1 |
The solution set of equation = 0 is ………. a) {0} b) {1, 2} c) {−1, 2} d) {−1, −2}
The solution set of equation = 0 is ………. a) {0} b) {1, 2} c) {−1, 2} d) {−1, −2}
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IIT 1981 |
02:12 min
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2 |
The equation of the common tangent to the curves and is a)  b)  c)  d) 
The equation of the common tangent to the curves and is a)  b)  c)  d) 
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IIT 2002 |
03:51 min
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3 |
The equation has a) no real solutions b) one real solution c) two real solutions d) infinite real solutions
The equation has a) no real solutions b) one real solution c) two real solutions d) infinite real solutions
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IIT 1982 |
03:09 min
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4 |
For positive numbers x, y and z the numerical value of the determinant is ……….. a) 1 b) –1 c) ±1 d) 0
For positive numbers x, y and z the numerical value of the determinant is ……….. a) 1 b) –1 c) ±1 d) 0
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IIT 1993 |
02:04 min
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5 |
(Multiple choice) The equation of common tangent to the parabolas and is/are a)  b)  c)  d) 
(Multiple choice) The equation of common tangent to the parabolas and is/are a)  b)  c)  d) 
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IIT 2006 |
04:15 min
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6 |
If a > 0, b > 0, c > 0, prove that
If a > 0, b > 0, c > 0, prove that
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IIT 1984 |
02:45 min
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7 |
The third term of Geometric Progression is 4. The product of the five terms is a)  b)  c)  d) 
The third term of Geometric Progression is 4. The product of the five terms is a)  b)  c)  d) 
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IIT 1982 |
01:07 min
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8 |
Three normals are drawn from the point (c, 0) to the curve . Show that c must be greater than . One normal is always the X-axis. Find c for which the other two normals are perpendicular.
Three normals are drawn from the point (c, 0) to the curve . Show that c must be greater than . One normal is always the X-axis. Find c for which the other two normals are perpendicular.
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IIT 1991 |
05:44 min
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9 |
Find the set of all x for which 
Find the set of all x for which 
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IIT 1987 |
05:05 min
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10 |
Sum of the first n terms of the series is a) 2n – n – 1 b) 1 – 2− n c) n + 2− n – 1 d) 2n + 1
Sum of the first n terms of the series is a) 2n – n – 1 b) 1 – 2− n c) n + 2− n – 1 d) 2n + 1
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IIT 1988 |
03:20 min
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11 |
Let be in Arithmetic Progression and be in Harmonic Progression. If and then is a) 2 b) 3 c) 5 d) 6
Let be in Arithmetic Progression and be in Harmonic Progression. If and then is a) 2 b) 3 c) 5 d) 6
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IIT 1999 |
04:53 min
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12 |
Match the following Normals are drawn at the points P, Q and R lying on the parabola which intersect at (3, 0) then Column 1 | Column 2 | i) Area of ΔPQR | A. 2 | ii) Radius of circumcircle of ΔPQR | B.  | iii) Centroid of ΔPQR | C.  | iv) Circumcentre of ΔPQR | D.  |
Match the following Normals are drawn at the points P, Q and R lying on the parabola which intersect at (3, 0) then Column 1 | Column 2 | i) Area of ΔPQR | A. 2 | ii) Radius of circumcircle of ΔPQR | B.  | iii) Centroid of ΔPQR | C.  | iv) Circumcentre of ΔPQR | D.  |
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IIT 2006 |
07:33 min
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13 |
If α, β are roots of and are roots of for some constant δ, then prove that
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IIT 2000 |
03:16 min
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14 |
Let the positive numbers a, b, c, d be in Arithmetic Progression. Then abc, abd, acd, bcd are a) Not in Arithmetic Progression/Geometric Progression/Harmonic Progression b) In Arithmetic Progression c) In Geometric Progression d) In Harmonic Progression
Let the positive numbers a, b, c, d be in Arithmetic Progression. Then abc, abd, acd, bcd are a) Not in Arithmetic Progression/Geometric Progression/Harmonic Progression b) In Arithmetic Progression c) In Geometric Progression d) In Harmonic Progression
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IIT 2001 |
01:12 min
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15 |
(Assertion and reason) The question contains statement – 1 (assertion) and statement 2 (reason). Of these statements mark correct choice if a) Statement 1 and 2 are true. Statement 2 is a correct explanation for statement 1. b) Statement 1 and 2 are true. Statement 2 is not a correct explanation for statement 1. c) Statement 1 is true. Statement 2 is false. d) Statement 1 is false. Statement 2 is true Statement 1 – The curve is symmetric with respect to the line x = 1 Statement 2 – The parabola is symmetric about its axis.
(Assertion and reason) The question contains statement – 1 (assertion) and statement 2 (reason). Of these statements mark correct choice if a) Statement 1 and 2 are true. Statement 2 is a correct explanation for statement 1. b) Statement 1 and 2 are true. Statement 2 is not a correct explanation for statement 1. c) Statement 1 is true. Statement 2 is false. d) Statement 1 is false. Statement 2 is true Statement 1 – The curve is symmetric with respect to the line x = 1 Statement 2 – The parabola is symmetric about its axis.
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IIT 2007 |
01:47 min
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16 |
If is the area of a triangle with sides a, b, c then show that . Also show that equality occurs if a = b = c
If is the area of a triangle with sides a, b, c then show that . Also show that equality occurs if a = b = c
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IIT 2001 |
05:12 min
|
17 |
An infinite Geometric Progression has first term x and sum 5 then a)  b)  c)  d) 
An infinite Geometric Progression has first term x and sum 5 then a)  b)  c)  d) 
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IIT 2004 |
01:34 min
|
18 |
Let P = (x, y) be any point on with focii and equals a) 8 b) 6 c) 10 d) 12
Let P = (x, y) be any point on with focii and equals a) 8 b) 6 c) 10 d) 12
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IIT 1998 |
01:38 min
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19 |
If a < b < c < d then the roots of the equation are real and distinct. a) True b) False
If a < b < c < d then the roots of the equation are real and distinct. a) True b) False
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IIT 1984 |
03:45 min
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20 |
The angles of a triangle are in Arithmetic Progression and let . Find the angle A.
The angles of a triangle are in Arithmetic Progression and let . Find the angle A.
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IIT 1981 |
03:20 min
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21 |
If α, β, γ are the cube roots of P, P < 0, then for any x, y, z, ………..
If α, β, γ are the cube roots of P, P < 0, then for any x, y, z, ………..
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IIT 1989 |
07:21 min
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22 |
If n is a natural number such that and are distinct primes, then show that
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IIT 1983 |
03:00 min
|
23 |
An ellipse has OB as a semi-minor axis. F, F’ are its focii and the angle FBF’ is a right angle. Then the eccentricity of the ellipse is . . . . .
An ellipse has OB as a semi-minor axis. F, F’ are its focii and the angle FBF’ is a right angle. Then the eccentricity of the ellipse is . . . . .
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IIT 1997 |
02:22 min
|
24 |
The least value of the expression for x > 1 is a) 10 b) 2 c) −0.01 d) none of these
The least value of the expression for x > 1 is a) 10 b) 2 c) −0.01 d) none of these
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IIT 1980 |
02:59 min
|
25 |
If x = 9 is the chord of contact of the hyperbola then the equation of the corresponding pair of tangents is a)  b)  c)  d) 
If x = 9 is the chord of contact of the hyperbola then the equation of the corresponding pair of tangents is a)  b)  c)  d) 
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IIT 1999 |
03:20 min
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