11/7/21
1) If (a-x)/px =(a-y)/qy=(a-z)/rz and p,q,r are three consecutive terms of an AP, then 1/x + 1/z is
A) 1/y B) 2/y. C) -1/y D) -2/y
2) There are even number of terms in a GP. If the sum of the progression is thrice the sum of odd terms, then the common ratio of the GP.
A) 2. B) 4 C) 6 D)
3) The product of n geometric mean between a and b is
A) ab B) a/b C) b/a D) none
4) the arithmetic mean of two number is A and the geometric mean is G find the numbers.
A) √(A²+B²) B) √(A²-B²)
C) A+ √(A²+B²) D) A- √(A²+B²)
5) Find the least value for n for which 1+3+3³+....+3ⁿ⁻¹ >900.
A) 7. B) 7/2 C) 8 D) 8/3
6) if tₙ be the nth term of a GP and t₁ = 2, find the minimum value of 2t₂ + 3t₃. find also the value of the common ratio for which the expression will be meaning.
A) 2/3, 1/3 B) -2/3, 1/3
C) 2/3, -1/3 D) -2/3, -1/3
7) If {(1+i)/(1-i)}³ - {(1- i)/(1+i)}³= p + iq, then p and q is..
A) 0,2 B) 2,0 C) 0, -2. D) -2,0
8) If x= 2+ 3i and y= 2 - 3i, then the value of (x³-y³)/(x³+y³) is
A) 9/46 B) -9/46. C) 4/47 D) none
10/7/21
1) If the point (x,y) is equidistant from the point (2,3) and (1,2) then the value of 3x + y is..
A) 4. B) 3 C) 2 D) 1
2) The coordinate of the triangle are (2a,4a),(2a,6a) and (2a+ √3 a, 5a) respectively. make a
A) equilateral triangle.
B) isosceles triangle
C) isosceles-right angled triangle
D) scalene triangle.
3) The Circum-cetre of the triangle (5,0),(0,5) and (3,4) is..
A) (0,0). B) (1,2) C)(2,3) D) (4,0).
4)The Circum-radius of the triangle (5,0),(0,5) and (3,4) is..
A) 4 B) 5. C) 6 D) 7
5) The three points (a, bc-a²), (b, ca- b²) and (c, ab - c²) make
A) equilateral triangle
B) isosceles triangle
D) right angled triangle
D) collinear.
6) A line segment joining the points (-4,10) and (2,1) is a divided internally (0,4) in a definite ratio. The point which divides the segment externally in the same ratio is..
A) (6,-6) B) (7,-7) C) (8,-8). D) none
7) If the coordinates of three vertices of a triangle are (p-4,p+5), (p+3, p-2) and (p,p), then the area of the triangle will remain___with the change of the value of p.
A) changed B) unchanged
C) similar D) none
8) The area of the triangle whose vertices are (ka, k/a), (kb, k/b) and (kc, k/c) is
A) (a-b) B) k/2abc D) 2abck D) n.
9) In a triangle ABC the coordinates of the point A,B,C are respectively (3,1),(9,7) and (-3,7). If D, E, F are respectively the midpoints of the sides BC ,CA and AB, then the ratio of the area of the ∆ DEF: ∆ ABC is..
A) 1:4 B) 4:1. C) 1:2 D) 2:1
** P(x,y) is any point on the line segment joining the points P₁(x₁,y₁) and P₂(x₂,y₂). And x= x₁+ k(x₂ - x₁) and y= y₁ + k(y₂ - y₁) where P₁P/P₁P₂ = k.
what conclusion can be drawn about the position P, if
10) 0<k<1
A) P is 0 B) P is between P₁and P₂.
C) P₁ is between P and P₂
D) P₂ is between P and P₂
11) k>1
A) P is on P₁and P₂ produced
B) P is between P₁ and P₂
C) P₁ is between P and P₂
D) P₂ is between P and P₂
12) k=0
A) P is between P₁ and P₂
B) P is on P₁and P₂ produced
C) P coincides with P₁.
D) P coincides with P₂
13) k=1
A) P is between P₁ and P₂
B) P is on P₁and P₂ produced
C) P coincides with P₁.
D) P coincides with P₂
14) k= 1/2
A) P is between P₁ and P₂
B) P is on P₁and P₂ produced
C) P coincides with P₁.
D) P is the midpoint of P₁P₂ .
** 15) A point moves so that the sum of the squares of its distances from two points (a,0) and (-a,0) is 2b². Then the locus of the moving point.
A) x²+y²+b²+a²= 0 B)x²+y²- b²+a²= 0.
C) x²-y²+b²+a²=0 D) x²-y²-b²-a²= 0
16) A point moves so that the sum of the squares of its distances from two points (a,0) and (-a,0) is 2b². If a= b, then what will be the locus of the moving point ?
