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Worksheets11 th maths vol I EM
Total questions: 134
Worksheet time: 1hrs 7mins
The equation of the locus of the point whose distance from y axis is half the distance from origin is
x2 +3y2 = 0
x2 - 3y2 = 0
3x2 +y2 = 0
3x2 - y2 = 0
Which of the following is the locus of (at2,2at)
x2/a2 - y2/b2 = 1
x2/a2 + y2/b2 = 1
x2+y2 = a2
y2 = 4ax
Which of the following point lie on the locus of 3x2 3y2 -8x-12y+17 = 0
(0,0)
(-2,3)
(1,2)
(0-1)
If the point (8,-5) lies on the locus x2/16 - y2/25 = k, then the value of k is
0
1
2
3
Straight line joining the point (2,3) and (-2,4) passes through the point (α,β) if
α+2β=7
3α+β=9
α+3β=11
3α+β=11
The slope of the line which makes an angle 450 with the line 3x-y = -5 are
1, -1
1/2, -2
1, 1/2
2, -1/2
Equation of the straight line that form an isosceles with coordinate axis in the I-quadrant with perimeter 4+2√2 is
x+y+2 = 0
x+y-2 = 0
x+y-√2 = 0
x+y+√2 = 0
The coordinates of the four vertices of a quadrilateral are (-2,4), (-1.2), (1,2) and (2,4) taken in order. The equation of the line passing trough the vertex (-1,2) and dividing the quadrilateral in the equal areas is
x+1 = 0
x+y = 1
x+y+3 = 0
x-y+3 = 0
The intercept of the perpendicular bisector of the line segment joining (1,2) and (3,4) with coordinate axes are
5, -5
5, 5
5, 3
5, -4
The equation of the line with slope 2 and the length of the perpendicular from the origin equal to √5 is
x-2y = √5
2x-y = √5
2x-y = 5
x-2y-5 = 0
A line perpendicular to the line 5x-y=0 forms a triangle with the coordinate axes. If the are of the triangle is 5 sq. units, then its equation is
x+5y±5√2=0
x-5y±5√2=0
5x-y±5√2=0
x5+y±5√2=0
Equation of the straight line perpendicular to the line x-y+5=0, through the point of intersection the y axis and the given line
x-y-5 = 0
x+y-5 = 0
x+y+5 = 0
x+y+10 = 0
If the equation of the base opposite to the vertex (2,3) of an equilateral triangle is x+y=2, then the lenght of a side is
√3/2
6
√6
3√2
The line (p+2q)x + (p-3q)y = p-q for different values of p and q passes through the point
(3/2, 5/2)
(2/5, 2/5)
(3/5, 3/5)
(2/5, 3/5)
The point on the line 2x-3y=5 is equidistance from (1,2) and (3,4) is
(7,3)
(4,1)
(1,-1)
(-2,3)
The image of the point (2,3) in the line y=-x is
(-3,-2)
(-3,2)
(-2,-3)
(3,2)
The length of ⊥ form the origin to the line x/3 - y/4 = 1, is
11/5
5/12
12/5
- 5/12
The y intercept of the straight line passing through (1,3) and perpendicular to 2x-3y+1=0 is
3/2
9/2
2/3
2/9
If the two straight line x+ (2k-7)y + 3 = 0 and 3kx+9y-5=0 are perpendicular then the value of k is
k = 3
k = 1/3
k = 2/3
k = 3/2
If a vertex of a square is at the origin and its one side lies along the line 4x+3y-20=0, then the area of the square is
20 sq. units
16 sq. units
25 sq. units
4 sq. units
If the line represented by the equation 6x2 + 41xy - 7y2 = 0 makes angle α and β with x axis, then tanαtanβ =
- 6/7
6/7
7/6
- 7/6
The area of the triangle formed by the line x2-4y2=0 and x=a is
