### Andhra University Engineering Entrance Test Mathematics Practice Sample Paper:

**Ques.** If the portion of the line lx + my = 1 falling inside the circle x^{2} + y^{2} = a^{2} subtends an angle of 45^{o} at the origin, then

(a) 4[a^{2} (l^{2} + m^{2}) – 1] = a^{2} (l^{2} + m^{2})

(b) 4[a^{2} (l^{2} + m^{2}) – 1] = a^{2} (l^{2} + m^{2}) – 2

(c) 4[a^{2} (l^{2} + m^{2}) – 1] = [a^{2} (l^{2} + m^{2}) – 2]^{2
}(d) None of these

**Ques. **Let *S* be the set of all real numbers. Then the relation *R* = {(*a*, *b*) : 1 + *ab* > 0} on *S* is

(a) Reflexive and symmetric but not transitive

(b) Reflexive and transitive but not symmetric

(c) Symmetric, transitive but not reflexive

(d) Reflexive, transitive and symmetric

**Ques.** To expand (1 + 2x)^{–1/2} as an infinite series, the range of *x* should be

(a) [–1/2, 1/2]

(b) (–1/2, 1/2)

(c) [–2, 2]

(d) (–2, 2)

**Ques.** The vector b = 3j + 4k is to be written as the sum of a vector b_{1} parallel to a = i + j and a vector b_{2} perpendicular to **a**. Then b_{1} =

(a) 3/2(i + j)

(b) 2/3(i + j)

(c) 1/2(i + j)

(d) 1/3 (i + j)

**Ques.** A lady gives a dinner party for six guests. The number of ways in which they may be selected from among ten friends, if two of the friends will not attend the party together is

(a) 112

(b) 140

(c) 164

(d) None of these

**Related:** Coordinate geometry questions and answers

**Ques. **The quartile deviation of daily wages (in *Rs.*) of 7 persons given below 12, 7, 15, 10, 17, 19, 25 is

(a) 14.5

(b) 5

(c) 9

(d) 4.5

**Ques.** If the equation y^{3} – 3x^{2} y + m (x^{3} – 3xy^{2}) = 0 represents the three lines passing through origin, then

(a) Lines are equally inclined to each other

(b) Two lines makes equal angle with *x*-axis

(c) All three lines makes equal angle with *x*-axis

(d) None of these

**Ques.** If (sec A + tan A) (sec B + tan B) (sec C + tan C) = (sec A – tan A) (sec B – tan B) (sec C – tan C), then each side is equal to

(a) 1

(b) – 1

(c) 0

(d) None of these

**Ques.** If |a x b| = 4 and |a . b| = 2, then | a |^{2} | b |^{2} =

(a) 2

(b) 6

(c) 8

(d) 20

**Ques.** A river is 80 *metre* wide. Its depth *d* *metre* and corresponding distance *x* *metre* from one bank is given below in table

x : |
0 | 10 | 20 | 30 | 40 | 50 | 60 | 70 | 80 |

d : |
0 | 4 | 7 | 9 | 12 | 15 | 14 | 8 | 3 |

Then approximate area of cross-section of river by Trapezoidal rule, is

(a) 710* sq. m*

(b) 730* sq. m
*(c) 705

*sq. m*

(d) 750

*sq. m*

**Related:** Coordination compounds question bank

**Ques.** If the sum of the roots of the equation ax^{2} + bx + c = 0 be equal to the sum of the reciprocals of their squares, then bc^{2}, ca^{2}, ab^{2} will be in

(a) A.P.

(b) G.P.

(c) H.P.

(d) None of these

**Ques.** The value of x_{o} (the initial value of *x*) to get the solution in interval (0.5, 0.75) of the equation x^{3} – 5x + 3 = 0 by Newton-Raphson method, is

(a) 0.5

(b) 0.75

(c) 0.625

(d) None of these

**Ques.** 49^{n} + 16n – 1 is divisible by

(a) 3

(b) 19

(c) 64

(d) 29

**Ques.** If a, b and c are the three non-coplanar vectors, then (a + b + c) . [(a + b) x (a + c)] is equal to

(a) [a b c]

(b) 2 [a b c]

(c) – [a b c]

(d) 0

**Ques. **From the following table, using Trapezoidal rule, the area bounded by the curve, the *x-*axis and the lines x = 7.47, x = 7.52, is

x : : |
7.47 | 7.48 | 7.49 | 7.50 | 7.51 | 7.52 |

f(x) : |
1.93 | 1.95 | 1.98 | 2.01 | 2.03 | 2.06 |

(a) 0.0996

(b) 0.0896

(c) 0.6977

(d) 0.0776

**Ques.** Let z_{1} and z_{2} be two roots of the equation z^{2} + az + b = 0, *z* being complex. Further, assume that origin, z_{1 }and z_{2} form an equilateral triangle. Then

