YUVASENA MOCK CET EXAM
7
-1-
MATHS
1.
2.
For every point (x, y,z) on X - axis
A) y = 0, z = 0
C) x = 0, y = 0
The straight line is
B) x = 0
D) x = 0, z = 0
x − 3 y − 2 z −1
=
=
is
3
1
0
A) parallel to x - axis
C) parallel to z - axis
B) parallel to y - axis
D) perpendicular to z - axis
3.
The degree and order of the differential equation of the family of all parabolas
whose axis is x - axis are respectively
A) 2 , 1
B) 1 , 2
C) 3 , 2
D) 2 , 3
4.
In the examination of C. E.T. the total marks of mathematics are 300 . If the
answer is right, marks provided 3 and if the answer is wrong, marks provided - 1.
A student knows the correct answer of 67 question and remaining questions are
doubtful for him. He takes the time 1½ min. to give correct answer and 3 min. that
for doubtful. Total time is 3 hours. In the questions paper after every two simple
questions, one question is doubtful. He solve the questions one by one, then the
number of questions solved by him, are
A) 67
B) 90
C) 79
D) 80
SPACE FOR ROUGH WORK
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5.
If sec θ + tan θ =
(θ +
π
6
, then the principal value of
) is :
A) π / 3
C) 3 π / 4
B) π / 4
D) 2π / 3
6.
If y = x - x2, then the derivatives of y2 with respect to x2 is
A) 2x2 + 3x - 1
B) 2x2 - 3x + 1
C) 2x2 + 3x + 1
D) none of these
7.
The point (1,1) (-1, -1) and (- 3 , 3 ) are angular points of a triangle, then it is
........triangle
A) Right angled
B) Isosceles
C) Equilateral
D) none of these
8.
For the following pair of observations :
(1 , 6), (2 ,9), (3, 6), (4, 7), (5, 8), (6, 5), (7, 12), (8, 3), (9, 17), (10, 1) ; cov (X , Y)
is :
A) 0.6
B) 0.5
C) 0.4
D) None pf these
9.
Equation of circle of radius 5 units concentric with the circle x2 + y2 - 2x - 4y + 1
= 0 is
A) x2 + y2 - 2x - 4y + 5 = 0
B) x2 + y2 - 2x - 4y + 4 = 0
D) x2 + y2 - 2x - 4y + 20 = 0
C) x2 + y2 - 2x - 4y - 20 = 0
SPACE FOR ROUGH WORK
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10.
If point P (x, y) is equidistant from A ( a + b, a - b) B ( a - b, a + b) then,
A) ax = by
B) bx = by
C) xy = ab
D) none of these
11.
The locus of the point which moves so that the tangents from it to two circles
x2 + y2 - 5x - 3 = 0
3x2 + 3y2 + 2x + 4y - 6 = 0 are equal is
A) 2x2 + 2y2 + 7x + 4y -3 = 0
B) 17x + 4y + 3 = 0
2
2
C) 4x + 4y - 3x + 4y - 9 =0
D) 13x - 4y + 15 = 0
12.
The points on the curve y = 12x - x3 at which the gradient is zero are
A) (0 , 2), (2, 16)
B) ( 0, -2) , (2, -16)
C) (2, 16), ( −2, −16)
D) (2, 16) , (2, 16)
13.
Two perpendicular tangents drawn to ellipse
x2 y2
+
= 1 intersect on the curve.
25 16
B) x2 + y2 = 41
D) x2 - y2 = 9
A) x = 25 /3
C) x2 + y2 = 9
14.
f (x) = xx then (x) equals,
A) xx
C) x log x+ 1
B) log x
D) e x log x. log ex
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15.
Let the vectors 2i + 3j - 4k and ai + bj + ck be perpendicular then
A) a = 2, b = 3, c = -4
B) a = 4, b = 4, c = 5
C) a = 2, b = 4, c = 5
D) None of these
16.
