Cat De Quant Test 42

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Quant Test 42

1. If p and q are the roots of x2 + px + q = 0, then

p=1 p = 1 or 0 p=–2 p = – 2 or 0 p = 1 or – 2 Skip this question

2. If a1, a2, a3 are the first three terms of an arithmetic progression containing 100 terms, what is the possible common ratio when a2, a1 and a3 are in geometric progression?

–2 2 1 both (1) and (3) impossible Skip this question

3. Let P(x) = kx3 + 2k2x2 + k3. Find the sum of all possible real numbers k for which (x – 2) is a factor of P(x).

–8 16 4 32 None of these Skip this question

4. Let S be the set of integers 4, 12, 20, 28, ……., 516 and S’ be the subset of S such that the sum of no two elements of S’ is 520. The maximum possible number of elements in S’ is

30 31 32 33 35 Skip this question

5. a, b, c are consecutive natural numbers and x = LCM (a!, b!, c!) y = HCF (b!, c!) z = LCM (a!, b!) Which of the following is/are true if a < b < c? I. x = z II. x = cy III. x + y + 2y

only I I and II only only II I and III only all the three Skip this question

6. If the area of a triangle is given by 1/2 xy, where x and y are the values (in sq. units) on x-axis and y-axis respectively. What will be the maximum possible area of the

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triangle formed and satisfying the equation 5x – 2y ≤ 30?

50 100 45 90 data insufficient Skip this question

7. In the equation x2 + ax + b = 0, the coefficients a and b are real. If one of the roots is 2 + sqrt3 , what is the value of a?

2 – sqrt3 2 + sqrt3 3 none of these data insufficient Skip this question

8. If N is a natural number having total number of divisors 18, which of the following can’t be the number of divisors of N2?

35 51 75 65 55 Skip this question

9. ABCD is a cyclic quadrilateral with three angles in the ratio 1 : 2 : 3. If both its diagonals are shorter than the diameter of its circumcircle, what is the measure of the smallest angle of the quadrilateral?

36 45 60 90 cannot be determined Skip this question

10. Find the number of digits in 10011001.

3004 1001 3003 3030 3000 Skip this question

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