2a2
√3/2 a2
1/2 a2
2/√3 a2
If one of the lines given by 6x2-xy+4cy2=0 is 3x+4y=0, then c =
-3
-1
3
1
θ is acute angle between the line x2-xy-6y2=0, then 2cosθ +3sinθ/4sinθ +5cosθ
1
-1/9
5/9
1/9
One of the equation of the lines given by x2 + 2xycotθ - y2 = 0 is
x - ycotθ = 0
x + ytanθ = 0
xcosθ + y (sinθ + 1) = 0
xsinθ + y(cosθ + 1) = 0
1/cos 800 - √3/ sin 800 =
√2
√3
2
4
If cos 280 + sin 280 = k3, then cos 170 =
k3/√2
- k3/√2
± k3/√2
- k3/√3
The maximum value of 4sin2x + 3 cos 2x + sin x/2 + cos x/2 is
4 + √2
3 + √2
9
4
(1 + cos π/8) (1 + cos 3π/8) (1 + cos 5π/8) (1 + cos 7π/8) =
1/8
1/2
1/√3
1/2
If π<2θ>3π/2, then √2+√2+2cos4θ =
-2 cosθ
-2 sinθ
2 cosθ
2 sinθ
If tan 400 = λ, then tan1400 - tan1300 / 1 + tan1400 tan1300 =
1-λ2/λ
1+λ2/λ
1+λ2/2
1-λ2/2λ
cos10 + cos20 cos30 + ....+ cos1790 =
0
1
-1
89
Let fk(x) = 1/k [sinkx + coskx] where x∊R and k≥1. Then f4(x) - f6(x) =
1/4
1/12
1/6
1/3
Which of the following is not true?
sinθ = -3/4
cosθ -1
tanθ = 25
secθ = 1/4
cos2θcos2Φ + sin2(θ-Φ) - sin2(θ-Φ) =
sin2(θ+Φ)
cos2(θ+Φ)
sin2(θ-Φ)
cos2(θ-Φ)
sin(A-B)/cosAcosB + sin (B-C)/cosBcosC + sin(C-A)/cosCcosA is
sinA + sinB+ sinC
1
0
cosA + coB + cosC
If cospθ + cosqθ = 0 and if p≠q, then θ is equal to ( n is any integer)
π(3n+1)/p-q
π(2n+1)/p±q
π(n±1)/p±q
π(n+2)/p+q
If tanα and tanβ are the roots of x2 ax + b = 0, then sin(α+β)/sinαsinβ is equal to
b/a
a/b
- a/b
- b/a
In a triangle ABC, sin2A +sin2B + sin2C = 2, then the triangle is
equilateral triangle
isosceles triangle
right triangle
scalene triangle
If f(θ) = |sinθ| + |cosθ|, θ∊R, then f(θ) is in the interval
[0, 2]
[1, √2]
[1, 2]
[0, 1]
cos6x + 6cos4x + 15cos2x + 10/cos5x + 5cos3x + 10cosx is equal to
cos2x
cosx
cos3x
2 cosx
Th triangle of maximum area with constant perimeter 12m
is an equilateral triangle with side 4m
is an isosceles triangle with sides 2m, 5m, 5m
is an triangle 3m, 4m, 5m
does not exist
A wheel is spinning at 2 radians/second. How many seconds will it take to make 10 complete rotations?
10π seconds
20π seconds
5π seconds
15π seconds
If sinα + cosα = b, then sin2α is equal to
b2 - 1, if b≤√2
b2 - 1, if b>√2
b2 - 1, if b≥√2
b2 - 1, if b≤1
In a ∆ABC, if
i) sinA/2 sinB/2 sinC/2 > 0
ii) sinA sinB sinC > 0 then
Both i) and ii) are true
only i) is true
only ii) is true
neither i) nor ii) is true
The sum of the digit at the 10th place of all numbers formed with the help of 2, 4, 5, 7 taken all at a time is
432
108
36
18
In an examination there are three multiple choice question and each question has 5 choices. Number of ways in which a student can fail to get all answer correct is
125
124
64
63
The number of ways in which the following prize be given to a class of 30 boys first and second in mathematics, first and second in physics, first in chemistry and first in English is
304 x 292
303 x 293
302 x 294
30 x 295
The number of 5 digit number all digits of which are odd is
25
55
56
625
In 3 figure, the number of ways four rings can be worn is ...... ways.
