Reference no: EM131663997
FUNCTIONS AND LIMITS
1. A rule that assigns to each element x in X a unique element y in Y is called a function from
a) X to X b) X to Y c) Y to Y
2. If f : X → Y is a function, then the elements of X are called
a) pre-images b) images c) constantans d) ranges
3. If f : X → Y is a function and x∈X, then
a) f (x) = 1 b) f(x) ∈Y c) f (x) ∈ X d) f(x) ∉Y
4. If f: X → f(X) is a function, then the elements of f(X) are called
a) pre-images b) images c) constantans d) ranges
5. If f : x → (3x - 5)/(x + 3) is a function, then f (0) =
a) 5 b) 3 c) - 3/5 d) - 5/3
6. If f : x → (2x2 + 5x -1)/(x + 3) is a function, then f(o) =
a) - 1/3 b) - 1/4 c) - 1/5 d) 0
7. If f : x → x2 - 2x +1 is a function, then f (t + 1) =
a) t + 1 b) t2 + 1 c) t - 1 d) t2 - 1
8. If f : X → Y is a function, then domain of f is
a) Y b) X c) - X d) - Y
9. If f : X → Y is a function, then the subset of Y containing all images is called the
a) domain of f b) range of f c) subset of X d) Superset of X
10. If f : X → Y is a function, then x∈X is called the
a) Dependent variable of f b) independent variable of f c) Value of f d) range of f
11. f (x) = x2 - 4x + 1 is
a) trigonometric function b) logarithmic function c) exponential function d) algebraic function
12. f (x) = log x is
a) trigonometric function b) logarithmic function c) exponential function d) algebraic function
13. f (x) = ex is
a) trigonometric function b) logarithmic function c) exponential function d) algebraic function
14. f (x) = ax + b, a ≠ 0 is
a) trigonometric function b) cubic function c) quadratic function d) linear function
15. The graph of a linear function is
a) parabola b) ellipse c) hyperbola d) straight line
16. A function f : X → X defined by f(x) = x, ∀ x∈ X is called the [1/2 f-1 (x)]
a) trigonometric function b) cubic function c) quadratic function d) identity function
17. The linear function f (x) = ax +b is an identity function if
a) a = 0, b =1 b) a = 1, b =0 c) a = 1, b =1 d) a = 0, b =0
18. If K is a constant, then the function f : x → k is
a) constant function b) cubic function c) quadratic function d) identity function
19. sinh x =
a) (ex + e- x)/2 b) (ex - e- x)/2 c) (ex - e- x)/(ex + e- x) d) (ex + e- x)/(ex - e- x)
20. tanh x =
a) (ex + e- x) 2 b) (ex - e- x)/2 c) (ex - e- x)/(ex + e- x) d) (ex + e- x)/(ex - e- x)
21. cosh 2 x - sinh 2 x =
a) - 2 b) -1 c) 1 d) 2
22. sinh -1 x =
a) In(x + √(x2+1)) b) In(x + √(x2 - 1)) c) 1/2 In ( 1+ x )/(1- x) d) 1/2 In ( x +1 )/(x -1)
23. Equations x = 3cos t and y = 3 sin t represent the equation of
a) line b) circle c) parabola d) hyperbola
24. If f(-x) = f(x) for every number x in the domain of f, then f is
