MATHS - (BCA-1)

Maths- Sample Paper

Q (1). x->f(x) = 3x+1 is continuous at x=?
(a) 2 (b) 4 (c) -1 (d) 1 ( )
Q (2). Evaluate lim 2x2 – 4x
x->2 x-2
(a) 2 (b) 1 (c) 4 (d) 0 ( )
Q (3). What would be the lim x->4 x2 – 16
x-4
(a) 8 (b) 7 (c) 3 (d) -1 ( )
Q (4). Value for ∫cosec2 x.dx =?
(a) sec x (b) –cotx (c) sinx (d) –cosx ( )
Q (5). ∫01 xex dx =?
(a) e-(e-1) (b) 0 (c) 1/6 (d) –x ( )
Q (6). What would be the value for tan 300=?
(a) 0 (b) 1/√3 (c) √2 (d) -1 ( )
Q (7). Evaluate tan (900 + )=?
(a) -Sin (b) cot (c) cosec  (d) –cot  ( )
Q (8) what is the value for cos 17700 ?
(a)- 1/√3 (b) 1/√2 (c) √3/2 (d)-2 ( )
Q (9). Evaluate sin 750 ?
(a) √3+1/2+1 (b) √3+1/2√2 (c) ½ (d) 3 ( )
Q (10). Sin (A+B) is Equal to
a) cos a cos b –sin a sin b (b)sin a cos b +cos a sin b
(c) 2sin a cos a (d)none ( )
Q (11). A number of the form x+iy, where x and y are two real numbers and I=√-1, is called
(a) Imaginary part (b) conjugate numbers (c) analytic functions (d) Complex numbers ( )

Q (12). If x be a real or complex then ex+e-x is defined as
2
(a) Hyperbolic sine of x (b) hyperbolic cosine of y
(c) Hyperbolic cosine of x (b) hyperbolic cosine of z ( )
Q (13). Evaluate sinh3x
(a) 3 tanhx +2tanhx (b) 3 sinh x+ 4 sinh3x
(b) (c) 2 sinh +4 sinh x (d)3 sinh –sinh x ( )
Q (14). In square matrix the diagonal from left top to right bottom corner is Called?
(a) Principal diagonal (b) leading diagonal (c) a, b (d) none of the above ( )
Q (15). A square matrix all of whose elements below the leading diagonal Are zero, is called
(a) Lower triangular matrix (b) upper triangular matrix (c) a, b (d) all ( )
Q (16). Which is true for skew matrices?
(a)aij= -aji (b) null (c) aij = aij (d) none of them ( )
Q (17). Which of the following is true for matrices?
(a) Every scalar matrix is a diagonal matrix (b) a unit matrix is denoted by p
(c) Unit matrix is not scalar matrix (d) unit matrix is not diagonal matrix ( )
Q (18). Find the derivative of function defined by √ (1+x2)
(a) x/√ (1-x2) (b) -√ (1+x2) (c) x/√ (1+x2) (d) √ (1-x2) ( )
Q (19). What would be pedal equation to the parabola y2=4a(x+a)
(a)p= ar (b) p=-ar (c) y= pr (d) p2=ar ( )


