**Ques.** A root of equation x^{3} + 2x – 5 = 0 lies between 1 and 1.5. Its value as obtained by applying the method of false position only once is

(a) 4/3

(b) 35/27

(c) 23/25

(d) 5/4

**Ans. **(b)

**Ques.** A particle possess two velocities simultaneously at an angle of tan^{–1} 12/5 to each other. Their resultant is 15 m/s. If one velocity is 13 m/s, then the other will be

(a) 5 m/s

(b) 4 m/s

(c) 12 m/s

(d) 13 m/s

**Ans.** (b)

**Ques.** If y = 2x is a chord of the circle x^{2} + y^{2} – 10x = 0, then the equation of the circle of which this chord is a diameter, is

(a) x^{2} + y^{2} – 2x + 4y = 0

(b) x^{2} + y^{2} + 2x + 4y = 0

(c) x^{2} + y^{2} + 2x – 4y = 0

(d) x^{2} + y^{2} – 2x – 4y = 0

**Ans.** (d)

**Related:** Bhartiya Vidyapeeth Mathematics Sample Paper

**Ques.** If sin x + sin^{2} x = 1, then the value of expression cos^{12} x + 3 cos^{10} x + 3 cos^{8} x + cos^{6} x – 1 is equal to

(a) 0

(b) 1

(c) –1

(d) 2

**Ans.** (a)

**Ques.** If the coefficient of the second, third and fourth terms in the expansion of (1 + x)^{n} are in A.P., then *n* is equal to

(a) 7

(b) 2

(c) 6

(d) None of these

**Ans.** (a)

**Ques.** Let function f(x) = x^{2} + x + sin x – cos x + log (1 + |x|) be defined over the interval [0, 1]. The odd extensions of f(x) to interval [–1, 1] is

(a) x^{2} + x + sin x + cos x – log (1 + |x|)

(b) –x^{2} + x + sin x + cos x – log (1 + |x|)

(c) –x^{2} + x + sin x – cos x + log (1 + |x|)

(d) None of these

**Ans.** (b)

**Ques.** A variable chord is drawn through the origin to the circle x^{2} + y^{2} – 2ax = 0. The locus of the centre of the circle drawn on this chord as diameter, is

(a) x^{2} + y^{2} + ax = 0

(b) x^{2} + y^{2} + ay = 0

(c) x^{2} + y^{2} – ax = 0

(d) x^{2} + y^{2} – ay = 0

**Ans.** (c)

**Related:** VITEEE Practice paper (Chemistry)

**Ques.** If in a frequency distribution, the mean and median are 21 and 22 respectively, then its mode is approximately

(a) 25.5

(b) 24.0

(c) 22.0

(d) 20.5

**Ans.** (b)

**Ques.** One root of x^{3} – x – 4 = 0 lies in (1, 2). In bisection method, after first iteration the root lies in the interval

(a) (1, 1.5)

(b) (1.5, 2.0)

(c) (1.25, 1.75)

(d) (1.75, 2)

**Ans. (b)**

**Ques.** Coordinates of the vertices of a quadrilateral are (2, – 1), (0, 2), (2, 3) and (4, 0). The angle between its diagonals will be

(a) 90^{o}

(b) 0^{o
}(c) tan^{–1} (2)

(d) tan^{–1} (1/2)

**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)

**Ques.** For the curve y^{n} = a^{n – 1} x, the subnormal at any point is constant. The value of *n* must be

(a) 2

(b) 3

(c) 0

(d) 1

**Ans.** (a)

**Ques.** The average weight of students in a class of 35 students is 40 *kg*. If the weight of the teacher be included, the average rises by 1/2kg; the weight of the teacher is

(a) 40.5 *kg*

(b) 50* kg
*(c) 41

*kg*

(d) 58

*kg*

**Ans.**(d)

**Ques.** Two masses are projected with equal velocity *u* at angle 30° and 60° respectively. If the ranges covered by the masses be R_{1} and R_{2} then**
**(a) R

_{1}> R

_{2}

(b) R

_{1}= R

_{2}

(c) R

_{1}= 4R

_{2}

(d) R

_{2}> R

_{1 }

**Ans.**(b)

**Ques.** If the normal at any point *P* on the ellipse x^{2} / a^{2} + y^{2}/b^{2} = 1 meets the co-ordinate axes in *G* and *g* respectively, then PG = Pg =

