This BCECE Maths Practice sample paper is based on BCECE Maths syllabus and consist 34 questions

**Ques.** Let and be roots of x^{2} – 3x + p = 0 and let c and d be the roots of x^{2} – 12x + q = 0, where a, b, c, d form an increasing G.P. Then the ratio of (q + p) : (q – p) is equal to

(a) 8 : 7

(b) 11 : 10

(c) 17 : 15

(d) None of these

Ans:- (c)

**Ques.** The octal number 473 in the decimal representation is equal to

(a) (312)_{10}

(b) (308)_{10}

(c) (315)_{10}

(d) None of these

Ans:- (c)

**Ques.** How many numbers can be made with the help of the digits 0, 1, 2, 3, 4, 5 which are greater than 3000 (repetition is not allowed)

(a) 180

(b) 360

(c) 1380

(d) 1500

Ans:- (c)

**Ques.** If roots of the equation a(b – c)x^{2} + b(c – a)x + c(a – b) = 0 are equal, then a, b, c are in

(a) A.P.

(b) G.P.

(c) H.P.

(d) None of these

Ans:- (c)

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**Ques.** Two tangents are drawn from a point *P* on radical axis to the two circles touching at *Q* and *R* respectively then triangle formed by joining *PQR* is

(a) Isosceles

(b) Equilateral

(c) Right angled

(d) None of these

Ans:- (a)

**Ques.** If for positive integers r > 1, n > 2 the coefficient of the (3r)^{th }and (r + 2)^{th} powers of *x *in the expansion of (1 + x)^{2n }are equal, then

(a) n = 2r

(b) n = 3r

(c) n = 2r + 1

(d) None of these

Ans:- (c)

**Ques.** The lines x = ay + b, z = cy + d and x = a’y + b’, z = c’y + d’ are perpendicular to each other, if

(a) aa’ + cc’ = 1

(b) aa’ + cc’ = –1

(c) ac + a’c’ = 1

(d) ac + a’c’ = –1

Ans:- (b)

**Ques.** The image of the pair of lines represented by ax^{2} + 2hxy + by^{2} = 0 by the line mirror y = 0 is

(a) ax^{2} – 2hxy – b^{2}y = 0

(b) bx^{2} – 2hxy + ay^{2} = 0

(c) bx^{2} + 2hxy + ay^{2} = 0

(d) ax^{2} – 2hxy + by^{2} = 0

Ans:- (d)

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**Ques.** A gun projects a ball at an angle of 45 degree with the horizontal. If the horizontal range is 39.2 *m*, then the ball will rise to

(a) 9.8 *m*

(b) 4.9 *m*

(c) 2.45 *m*

(d) 19.6* m*

Ans:- (a)

**Ques.** What will be the equation of that chord of ellipse x^{2} / 36 + y^{2} / 9 = 1 which passes from the point (2, 1) and bisected on the point

(a) x + y = 2

(b) x + y = 3

(c) x + 2y = 1

(d) x + 2y = 4

Ans:- (d)

**Ques.** The central value of the set of observations is called

(a) Mean

(b) Median

(c) Mode

(d) G.M.

Ans:- (b)

**Ques.** If y = a log |x| + bx^{2} + x has its extremum values at x = –1 and x = 2, then

(a) a = 2, b = –1

(b) a = 2, b = – ½

(c) a = –2, b = ½

(d) None of these

Ans:- (b)

**Ques.** Karl Pearson’s coefficient of correlation between *x* and *y* for the following data is

x : |
3 | 4 | 8 | 9 | 6 | 2 | 1 |

y : |
5 | 3 | 7 | 7 | 6 | 9 | 2 |

(a) 0.480

(b) – 0.480

(c) 0.408

(d) – 0.408

Ans:- (c)

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**Ques.** If *R* and R’ are the resultants of two forces P / Q and Q/P (P > Q) according as they are like or unlike such that R : R’ = 25 : 7, then P : Q =

(a) 2 : 1

(b) 3 : 4

(c) 4 : 3*
*(d) 1 : 2

Ans:- (c)

**Ques.** In the group *G* = {2, 4, 6, 8} under multiplication modulo 10, the inverse of 4 is

(a) 2

(b) 4

(c) 6

(d) 8

Ans:- (b)

**Ques.** A student appears for test I, II and III. The student is successful if he passes either in tests I and II or test I and III. The probabilities of the student passing in tests I, II, III are *p*, *q* and 1/2 respectively. If the probability that the student is successful is 1/2, then

(a) p = 1, q = 0

(b) p = 2/3, q = ½

(c) There are infinitely many values of *p *and *q
*(d) All of the above

Ans:- (d)

**Ques.** Which of the following is the inverse of the proposition : “If a number is a prime then it is odd.”

(a) If a number is not a prime then it is odd

(b) If a number is not a prime then it is odd

(c) If a number is not odd then it is not a prime

(d) If a number is not odd then it is a prime

Ans:- (b)

**Ques.** In the above question the iso-profit line is

(a) 3x + y = 30

(b) x + 3y = 20

(c) 3x – y = 20

(d) 4x + 3y = 24

Ans:- (a)

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