Q (20). If x= a (cos +sin), y= a (sin -cos), find d2y/dx2
(a) Sec2  (b) sec3  (c) a, b (d) none of them ( )
a 
Q (21) if any repetition allowed them how many sampal will arise in four element selecting there ?
(a) 4 (b) 24 (c) 1000 (d) none of these ( )
Q (22) 52 P0 = ?
(a) 52 (b)51 (c) 52/0 (d) 1 ( )
Q (23) nc5 = nc8 then n = ?
(a) 13 (b) 8 (c) 5 (d)3 ( )
Q (24) 52c 48 = ?
(a) 52x51x50x49 (b) 52c5 (c) 52x51x50x49/4x3x2x1 (d) none of these ( )
Q (25.) 957C954=?
(a) 957 (b) 145620310 (c) 457446 (d) none of these ( )
Q(26) nc4 +nc3
(a) n+1C3 (b) nC3 (c) n+1c4 (d) None of these ( )
Q(27) three students X,Y,Z wright an examination there chance of passing are 1/2 ,1/3,1/4, respectively find the probability of all will fail is
(a) ¼ (b) ¾ (c) 2/4 (d) none of these ( )
Q(28) In a deck of card , probability of getting a clover is ……
(a) 4/52 (b) ¼ (c) 14/52 (d) 15/52 ( )
Q(29) The value of P(S/A) is …..
(a) 0 (b) 1 (c) P(A) (d) None ( )
Q(30) the probability of getting head from two headed coin is
(a) 0 (b) ½ (c) 1 (d) none of these ( )
Q (31) the graph represent by K 8.16 contain ….. vertices
a) 8 b) 16 c) 24 D) 128 ( )
Q32. All sets are sub sets of …..
a) null set b) super set c) universal set d) none ( )
Q 33) Degree of every vertex in K10 is ….
a) 13 b) 5 c) 20 d) none ( )
Q 34) if Ax(BxC) =(AxB)xC then the law is called
A) De Morgan’s Law b) Distributive law c) Commutative Law d) Associative law( )
Q35) the value of P1 +P2 +P3(where Pi is probability associated with same E) is………….
a) 0 b) 1 c) K d) Pk ( )
Q36) if n (A) = 4,n(B)= 2 then n (AxB) IS ……..
A) 6 b) 2 c) 4 d) none ( )
Q37) the inventer of set theory was born in the ………..country
a) India b) America c) Japan d) none ( )
Q38) if A = {1,2,3} , B{2,4,5} then (A-B) x a is…….
a) {(1,1),(1,3),(2,1)(2,3), (3,1),(3,3)} b) {(1,1),(1,2),(1,3)(3,1), (3,2),(3,3)}’
c) {(1,1),(2,1),(3,1)(1,3), (3,2),(3,3)}’ d) none ( )
Q39) if A = { y / y Є N and Y < 3} , B= { y / y² - 16 =0and y > 0 } then ( A∩B ) IS …
a) {1,2} b) {-4,4} C) {} d) None ( )
Q40) The value of P(S/A) is …..
a) 0 b) 1 c) P(A) d) none ( )
Section-B
Q (41). The Process of finding the actual rate of change of one variable with respect to The other is called:?
(a) Derivatives (b) Theorems (c) Differentiation (d) all of them ( )
Q (42). Integrate ∫ tan2 x.dx
(a) I= tan+x+c (b) I= tan x-x+c (c) a, b (d) sin2x ( )
Q (43). Evaluate Lim [ 1 + 8 + 27 +……….+ 1 ]
n->∞ 1+n4 16 + n4 81 + n4 2n4
(a) ¼ log2 (b)1/2 log 4 (c) ¼ log3 (d) ½ log-4 ( )

Q (44). Integrate ∫ tan x. .dx
cotx
(a) cotx-x (b) cotx+x (c) tanx+x (d) tanx-x ( )
Q (45). What would be the derivative for?
(1) 2x2-3x3 (2) sin3x
(a) 4x+5x, 3sin2x.cosx (b) 4x-9x2 , 4 sin2x.cosx (c) 4x-9x2 , 3sin2x.cosx (d) None of them ( )
Q (46). Find x from (2x-3) (cosec2 π/3–sin2 π/4) = x tan2 (π/4) – sec2 (π/6) -2
(a) x= (5/2) (b) x=(4/5) (c) x= - (5/4) (d)x=(2/4) ( )
Q (47) What is the value for cosec (900+ ) and cot (900+ )?
(a) sec , - tan (b) tan, sin (c) cot, cos  (d) cosec , tan  ( )
Q(48). Find the value for sec 3000 and tan 2400 ?
(a)√3 , -√ 2 (b) 2 , √3 (c) -1 ,0 (d) 2, -3 ( )
Q(49). Sin 1350+cos 4800
Sin 1350 –cos 1200 = ?
(a) √ 2 -2 (b) ½ -√ 2 (c) 3+2√2 (d)3-2√2 ( )
Q(50). If tan =1/3 and tan ß =1/7 then 2 + ß=?
(a) – π/2 (b) π/4 (c) 1/3 (d)2/3 ( )
Q(51). What would be the value for sin(a+ π/4) +cos (a+ π/4)=?
(a) √ 2 cos a (b) -√ 2 sin a (c) -√ 2 tan a (d) -√ 1 cos a ( )
Q(52). If tan a=5/6 , tan b= 1/11 , then a+b=?
(a) - π/4 (b) π/2 (c) π/3 (d) π/4 ( )
Q(53). Find the Modulus for (3 - √ 2)2
1+ 2i
(a) 11√ 5/5 (b) -√ 2/11 (c) √ 2-√ 2/5 (d) √ 2+1 ( )
Q(54). If 2 cos= x+1/x then what would be the value for 2 cos r=?
(a) 2x+r (b)xr +1/xr (c)xr-2x (d) x2-xr ( )
Q(55). Match the following?
(1)cosh2 x-sinh2 x (2) sech2 x + tanh2 x (3)coth2 x –cosech2 x
(a) 1,-1, 2 (b) 1, 0, 1 (c) 1, 1, 1 (d)-1, 2, 1 ( )
Q56) 52 P0 = ?
a)52 b) 1 c) 51 d) none ( )
Q57) The power set concept is discovered by
a) Newton b) fuller c) cantor d) none ( )
Q58 ) the graph represent by K 8.16 contain ….. vertices
a) 8 b) 16 d) 24 d) 128
Q59) Three students X,Y,Z weight an examination there chance of passing are 1/2 ,1/3,1/4, respectively find the probability of all will fail is
a) ¼ b) ¾ c) 2/4 d) none
Q60) From 6 positive and 8 negative numbers, 4 are chosen random and multiplied . what is the probability that product is positive number
a) 4/21 b) 0.5045 c) 0.6012 d) none