a) linear function b) periodic function c) odd function d) even function
25. If f(-x) = -f(x) for every number x in the domain of f, then f is
a) linear function b) periodic function c) odd function d) even function
26. f (x) = cos x is
a) linear function b) quadratic function c) odd function d) even function
27. f (x) = x cotx is
a) linear function b) quadratic function c) odd function d) even function
28. if f (x) = x4 - 4x2 + 4, then f (√(x +1))=
a) x -1 b) (x-1)2 c) x2 - 1 d) x2 + 1
29. If f(x) = √(Cos(2Π sin x)) , then f ( Π/2 ) =
a) - 1 b) 0 c) 1 d) √2
30. If f(x) = √(2cos(2Πsinx)), then f ( Π/2 ) =
a) - 1 b) 0 c) 1 d) √2
31. If f(x) = √(x+4), then f (x2 + 4) =
a) x2 - 8 b)√(x2 - 8) c) √(x2 + 8) d) x2 + 8
32. If f(x) = x3 + 2x2 - 1, then (f (a + h) - f (a))/h
a) 0 b) 1 c) h2 +a2 d) h2+(3a+2)h+3a2+4a
33. If f(x) = x3 + 2x2 - 1, then (f (1+ h) - f (1))/h
a) h b) h2- 5h + 7 c) h2 + 5h + 7 d) h2 + 5h - 7
34. If P is the perimeter of a square and A is its area, then P=
a) √A b) 2√A c) 3√A d) 4√A
35. If A is the area of the circle and C is its circumference C, then C =
a) 8√(ΠA) b) 4√(ΠA) c) 2√(ΠA) d) √(ΠA)
36. The volume of a cube of side length 2 is
a) 2 cubic units b) 4 cubic units c) 8 cubic units d) 16 cubic units
37. If f(x) = √(x2 - 4) , then domain of f is
a) (-∞, -2] ∪ [2, ∞) b) (-∞, ∞) c) [-2, 2] d) [-3, 3]
38. if f (x) = |x|, then range of f is
a) (-∞, 0] b) [0, ∞) c) (-∞, ∞) d) none of these
39. x = a secθ, y = b tanθ are perimeter equations of
a) circle b) parabola c) ellipse d) hyperbola
40. If f(x) = x - 2 and f(x) = √(x2 + 1), then (f o g) (x) =
a)√(x2 +1) - 2 b) √(x2 - 4x + 5) c) x2 - 1 d) x2 - 4x + 5
41. If f(x) = (2x +1)/(x -1) , then f-1 (x)
a) x -1/2x +1 b) x - 2/x +1 c) x +1/x - 2 d) 2x - 6/
42. f : x → √(3x2 -1) and g : x → sin x , then f o g : x →
a) sin(3x2 - 1) b) sin√(3x2 - 1) c) √(3sinx2 -1) d) √(3x2 - 1sinx)
43. lim (x3 - x)/(x +1) =
x→-1
a) 5 b) 3 c) 2 d) 0
44. lim (2x2 - 32)/(3 + 4x2 ) =
x→4
a) 5 b) 3 c) 2 d) 0
45. lim (x - 2)/(√x - √2) =
x→2
a)√2 b) 2 c) 2√2 d) 0
46. lim (tanx)/x =
x→0
a) 0 b) 1 c) 2 d) 6
47. lim (sin6x)/x =
x→0
a) 0 b) 1 c) 2 d) 6
48. lim sin x0/x =
x→0
a) Π/180 b) 180/Π c) 180Π d) 1
49. lim (sin ax)/(sin bx) =
x→0
a) 1/ab b) b/a c) a/b d) 1
50. lim x2/(sin axsin bx) =
x→0
a) 2/3 b) 3/2 c) 1/6 d) 1
51. lim (1 + 1/x)x =
x→∞
a) 2/3 b) 3/2 c) 1/6 d) 1
52. lim (x/(1 + x))x =
x→0
a) e-1 b) e1/2 c) e2 d) e3
53. lim = (√(1+sinx - √(1 - sinx))/x =
x→0
a) -1 b) 0 c) 1 d) 2
DIFFERENTIATION
1. lim f (x + δ x) - f (x)/δx =
δx→0
a) f'(x) b) f'(a) c) f'(2) d) f'(0)
2. d/dx (axm + bxn ) =
a) axm-1 + bxn-1 b) amxm-1 + bnxn-1 c) xm-1 + xn-1 d) mxm-1 + nxn-1
3. f (x) = 1/x -1 ⇒ f'(2) =
