BITSAT Maths Sample Question paper 1 consist questions with answers based on 11th and 12th Mathematics syllabus of CBSE Board. You can download PDF of this BITSAT Math sample paper by using the link below 10th question.

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**Ques. **If the point (1, 4) lies inside the circle x^{2} + y^{2}– 6x – 10y + p = 0 and the circle neither touches nor intersects the coordinate axes, then

(a) 0 < p < 39

(b) 25 < p < 29

(c) 9 < p < 25

(d) 9 < p < 29

**Ques. **The sides *AB,* *BC*, *CA* of a triangle *ABC* have respectively 3, 4 and 5 points lying on them. The number of triangles that can be constructed using these points as vertices is

(a) 205

(b) 220

(c) 210

(d) None of these

**Ques. **A student is allowed to select utmost *n *books from a collection of (2n + 1) books. If the total number of ways in which he can select one book is 63, then the value of *n* is

(a) 2

(b) 3

(c) 4

(d) None of these

**Ques. **If (1 + x)^{n} = C_{0} + C_{1}x + C_{2}x^{2} + … + C_{x}x^{x}, then the value of C_{0} + 2C_{1} + 3C_{2} + … + (n + 1)C_{n} will be

(a) (n + 2)2^{n – 1}

(b) (n + 1)2^{nj}

(c) (n + 1)2^{n – 1}

(d) (n + 2)2^{n}

**Ques. **If the pair of straight lines xy – x – y + 1 = 0 and the line ax + 2y – 3 = 0 are concurrent, then *a* =

(a) – 1

(b) 0

(c) 3

(d) 1

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**Ques. **Equation of chord (AB) of circle x^{2} + y^{2} = 2 passing through the point *P* (2, 2), such that PB/PA = 3, is

(a) x = 3y

(b) x = y

(c) y = (x – 2)

(d) none of these

**Ques. **The mean and the variance of a binomial distribution are 4 and 2 respectively. Then the probability of 2 successes is

(a) 28/256

(b) 219/256

(c) 128/256

(d) 37/256

**Ques. **Two uniform solid spheres composed of the same material and having their radii 6 *cm* and 3 *cm* respectively are firmly united. The distance of the centre of gravity of the whole body from the centre of the larger sphere is

(a) 1 *cm**
*(b) 3

*cm*

*(c) 2*

*cm*

*(d) 4*

*cm*

**Ques. **A point *P* moves in such a way that the ratio of its distances from two coplanar points is always fixed number (≠1). Then its locus is

(a) Straight line

(b) Circle

(c) Parabola

(d) A pair of straight lines

**Ques. **An unbiased die with faces marked 1, 2, 3, 4, 5 and 6 is rolled four times. Out of four face values obtained the probability that the minimum face value is not less than 2 and the maximum face value is not greater than 5, is

(a) 16/81

(b) 1/81

(c) 80/81

(d) 65/81

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**Ques. **Volume of tetrahedron formed by the planes x + y = 0, y + z = 0, z + x = 0, x + y + z – 1 = 0 is

(a) 1/6

(b) 1/3

(c) 2/3

(d) none of these

**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

**Ques. **In a room there are 12 bulbs of the same voltage, each having a separate switch. The number of ways to light the room with different amount of illumination is

(a) 12^{2 }– 1

(b) 2^{12}

(c) 2^{12} – 1

(d) none of these

**Ques. **The maximum value of objective function in the above question is

(a) 100

(b) 92

(c) 95

(d) 94

**Ques. **The value of *c* so that for all real *x*, the vectors cxi + 6j + 3k, xi + 2j + 2cxk make an obtuse angle are

(a) c < 0

(b) 0 < c < 4/3

(c) –4/3 < c < 0

(d) c > 0

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**Ques. **The ends of the latus rectum of the conic x^{2} + 10x – 16y + 25 = 0 are

(a) (3, – 4), (13, 4)

(b) (- 3, – 4), (13, – 4)

(c) (3, 4), (- 13, 4)

(d) (5, – 8), (- 5, 8)

**Ques. **A pregnancy test is done on 100 pregnant women and 100 non-pregnant women. Test suggests out of 100 pregnant woman, 2 are pregnant and 8 out of 100 non-pregnant woman are pregnant. A woman is selected randomly and test is done which says woman is pregnant. What is the probability woman is non-pregnant.