If I is a unit matrix of order 10, then the determinant of I is equal to
A) 10
B) 1
C) 1/10
D) 9
17.
The number of real tangents that can be drawn to curve y2 + 2xy + x2 + 2x + 3y + 1
= 0 from the point (1, -2) is
A) One
B) Two
C) Nil
D) None of these
18.
Which of the following is not true on linear programming problems ?
A) A slack variable is a variable added to the left hand side of a less than or
equal to constraint to convert it into an equality.
B) A surplus variable is a variable subtracted from the left hand side of a greater
than or equal to constraint to convert it in to an equality.
C) A basic solution which is also in the feasible region in called a basic feasible
region.
D) A column in the simplex table that contains all of the variables in the solution
is called pivot or key column.
19.
The direction - consines of any normal to the xy - plane are
A) < 0 , 0 , 1 >
B) < 1 , 0 , 0 >
C) < 1 , 1 , 0 >
D) < 0 , 1 , 0 >
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20.
f ( x) =
=
1 + px − 1 − px
,−1 ≤ x ≤ 0
x
2x + 1
,0 ≤ x ≤ 1
x−2
is continuous in the interval [ -1, 1], then p is :
A) -1
B) -1/2
C) 1/2
D) 1
21.
If a matrix A is type 2 × 3 and the product ABC is defined then the number of
elements in matrix BC can be
A) 8
B) 4
C) 12
D) 32
22.
The equation of the unit circle concentric with x2 + y2 - 4x + 6y -12 = 0 is
B) x2 + y2 - 4x + 6y -15 = 0
A) x2 + y2 - 4x + 6y + 12 = 0
C) x2 + y2 - 4x + 6y + 25 = 0
D) x2 + y2 - 4x - 6y - 25 = 0
23.
Two unbiased dice are thrown. If it is known that one die shows a 3, what is the
probability that the sum of the two dice is greater that 7 ?
A) 1/4
B) 2/3
C) 1/3
D) None of these
24.
The chance of throwing a five first only of two successive throws with an
ordinary dice is
A) 1 / 36
B) 5 / 36
C) 25 / 36
D) 1 / 6
SPACE FOR ROUGH WORK
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25.
Equation of parabola, having (4, - 8) and (4, 8) as ends of its latus - rectum, is
A) y2 = 8x
B) y2 = 16x
D) x2 = 16 y
C) y2 = 32 x
26.
When two or more logical statements are combined by logical connective 'and', '
or', 'not' 'if then' ' if and only if ', then that statement is called :
A) simple logical statement
B) compound statement
C) simple and compound statement D) None of these
27.
The vertices of the feasible region { ( x, y) / x ≤ 4, x - y ≥ 0, 3x + y ≥ 3 } are
A) (1, 0), (4, 0), (4, 4) , and (¾ , ¾ )
B) (1, 0), (0, 4), (4, 4) , and (3, 3 )
C) (0, 1), (4, 0), (0, 4) , and (¾ , ¾ )
D) (0, 1), (1, 4), (4, 4) , and (3, 3 )
28.
The area of the region bounded by the curve y = 16 − x 2 and x - axis is :
A) 8π sq. units
B) 20π sq. units
C) 16π sq. units
D) 256π sq. units
29.
Any tangent to the curve y = 3x7 + 5x + 3
A) is parallel to X - axis
B) is parallel to Y - axis
C) makes an acute angle with X - axis
D) makes an obtuse angle with X - axis
30.
if A and B are square matrices of order 3, such that |A| = -1 |B| = 3 then the
determinant of 3 AB equal to
A) -9
B) -27
C) -81
D) 81
SPACE FOR ROUGH WORK
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31.
When two statement are connected by logical connective 'and ', then the compound
statement is called :
A) conjuctive statement
B) disjunctive statement
C) negation statement
D) conditional statement
32.
A sentence is a logical statement, when it is
A) either true or false
B) neither true nor false
C) true and false
D) None of these
33.