A) triangle B) circle
C) point circle. D) parabola
17) A point moves such that the sum of its distance from two fixed points (c,0) and (-c,0) is 2a. Then the equation of the locus of the point is..
A) x²/a² + y²/b²=1 B) x²/a²- y²/b² = 1
C) x²/a² + y²/(a²- c²) = 1. D) none
18) The coordinates of the two ends of the base of a triangle are (2,5) and (-1,3). If the height of the triangle is 2√13, then equation of the locus of the vertex of the triangle.
A) 2x-3y+37=0. B) 2x+3y-37=0
C) 2x+3y+37=0 D) 2x-3y-37=0
9/7/21
1) Two equal arcs of two circles subtend angles of 60 and 75 at the centre. Then the ratio of radii of the two circles.
A) 4:5 B) 5:4. C) 3:2 D) 2:3
2) If cosx - sinx =√2 sinx, then sinx + cosx is..
A) √2 B) √2cosx. C) - √2cosx D) 1
3) If 7 cosx + 5 sinx = 5, then 5 cosx - 7 sinx is .
A) ±4 B) ± 5 C) ± 6 D) ±7.
4) If sinx + Cosecx= 2, then sin¹⁰x + cosec¹⁰x is
A) 1 B) 2 C) 0 D) none
5) If tan⁴x + tan²x = 1, then cos⁴x + cos²x is
A) 0 B) 1. C) 2 D) 3
6) If cos⁴x + cos²x = 1, then tan⁴x + tan²x is
A) 0 B) 1. C) 2 D) 3
7) if sinx, cosx, tanx are in GP. Then cot⁶x - cot²x is..
A) 0 B) 1. C) 2 D) 3
8) If (secx -1)(secy -1)(secz -1)= (secx +1)(secy +1)(secz +1) then the value of each side is
A) ± tanx B) ± tany C) ± tan z D) ± tanx tany Tanz.
9) If (a² - b²) sinx + 2ab cosx = a²+b³, then tanx is.
A) a²+ b² B) a²-b² C) (a²+b²)/2ab D) (a²-b²)/2ab.
10) If tanx + sinx= m and tanx - sinx= n, then m²-n² is
A) m B) n C) mn D) 4√(mn).
11) If x sin³a + y cos³a= sina cos a and x sina - y cosa= 0 then x²+y² is
A) 0 B) 1. C) 2 D) none
12) If x= coseca - sina and y= seca - cos a, then x²+y²+3 is
A) 1 B) xy C) x²y² D) 1/x²y².
13) If coseca + cosecb + cosec c= 0 then (sina+ sin b+ sin c)²- sin²a - sin² b - sin²c is
A) 0. B) 1 C) 2 D) none
14) least value of 9 tan²x+ 4 cot²x is
A) 14 B) 13 C) 12 D) 11.
8/7/21
1) The 2nd, 3rd and 6th terms of an AP are three consecutive terms of a G. P. Then common ratio of the GP
A) 3. B) 4 C) 5 D) 6
2) Find the sum of:
1+11+111+1111+... to n terms
3) If the 1st, 2nd, and last terms of a G. P are a, b, and l respectively. Then sum of the terms is..
A) a+b B) b+l C) a+b+l D) none.
4) If the pth, qth and rth terms of an AP are in GP., Then common ratio is
A) q-r B) p-q C) (q-r)(p-q) D) (q-r)/(p-q)..
5) If the pth, qth rth and sth terms of an AP are in GP., Then p-q, q--r, r-s are in
A) AP B) GP. C) HP D) none
6) If 1+3+3²+....3ˣ= 1093.then x is..
A) 5 B) 6. C) 7 D) 10
7) If a, b, c, d are in AP and a, c, d are in GP. Then 3(b² - ad) is
A) a² B) d² C) a²+ d² D) a² - d².
8) The product of 3 numbers in GP is 512. If 8 be added to the 1st and 6 to the 2nd, the resulting numbers with the third number form an AP. Find the numbers.
A)4,8,16. B) 2, 8, 32 ac) 6,12,24 D) n
9) If a, b, c are in AP and a, b-a, c-a are in GP., Then a= b/3= c/5. T./F
7/7/21
1) If b²+bc+c², c²+ca+a², a²+ab+ b² are in AP then a,b,c are in
A) AP. B) GP C) HP D) none
2) If a, b, c are in AP then 1/a(1/b + 1/c), 1/b (1/c + 1/a), 1/c(1/a + 1/b) are in
A) AP. B) GP C) HP D) none
3) If a,b,c,d are in AP. Then ab+cd + ad is...
A) 3abcd B) 3abc C) 3ab D) 3bc.