(a) ½

(b) 92/100

(c) 8/100

(d) none of these

**Ques. **Let *E* and *F* be two independent events. The probability that both *E* and *F* happens is 1/12 and the probability that neither *E* nor *F* happens is ½, then

(a) P(E) = 1/3, P(F) = ¼

(b) P(E) = ½, P(F) = ⅙

(c) P(E) = 1/6, P(F) = ½

(d) None of these

**Ques. **Two cards are drawn from a well shuffled pack of cards with replacement. The probability of drawing both aces is

(a) (1/13)^{2}

(b) 1/13 + 1/17

(c) 1/12 x 1/51

(d) 1/13 x 4/51

**Ques. **Let S_{n} denote the sum to *n* terms of an arithmetic progression whose first term is *a*. If the common difference is equal to S_{n} – kS_{n – 1} + S_{n – 2}, then *k* =

(a) 1

(b) 2

(c) 3

(d) none of these

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**Ques. **If ax^{2} + bx + c = 0 and bx^{2} + cx + a = 0, a ¹ 0, b ¹ 0 have a common root, then the value of a^{3} + b^{3} + c^{3} – 3abc is

(a) 0

(b) 1

(c) 2

(d) 10

**Ques. **The control unit and arithmetic logic unit is called

(a) Arithmetic Logic Unit (ALU)

(b) Central Processing Unit (CPU)

(c) Memory Unit

(d) Input Unit

**Ques. **The motion of a particle along a straight line is described by the function x = (2t – 3)^{2}, where x is in metre and t is in second. Then the velocity of the particle at origin is :

(a) 0

(b) 1

(c) 2

(d) none of these

**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

** Ques. **If

*m*is the root of the equation (1 – ab)x

^{2}– (a

^{2}+ b

^{2})x – (1 + ab) = 0, and

*m*harmonic means are inserted between

*a*and

*b*, then the difference between the last and the first of the means equals

(a) ab(a – b)

(b) a(b – a)

(c) ab(b – a)

(d) b – a

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**Ques. **If z = , then

(a) Re(z) = 0

(b) Im z = 0

(c) Re(z) > 0, Im(z) > 0

(d) Re(z) > 0

**Ques. **The solution of differential equation (e^{x} + 1)ydy = (y + 1)e^{x}dx is :

(a) (e^{x} + 1) (y + 1) = ce^{y}

(b) (e^{x} + 1) | (y + 1) | = ce^{–y
}(c) (e^{x} + 1) (y + 1) = ±ce^{y}

(d) none of these

**Ques. **Find the integral factor of equation

(a)

(b)

(c)

(d) None of these

**Ques. **In any triangle AB = 2, BC = 4, CA = 3 and D is mid-point of BC, then

(a) cos B = 11/6

(b) cos B = 7/8

(c) AD = 2.4

(d) AD^{2} = 2.5

**Ques. **Equation of ellipse with foci (5, 0) and (-5, 0) and 5x – 36 = 0 as one directrix, is

(a) 11x + 36y = 196

(b) 11x + 18y = 396

(c) 11x + 18y = 198

(d) 11x + 36y = 396

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**Ques. **The angle between the pair of straight lines represented by 2x^{2} – 7xy + 3y^{2} = 0 is

(a) 60^{o}

(b) 45^{o}

(c) tan^{–1} (7/6)

(d) 30^{o}

**Ques. **The intercept of a line between the coordinate axes is divided by point (– 5, 4) in the ratio 1 : 2. The equation of the line will be

(a) 5x – 8y + 60 = 0

(b) 8x – 5y + 60 = 0

(c) 2x – 5y + 30 = 0

(d) None of these

**Ques. **If the vertex and the focus of a parabola are (–1, 1) and (2, 3) respectively, then the directrix is

(a) 3x + 2y + 14 = 0

(b) 3x + 2y – 25 = 0

(c) 2x – 3y + 10 = 0

(d) none of these

**Ques. **A bag contains (2n + 1) coins. It is known that n of these have a head on both the sides, whereas the remaining (n + 1) coins are fair. A coin is picked up at random from the bag and tossed. If the probability that the toss results in a head is 31/42, then value of n is

(a) 10

(b) 8

(c) 76

(d) 25

**Ques. **The equation of plane passing through (1, 2,3) and at the maximum distance from origin is

(a) x + 2y + 3z = 14

(b) x + y + z = 6

(c) x + 2y + 3z = –14

(d) 3x + 2y + z = 14

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**Ques. **Workers work in three shifts I, II, III in a factory. Their wages are in the ratio 4 : 5 : 6 depending upon the shift. Number of workers in the shifts are in the ratio 3 : 2 : 1. If total number of workers working is 1500 and wages per worker in shift I is $400. Then mean wage of a worker is