43-1
34
68
64
If (n+5)P(n+1) = (11(n-1)/2) (n+3)Pn, then the value of n are
7 and 11
6 and 7
2 and 11
2 and 6
The product of r consecutive positive integer is divisible by
r!
(r-1)!
(r+1)!
rr
The number of five digit telephone number having at leas one of their digit repeated is
90000
10000
30240
69760
If a^2-aC2 = a^2-aC4 then the value of 'a' is
2
3
4
5
There are 10 points in a plane and 4 of them are collinear. The number of straight lines joining any two points is
45
40
39
38
The number of ways in which a host lady invite 8 people for a party 8 out of 12 people of whom two do not want to attend the party together is
2 x 11C7 + 10C8
11C7 + 10C8
12C8 - 10C6
10C6 + 2!
The number of parallelogram that can be formed from a set of four parallel lines interecting another set of three parallel lines
6
9
12
18
Everybody in a room shakes hands with everybody else. The total number of shake hand is 66. The number of persons in the room is........
11
12
10
6
Number of sides of a polygon having 44 diagonals is........
4
4!
11
22
If 10 lines are drawn in a plane such that no two of them are parallel and no three are concurrent, then the total number of points of intersection are
45
40
10!
210
In a plane there are 10 points are there out of which 4 points are collinear, then the number of triangles formed is
110
10C3
120
116
In 2nC3 : nC3 = 11 : 1 then n is
5
6
11
7
(n-1)Cr + (n-1)C(r-1) is
(n+1)Cr
(n-1)Cr
nCr
nC(r-1)
The number of rectangle that a chessboard has........
81
99
1296
6561
The number of 10 digit number that can be written by using the digit 2 and is
10C2 + 9C2
210
210 - 2
10!
If Pr stands for rPr then the sum of the series 1 + P1 +2P2 + 3P3 + ...... + nPn is
Pn+1
Pn+1 - 1
Pn-1 + 1
(n-1)P(n+1)
The product of first n odd natural numbers equals
2nCn x nPn
(1/2)n x 2nCn x nPn
(1/4)n x 2nCn x nPn
nCn x nPn
If nC4, nC5, nC6 are in AP the value of n can be
14
11
9
5
1 + 3+5 + 7+ ........ + 17 =
101
81
71
61
If A = {(x, y) : y = ex, x∈R} and B = {(x, y) : y = e-x, x∈R} then n(A∩B) is
Infinity
0
1
2
If A {(x. y) : y = sinx, x∈R} and B = {(x, y) : y = cosx, x∈R} then A∩B contains
no element
infinitely many element
only one element
cannot be determined
The relation R defined on a set A = {0, -1, 1, 2} by xRy if |x2+y2| ≤ 2, then which one of the following is true?
R = {(0,0), (0,-1), (0,1), (-1,0), (-1,1), (1,2), (1,0)}
R-1 = {(0,0), (0,-1), (0,1), (-1,0), (-1,1), (1,0)}
domain of R is {0, -1, 1 2}
range of R is {0, -1, 1 }
If f(x) = |x-2| + |x+2, x∈ℝ, then
Let ℝ be the set of all real number. Consider the following subset of the plane ℝxℝ : S = {(x, y) : y = x+1 and 0<x<2} and T = {(x, y) : x-y is an integer} Then which of the following is true?
T is an equivalence relation but S is not an equivalence relation.
Neither S nor T is an equivalence relation
Both S and T are equivalence relation
S is an equivalence relation but T is not an equivalence relation.