(a) a^{2} = b

(b) a^{2} = 2b

(c) a^{2} = 3b

(d) a^{2} = 4b

**Related:** Fluid Mechanics (Physics) Question Bank

**Ques.** If cosh^{–1} (p + iq) = u + iv, then the equation with roots cos^{2} u and cosh^{2} v

(a) x^{2} – x (p^{2} + q^{2}) + p^{2} = 0

(b) x^{2} – x(p^{2} + q^{2} + 1) + 1 = 0

(c) x^{2} + x(p^{2} + q^{2} + 1) + 1 = 0

(d) x^{2} – x (p^{2} + q^{2} + 1) = 0

**Ques.** In a college of 300 students, every student reads 5 newspaper and every newspaper is read by 60 students. The no. of newspaper is

(a) At least 30

(b) At most 20

(c) Exactly 25

(d) None of these

**Ques.** If the circle x^{2} + y^{2} = a^{2} intersects the hyperbola xy = c^{2} in four points P (x_{1}, y_{1}), Q (x_{2}, y_{2}), R (x_{3}, y_{3}), S (x_{4}, y_{4}), then

(a) x_{1} + x_{2} + x_{3} + x_{4} = 0

(b) y_{1} + y_{2} + y_{3} + y_{4} = 0

(c) x_{1} x_{2} x_{3} x_{4} = c^{4
}(d) y_{1 }y_{2} y_{3} y_{4} = c^{4
}

**Ques.** Let *p* a non singular matrix 1 + p + p^{2} + … + p^{n} = O (*O* denotes the null matrix), then p^{–1} =

(a) p^{n
}(b) –p^{n
}(c) – (1 + p + … + p^{n})

(d) None of these

**Ques.** The real root of the equation *x*^{3 }– 5 = 0 lying between 1 and 2 after first iteration by Newton-Raphson method is

(a) 1.909

(b) 1.904

(c) 1.921

(d) 1.940

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**Ques.** If the length of the tangents drawn from the point (1,2) to the circles x^{2} + y^{2} + x + y – 4 = 0 and 3x^{2} + 3y^{2} – x – y + k = 0 be in the ratio 4 : 3, then *k* =

(a) 7/2

(b) 21/ 2

(c) – 21/ 4

(d) 7/ 4

**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

**Ques.** If the equation x^{2} + y^{2} + 2gx + 2fy + 1 = 0 represents a pair of lines, then

(a) g^{2} – f^{2} = 1

(b) f^{2} – g^{2} = 1

(c) g^{2} + f^{2} = 1

(d) f^{2} + g^{2} = ½

**Ques.** The range of following set of observations 2, 3, 5, 9, 8, 7, 6, 5, 7, 4, 3 is

(a) 11

(b) 7

(c) 5.5

(d) 6

**Ques.** The number of observations in a group is 40. If the average of first 10 is 4.5 and that of the remaining 30 is 3.5, then the average of the whole group is

(a) 1/5

(b) 15/4

(c) 4

(d) 8

**Related:** Square root questions

**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

**Ques.** The value of the nearest root of the equation x^{3} + x – 1 = 0 after third iteration by Newton-Raphson method near x = 1 is

(a) 0.51

(b) 0.42

(c) 0.67

(d) 0.55

**Ques.** x + y + z + 2 = 0 together with x + y + z + 3 = 0 represents in space

(a) A line

(b) A point

(c) A plane

(d) None of these

**Ques.** If the expression (mx – 1 + 1/x) is always non-negative, then the minimum value of *m* must be

(a) –½

(b) 0

(c) ¼

(d) ½

**Ques.** Let a and b 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

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**Ques.** Locus of the foot of the perpendicular drawn from the centre upon any tangent to the ellipse x^{2}/a^{2} + y^{2}/b^{2} = 1, is

(a) (x^{2} + y^{2})^{2} = b^{2}x^{2} + a^{2}y^{2
}(b) (x^{2} + y^{2})^{2} = b^{2}x^{2} – a^{2}y^{2
}(c) (x^{2} + y^{2})^{2} = a^{2} x^{2} – b^{2} y^{2
}(d) (x^{2} + y^{2})^{2} = a^{2}x^{2} + b^{2}y^{2
}

**Ques.** The number of integral points (integral point means both the coordinates should be integer) exactly in the interior of the triangle with vertices (0, 0), (0, 21) and (21, 0), is

(a) 133

(b) 190

(c) 233

(d) 105

**Ques. **Urn *A* contains 6 red and 4 black balls and urn *B* contains 4 red and 6 black balls. One ball is drawn at random from urn *A* and placed in urn *B*. Then one ball is drawn at random from urn *B* and placed in urn *A*. If one ball is now drawn at random from urn *A*, the probability that it is found to be red, is

(a) 32/55

(b) 21/55

(c) 19/55

(d) None of these

**Ques.** The length of subtangent to the curve x^{2} y^{2} = a^{4} at the point (–a, aa) is

(a) 3a

(b) 2a

(c) a

(d) 4a

**Ques.** If the two regression coefficient between *x* and *y* are 0.8 and 0.2, then the coefficient of correlation between them is