The separate equations of the lines represented by
3x2 - 4xy - 4y2 = 0 is,
A) 3x + 2y = 0 and x - 2y = 0
C) -2x + 3y = 0 and - 2x - 2y = 0
B) 2x + 2y = 0 and 2x - y = 0
D) -3x + 2y = 0 and x + 2y = 0
34.
If sum of two number is 3, then maximum value of the product of first and square
of second is :
A) 4
B) 3
C) 2
D) 1
35.
The value of k which means the function defined by :
sin (1/x), if x = 0
f(x) = k ,
if x = 0
continuous at x = 0 is :
A) 8
C) -1
B) 1
D) None of these
SPACE FOR ROUGH WORK
-8-
36.
∫
sin x − cos x
dx
sin 2 x
A) log (sin x + cos x + sin 2 x ) +c
B) - log (sin x + cos x + sin 2 x ) +c
C) log (sin x - cos x + sin 2 x ) +c
D) - log (sin x - cos x + sin 2 x ) +c
37.
The general solution of cos 2θ = sin α is given by :
A) θ =
nπ α
−
4
2
π
B) θ = 2nπ ± ( − α )
1
2
π α
D) θ = nπ ± ( − )
2
n
C) θ = [nπ + ( −1) α ]
38.
2
If 3 sin x + cos x = 3 ,then the general solution is x =
π
A) nπ + ( )
π
B) nπ + ( )
π
n π
C) nπ + (−1) ( ) +
π
n π
D) nπ + (−1) ( ) −
6
3
4
39.
4
3
3
6
The equation of curve whose length of subtangent is constant k, is
A) x = k log y + c
B) k = y log x + c
C) y = k log x + c
D) none of these
SPACE FOR ROUGH WORK
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40.
The area bounded by the curve y = , the x2 - axis and line x = 2 1/3 is divided into
two equal areas by the line x = k. The value of k is :
B) 1
A) 2 1/3-1
−2/3
C) 2
D) 2 1/3-1
41.
If ∫ (1 / f ( x )) dx = log{ f ( x )}2 + c, then f (x) =
A) x + a
C) (x/2 ) + a
42.
B) 2x + a
D) x2+ a
One of the following is not a vector
A) displacement
C) centrifugal force
B) work
D) None of these
43.
Three non - zero, non - parallel coplanar vetcors are always
A) Linearly dependent
B) Linearly independent
C) either (A) and (B)
D) None of these
44.
Let f (x) = 2a - x, - a < x < a = 3x - 2a, a ≤ x. Then
A) f is discontinuous at x = a
B) f is continuous at x = a but is not differentiable at x = a
C) f is differentiable at x = a
D) none of these
45.
If the coefficient of correlation between x and y is 0.28, co- variance between x and y
is 7.6 and the variance of x is 9, then the S.D. of y series is :
A) 9.8
B) 10.1
C) 9.05
D) 10.05
SPACE FOR ROUGH WORK
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46
A fair die is tossed. If the number is even, th the probability that is prime is
A) 1 / 2
C) 1 / 4
47.
B) 1 / 3
D) 1 / 5
ex + log y = c is a constant of
dy
+ yex = 0
dx
dy
x
C) y
dx = e
A)
B)
dy
= yex
dx
D) none of these
48.
The area of a parabola y2 = 4αx bounded by its latus - rectum is
A) 8 / 3 α2
B) 16 / 3 α2
C) 4 / 3 α2
D) 2 / 3 α2
49.
If f " (x) = 60 x3, then
A) f (x) is a polynomial of degree 5
B) f 9x) is a polynomial of degree 5 with leading coefficient 3
C) f (x) is a polynomial of degree 5 with integral coefficients
D) f (x) is a polynomial of degree with leading coefficient 60.
50.
The co - efficient of correlation between two variables x and y is 0.5 , their co variance is 16, S. D. of x is 4, then S. D. of x is 4, then S. D. of y is equal to :
A) 4
B) 8
C) 16
D) 64
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