Sample BITSAT Maths Test
45 Questions MCQ Test BITSAT Mock Tests Series & Past Year Papers | Sample BITSAT Maths Test
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What is the area under the curve y = |x| + | x - 1| between x = 0 and x = 1 ?
The greatest term in the expansion of (3 + 2x)9, when x = 1, is
The coordinates of the pole of the line lx+my+n=0 with respect to the circle x2+y2=1 are
ANSWER :- d
Solution :- Let (x1,y1) be the pole of the line lx+my+n=0 with respect to the hyperbola x2a2−y2b2=1. Then, the equation of the polar is
xx1/ + yy1/ = 1………(i)
Since, (x1,y1) is the pole of the line lx+my+n=0. So, the polar of (x1,y1) is also the line
lx+my+n=0...(ii)
clearly, (i) and (ii) represent the same line. Therefore,
x1(l) = y1(m) = 1/(−n)
⇒x1 = −l/n, y1 = -m/n.
Hence, the pole of the given line with respect to the given hyperbola is
(−l/n, -m/n)
If the line 2x - y + k = 0 is a diameter of the circle x2 + y2 + 6x -6y + 5 =0, then k is equal to
The differential equation of the family of lines passing through the origin is
The equation of line passing through the origin is y = mx , when m is constant
Diffrence w.r.t x
Which of the following is a solution of the differential equation 
dy/dx= x−y/x+y
Put,y=vx
⟹dy/dx=v+x(dv/dx)
⟹v+xdv/dx=1−v/1+v
⟹xdv/dx = 1−2v−v^2/(1+v)
⟹∫v+1/(v+1)^2−2dv=−∫1/xdx
⟹1/2ln|[(v+1)^2−2]| = 2ln|c1/x|
⟹x^2(v^2+2v−1)=C
Where C = 2ln|c1/x|
Since,v=y/x, we get
⟹ y2+2xy−x2=C
Value of 1 + log x + (log x)2/2! + (log x)3/3! + ..... ∞ is
The angle of elevation of a cloud from a point h mt above the surface of a lake is θ and the angle of depression of its reflection in the lake is φ . The height of the cloud is
The eccentricity of the conjugate hyperbola of the hyperbola x2 - 3y2 = 1 is
Which of the following functions is a solution of the differential equation (dy/dx)2 - x (dy/dx) + y = 0?
The solution of the differential equation (dy/dx) = (y/x) + (φ (y/x)/φ' (y/x)) is
ANSWER :- c
Solution :- 23n−7n−1=8n−7n−1
=(7+1)n−7n−1
=C(n,0)7n+C(n,1)7n−1+...+C(n,n−2)72+C(n,n−1)71+C(n,n)70−7n−1
Now, C(n,0)7n+C(n,1)7n−1+...+C(n,n−2)72 is clearly divisible by 49.
So, we can write it as 49k.
So, our expression becomes,
=49k+C(n,n−1)71+C(n,n)70−7n−1
=49k+7n+1−7n−1
=49k
∴23n−7n−1=49k
So, clearly 23n−7n−1 is divisible by 49.
If A, B are two square matrices such that AB = A and BA = B, then
For a square matrix A, it is given that AA' = I, then A is a
The real value of α for which the expression 1-i sin α/1+2 i sin α is purely real is
For xy = 0
The lines are: x = 0 & y = 0 which are the Y and X axis respectively which are perpendicular.
The equation of the normal to the curve x2 = 4y at (1, 2) is
Two finite sets have m and n elements, the total number of subsets of the first set is 56 more than the total number of subsets of the second. The value of m and n are respectively
Let A denote the first set and B denote the second set
We have, n(A) = 2m and n(B) = 2n
As per the question, we have
n(A) = 56 + n(B)
⇒ n(A) - n(B) = 56
⇒ 2m - 2n = 56
⇒ 2n (2m - n - 1)
⇒ 2n (2m - n - 1) = 8 x 7
⇒ 2n = 8 = 23 or (2m - n - 1) = 7
⇒ n = 3 or 2m - n = 8 = 23 = 26 - 3
⇒ n = 3 or m - n = 3
⇒ n = 3 or m = 6
Hence, the required values of m and n are 6 and 3 respectively
In how many ways can the letters of the word ARRANGE be arranged so that R's are never together?
Reqd. ways = 
= 1260 - 360 = 900
A and B are events such that P(A ∪ B) = 3/4, P(A ∩ B) = 1/4, P(A̅)= 2/3, then P(A̅ ∩ B) is
The probability that a number selected at random from the set of numbers {1,2,3,....,100} is a cube is
A = B = C = 60o
r : R : r1 = 4R sin (A/2) sin (B/2) sin (C/2) : R : 4R sin (A/2) cos (B/2) cos (C/2)
= 4 (1/2) (1/2) (1/2) : 1 : 4 (1/2) (√3 /2) (√3 /2) = (1/2) : 1 : (3/2) = 1 : 2 : 3
The perimeter of a triangle is 16cm. One of the sides is of length 6cm. If the area of the triangle is 12sq.cm, then the triangle is
11,13,15,...., 99
a = 11, n = 45, d = 2
Sn = n/2[2a + (n-1)d}]
= 45/2 [22 + 44 × 2]
= 45/2 × 110
= 45 × 55
= 2475
If the sum of first n terms of an A.P. be 3n2 - n and its common difference is 6, then its first term is
In a town of 10,000 families it was found that 40% family buy newspaper A, 20% buy newspaper B, and 10% families buy newspaper C, 5% families buy A and B, 3% buy B and C and 4% buy A and C. If 2% families buy all the three newspapers, then number of families which buy A only is
If f : N x N → N is such that f (m,n) = m + n where N is the set of natural numbers, then which of the following is true?
The ortho centre of triangle whose vertices are (0,0), (3,0) and (0,4) is
The acute angle between the planes 2x-y+z=6 and x+y+2z=3 is
Max. value will occur when cosx=cosy=1 and cosz=0
If 3i+4j and -5i+7j represent the sides of a triangle, then its area is
and 
are mutually perpendicular, then (a+b)2=|
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