(a) 0.4

(b) 0.6

(c) 0.3

(d) 0.5

**Related:** Trigonometry Ratio Sample Paper (Maths)

**Ques.** A root of the equation x^{3} – x – 4 = 0 lies between 1 and 2. Its approximate value, as obtained by applying bisection method 3 times, is

(a) 1.375

(b) 1.750

(c) 1.975

(d) 1.875

**Ques.** The total expenditure incurred by an industry under different heads is best presented as a

(a) Bar diagram

(b) Pie diagram

(c) Histogram

(d) Frequency polygon

**Ques.** A root of the equation *x*^{3 }– 18=0 lies between 2 and 3. The value of the root by the method of false position is

(a) 2.526

(b) 2.536

(c) 2.546

(d) 2.556

**Ques.** A ball is thrown vertically upwards from the ground with velocity 15 *m*/*s* and rebounds from the ground with one-third of its striking velocity. The ratio of its greatest heights before and after striking the ground is equal to**
**(a) 4 : 1

(b) 9 : 1

(c) 5 : 1

(d) 3 : 1

**Ques.** Let E = {1, 2, 3, 4} and F = {1, 2}.Then the number of onto functions from *E* to *F* is

(a) 14

(b) 16

(c) 12

(d) 8

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**Ques.** If *a* and a + h are two consecutive approximate roots of the equation f(x) = 0 as obtained by Newtons method, then *h* is equal to

(a) f(a)/f’(a)

(b) f’(a)/f(a)

(c) –f’(a)/f(a)

(d) –f(a)/f’(a)

**Ques.** One side of a rectangle lies along the line 4x + 7y + 5 = 0. Two of its vertices are (–3, 1) and (1, 1). Then the equations of other two sides are

(a) 7x – 4y + 25 = 0, 4x + 7y = 11 and 7x – 4y – 3 = 0

(b) 7x + 4y + 25 = 0, 7y + 4x – 11 = 0 and 7x – 4y – 3 = 0

(c) 4x – 7y + 25 = 0, 7x + 4y – 11 = 0 and 4x – 7y – 3 = 0

(d) None of these

**Ques.** In group *G* = {0, 1, 2, 3, 4, 5} under addition modulo 6, a subgroup is

(a) {0, 2, 4}

(b) {0, 1, 3}

(c) {0, 3, 5}

(d) {0, 4, 5}

**Ques.** A pack of playing cards was found to contain only 51 cards. If the first 13 cards which are examined are all red, then the probability that the missing cards is black, is

(a) ⅓

(b) ⅔

(c) ½

(d) ⅛

**Ques. **If in a triangle *ABC*, *c* = 3*b* and *C* – *B* = 90°, then tan*B* equals (The symbols have their usual meanings)

(a) 2 + √3

(b) 2 – √3

(c) 3

(d) ⅓

**Related:** Chemical Equilibrium Sample Paper

**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

**Ques.** The domain of the function f(x) = ^{16 – x} C_{2x – 1} +^{ 20 – 3x} P_{4x – 5}, where the symbols have their usual meanings, is the set

(a) {2, 3}

(b) {2, 3, 4}

(c) {1, 2, 3, 4}

(d) {1, 2, 3, 4, 5}

**Ques.** If cosh y = sec x, then the value of tanh^{2} (y/2) is

(a) tan^{2} (x/2)

(b) cot^{2} (x/2)

(c) sin^{2} (x/2)

(d) tan^{2} x/2

**Ques.** The area of the triangle formed by the line 4x^{2} – 9xy – 9y^{2} = 0 and x = 2 is

(a) 2

(b) 3

(c) 10/3

(d) 20/3

**Ques.** The mean deviation from the median is

(a) Greater than that measured from any other value

(b) Less than that measured from any other value

(c) Equal to that measured from any other value

(d) Maximum if all observations are positive

Related: set theory questions

**Ques.** The sum of three consecutive terms in a geometric progression is 14. If 1 is added to the first and the second terms and 1 is subtracted from the third, the resulting new terms are in arithmetic progression. Then the lowest of the original term is

(a) 1

(b) 2

(c) 4

(d) 8

**Ques.** The number of ways in which five identical balls can be distributed among ten identical boxes such that no box contains more than one ball, is

(a) 10 !

(b) 10! / 5!

(c) 10! / (5!)^{2}

(d) None of these

**Ques. **16 R^{2} r r_{1} r_{2} r_{3} =

(a) *abc*

(b) a^{3} b^{3} c^{3}

(c) a^{2} b^{2} c^{2}

(d) a^{2} b^{3} c^{4
}

**Ques. **If *T*_{1} is the period of the function *y* = *e*^{3(x }^{– [x]) } and *T*_{2} is the period of the function

*y* = *e*^{3x }^{– [3x]} ([.] denotes the greatest integer function), then

(a) *T*_{1} = *T*_{2}

(b) *T*_{1} = T_{2}/3

(c) *T*_{1} = 3*T*_{2}

(d) none of these

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