Let A and B be subset of the universal set ℕ, the set of natural numbers. Then A'∪[(A∩B)∪B'] is
A
A'
B
ℕ
The number of students who take both subjects Mathematics and Chemistry is 70. This represents 10% of the enrollment in mathematics and 14% of the enrollment in chemistry. The number of students take at least one of these two subjects is
1120
1130
1100
insufficient data
If n((AxB) ∩ (AxC)) = 8 and n(B∩C) = 2, then n(A) is
6
4
8
16
If n(A) = 2 and n(BUC) = 3, then n[(AxB) U (AxC)] is
23
32
6
5
If two sets A and B have 17 elements in common, then the number of elements common to the set AxB and BxA is
217
172
34
insufficient data
For non-empty sets A and B, if A⊂B then (AxB) ∩ (BxA) is equal to
A∩B
AxA
BxB
none of these
The number of relation on a set containing 3 elements is
9
81
512
1024
Let R be the universal relation on a set X with more than one element. Then R is
not reflexive
not symmetric
transitive
none of these
Let X = {1,2,3,4} and r = [(1,1), (1,2), (1,3), (2,2), (3,3), (2,1), (3,1), (1,4), (4,1)}. Then R is
reflexive
symmetric
transitive
equivalence
The range of the function 1/1-2sinx is
(-∞, -1) U (1/3, ∞)
(-1, 1/3)
[-1, 1/3]
(-∞, -1] U [1/3, ∞)
Let range of the function f(x) = |⌊x⌋ - x|, x∊ℝ is
[0,1]
[0,∞)
[0,1)
(0,1)
The rule f(x) = x2 is a bijection if the domain and the co-domain are given by
ℝ,c
ℝ, (0,∞)
(0,∞), ℝ
[0,∞), [0,∞)
The number of constant function from a set containing m element to a set containing n elements is
mn
m
n
m+n
The function f: [-3,3]→S defined by f(x) = x2 is onto, then S is
[-9, 9]
ℝ
[-3, 3]
[0, 9]
The function f: [0, 2π]→[-1, 1] defined by f(x) = sinx is
one-to-one
onto
bijection
cannot be defined
Let X = {1,2,3,4}, Y = {a,b,c,d} and f = {(1,a), (4,b), (2,c), (3,d), (2,d)}. Then f is
an one-to-one function
an onto function
a function which is not one-to-one
not a function
Let f : ℝ→ℝ be defined by f(x) = 1-|x|. Then the range is
ℝ
(1,∞)
(-1, ∞)
(-∞, 1]
The function f : ℝ→ ℝ is defined by f(x) = sinx + cosx is
an odd function
neither an odd function nor an even function
an even function
both odd function and even function
an odd function
neither odd function nor even function
an even function
both odd function and even function
If |x+2|≤9, then x belongs to
(-∞, -7)
[-11, 7]
(-∞, -7) U [11, ∞)
(-11, 7)
Given that x, y and b are real numbers x<y, b<0, then
xb<yb
xb>yb
xb≤yb
xb≥yb
If |x-2|/x-2 ≥ 0, then x belongs to
[2,∞)
(2,∞)
(-∞, 2)
(-2,∞)
The solution of 5x-1 < 24 and 5x+1 > -24 is
(4, 5)
(-5, -4)
(-5, 5)
(-5, 4)
The solution set of the following inequality |x-1| ≥ |x-3| is
[0, 2]
[2, ∞)
(0, 2)
(-∞, 2)
The value of log√2512
16
18
9
12
The value of log3 1/81 is
-2
-8
-4
-9
If log√x0.25 =4, then the value of x i
0.5
2.5
1.5
0.25
The value of logab logbc logca is
2
1
3
4