(a) a : b

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

(d) b : a

**Ans.** (c)

**Ques.** Equation of one of the sides of an isosceles right angled triangle whose hypotenuse is 3x + 4y = 4 and the opposite vertex of the hypotenuse is (2, 2), will be

(a) x – 7y + 12 = 0

(b) 7x + y – 12 = 0

(c) x – 7y + 16 = 0

(d) 7x + y + 16 = 0

**Ans.** (a)

**Related:** BITSAT Physics Question Bank

**Ques.** Two candidates attempt to solve the equation x^{2} + px + q = 0. One starts with a wrong value of *p* and finds the roots to be 2 and 6 and the other starts with a wrong value of *q* and find the roots to be 2 and – 9. The roots of the original equation are

(a) 2, 3

(b) 3, 4

(c) –2, – 3

(d) – 3, – 4

**Ans.** (d)

**Ques.** In a moderately asymmetrical distribution the mode and mean are 7 and 4 respectively. The median is

(a) 4

(b) 5

(c) 6

(d) 7

**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 = –1/2

(c) a = –2, b = ½

(d) None of these

**Ans.** (b)

**Ques. **The probability of happening an event *A* is 0.5 and that of *B* is 0.3. If *A* and *B* are mutually exclusive events, then the probability of happening neither *A* nor *B* is

(a) 0.6

(b) 0.2

(c) 0.21

(d) None of these

**Ans.** (b)

**Ques.** If there are n harmonic means between 1 and 1/31 and the ratio of 7^{th} and (n – 1)^{th} harmonic means is 9 : 5 then the value of n will be

(a) 12

(b) 13

(c) 14

(d) 15

**Ans.** (c)

**Ques.** The number 3.14150 rounded to 3 decimals is

(a) 3.14

(b) 3.141

(c) 3.142

(d) None of these

**Ans. **(c)

**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.** A school has four sections of chemistry in class XII having 40, 35, 45 and 42 students. The mean marks obtained in chemistry test are 50, 60, 55 and 45 respectively for the four sections, the overall average of marks per students is

(a) 53

(b) 45

(c) 55.3

(d) 52. 25

Ans. (d**)**

**Ques.** The upper 34^{th} portion of a vertical pole subtends an angle tan^{‑1} (3/5) at a point in the horizontal plane through its foot and at a distance 40 *m *from the foot. A possible height of the vertical pole is

(a) 20 *m*

(b) 40 *m*

(c) 60 *m
*(d) 80

*m*

**Ans.**(b)

**Ques.** The median of a set of 9 distinct observations is 20.5. If each of the largest 4 observation of the set is increased by 2, then the median of the new set

(a) Is increased by 2

(b) Is decreased by 2

(c) Is two times the original median

(d) Remains the same as that of the original set

**Ans.** (d)

**Related:** Probability Practice Questions

**Ques.** If the variance of x = 9 and regression equations are 4x – 5y + 33 = 0 and 20x – 9y – 10 = 0, then the coefficient of correlation between *x* and *y* and the variance of *y* respectively are

(a) 0.6; 16

(b) 0.16; 16

(c) 0.3; 4

(d) 0.6; 4

Ans. (a)

**Related:**

**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 – by^{2} = 0

(b) bx^{2} – 2hxy + ay^{2} = 0

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

(d) ax^{2} – 2hxy + by^{2} = 0

**Ans.** (d)

**Ques.** The function (e^{2x} – 1) / (e^{2x} + 1) is

(a) Increasing

(b) Decreasing

(c) Even

(d) Odd

**Ans.** (a,d)

**Ques.** The lines ax + by + c = 0, where 3a + 2b + 4c = 0 are concurrent at the point

(a) (1/2, 3/4)

(b) (1, 3)

(c) (3, 1)

(d) (3/4, 1/2)

**Ans.** (d)

**Ques.** If a party of *n* persons sit at a round table, then the odds against two specified individuals sitting next to each other are

(a) 2 : (n – 3)

(b) (n – 3) : 2

(c) (n – 2) : 2

(d) 2 : (n – 2)

**Ans.** (b)

**Ques.** The differential equation for the family of curves x^{2} + y^{2} – 2ay = 0, where *a* is an arbitrary constant, is

