The lines 2x-3y=5 and 3x-4y=7 are two diameters of a circle of area 154 sq unit. Then the equation of this circle is
x2+y2+2x-2y-62=0
x2+y2+2x+2y-47=0
x2+y2-12x-2y-7=0
x2+y2-2x+2y-62=0
Equation of the circle passing through (0,0),(a,b) and (b,a) is
(a+b)(x2+y2)-(a2+b2)(x+y)=0
(a+b)(x2+y2)-(a+b)(x+y)=0
(a+b)(x2+y2)+(a2+b2)(x+y)=0
(a2+b2)(x2+y2)+(a+b)(x+y)=0
A student has to answer 10 out of 13 questions in an examination choosing at least 5 questions from the first 6 questions. The number of choice available to the student is
63
91
161
196
The distance between the foci of the hyperbola x2- 3y2- 4x - 6y - 11 = 0 is
4
6
8
10
A bag contain 12 two rupee coins, 7one rupee coins and 4 half rupee coins. If 3 coins are selectedat random, then the probability that each coin is of different value is
4C3/23C3
12C3/ 23C3
12*7*4/23C3
none
If f(x)=cos2x+cos2(600+x) + cos2(600-x) and g(3/2)=5 then gof(x)=
0
1
5 d) 15/2
15/2
The multiplicative inverse of (4+3i) is
4/25+(3/25)i
4/25-(3/25)i
-4/25+(3/25)i
-4/25-(3/25)i
If (1, 2) is the mid point of chords of the circle (x -2)2 +(y -4)2=10 and the equation of the chord is ax + by + c=0(a > 0) then a – b + c=
2
-2
-6
If tan (cot x) = cot (tan x), then sin 2x=
(2n+1) π/4
4/ (2n+1) π
4π/ (2n+1)
If sum of the roots of the equation 2x9-11x7+6x4+8=0 is ‘a’ then ‘a’=
11/2
-11/2
2/11
The locus of the poles w.r.t the ellipse x2/a2+y2/b2=1 of tangents to its auxiliary circle is
x2/a2+y2/b2=1/a2
x2/a2+y2/b2=1/b2
x2/a4+y2/b4=1/a2
x2/a4+y2/b4=1/b2
If the sum of two of the roots of x4-2x3-3x2+10x-10=0 is zero then the roots are
±√5, 1±i
±√5,1,-1
1/2,-1/5,±1
√2,√5, ±2
The number of terms in the expansion of (a+b+c+d)5 is
20
120
336
56
The points (-a, -b), (0, 0), (a, b), (" a^2 ",ab) are
The vertices of a rectangle
The vertices of a square
The vertices of rhombus
collinear
Let f(x+y)= f(x)f(y) for all x,y ε R. If f is differentiable at x=0, then
f is differentiable everywhere
f is not differentiable everywhere
f is not differentiable at x=1
If tan β= n tan α / 1+(1-n)tan2 α, then tan(α - β)=
(1+n)tan α
(1-n)tan α
-(1+n)tan α
–(1-n) tan α
The multiple roots of x4-2x3+11x2-12x+36=0 are
1,2
-1,2
2.3
-2,3
(cosh x/1- tanh x)+(sinh x/ 1- coth x)=
2 cosec hx
sinh x+ cosh x
sech x
tanh x
If A+B+C= 1800 then sin2 A/2+ sin 2 B/2 - sin2 C/2=
1- 2 sin A/2 sin B/2 sin C/2
1- 2 cos A/2 cos B/2 cos C/2
1- 2 cos A/2cos B/2 sin C/2
1- 2 sin A/2cos B/2 sin C/2
If sinh 9- k sinh k=(k+1)sinh3 k,then k=
3
9
noneof these
49n+16n+k is divisible by 64 for n?N. Then the numerically least –ve integer value of k is
-1
-3
-4
The distance between the limiting points of the coaxial system x2 + y2 – 4x – 2y – 4 + 2λ(3x + 4y + 10)=0
2√7
√7
4√7
8√7