4) The sum of first n terms of an AP is denoted by Sₙ. If Sₙ= n²p and Sₘ = m²p, m≠ n, then Sₚ is
A) p B) p² C) p³. D) p⁴
5) There are 100 terms in an AP. If the sum of the terms occupying the even places is 1600 and the sum of the terms occupying the odd places is 1300. Then the middle two terms are..
A) 26, 32. B) 27, 33 C) 28,34 D) n
6) If the sum of first p terms of an AP be P and the sum of first q terms be Q, then first term will be -------
7) If the first and the last terms of an AP are a and l respectively and the sum of the terms is S, then the common difference is____.
8) The sum of three numbers in GP is 7 and the sum of their squares is 21; then sum of their cubes is..
A) 70 B) 71 C) 72 D) 73.
9) The sum of three numbers in GP is 65 and the product of first and the third number is 225; then the numbers are..
A) 5,15,45 B) 15, 45, 225
C) 5, 10, 15 D) 15, 30, 45
10) 2+4+8+.... to 20 terms is
A) 2²⁰-1 B) 2²⁰ C) 2(2²⁰-1). D) n
11) If (a+bx)/(a- bx)= (b+cx)/(b- cx)= (c+dx)/(c- dx) (x≠0), then a, b, c, d are in
A) AP B) G.P C) HP D) none
12) If a, b, c, d are in GP then 1/(a²+b²), 1/(b² + c²) + 1/(c²+ d²) are in..
A) AP B) G.P C) HP D) none
13) The 5th term of a GP is 8 and the 13th term is 128. Sum upto 12th term is..
A) 126 B)126.√4 C)126(√4+1) D)n
14) The sum of three consecutive terms of an AP is 15, if 1 is substracted from the second term, the resulting numbers form a GP. Then terms are..
A) 2,5,8. B) 3, 6,9 C) 4, 6,8 D) none
6/7/21
15) If the pth, qth and rth terms of an AP are respectively 1/a, 1/b and 1/c, then (q-r) bc +(r-p)ca +(p-q)ab isA) 0. B) 1 C) a D) b E) ab
2) How many terms of the series 1/2+ 1/3+ 1/6+.... must be taken so that the sum may be...
A) 1/2 B) -1/2 C) 3/2 D) -3/2.
3) sum of 1-3+5-7+9-11+...to n terms.
A) n+1 B) n+2 C) 2(n+1) D) none
4) How many even numbers are there between 15 and 115 ? And the sum of all these numbers are..
A) 50, 3250. B) 100, 10200
C) 20, 1490 D) none
5) Find the sum of all the numbers between 200 and 300 which are multiple of 7
A) 3479. B) 3749 C) 3947 D) 7777
6) If (p+1)th term of an AP be a, the sum of first (2p+1) terms of AP is
A) 2ap B) 2p+1 C) (2p+1)a. D) n
7) If the 11th term of an AP be 25, then the sum of first 21 terms of the AP is .
A) 255 B) 525. C) 552 D) none
8) There are (2n+1) terms in an AP. Then the ratio of the sum of odd terms the sum of even terms is..
A) (n+1):n. B) n:(n+1)
C) (n-1): n D) n/(n-1)
9) 99th term of the series 2+7+14+ 23+34+.... Is
A) 9899 B) 9998. C) 8999 D) n
10) The sum of four numbers in AP is 20 and the sum of their squares is 120. Find the numbers
A) 2,4,6,8. B) 3,5,7,9
C) 4,6,7,10 D) 2, 5, 8, 11
11) The sum of 6 numbers in AP is 345 and the difference between the first and the sixth is 55. the numbers are...
A) 30, 41, 52, 63, 74, 85.
B) 30, 40, 50, 60, 70, 80
C) 31, 43, 53, 74, 75, 86. D) n
12) the fourth term of an AP is thrice the first term and the 7th term exceeds twice the third term by 2. the sum of first n terms of the AP. is...
A) 200 B) 210 C) 230 D) 240.
13) If the sum of first n terms of an AP is 40, and the common difference is 2 and the last term is 13, value of n is ..
A) 4 or 10. B) 4 or 20
C) 5 or 15 D) 5 or 20
14) If the sum of the first n terms of two AP's are find the ratio (3n+1):(3n-1). Then the ratio of their 10th terms is...
A) 28:29 B) 29:28 C) 30:31 D) n
15) Sum of n arithmetic means between two numbers is n times the Arithmetic mean of those two numbers. T./F
16) n arithmetic means are inserted between 1 and 41. If the sum of the means and the two numbers be 189, then the value of n is...
A) 7. B) 8 C) 9 D) 10
17) If (b+c)/a, (c+a)/b, (a+b)/c are in AP and a+b+c ≠ 0, then 1/a, 1/b, 1/c are in
A) AP B) GP C) HP D) NONE
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