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Practice Test - Mathematics 13

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Question 1

and

are three non−coplanar vectors, then

equals

Question 2

In a triangle, if the sum of two sides is x and their product is y such that y = (x – z) (x + z), where z = third side, then triangle is

Question 3

The trigonometric equation sin⁻¹ x = 2 sin⁻¹ a, has a solution for

Question 4

Let PS be the median of the triangle with vertices P(2, 2), Q(6, –1) and R(7, 3). The equation of the line passing through (1, -1) and parallel to PS is

Question 5

If the standard deviation of the numbers 2, 3, a and 11 is 3.5, then which of the following is true?

Question 6

In a triangle ABC, medians AD and BE are drawn. If AD = 4, ∠ DAB =

and ∠ ABE =

, then the area of the Δ ABC is

Question 7

and

then S :

Question 8

Given P(x) = x⁴ + ax³ +bx² cx + d such that x = 0 is the only real root of P'(x) = 0. If P(–1) < P(1), then in the interval [–1, 1].

Question 9

If 100 times the 100^th term of an AP equals 50 times its 50^th term, then the 150^th term of this AP is

Question 10

Let two fair six-faced dice A and B be thrown simultaneously. If E₁ is the event that die A shows up four, E₂ is the event that die B shows up two and E₃ is the event that the sum of numbers on both dice is odd, then which of the following statements is TRUE?

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