C0-2. C1+3. C2………..+(-1)n(n+1).Cn =
A unit vector perpendicular to the plane of a=2i-6j-3k, b=4i+3j-k is
4i+3j-k /√26
2i-6j-3k/7
3i-2j+6k/7
2i-3j-6k/7
It is given that there are 52 Fridays in a leap year. The probability that it will have 53 Saturdays is
3/5
4/5
2/5
1/5
The lines 2x+y-1=0, ax+3y-3=0, 3x+2y-2=0 are concurrent
for all a
for a=4 only
for -1≤a≤3
for a>0 only
(cosh x+ sinh x)n=
cosh nx+ sinh nx
tanh nx6coth nx
coth nx+sech nx
sinh nx+cosech nx
cos π/11 cos 2π/11 cos 3π/11 cos 4π/11 cos 5π/11=
1/4
1/8
1/16
1/32
If the first three terms of (1+ax)n are 1,6x,6x2 then (a,n)=
(2/3, 9)
(2/5, 8)
(3/2, 6)
(5/2, 3)
(cos A+ cos 3A+cos 5A+cos 7A)/ (sin A+sin 3A+sin 5A+sin 7A)=
sin 4A
cos 4A
tan 4A
cot 4A
An equilateral triangle is inscribed in the circle x2+y2=a2 . The length of the side of the triangle is
a√2
a√3
2a
The locus of a point P such that the distances from P to the points (2,3,5) ,( 1,2,-1) are in the ratio 5:2 is
21x2+21y2+21z2-34x-76y+90z-2=0
21x2-21y2+21z2-34x-76y+90z-2=0
21x2+21y2+21z2-34x+76y+90z+2=0
21x2-21y2-21z2-34x-76y+90z-2=0
If the orthocenter of the angle formed by the lines 2x+3y-1=0, x+2y-1=0, ax+by-1=0 is at the origin, then (a, b) is given by
(6, 4)
(-3, 3)
(-8, 8)
(0, 7)
A bag containing 12 two rupee coins, 7 one rupee coins and 4 half rupee coins.If 3 coinsare selected at random, then the probability that the sum of 3 coins is maximum is
If x=sin-1t, y= √(1-t2) then d2y/dx2=
-√(1-t2)
t2
If a tangent to the circle x2 + y2 + 4x - 4y+4=0 makes a equal intercepts on the coordinate axes then the equation of that tangent is
x + y=1
x +y =2√2
x + y=√2
x +y=2
The area (in square unit) of the region enclosed by the curves y=x2 and y=x3 is
1/12
1/6
1/3
d/dx{Tan-1(x-√x/1+x3/2}=
(1/1+x2)-(1/2(1+x)√x)
1/2√(1+x2)
1/√1+x2
1/2√1-x2
The area of the triangle formed by the lines 3x+4y+5=0, (3x+4y)2-3(y-4x)2=0 is
1/√3
1/5√3
16/13√3
5/√3
7/5(1+1/?102 +1.3/1.2.1/104 +1.3.5/1.2.3.1/106 +...........∞)
√(2/3)
21/3
2√2
√2
The lines represented by the equation 3x2-5xy+2y2=0 are
x-y=0,3x+y=0
x+y=0,x-y=0
x-y=0,3x-2y=0
x+y=0,3x-y=0
In ΔABC, tan (A/2)tan (B/2)+ tan (B/2)tan (C/2)+ tan (C/2) tan (A/2)=
If a tangent drawn from the point (4, 0) to the circle x2+y2=8 touches it at a point in the first quadrant, then the coordinates of another point B on the circle such that AB=4 are
(2, -2) or (-2, 2)
(1, -2) or (-2, 1)
(-1, 1) or (1, -1)
(3, -2) or (-3, 2)
If tan2 θ=3 cosec2 θ-1 then θ=
nπ ± π/3: n ε Z
nπ + π/4: n ε Z
nπ+ (-1)nπ/6: n ε Z
nπ - π/3: n ε Z
The equations whose roots are opposite in sign and equal in magnitude of the roots of x7+3x5+x3-x2+7x+2=0 is
x5-4x4+12x3-16x2+64x+96=0
x7+3x5+x3+x2+7x-2=0
x5+11x4+42x3+57x2-13x-60=0