a) 1 b) 0 c) - 1 d) - 2
4. d/dx [ f (x) sin x] =
a) f' (x) sin x + f(x) cos x b) f' (x) sin x - f(x) cos x c) f' (x) cos x + f(x) sin x d) f' (x) cos x
5. d/dx (- cosec x) =
a) -cosecx cotx b) cosecx cotx c) - sin x d) sec x tan x
6. d/dx (cosec-1x)
a) 1/x√(x2 -1) b) - 1/x√(x2 -1) c) 1/1+ x2 d) cot-1 x
7. 3x + 4y + 7 = 0 ⇒ dy/dx =
a) 3/4 b) - 3/4 c) - 4/3 d) 0
8. (1+ x2) d/dx (tan-1 x - cot-1 x) =
a) -1 b) 0 c) 1 d) 2
9. If f(x) = √(x + 1), then d/dx ((1/2 f-1 (x)) =
a) 0 b) x c) 2x d) 3x
10. 1/x d/dx (sin x2 ) =
a) 2xcosx2 b) cosx2 c) 2xcos2x d) 2cosx2 1/3
11. 1/3x2 d/dx (t in x3 ) =
a) sec2x3 b) 3x2 sec2 x3 c) sec2 x d) 3sec2 x
12. 2√tan x d/dx √tan x =
a) 1/√tan x.sec2x b) 0 c) sec2 x d) √tan x
13. if f(x) = tanx, then f' (x) cos2 x =
a) sec2 x b) sec x c) 0 d) 1
14. If f(x) = √(x +1), then d/dx (1/2 f -1 (x) )
a) 0 b) x c) 2x d) 3x
15. 1/3x2 d/dx (tan x2 ) =
a) sec2 x3 b) 3x2 sec2 x3 c) sec2 x d) 3sec2 x
16. If f(x) = tanx, then f' (x) cos2x =
a) sec2 x b) sec x c) 0 d) 1
17. d/dx tan-1 (sin 2x/1 + cos x ) =
a) 0 b) 2 c) 1 d) 0
18. d/dx cot-1 ((1+ cos x)/sin2x) =
a) 3 b) 2 c) 1 d) 0
19. d/dx [tan-1 √(1- cos x)/√(1+ cos x) ] =
a) 1 b) 1/2 c) 0 d) -1
d [ ( -1 cot2 x +1 )]
20. d/dx [tan (sec-1(√(cot2x + 1)/cot2x)] =
21. d/dx (ax) =
a) - cosec2 x b) sec2 x c) sec x d) sec x tan x
22. d/dx(5x - 2x) =
a) 5xln5- 2x ln2 b) 5x ln5 + 2x ln 2 c) 5x + 2x d) 5x - 2x
23. d/dx (cosh 3x) =
a) 3cosech3x b) -3 sinh 3x c) 3 sinh 3x d) 3 coth 3x
24. d/dx (coth x) =
a) sec h2 x b) -sec h2 x c) coth x d) cosechx
25. d/dx (cosech x) =
a) - cosechxcothx b) cosechxcothx c) sechx tanh x d) - sechx tanhx
26. d/dx (coth-1 x) =
a) 1/(1- x2) b) 1/(1+ x2) c) -1/(1- x2) d) -1/(1+ x2)
27. If f (x) = sinx, then f' (cos-1 3x) =
a) cos x b) - 3/√(1 - 9x2) c) 3/√(1- 9x2) d) 3x
28. If f (x) = tan-1x, then f' (tan x) =
a) 1/(1+ x2) b) sin2 x c) cos2 x d) sec2 x
29. d/dx [e f(x) ] =
a) e f( x) b) e(x) c) ef(x)/f'(x) d) ef(x)f'(x)
30. d/dx [10sin x ] =
a) 10cos x b) 10sin x cos x ln10 c) 10sin x ln10 d) 10cos x ln10
31. If y = sin3x, then y4 =
a) 3sin 3x b) 9sin3x c) 27sin 3x d) 81 sin 3x
32. If f= ex, then y4 =
a) 0 b) ex c) 2ex d) 4ex
33. If f (x) = sinx, then f (sin-1 x) =
a) 1/√(1-x2) b) cos x c) - sin x d) -x
34. ln (1 - x ) =
a) x- x3/3! + x5/5! - x7/7! +...... b) 1 - x2/2! + x4/4! - x6/6! +...... c) - x - x2/2 - x3/3 - x4/4 d) x - x2/2 + x3/3 - x4/4 + ......
35. cos x
a) x- x3/3! + x5/5! - x7/7! +...... b) 1 - x2/2! + x4/4! - x6/6! +...... c) - x - x2/2 - x3/3 - x4/4 d) x - x2/2 + x3/3 - x4/4 + ......
36. ex
a) x + x2/2 + x3/3 + x4/4 +...... b) 1 - x2/2! + x4/4! - x6/6! +...... c) 1 + x + x2/2! + x3/3! +.... d) 1 - x + x2/2! - x3/3!
