Mathematics Entrance Test

Mathematics Objective Type Questions with Answers for the preparation of Engineering Entrance Test like AIEEE, IIT-JEE, CET etc. (Important for Students of Class 10+1 & 10+2)

Test 6

(1) The area enclosed between the curve y = loge (x + e) and the coordinate axes is

(a) 1

(b) 2

(c) 3

(d) 4

Answer (a) 1

(2) If x dy/dx = y (log y − log x + 1), then the solution of the equation is

(a) y log(x/y) = cx

(b) x log(y/x) = cy

(c) log(y/x) = cx

(d) log(x/y) = cy

Answer (c) log(y/x) = cx

(3) The line parallel to the x−axis and passing through the intersection of the lines ax + 2by + 3b = 0 and bx − 2ay − 3a = 0, where (a, b) ≠ (0, 0) is

(a) below the x−axis at a distance of 3/2 from it

(b) below the x−axis at a distance of 2/3 from it

(c) above the x−axis at a distance of 3/2 from it

(d) above the x−axis at a distance of 2/3 from it

Answer (a) below the x−axis at a distance of 3/2 from it

(4) ∫ cosx

(a) tanx

(b) secx

(c) sinx

(d) -sinx

Answer (c) sinx

(5) The angle between the lines 2x = 3y = − z and 6x = − y = − 4z is

(a) 0 Degree

(b) 90 Degree

(c) 45 Degree

(d) 30 Degree

Answer (b) 90 Degree

(6) If the plane 2ax − 3ay + 4az + 6 = 0 passes through the midpoint of the line joining the centres of the spheres

x2 + y2 + z2 + 6x − 8y − 2z = 13 and

x2 + y2 + z2 − 10x + 4y − 2z = 8, then a equals

Here 2 is read as Square

(a) − 1

(b) 1

(c) − 2

(d) 2

Answer (c) − 2

(7) If non-zero numbers a, b, c are in H.P., then the straight line x/a + y/b + z/c always passes through a fixed point. That point is

(a) (-1, 2)

(b) (-1, -2)

(c) (1, -2)

(d) (1, -1/2)

Answer (c) (1, -2)

(8) If a vertex of a triangle is (1, 1) and the mid-points of two sides through this vertex are (-1, 2) and (3, 2), then the centroid of the triangle is

(a) (-1, 7/3)

(b) (-1/3, 7/3)

(c) (1, 7/3)

(d) (1/3, 7/3)

Answer (c) (1, 7/3)

(9) If the circles x2 + y2 + 2ax + cy + a = 0 and x2 + y2 – 3ax + dy – 1 = 0 intersect in two distinct points P and Q then the line 5x + by – a = 0 passes through P and Q for

(a) exactly one value of a

(b) no value of a

(c) infinitely many values of a

(d) exactly two values of a

Here 2 is read as Square

Answer (b) no value of a

(10) A circle touches the x-axis and also touches the circle with centre at (0, 3) and radius 2. The locus of the centre of the circle is

(a) an ellipse

(b) a circle

(c) a hyperbola

(d) a parabola

Answer (d) a parabola

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Mathematics Objective Type Questions with Answers for the preparation of Engineering Entrance Test like AIEEE, IIT-JEE, CET etc. (Important for Students of Class 10+1 & 10+2)

Test 6

(1) The area enclosed between the curve y = loge (x + e) and the coordinate axes is

(a) 1

(b) 2

(c) 3

(d) 4

Answer (a) 1

(2) If x dy/dx = y (log y − log x + 1), then the solution of the equation is

(a) y log(x/y) = cx

(b) x log(y/x) = cy

(c) log(y/x) = cx

(d) log(x/y) = cy

Answer (c) log(y/x) = cx

(3) The line parallel to the x−axis and passing through the intersection of the lines ax + 2by + 3b = 0 and bx − 2ay − 3a = 0, where (a, b) ≠ (0, 0) is

(a) below the x−axis at a distance of 3/2 from it

(b) below the x−axis at a distance of 2/3 from it

(c) above the x−axis at a distance of 3/2 from it

(d) above the x−axis at a distance of 2/3 from it

Answer (a) below the x−axis at a distance of 3/2 from it

(4) ∫ cosx

(a) tanx

(b) secx

(c) sinx

(d) -sinx

Answer (c) sinx

(5) The angle between the lines 2x = 3y = − z and 6x = − y = − 4z is

(a) 0 Degree

(b) 90 Degree

(c) 45 Degree

(d) 30 Degree

Answer (b) 90 Degree

(6) If the plane 2ax − 3ay + 4az + 6 = 0 passes through the midpoint of the line joining the centres of the spheres

x2 + y2 + z2 + 6x − 8y − 2z = 13 and

x2 + y2 + z2 − 10x + 4y − 2z = 8, then a equals

Here 2 is read as Square

(a) − 1

(b) 1

(c) − 2

(d) 2

Answer (c) − 2

(7) If non-zero numbers a, b, c are in H.P., then the straight line x/a + y/b + z/c always passes through a fixed point. That point is

(a) (-1, 2)

(b) (-1, -2)

(c) (1, -2)

(d) (1, -1/2)

Answer (c) (1, -2)

(8) If a vertex of a triangle is (1, 1) and the mid-points of two sides through this vertex are (-1, 2) and (3, 2), then the centroid of the triangle is

(a) (-1, 7/3)

(b) (-1/3, 7/3)

(c) (1, 7/3)

(d) (1/3, 7/3)

Answer (c) (1, 7/3)

(9) If the circles x2 + y2 + 2ax + cy + a = 0 and x2 + y2 – 3ax + dy – 1 = 0 intersect in two distinct points P and Q then the line 5x + by – a = 0 passes through P and Q for

(a) exactly one value of a

(b) no value of a

(c) infinitely many values of a

(d) exactly two values of a

Here 2 is read as Square

Answer (b) no value of a

(10) A circle touches the x-axis and also touches the circle with centre at (0, 3) and radius 2. The locus of the centre of the circle is

(a) an ellipse

(b) a circle

(c) a hyperbola

(d) a parabola

Answer (d) a parabola

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