1 
The equation of the common tangent touching the circle and the parabola , above X–axis is a) b) c) d)
The equation of the common tangent touching the circle and the parabola , above X–axis is a) b) c) d)

IIT 2001 
05:54 min

2 
Evaluate a) 0 b) c) 1 d) 2
Evaluate a) 0 b) c) 1 d) 2

IIT 1979 
00:54 min

3 
The angle between the tangents drawn from the point (1, 4) to the parabola is a) b) c) d)
The angle between the tangents drawn from the point (1, 4) to the parabola is a) b) c) d)

IIT 2004 
02:56 min

4 
Determine the values of a, b, c for which the function is continuous at x = 0 a) b) c) d)
Determine the values of a, b, c for which the function is continuous at x = 0 a) b) c) d)

IIT 1982 
04:00 min

5 
If a) b) [2, ∞) c) d)

IIT 2002 
06:15 min

6 
A is a point on the parabola . The normal at A cuts the parabola again at B. If AB subtends a right angle at the vertex of the parabola, find the slope of AB.
A is a point on the parabola . The normal at A cuts the parabola again at B. If AB subtends a right angle at the vertex of the parabola, find the slope of AB.

IIT 1982 
06:08 min

7 
Show that the locus of a point that divides a chord of slope 2 of the parabola internally in the ratio 1:2 is a parabola. Find its vertex.
Show that the locus of a point that divides a chord of slope 2 of the parabola internally in the ratio 1:2 is a parabola. Find its vertex.

IIT 1995 
06:25 min

8 
Let ℝ be the set of real numbers and f : ℝ → ℝ such that for all x and y in ℝ, . Then f (x) is a constant. a) True b) False
Let ℝ be the set of real numbers and f : ℝ → ℝ such that for all x and y in ℝ, . Then f (x) is a constant. a) True b) False

IIT 1988 
01:50 min

9 
Three normals with slopes are drawn from a point P not on the axis of the parabola . If results in the locus of P being a part of the parabola, find the value of α.

IIT 2003 
05:59 min

10 
Find a) 0 b) e c) e^{z} d) e^{3}
Find a) 0 b) e c) e^{z} d) e^{3}

IIT 1993 
05:49 min

11 
The relatives of a man comprise 4 ladies and 3 gentlemen and his wife has 7 relatives 3 of them are ladies and 4 gentlemen. In how many ways can they invite a dinner party of 3 ladies and 3 gentlemen so that so that three of man’s relatives and three of wife’s relatives are included?
The relatives of a man comprise 4 ladies and 3 gentlemen and his wife has 7 relatives 3 of them are ladies and 4 gentlemen. In how many ways can they invite a dinner party of 3 ladies and 3 gentlemen so that so that three of man’s relatives and three of wife’s relatives are included?

IIT 1985 
04:27 min

12 
For a fixed value of n D = Then show that is divisible by n
For a fixed value of n D = Then show that is divisible by n

IIT 1992 
07:32 min

13 
Let E be the ellipse and C be the circle . Let P and Q be the points (1, 2) and (2, 1) respectively. Then a) Q lies inside C but outside E b) Q lies outside both C and E c) P lies inside both C and E d) P lies inside C but outside E
Let E be the ellipse and C be the circle . Let P and Q be the points (1, 2) and (2, 1) respectively. Then a) Q lies inside C but outside E b) Q lies outside both C and E c) P lies inside both C and E d) P lies inside C but outside E

IIT 1994 
04:15 min

14 
For any positive integers m, n (with n ≥ m), prove that
For any positive integers m, n (with n ≥ m), prove that

IIT 2000 
05:45 min

15 
If tangents are drawn to the ellipse then the locus of the midpoints of the intercepts made by the tangents between the coordinate axes is a) b) c) d)
If tangents are drawn to the ellipse then the locus of the midpoints of the intercepts made by the tangents between the coordinate axes is a) b) c) d)

IIT 2004 
03:11 min

16 
A = is equal to a) 0 b) 1 c) d)
A = is equal to a) 0 b) 1 c) d)

IIT 1978 
02:30 min

17 
Let P be a variable point on the ellipse with foci F_{1} and F_{2.} . If A is the area of then the maximum value of A is . . . . .
Let P be a variable point on the ellipse with foci F_{1} and F_{2.} . If A is the area of then the maximum value of A is . . . . .

IIT 1994 
02:27 min

18 
For the function The derivative from right . . . . and the derivative from the left . . . . a) 0, 0 b) 0, 1 c) 1, 0 d) 1, 1
For the function The derivative from right . . . . and the derivative from the left . . . . a) 0, 0 b) 0, 1 c) 1, 0 d) 1, 1

IIT 1983 
03:28 min

19 
Let z_{1} and z_{2} be n^{th} roots of unity which subtend a right angle at the origin then n must be of the form a) 4k + 1 b) 4k + 2 c) 4k + 3 d) 4k
Let z_{1} and z_{2} be n^{th} roots of unity which subtend a right angle at the origin then n must be of the form a) 4k + 1 b) 4k + 2 c) 4k + 3 d) 4k

IIT 2001 
05:59 min

20 
The equation represents a) An ellipse b) A hyperbola c) A circle d) None of these
The equation represents a) An ellipse b) A hyperbola c) A circle d) None of these

IIT 1981 
01:03 min

21 
a) 0 b) 1 c) e^{3} d) e^{5}
a) 0 b) 1 c) e^{3} d) e^{5}

IIT 1990 
04:42 min

22 
If z = 1 and then Re (w) is a) 0 b) c) d)
If z = 1 and then Re (w) is a) 0 b) c) d)

IIT 2003 
02:36 min

23 
For the hyperbola which of the following remains constant with change in α a) Abscissae of vertices b) Abscissae of focii c) Eccentricity d) Directrix
For the hyperbola which of the following remains constant with change in α a) Abscissae of vertices b) Abscissae of focii c) Eccentricity d) Directrix

IIT 2003 
01:32 min

24 
If w ( ≠1 ) is cube root of unity, then a) 0 b) 1 c)  1 d) w
If w ( ≠1 ) is cube root of unity, then a) 0 b) 1 c)  1 d) w

IIT 1995 
01:46 min

25 
India played two matches each with Australia and West indies. In any match the probability of India getting the points 0, 1, and 2 are 0.45, 0.05 and 0.50 respectively. Assuming that the outcomes are independent, the probability of India getting at least seven points is a) 0.8730 b) 0.0875 c) 0.0625 d) 0.0250
India played two matches each with Australia and West indies. In any match the probability of India getting the points 0, 1, and 2 are 0.45, 0.05 and 0.50 respectively. Assuming that the outcomes are independent, the probability of India getting at least seven points is a) 0.8730 b) 0.0875 c) 0.0625 d) 0.0250

IIT 1992 
03:03 min
