Xavier's College +2 Science Entrance Exam Past Questions

24 Questions

If tanθ + tan²θ + tan³θ = θ, what is the value of θ?

If 4sinx + cosx = π, what is the value of x?

1/2

If A + B + C = π, what is the value of cotA.cotB + cotB.cotC + cotC.cotA?

What is the value of A³ if A = [x x; x x]?

[4x³ 4x³; 4x³ 4x³]

If a, b, c are in GP and a¹/x = c¹/z, what can be said about x, y, z?

x, y, z are in GP

If m times the mth term of an AP is equal to n times the nth term, what is the value of the (m+n)th term?

What is the value of K so that the equation 3x² + 7x + 6 - K = 0 has one of its roots equal to zero?

If both roots of x² + bx + c = 0 and x² + dx + e = 0 are common, what can be said about b, c, d, e?

be = cd

What is the function of the annulus of sporangium of a fern?

To assist in dispersal of spores

Which enzyme is responsible for fermentation in yeast?

Zymase

What is a plant that produces flowers and fruits only once in its lifetime called?

Monocarpic

What is the radius of the circle x + y + 2cos(0)x + 2sin(0)y - 8 = 0?

2√3

What is the equation of the circle passing through points (0, 0), (a, 0) and (0, b)?

x² + y² + 2ax + 2by = 0

What is the distance between the pair of lines represented by x - 6y + 3x - 9y - 4 = 0?

√5

For what value of k are points (1, -1), (k, 1) and (4, 5) collinear?

k = -4

What is the angle between vectors a and a + b + c, if a, b, and c are mutually perpendicular vectors of equal magnitudes?

cos⁻¹(1/√3)

If waste pipe R is opened with P and Q, the empty tank is filled in 24 hours. In what time does waste pipe R empty a full tank of water?

4 hours

If a business man marked the selling price of an article 20% above the cost price, and he sells the article at 10% discount on marked price, what is the profit percentage?

A set of furniture is bought at Rs. 12000. The rate of compound depreciation is 10%. In how many years will the value of this furniture be set at Rs. 9720?

2 years

If 4x - 9.2x + 32 = 0, what is the value of x?

0, 2

If the length of a rectangle is increased by 3m and its breadth is decreased by 3m, its area decreases by 1m^2. If its both length and breadth are increased by 3m, area increases by 60m^2. What are the length and breadth of the rectangle?

10m, 8m

ABCD is a square of side 14cm. Taking each of its vertices as the centre of circles, four circles have been drawn which touch each other. What is the area between the circles?

44 cm^2

If the perimeter of a square field is 4x + 8, what is the diagonal of the field?

2(x + 2)

A bag contains 4 red marbles, 5 blue marbles, and 2 yellow marbles. Two marbles are drawn, first replaced before the second is drawn. What is the probability that they are of the same color?

76/121

Study Notes

Mathematics

1. If tanθ + tan2θ + tan3θ = θ, then θ = π/3.
1. If 4sin x + cos x = π, then x = π/2.
1. If A + B + C = π, then cotA.cotB + cotB.cotC + cotC.cotA = -1.
1. A = {x : 2x + 1 = 0 and x is an integer} is a null set.
1. If f(x) = x + 2 and g(x) = x3, then fog(1) = 4.
1. If A and B are arbitrary square matrices of the same order, then (AB)T = ATBT.
1. If A = x x, then A3 = x3 x3.
1. If a, b, c are in G.P. and a1/x = c1/z, then x, y, z are in G.P.
1. If m times the mth term of an A.P. is equal to n times the nth term, then the (m+n)th term is 0.
1. The value of K so that the equation 3x2 + 7x + 6 - K = 0 has one of its roots equal to zero is 6.
1. Both roots of x + bx + c = 0 and x2 + dx + e = 0 are common, then be = cd.
1. Pipes P and Q take 4 hrs and 6 hrs to fill a tank respectively. Waste pipe R empties a full tank in 2 hrs 40 mm.
1. A businessman marks the selling price of an article 20% above the cost price. If he sells the article at 10% discount on marked price, the profit percent is 8%.
1. A set of furniture is bought at Rs. 12000. The rate of compound depreciation is 10%. The value of the furniture will be set at Rs.9720 in 2 years.
1. If 4x2 - 9x + 2 = 0, then x = 0, 2 or x = 1, 3.

Algebra

1. If the length of a rectangle is increased by 3m and its breadth is decreased by 3m, its area decreases by 1Bm2. If both length and breadth are increased by 3m, area increases by 60m2.
1. The area between four circles drawn from each vertex of a square of side 14cm is 44 cm2.
1. If perimeter of a square field is 4x + 8, then the diagonal will be 2(x + 2).
1. The probability that two marbles drawn from a bag, with replacement, are of the same colour is 76/121.

Biology

1. The annulus of sporangium of fern assists in the dispersal of spores by losing water from its cells.
1. Yeast produces an enzyme that is responsible for fermentation, which is Zymase.
1. A plant producing flowers and fruits once in its life is called Monocarpic.

Geometry

1. The radius of the circle x + y + 2cos0x + 2sin0y - 8 = 0 is 10.
1. The equation of the circle passing through points (0, 0), (a, 0) and (0, b) is x2 + y2 + 2ax + 2by = 0.
1. The distance between the pair of lines represented by x - 6xy + 9y + 3x - 9y - 4 = 0 is 5/√2.
1. For what value of k points (1,-1), (k, 1) and (4,5) are collinear? k = -4.

Vector Algebra

1. If a, b, c are mutually perpendicular vectors of equal magnitudes, then angle between a and a + b + c is π/3.

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