Section-C
Q(61). If u=log tan (π/4+/2), tanh (u/2) =?
(a)tan(/2) (b)cot (/2) (c) sin(/2) (d)cosec(/2) ( )

Q(62). Match the following functions to their derivatives?
(1) Sin 2x (2) cos3 x
(a) 2.cos2x, -3sinx.cos2x (b) cos 2x, -2 sinx.cosx (c) sin 2x, -2 cosx. Sin x (d) none of them ( )
Q (63). If u=tan-1 x3+y3 , then x du + y du = ?
(x-y) dx dx
(a) sin-2u (b) cosec2u (c) sin 2u (d) tan 2u ( )

Q (64). What would be the value for ∫ x. log (1+x) dx?
(a) x2 -1 log (1+x) – x2 + x (b) x2 -1 log (1+x) – x2 + x
2 4 2 3 1 4
(c) x2 -1 log (1+x) – x2 + x (d) x2 -1 log (1+x) – x2 + x ( )
2 4 2 2 3 1
Q(65). Match the followings ?
(1) sin 90 (2) cosec 30 (3) cot 45 (4) tan 0
(a) 1 , 2 , 1 , 0 (b) 1 , 2 , 1 ,0 (c) 2 , 1, 0 ,1 (d) 1 , 0 , 1 , 2 ( )
Q(66). Solve the following equation ?
(1) Sin 135 + cos 480 and (2) sin (270 +)=?
Sin 135 – cos 120
(a) (1) 3-2√2 , (2) –tan  (b) (1) 3-2√3 (2) –cos 
(c ) (1) 3-2√2 , (2) sin  (d) (1) 3-1√2 , (2) –sin  ( )
Q(67). If we expand sin7 cos 3  in a series of sines of multiples of  what would be right option?
(a) 2i sin 10- 4(2i sin8)+3(2i sin6)+8(2i sin 4)-14 (2i sin 2)
(b) 2i sin 11- 5(2i sin8)+3(6i sin6)+8(2i sin 4)-4 (2i sin 2)
(c) 2i sin - 4(2i sin8)+5(2i sin6)+9(2i sin 3)-14 (2i sin 2)
(d) None of the above ( )
Q(68). Match the sequence of the following categories ?
(1) row matrix (2) null matrix (3) column matrix
(a) (1) having only one column (2) having only one row (3) all elements are zero
(b) (1) having only one row (2) having only one column (3) all elements are zero
(c ) (1)having only one row (2) all elements are zero (3) having only one column
(d) all of the above are right ( )
Q(69) how many 7 persons committees can be formed each containing three females members from a available set of 20 , females and four males members from available set of 30 males
(a) 1140 (b) 27405 (c) 31,241,700 (d) none of these ( )
Q(70) In the non leap year the probability of having 53 Mondays is…..
(a) 1/7 (b) 2/7 (c) 3/7 (d) none of these ( )
Q71) a student A can solve 75 % of the problem given in this book and another student B can solve 70 % what is the probability that A or B can solve a problem chosen at random
a) 37/40 b) 3/40 c) 7/10 d) none ( )
Q72) how many password are possible of four character which consist at first latter an alphabet and remaining 3 character are letter from English alphabet or from the set of digit { 0,1,2,………9}
a) 46656 b) 279936 c) 278859 d) none ( )
Q73) how many 7 persons committees can be formed each containing three females members from a available set of 20 , females and four males members from available set of 30 males
a) 1140 b) 27405 c) 31241700 d) none ( )
Q74) In a certain college, 4% of men students & 1% of women students are taller than 1.8 m. furthermore 60% of students are women. If a student is selected at random & is found taller than 1.8 m. what is the probability that student is a women?
a) .2727 b) .3347 c) .43621 d) 0.1523 ( )
Q75) One integer is chosen at random from the numbers 1, 2, 3, ……. 100. what is the probability that chosen number is divisible 6 or 8?
a) 5/8 b) 1/5 c) 4/5 d) none ( )


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