37. If f (x) = x3 = cos x , then f' (x) =
7 = 4
a) 3x2 - sinx b) 3x2 - sinx c) 3x2 - sinx d) 0
0 4 0 0 7 4
38. The function f (x) = x3 is
a) increasing for x>0 b) decreasing for x < 0 c) decreasing for x > 0 d) constant x > 0
39. The minimum value of the function f (x) = 5x2 - 6x + 2 is
a) 1/5 b) 1/4 c) 1/3 d) 0
INTEGRATION
1. The integration is the reverse process of
a) tabulation b) sublimation c) classification d) differentiation
2. ∫d/dx xn dx =
a) xn+1/n + c b) xn-1/n -1 + c c) xn+1/n +1 + c d) xn + c
3. ∫cos ecxdx = ∫- cosec2 xdx
a) cosx + c b) -cosx + c c) tanx + c d) cotx + c
4. ∫ -3cos ec23xdx =
a) -cot3x + c b) -cos3x + c c) tan3x + c d) cot3x + c
5. ∫(n +1)[x2 + 2x -1]n (2x + 2)dx =
a) (x2 + 2x -1)n+1 + c b) (x2 + 2x -1)n +1 c) (x2 + 2x -1)n-1 d) n(x2 + 2x -1)n-1
6. ∫ (x -1)/(x2 - 2x +1)dx =
a) 1/2 ln(x2 - 2x +1) + c b) 1/4ln(x2 - 2x +1) + c c) ln(x2 - 2x +1) + c d) ln(2x - 2) + c
7. ∫ cosec2 x/ cot x dx =
a) ln tanx + c b) ln cotx + c c) 2 ln cotx + c d) 2 ln tanx + c
8. ∫ sec2 x/tan x + ∫cosec2 x/cot x dx =
a) ln tanx + c b) ln cotx + c c) 2 ln cotx + c d) 2 ln tanx + c
9. ∫(1/x - cosec2x/cot x)dx =
a) ln(x sinx) + c b) ln(x sinx2x) + c c) ln (x tanx) + c d) ln (x cot x) + c
10. ∫ ( 1/x - sin 2x/tan x ) dx =
a) ln (x sinx) + c b) ln (x sinx2x ) + c c) ln ( x tanx )+ c d) ln (x cot x) + c
11. ∫ ( ex + sin 2x/( sin2 x ) dx =
a) ln(ex sin2 x) + c b) ln(x sin2 x) + c c) ln(x cos2 x) + c d) ln(ex cos2 x) + c
12. ∫ etan x sec2 xdx =
a) -ecot x + c b) etan x + c c) esin x + c d) ecos x + c
13. - ∫ecot -1x/1+ x2 dx =
a) esec x + c b) etan x + c c) ecot -1x + c d) etan -1x + c
14. ln a ∫ axdx =
a) ax / ln a + c b) lna/ax + c c)1/axln a + c d) ax + c
15. ∫ a f(x) f' (x)dx =
a) 1/af(x).ln a b) ln a/af(x) + c c) af(x)/ln a + c d) a f(x).ln a + c
16. ln a∫asin x cos xdx
a) asinx/ln a + c b) ln a/ asin x + c c) asin x ln a + c d) asin x + c
17. ∫-1/√(1 - x2) dx =
a) tan-1 x + c b) cot-1 x + c c) cos-1 x + c d) sin-1 x + c
18. ∫1/x√(x2 - 1) dx =
a) tan-1 x + c b) cosec-1x + c c) sec-1 x + c d) sin-1 x + c
19. ∫ tan xdx =
a) ln secx + c b) ln cosecx + c c) ln sinx + c d) ln cotx + c
20. ∫1/ax + b .dx =
a) 1/a.ln(ax + b) + c b) 1/b.ln(ax + b) + c c) 1/ab .ln(ax + b) + c d) 1/x ln(ax + b) + c
21. ∫dx/√(a2 - x2) =
a) cos-1 ( x/a ) + c b) sin-1 ( a/x ) + c c) sin-1 ( x/a ) + c d) sin-1 x + c
22. ∫dx/√(a2 + x2) =
a) sinh-1 ( x ) + c b) cosh-1 ( x/a ) + c c) sin-1 ( x/a ) + c d) sin-1 x + c
23. ∫dx/ 9 - x2
a) 1/6 ln x - 3/x + 3 + c b) 1/6 ln (3 + x)/(3 -x) + c c) 1/9 tan-1 ( x ) + c d) 1/3 tan-1 ( x ) + c
24. ∫cos ecxdx =
