

(a) b = Ö2a

(b) a = Ö2b

(c) b = –Ö2a

(d) none of these

Ans. (b)

**Ques. **Consider the equation y – y_{1} = m(x – x_{1}). If m and x_{1} are fixed and different lines are drawn for different values of y_{1}, then

(a) the line will pass through a fixed point

(b) there will be a set of parallel lines

(c) all the lines will be parallel to the line y = y_{1}

(d) none of these

Ans. (b)

**Ques. **For what value of ‘*a*’ the lines x = 3, y = 4 and 4x – 3y + a = 0 are concurrent

(a) 0

(b) –1

(c) 2

(d) 3

Ans. (a)

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**Ques.** The nearest point on the line 3x + 4y = 25 from the origin is**
**(a) (-4, 5)

(b) (3, -4)

(c) (3, 4)

(d) (3, 5)

Ans. (c)

**Ques. **The intercept of a line between the coordinate axes is divided by point (– 5, 4) in the ratio 1 : 2. The equation of the line will be

(a) 5x – 8y + 60 = 0

(b) 8x – 5y + 60 = 0

(c) 2x – 5y + 30 = 0

(d) None of these

Ans. (b)

**Ques. **The points (-a, -b), (0, 0), (a, b) and (a^{2}, ab) are

(a) collinear

(b) vertices of a parallelogram

(c) vertices of a rectangle

(d) none of these

Ans. (a)

**Ques. **The lines 15x – 18y + 1 = 0, 12x + 10y – 3 = 0 and 6x + 66y – 11 = 0 are

(a) Parallel

(b) Perpendicular

(c) Concurrent

(d) None of these

Ans. (c)

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**Ques. **The point of intersection of the lines x/a + y/b = 1 and x/b + y/a = 1 lies on the line

(a) x – y = 0

(b) (x – y) (a + b) = 2ab

(c) (lx + my) (a – b) = (l + m)ab

(d) (lx – my) (a – b) = (1 – m)ab

Ans. (a)

**Ques. **The three lines 4x – 7y + 10 = 0, x + y = 5 and 7x + 4y = 15 form the sides of a triangle. Then the point (1, 2) is its

(a) centroid

(b) incentre

(c) orthocenter

(d) none of these

Ans. (c)

**Ques. **The straight lines x + 2y – 9 = 0, 3x + 5y – 5 = 0 and ax + by – 1 = 0 are concurrent, if the straight line 35x – 22y + 1 = 0 passes through the point

(a) (a, b)

(b) (b, a)

(c) (–a, –b)

(d) None of these

Ans. (a)

**Ques. **Points on the line x + y = 4 that lie at a unit distance from the line 4x + 3y – 10 = 0 are

(a) (3, 1) and (-7, 11)

(b) (-3, 7) and (2, 2)

(c) (-3, 7) and (-7, 11)

(d) none of these

Ans. (a)

**Ques. **In a rhombus ABCD, the diagonals AC and BD intersect at the point (1, 2). If the point B is (2, 3), the diagonal AC has equation

(a) x + y = 0

(b) x – y = 3

(c) x – y = 0

(d) x + y = 3

Ans. (d)

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**Ques. **The solution of equations x + y = 10, 2x + y = 18 and 4x – 3y = 26 will be

(a) Only one solution

(b) No Solution

(c) Infinite solution

(d) None of these

Ans. (a)

**Ques. **The straight line passing through the point of intersection of the straight lines x – 3y + 1 = 0 and 2x + 5y – 9 = 0 and having infinite slope and at a distance of 2 units from the origin, has the equation

(a) x = 2

(b) 3x + y – 1 = 0

(c) y = 1

(d) None of these

Ans. (a)

**Ques. **The equations of the lines through (-1, -1) and making angle 45° with the line x + y = 0 are given by

(a) x + 1 = 0, x – y = 0

(b) y + 1 = 0, x – y = 0

(c) x + 1 = 0, y + 1= 0

(d) none of these

Ans. (c)

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**Ques. **Let the vertices of a triangle be (0, 0), (3, 0) and (0, 4). Its orthocentre is

(a) (0, 0)

(b) (1, 4/3)

(c) (3/2, 2)

(d) none of these

Ans. (a)

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