# Mathematics Entrance Test 6

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

(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

(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

(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

(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

(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)

(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)

(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