a) ln(secx + tanx) + c b) ln(cosecx + cotx) + c c) ln(secx - tanx) + c d) -ln(cosecx - cotx) + c
25.∫ x2/a2 + x2 dx =
a) a tan-1 ( x/1 ) + c b) x - a tan-1 ( x/a) + c c) 1/a - tan-1 ( x/a) + c d) lan(a2 + x2 ) + c
26. ∫cos xdx/sin x ln sin x =
a) ln ln cosx +c b) ln ln sinx +c c) ln sinx +c d) ln cosx +c
27. ∫sec2 xdx/tan x ln tan x =
a) ln ln cosx +c b) ln ln sinx +c c) ln ln tanx + c d) ln ln cotx +c
28. ∫ -dx /((1+ x2 ) tan-1 x ln tan-1 x) =
a) ln ln tanx + c b) ln ln secx +c c) ln ln cot-1x + c d) ln ln tan-1x +c
29. ∫eax [af (x) + f' (x)]dx =
a) ex f' (x) + c b) ex f (x) + c c) f (x) + f' (x) + c d) aex f (x) + c
30. ∫ex [acosec-1x -1/(x(√x2 -1)) ]dx =
a) excosec-1x + c b) ex sec-1x + c c) ex tan-1 x + c d) ex cos-1 x + c
31. ∫ex [a sec-1x + 1/(x(√x2 -1)) ]dx =
a) ex sec-1 x + c b) eax sec-1x + c c) eax tan-1 x + c d)ex tan-1 x + c
32. ≠∫eax [a cot-1x - 1/(1+ x2) ]dx =
a) aeax cot-1 x + c b) eax sec-1 x + c c) eax tan-1 x + c d) eax cot-1 x + c
33. ∫sin xdx =
a) 0 b) 6 c) 8 d) 16
34. 1∫4 ex ( 1/x - 1/x2 ) dx =
a) e4/4 +e b) e - e4/4 c) e4/4 - e d) e4 - e
35. If f(x) = cosx, then Π/2∫Π/2 f (x)dx - f'(Π/2) =
a) -1 b) 0 c) 2 d) 3
36. 2 0∫Π/2 sec2 xdx =
a) 2 b) 1 c) 0 d) -1
37. 2 0∫Π/2 sec xtan xdx =
a) 4√2 - 4 b)3√2 -3 c) 2√2 - 2 d) √2 -1
38. 0∫1dx/1+ x2
a) Π/6 b) Π/4 c) Π/3 d) Π/2
39. 0∫1dx/√(1 - x2)
a) Π/6 b) Π/4 c) Π/3 d) Π/2
40. If d/dx (x√x+1 = 3x + 2/2√(x+1), then 0∫8 3x + 2/2√(x+1) dx =
a) 48 b) 36 c) 24 d) 18
41. If 0∫1 (4x + K )dx = 2, then k =
a) -1 b) 0 c) 1 d) 2
42. Π/4∫Π/4 cosec2 xdx =
a) 2 b) 1 c) -1 d) -2
43. 0∫Π/4 sin 2xdx =
a) 1 b) √3/2 c) 1/2 d) √3
ANALYTIC GEOMETRY
1. The distance between two pints A(x1, y1) and B(x2, y2) is
a) (x2 - x1 )2 + ( y2 - y1)2 b)√((x2 -x1) + (y2 - y1)) c) √((x1 - y1)2 + (x2 - y2)2) d) √((x2 -x1)2 + (y2 - y1)2)
2. The distance of the point (1,2) from x-axis is
a) -2 b) -1 c) 1 d) 2
3. The distance of the point (-1,2) from x-axis is
a) -2 b) -1 c) 1 d) 2
4. If d1 is the distance between points(0,0), (1,2) and d2 is the distance between points (1,2), (2,1), then d12 + d22
a) 1 b) 3 c) 5 d) 7
5. If the distance of the point (5,b) from x-axis is3, then b =
a) 7 b) 5 c) 3 d) 1
6. If the distance between the points (a,5) and (1,3) is √(2a + 1), then a =
a) 4 b) 2 c)√2 d) 1
7. The point P dividing internally the line joining the points A(x1, y1) and B (x2, y2) in the ratio AP: PB = k1: k2 has coordinates
a) ( (k1x1 + k2 x2)/(k1 + k2), (k1 y1 + k2 y2)/(k1 + k2) ) b) ( (k1x1 - k2 x2)/(k1 - k2) , (k1 y1 - k2 y2)/(k1 - k2) )
c) ( (k1x2 + k2 x1)/(k1 + k2), (k1 y2 + k2 y1)/(k1 + k2) d) ( (k1x2 - k2 x1)/(k1 - k2) , (k1 y2 - k2 y1)/(k1 - k2) )