f 3 is the logarithm of 343, then the base is
5
7
6
9
Find a so that the sum and product of the root of the equation 2x2 + (a-3)x +3a -5 = 0 are equal is
1
2
0
4
If a and b are the roots of the equation x2 - kx + 16 = 0 and satisfy a2 + b2 = 32, then the value of k is
10
-8
-8, 8
6
The number of solution of x2 + |x-1| = 1 is
1
0
2
3
The equation whose roots are numerically equal but opposite in sign to the roots of 3x2 - 5x - 7 = 0 is
3x2 - 5x - 7 = 0
3x2 + 5x - 7 = 0
3x2 - 5x + 7 = 0
3x2 - x - 7 = 0
If 8 and 2 are the roots of x2 + ax + c = 0 and 3, 3 are the roots of x2 + dx + b = 0, then the roots of the equation x2 + ax + b = 0 are
1, 2
-1, 1
9, 1
-1, 2
If a and b are the real roots of the equation x2 - kx + c = 0, then the distance between the points (a, 0) and (b,0) is
√k2 - 4c
√4k2 - c
√4c - k2
√k - 8c
If kx/(x+2)(x-1) = 2/x+2 + 1/x-1, then the value of k is
1
2
3
4
If 1-2x/3+2x-x2 = A/3-x + B/x+1, then the value of A+B is
-1/2
-2/3
1/2
2/3
The number of roots of (x+3)4 + (x+5)4 = 16 is
4
2
3
0
The value of log311 ⋅ log1113 ⋅ log1315 ⋅ log1527 ⋅ log2781 is
1
2
3
4
The value of 2+4+6+......+2n is
n(n-1)/2
n(n+1)/2
2n(n+1)/2
n(n+1)
The coefficient of x6 in (2+-2x)10 is
10C6
26
10C6 26
10C6 210
The coefficient of x8y12 in the expansion of (2x+-3y)20 is
0
28312
28312 + 21238
20C8 28312
If nC10 > nCr for all possible r, then the value of n is
10
21
19
20
If a is the arithmetic mean and g is the geometric mean of two numbers, then
a≤g
a≥g
a=g
a>g
If (1+x2)2 (1+x)n =a0 + a1x + a2x2 + ....... + xn+4 and if a0, a1, a2 are in AP, then n is
1
5
2
4
If a,8,b are in AP, a,4,b are in GP, and if a,x,b are in HP then x is
2
1
4
16
The sequence 1/√3, 1/√3+/√2, 1/√3+2√2, ..... form an
AP
GP
HP
AGP
The HM of two positive number whose AM and GM are 16,8 respectively is
10
6
5
4
If Sn denotes the sum if n term of an AP whose common difference id d, the value of Sn -2Sn-1 + Sn-2 is
d
2d
4d
d2
The remainder when 3815 is divided by 13 is
12
1
11
5
The nth term of the sequence 1,2,4,7,11,........ is
n3+3n2+2n
n3-3n2+23n
n(n+1)(n+2)/3
n2-n+2/2
The sum up to n term of the series 1/√1+1√5 + 1/√3+√5 + 1/√5+√7 +....... is
√2n +1
√2n +1/2
√2n +1 -1
√2n +1 -1/2
The nth term of the sequence 1/2, 3/4, 7/8, 1 5/16,...... is
2n-n-1
1-2-n
2-n +n-1
2n-1
The sum up to n terms of the series √2+√8+√18+√32+..... is
n(n+1)/2
2n(n+1)
n(n+1)/√2
1
The value of the series 1/2 + 6/4 + 13/8 + 19/16 + ..... is
14
7
4
6
The sum of an infinite GP is 18. If the first term is 6, the common ratio is
1/3
2/3
1/6
3/4
The coefficient of x5 in the series e-2x is
2/3
3/2
-4/16
4/15
The value of 1/2! + 1/4! + 1/6! + ..... is
e2+1/2e
(e+1)2/2e
(e-1)2/2e
e2-1/2e
The value of 1 - 1/2(2/3) + 1/3(2/3)2 - 1/4(2/3)3 + ..... is
log(5/3)
3/2 log(5/3)
5/3 log(5/3)
2/3 log(2/3)