(a) $467

(b) $500

(c) $600

(d) $400

**Ques. **Total number of books is 2n + 1. One is allowed to select a minimum of the one book and a maximum of n books. If total number of selections if 63, then value of n is :

(a) 3

(b) 6

(c) 2

(d) none of these

**Ques. **The number of different garlands, that can be formed using 3 flowers of one kind and 3 flowers of other kind, is

(a) 60

(b) 20

(c) 4

(d) 3

**Ques. **The major axis of the ellipse, whose axes are the coordinates with latus rectum 20, whose minor axis is the distance between the foci, is

(a) 18

(b) 20

(c) 36

(d) 40

**Ques. **A body is projected vertically upwards from a tower of height 192 ft. If it strikes the ground in 6 seconds, then the velocity with which the body is projected is

(a) 64 ft./sec

(b) 32 ft./sec

(c) 16 ft./sec

(d) none of these

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**Ques. **Let A(2, –3) and B(–2, 1) be vertices of a triangle *ABC*. If the centroid of this triangle moves on the line 2x + 3y = 1, then the locus of the vertex *C *is the line

(a) 2x + 3y = 9

(b) 2x – 3y = 7

(c) 3x + 2y = 5

(d) 3x – 2y = 3

**Ques. **The minimum marks required for clearing a certain screening paper is 210 out of 300. The screening paper consists of ‘3’ sections each of Physics, Chemistry and Maths. Each section has 100 as maximum marks. Assuming there is no negative marking and marks obtained in each section are integers, the number of ways in which a student can qualify the examination is (Assuming no cut-off limit for individual subject)

(a) ^{210}C_{3} – ^{90}C_{3}

(b) ^{93}C_{3
}(c) ^{213}C_{3}

(d) (210)^{3
}

**Ques. **A man firing at a distant target has 10%. Chance of hitting the target in one shot. The number of times he must fire at the target to have about 50% chance of hitting target is

(a) 11

(b) 9

(c) 7

(d) 5

**Ques. **In an examination, a candidate is required to pass four different subjects. The numbers of ways he can fail is

(a) 4

(b) 10

(c) 15

(d) 24

**Ques. **From a point A(1, 1) on the circle *x*^{2} + *y*^{2} – 4*x* – 4*y* + 6 = 0 two equal chords AB & AC of length 2 units are drawn. The equation of chord BC is

(a) 4*x* + 3*y* = 12

(b) *x* + *y* = 4

(c) 3*x* + 4*y* = 4

(d) *x* + *y* = 6

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**Ques. **For the function f(x) = 1 + 3^{x} log 3, find the antiderivative F which assumes the value 7 for x = 2. At what value of x does the curve y = F(x) cut the abscissa?

(a) x = 3

(b) x = 1

(c) x = 0

(d) None of these

**Ques. **f(x) = x^{3} +ax^{2} + bx + 5sin^{2}x is an increasing function in the set of real numbers if a and b satisfy the condition

(a) a^{2} – 3b – 15 > 0

(b) a^{2} – 3b + 15 > 0

(c) a^{2} – 3b + 15 < 0

(d) a > 0 b > 0

**Ques. **The expansion of (8 – 3x)^{3/2} in terms of power of x is valid only if

(a) x < 3/8

(b) |x| < 8/3

(c) x > 8/3

(d) none of these

**Ques. **A father with 8 children takes them 3 at a time to the Zoological gardens, as often as he can without taking the same 3 children together more than once. The number of times he will go to the garden is

(a) 336

(b) 112

(c) 56

(d) None of these

**Ques. **The equation of a parabola which passes through the intersection of a straight line

x + y = 0 and the circle x^{2} + y^{2} + 4y = 0 is

(a) y^{2} = 4x

(b) y^{2} = x

(c) y^{2} = 2x

(d) none of these

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**Ques. **Number of ways in which 3 boys and 3 girls (all are of different heights) can be arranged in a line so that boys as well as girls among themselves are in decreasing order of height (from left to right), is

(a) 1

(b) 6!

(c) 20

(d) none of these

**Ques. **An aircraft gun takes a maximum of fourshots at an enemy’s plane moving away from it. The probability of hitting the plane at first, second, third and fourth shots are 0.4, 0.3, 0.2 and 0.1 respectively. What is the probability that the gun hits the plane?

(a) 1

(b) 0.550

(c) 0.6976

(d) none of these

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