(a) (x^{2} + y^{2})y’ = 2xy

(b) 2 (x^{2} + y^{2})y’ = 2xy

(c) (x^{2} – y^{2})y’ = 2xy

(d) 2(x^{2} – y^{2})y’ = xy

**Ans.** (c)

**Ques.** A gun projects a ball at an angle of 45^{o} 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.** A train is running at 5 m/s and a man jumps out of it with a velocity 10 m/s in a direction making an angle of 60° with the direction of the train. The velocity of the man relative to the ground is equal to

(a) 12.24 m/s

(b) 11.25 m/s

(c) 14.23 m/s

(d) 13.23 m/s

**Ans.** (b)

**Related:** Chemical Equilibrium Question Bank

**Ques.** The class marks of a distribution are 6,10, 14, 18, 22, 26, 30 then the class size is

(a) 4

(b) 2

(c) 5

(d) 8

**Ans. (**a)

**Ques.** Two students while solving a quadratic equation in *x*, one copied the constant term incorrectly and got the roots 3 and 2. The other copied the constant term and coefficient of x^{2} correctly as –6 and 1 respectively. The correct roots are

(a) 3, –2

(b) –3, 2

(c) –6, –1

(d) 6, –1

**Ans.** (d)

**Ques.** The equation e^{–2x} – sin x + 1 = 0 is of the form

(a) Algebraic

(b) Linear

(c) Quadratic

(d) Transcendental

**Ans. **(d)

**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

**Ans.** (b)

**Ques.** The locus of the middle points of the chords of hyperbola 3x^{2} – 2y^{2} + 4x – 6y = 0 parallel to y = 2x is

(a) 3x – 4y = 4

(b) 3y – 4x + 4 = 0

(c) 4x – 4y = 3

(d) 3x – 4y = 2

**Ans.** (a)

**Ques.** 16. Six boys and six girls sit in a row. What is the probability that the boys and girls sit alternatively

(a) 1/462

(b) 1/924

(c) ½

(d) None of these

**Ans.** (a)

**Ques.** Solution of the equation ydx – xdy + log xdx = 0 is

(a) y = cx – (1 + log x)

(b) y = cx + (1 + log x)

(c) y + cx + (1 + log x) = 0

(d) None of these

**Ans.** (a)

**Ques.** Let PQR be a right angled isosceles triangle, right angled at p (2, 1). If the equation of the line QR is 2x + y = 3, then the equation representing the pair of lines PQ and PR is

(a) 3x^{2} – 3y^{2} + 8xy + 20x + 10y + 25 = 0

(b) 3x^{2} – 3y^{2} + 8xy – 20x – 10y + 25 = 0

(c) 3x^{2} – 3y^{2} + 8xy + 10x + 15y + 20 = 0

(d) 3x^{2} – 3y^{2} – 8xy – 10x – 15y – 20 = 0

**Ans.** (b)

**Ques.** Three distinct numbers are selected from first 100 natural numbers. The probability that all the three numbers are divisible by 2 and 3 is

(a) 4/25

(b) 4/35

(c) 4/55

(d) 4/1155

**Ans.** (d)

**Ques.** Let u = i + j, v = i – j and w = i + 2j + 3k. If n is a unit vector such that u.n = 0 and v.n = 0 then | w . n | is equal to

(a) 0

(b) 1

(c) 2

(d) 3

**Ans.** (d)

**Ques.** The median of 10, 14, 11, 9, 8, 12, 6 is

(a) 10

(b) 12

(c) 14

(d) 11

**Ans.** (a)

**Ques.** Solution of the differential equation y’ = y tan x – 2 sin x, is

(a) y = tan x + 2c cos x

(b) y = tan x + c cos x

(c) y = tan x – 2c cos x

(d) None of these

**Ans.** (d)

**Ques.** If the range of any projectile is the distance equal to the height from which a particle attains the velocity equal to the velocity of projection, then the angle of projection will be

(a) 60^{o}

(b) 75^{o
}(c) 36^{o}

(d) 30^{o
}**Ans.** (b)

**Ques.** The root of the equation 2x – log_{10} x = 7 lies between

(a) 3 and 3.5

(b) 2 and 3

(c) 3.5 and 4

(d) None of these

**Ans.** (c)

**Related:** UP B. Tech Entrance Exam Sample Paper

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

(a) Mean

(b) Median

(c) Mode

(d) G.M.

**Ans.** (b)

**Ques.** Three squares of a chess board are chosen at random, the probability that two are of one colour and one of another is

(a) 16/21

(b) 8/21

(c) 32/12

(d) None of these

**Ans.** (a)

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