8. The point P dividing externally the line joining the points A(x1, y1) and B (x2, y2) in the ratio AP: PB = k1: k2 has coordinates
a) ( (k1x1 + k2 x2)/(k1 + k2), (k1 y1 + k2 y2)/(k1 + k2) ) b) ( (k1x1 - k2 x2)/(k1 - k2) , (k1 y1 - k2 y2)/(k1 - k2) )
c) ( (k1x2 + k2 x1)/(k1 + k2), (k1 y2 + k2 y1)/(k1 + k2) d) ( (k1x2 - k2 x1)/(k1 - k2) , (k1 y2 - k2 y1)/(k1 - k2) )
9. The midpoint of the line segment joining the points (4, -1) and (2,7) is
a) (0, 0) b) (1, 1) c) (2, 2) d) (3, 3)
10. If (3,5) is the midpoint of (5,a) and (b,7) then
a) a =1, b =1 b) a =-4, b = -3 c) a =-3, b = 1 d) a = -2, b = - 5
11. If a rod of length l sides down against a wall and ground, the locus of middle point of the rod is
a) a straight line b) a circle c) a parabola d) an ellipse
12. The point which divides segment joining points (4, -2) and (8, 6) in the ration 7:5 externally is
a) ( 19/3 , 8/3 ) b) ( 8/3 , 19/3 ) c) ( - 8/3, - 19/3 ) d) (18, 26)
13. The point of concurrency of the medians of a triangle is called its
a) in-centre b) centroid c) circumcentre d) orthocenter
14. The point of concurrency of the angle bisectors of a triangle is called its
a) in-centre b) centroid c) circumcentre d) orthocenter
15. if A(x1, y1), B (x2, y2), C (x3, y3) are the vertices of the triangle then its centroid is
a) ( (x1 + x2 + x3)/4, (y1 + y2 + y3)/4 b) ((x1 + x2 + x3)/2, (y1 + y2 + y3)/2 )
c) (( x1 + x2 + x3)/3 , (y1 + y2 + y3)/3 ) d) (x1 + x2 + x3, y1 + y2 + y3 )
16. The slop of the line through the points (3, -2), (5, 11) is
a) 0 b) 1 c) 2 d) 3
17. The slop of the line through the points (a, 2), (3, b) is
a) 1/(b - a) b) (a - 3)/(2 - b) c) (2 - b)/(a - 3) d) b - a
18. If m1 is the slop of the line through the points (-2, 4), (5,11) and m2 is the slop of line through the points (3, -2), (2,7), then
a) m1 + m2 + 8 = 0 b) m1 + m2 - 8 = 0 c) m1 - m2 + 8 = 0 d) m1 - m2 - 8 = 0
19. If a straight line is parallel to x-axis, then its slop is
a) -1 b) 0 c) 1 d) undefined
20. If a is some fixed number, then the line y = a is
a) along y-axis b) parallel to y-axis c) parallel to y-axis d) perpendicular to y- axis
21. The line l1, l2 with slopes m1, m2 are perpendicular if
a) m1m2 = -1 b) m1 = m2 c) m1 + m2 = 0 d) m1m2 = 1
22. If - 1/2 is the slop of line l1 and l1 l2, then the slop of the line l2 is
a) 2 b) 0 c) -1 d) -2
23. Three points (x1, y1), (x2, y2), (x3, y3) are collinear if
a) x1 y1 1 b) x1 y1 1
x2 y2 1 ≠ 0 x2 y2 1 = 0
x3 y3 1 x3 y3 1
c) x1 y2 1 d) none of these
x2 y1 1 = 0
x3 y3 1
24. The equation of line through (-2, 5) with slop -1 is