2x4-5x3-7x2+3x-1=0
The solution of (x2y3+x2)+(y2x3+y2)dy=0 is
(x3+1)(y3+1)=c
(x3-1)(y3-1)=c
(x3-1)(y3+1)=c
(x3+1)(y3-1)=c
The point on the curve x2=2y which is closest to the point (0, 5) is
(±2√2, 3)
(±2√2, 4)
(±√2, 3)
(±√3, 4)
If y=(1+x2)Tan-1x then y2=
(2x/1+x2)+2 Tan-1x
(2x/1+x2)-2Tan-1 x
(2x/1-x2)+ 2 Tan-1x
(2x/1-x2)-2 Tan-1x
If two consecutive terms in the expansion of (x+a)n are equal where n is a positive integer then (n+1)a/x+a is
a positive integer
a negative integer
an even integer
an odd integer
If n is even then C02-C12+C22-……….+(-1)n Cn2 =
nC(n/2)(-1)n/2
2nCn(-1)n
(2n+1)Cn(-1)n
If the length of a chord of the circle x2 + y2=a2is 2K then the locus of the midpoint of that chord is a circle of radius
√(a2-k2 )
√(a2+k2)
√(k2-a2)
a2 – k2
If the acute angle between the lines 2x+3y-5=0, 5x+ky-6=0 is then the value of k is
The equation of the tangent to the parabola y2 = 12x at (3, -6) is
X + y + 3 = 0
X + y + 1 = 0
X – y + 2a = 0
The angles between tangents to the parabola y2 = 4ax at the points where it intersects with the line x – y –a = 0 is
π/3
π/4
π/6
π/2
The maximum value of a2-abx-b2x2 is
5a2/4
a2/2
a
-a
The centre of the circle passing through the points (0, 0), (1, 0) and touching the circle x2+y2=9 is
(3/2, 1/2)
(1/2, 3/2)
(-1/√2, 1/√2)
(1/2, -√2)
If ax+by+c=0 is the equation of the common radical axis of the coaxial system (3x2+3y2-2x-2y-1)+λ(x2+y2-x-2y-3)=0 then ab+bc+ca=
44
13
40
12
If x= a cos θ (1+cos θ), y=sin θ(1+cos θ) then (dy/dx)θ=π/2
The number of positive divisors of 253673 is
14
167
168
166
The modulus and principal argument of complex number (1+2i)/(1-2i) are respectively:
0,1
1,0
1,1
0,0
The point of intersection of straight lines represented by 6x2 + xy - 40y2 – 35x - 83y + 11 = 0 is:
(3, 1)
(3, -1)
(-3, 1)
(-3, -1)
The equation of the common chord of the two circles (x-a)2+(y-b)2=c2, (x-b)2+(y-a)2=c2 is
ax-by=10
ax-by=0
x-y=0
ax+by=1
Tan (tan-1 1/2+ tan-11/3) =
5
The value of k so that 3x4+4x3+2 x2+10x+k is divisible by x+2 is
If x= 2 cos t- cos 2t, y= 2 sin t- sin 2t then dy/dx=
tan t
–tan t
tan (3t/2)
–cot (3θ/2)
cosec2 θ. cot2 θ- sec2 θ. tan2 θ-( cot2 θ- tan2 θ)( sec2 θ. cosec2θ-1)=
If f(x)=3x-7/5x-3 then (fof)(x)=
x
–x
3x
f(x)
Let a, b, c be the distinct non-negative numbers. If the vectors ai+aj+ck, i+k and ci+cj+bk lie in a plane then c is
the arthematic mean of a and b
the geometric mean of a and b
the harmonic mean of a and b
equal to zero
If f(x)=√(x+2√(2x-4))+ )=√(x-2√(2x-4)) then
f is differentiable at all points of its domain except x=4
f is differentiable on(2,∞)
f is differentiable in (-∞,∞)
f'(x)=0 for all x ε[2,6)
The lines x+2y-3=0, x+2y+7=0, 2x-y-4=0 from three sides of two squares.