a) 2x - y +1 = 0 b) x + y - 3 = 0 c) x + y + 3 = 0 d) x - y - 3 = 0
25. Normal form of equation of line is
a) x sina + ycosa = p b) x sina - ycosa = p c) x cosa - ysina = p d) xcosa + ysina
26. In the normal form of equation of line xcosa + ysina = p, p is the length of perpendicular from
a) origin to line b) (1,1) to the line c) (2,2) to the line d) (3,3) to the line
27. If b = 0, then the line ax + by +c = 0 is parallel to
a) y-axis b) x-axis c) along x-axis d) none of these
28. If the lines a1x +b1y + c1 = 0 and a2x + b2y + c2 = 0 are perpendicular, then
a) a1a2 - b1b2 = 0 b) a1a2 + b1b2 = 0 c) a1b2 - a2b1 = 0 d) a1b2 + a2b1 = 0
29. 2x2 + 3xy - 5y2 = 0 If the lines a1x + b1 y + c1 = 0 and a2 x + b2 y + c2 = 0 are parallel, then
a) a1a2 - b1b2 = 0 b) a1a2 + b1b2 = 0 c) a1b2 - a2b1 = 0 d) a1b2 + a2b1 = 0
30. Altitudes of a triangle are
a) parallel b) perpendicular c) concurrent d) non- concurrent
31. The right bisectors of a triangle are
a) parallel b) perpendicular c) concurrent d) non- concurrent
32. The area of a triangle region with vertices A(x1, y1), B (x2, y2) , C (x3, y3) is
a) x1 x2 x3 b) x1 x2 x3
2 y1 y2 y3 y1 y2 y3
1 1 1 1 1 1
c) x1 x2 x3 x1 x2 x3
1/2 y1 y2 y3 1/4 y1 y2 y3
1 1 1 1 1 1
33. If θ is the angle between the lines represented by the homogeneous second degree equation ax2 + 2hxy + by2 = 0, then
a) tanθ = 2√(h2 +ab)/(a +b) b) tanθ = 2√(h2 - ab)/(a + b) c) tanθ = (a + b)/2√(h2 + ab) d) tanθ = (a + b)/2√(h2 - ab)
34. If the lines kx - 4y - 13 = 0, 8x - 11y - 33 = 0 and 2x - 3y - 7 = 0 are concurrent, then k =
a) 3 b) 0 c) - 1 d) - 2
35. The angle between the lines x/a + y/b = 1 and x/a - y/b = 1 is
a) tan -1(( a2 - b2 )/2ab) b) tan-1 (2ab/(a2 + b2)) c) tan-1 (2ab)/(a2 - b2) d) 0
36. The angle between the lines y = (2 - √3 ) x + 5 and y = (2 + √3 ) x - 7 is
a) 30° b) 45° c) 60° d) 90°
37. The angle between the lines √3 x + y = 1 and √3 x - y = 1 is
a) 90° b) 60° c) 30° d) - 60°
38. The perpendicular distance of a line 12x + 5y = 7 from the origin is
a) 1/13 b) 13/7 c) 7/13 d) 13
39. The lines 2x + 3ay - 1 = 0 and 3x + 4y +1 = 0 are perpendicular, then a =
a) - 1/2 b) - 1/4 c) 1/2 d) 1
40. The angle between lines 3x + y - 7 = 0 and x + 2y + 9 = 0 is
a) 135° b) 90° c) 60° d) 30°
41. The angle between pair of lines represented by x2 + 2xy - y2 = 0 is
a) Π/6 b) Π/3 c) Π/2 d) Π
42. Distance between the line x + 2y - 5 = 0 and 2x + 4y = 1 is
a) 9/2√5 b) 2√5/9 c) 5/4 d) 0
43. 2x2 + 3xy - 5y2 = 0 represents the lines
a) x + y = 0 , 2x - 5y = 0 b) x - y = 0 , 2x + 5y = 0
c) 3x - 2 y = 0 , 5x - 3y = 0 d) 3x + 2 y = 0 , 5x + 3y = 0