2x-y-14=0 or 2x-y+6=0
2x-y-8=0 or 2x-y+16=0
x-2y-14=0 or x-2y+6=0
x+2y-14=0 or x+2y+6=0
The solution of x2dy-y2dx=0 is
(1/x)-(1/y)=c
(1/x)+(1/y)=c
x3-y3=c
x2-y2=c
lf the centroid of the triangle formed by (p, q),(q,1),(1,p) is the origin, then p3+q3+1=
3pq
pq
2pq
If x+iy= cis α cis β then the value of x2+y2 is
The solution of y dx-x dy+log x dx=0 is
y- log x-1=cx
x+log y+1=cx
y+log x+1=cx
y+log x-1=cx
From 101 to 1000 natural numbers a number is taken at random. The probability that the number is divisible by 17 is:
58/900
58/100
53/900
53/1000
If there is an error of 0.05 cm, while measuring the side of equilateral triangles as 5 cm, then the percentage error in area is
2/3
If the foot of the perpendicular from (0,0,0) to a plane is (1,2,3), then the equation of the plane is
2x+y+3z =14
x+2y+3z =14
x+2y+3z+14=0
x+2y -3z =14
If the lines 4x+3y-1=0,x-y+5=0 and kx+5y-3=0 are concurrent,then k is equal to
7
If (3+i) is a root of the equation x2 + ax+ b=0 then a =
The angle between the pair of straight lines formed by joining the points of intersection of x2 + y2 = 4 and y = 3x + c to the origin is a right angle. Then c2 is equal to
sin A+sin 5A+sin 9A)/(cos A+ cos 5A+ cos 9A)=
tan 2A
tan 3A
tan 5A
If the length of the tangent from (h, k) to the circle x2+y2=16 is twice the length of the tangent from the same point to the circle x2+y2+2x+2y=0, then
h2+k2+4h+4k+16=0
h2+k2+3h+3k=0
3h2+3k2+8h+8k+16=0
3h2+3k2+4h+4k+16=0
A man 6 feet height walks at a uniform of 20 above the floor. An object falls freely under gravity, starting from rest at the same height as the lamp, put at a horizontal distance of 5 ft from it. The speed of the shadow of the object on the floor when it has fallen through 15 ft is
12 ft/sec
12.5 ft/sec
11 ft/sec
10 ft/sec
If A+B+C =900 then cos2 A+cos2B+ cos2 C=
1+ 4sin A sin B sin C
1- 2sin A sin B sin C
2+ 2sin A sin B sin C
4 sin Asin B cos C
If y√1+x2=log(x+√1+x2) then (1+x2)y1+xy=
If tan θ=-4/3 and θ is not in the fourth quadrant , then the value of 5 sin θ+10cos θ+ 9 secθ+16 cosec θ – 4 cot θ=
α and β are the roots of the equation x2+px+p3=0,(p≠0).If the points (α,β) lies on the curve x=y2,then the roots of the given equation are
4,-2
4,2
1,-1
A: The angle between the tangents drawn from origin to the circle x2+y2-14x+2y+25=0 is π/2 R: If θ is the angle between the pair of tangents drawn from (x1, y1) to the circle S=0 of radius r then tanθ/2=r/√S11
Both A and R are true and R is the correct explanation of A
Both A and R are true but R is not correct explanation of A
A is true but R is false
A is false but R is true
Sum of n brackets of (1)+(1/3+1/32)+(1/33+1/34+1/35)+…. Is
(3n-1)3/2.4n-1
(3n-1)/2.3 (n-1)(n+2)/2
(3n+1)/3.7n-1
Tangents are drawn from the Point (-2, -1) to the hyperbola 2x2-3y2=6. Their equations are
3x-y+5=0, x-y+1=0
3x+y+5=0, x+y+1=0
3x-y-5=0, x-y-1=0
3x+y-5=0, x+y-1=0
The value of sin[(1/2)cot-1(3/4)] is equal to
-1/√5
1/√5
-2/√5
2/√5
If the area of the triangle formed by the points (t,2t), (-2,6), (3,1) is 5sq.unit, then t is
½,2
2,2/3
77,83
½,-1
sin 1200 cos 1500-cos 2400 sin 3300 is equal to :
-2/3
If α,β,γ,δ are the roots of x4+px3+qx2+rx+s=0 then Σα2βγ
3r+pq
3r-pq
pr+4s
pr-4s
If p1,p2,p3 are the product of perpendiculars from (0,0) to xy+x+y+1=0, x2-y2+2x+1=0, 2x2+3xy-2y2+3x+y+1=0 respectively then ascending order of p1,p2,p3 is
p1,p2,p3
p3,p2,p1
p2,p3,p1
p1,p3,p2
If cos x+ cos y=4/5, cos x- cos y=2/7, then 14 tan(x-y/2)+ 5 cot (x+y/2)=
3/4
5/4
If the line 2x+3y+1=0 and 3x-y-4=0 lie along diameters of a circle of circumference 10π, then the equation of the circle is
x2+y2-2x+2y-23=0
x2+y2+2x-2y-23=0
x2+y2+2x+2y-23=0
x2+y2-2x-2y-23=0
If dx + dy =(x + y) ( dx- dy ) then log ( x + y ) is equal to
x + y + c
x +2 y + c
x - y + c
2x + y + c
(x+y+z)(x+yω+zω2)(x+yω2+zω)=
x3+y3+z3+3xyz
x3+y3+z3-3xyz
x3+y3+z3
Four tickets marked 00,01,11 respectively are placed in a bag. A ticket is drawn at random 5 times being replaced each time. The probability that the sum of the numbers on the tickets is 22 is
2/7
25/256
231/256