451 |
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.
|
IIT 1991 |
05:44 min
|
452 |
Eighteen guests have to be seated, half on each side of a long table. Four particular guests desire to be on a particular side and three others on the other side. Determine the number of ways in which the seating arrangements can be made?
Eighteen guests have to be seated, half on each side of a long table. Four particular guests desire to be on a particular side and three others on the other side. Determine the number of ways in which the seating arrangements can be made?
|
IIT 1991 |
03:05 min
|
453 |
If and = and f(0) = 0. Find the value of . Given that 0 < < a) b) c) d) 1
|
IIT 2004 |
03:29 min
|
454 |
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. |
|
IIT 2006 |
07:33 min
|
455 |
If exists then both the limits and exist a) True b) False
If exists then both the limits and exist a) True b) False
|
IIT 1981 |
03:33 min
|
456 |
(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.
|
IIT 2007 |
01:47 min
|
457 |
Total number of ways in which six ‘+’ and four ‘’ signs can be arranged in a line so that no two ‘’signs occur together is …..
Total number of ways in which six ‘+’ and four ‘’ signs can be arranged in a line so that no two ‘’signs occur together is …..
|
IIT 1988 |
01:55 min
|
458 |
Fill in the blank If f (x) = sin ln then the domain of f (x) is …………. a) (−2, −1) b) (−2, 1) c) (0, 1) d) (1, ∞)
Fill in the blank If f (x) = sin ln then the domain of f (x) is …………. a) (−2, −1) b) (−2, 1) c) (0, 1) d) (1, ∞)
|
IIT 1985 |
01:25 min
|
459 |
If x, y, z are real and distinct then 8u = is always a) Non–negative b) Non–positive c) Zero d) None of these
If x, y, z are real and distinct then 8u = is always a) Non–negative b) Non–positive c) Zero d) None of these
|
IIT 1979 |
02:14 min
|
460 |
If are any real numbers and n is any positive integer then a) b) c) d) none of these
If are any real numbers and n is any positive integer then a) b) c) d) none of these
|
IIT 1982 |
01:04 min
|
461 |
Let a + b + c = 0, then the quadratic equation has a) at least one root in (0, 1) b) one root in (2, 3) and the other in c) imaginary roots d) none of these
Let a + b + c = 0, then the quadratic equation has a) at least one root in (0, 1) b) one root in (2, 3) and the other in c) imaginary roots d) none of these
|
IIT 1983 |
02:32 min
|
462 |
If α and β are roots of and are roots of then the equation has always a) Two real roots b) Two positive roots c) Two negative roots d) One positive and one negative root
If α and β are roots of and are roots of then the equation has always a) Two real roots b) Two positive roots c) Two negative roots d) One positive and one negative root
|
IIT 1989 |
04:41 min
|
463 |
The number of points of intersection of the two curves y = 2sinx and y = is a) 0 b) 1 c) 2 d)
The number of points of intersection of the two curves y = 2sinx and y = is a) 0 b) 1 c) 2 d)
|
IIT 1994 |
01:51 min
|
464 |
The roots of the equation are real and less than 3, then a) a < 2 b) 2 < a < 3 c) 3 ≤ a ≤ 4 d) a > 4
The roots of the equation are real and less than 3, then a) a < 2 b) 2 < a < 3 c) 3 ≤ a ≤ 4 d) a > 4
|
IIT 1999 |
02:39 min
|
465 |
Let f(x) = and m(b) be the minimum value of f(x). As b varies, range of m(b) is a) b) [ 0, c) [ d)
Let f(x) = and m(b) be the minimum value of f(x). As b varies, range of m(b) is a) b) [ 0, c) [ d)
|
IIT 2001 |
03:22 min
|
466 |
The set of all real numbers x for which is a) b) c) d)
The set of all real numbers x for which is a) b) c) d)
|
IIT 2002 |
03:01 min
|
467 |
If one root is square of the other root of the equation then the relation between p and q is a) b) c) d)
If one root is square of the other root of the equation then the relation between p and q is a) b) c) d)
|
IIT 2004 |
03:14 min
|
468 |
If a ≠ p, b ≠ q, c ≠ r and = 0 Then find the value of + + a) 0 b) 1 c) 2 d) 3
If a ≠ p, b ≠ q, c ≠ r and = 0 Then find the value of + + a) 0 b) 1 c) 2 d) 3
|
IIT 1991 |
03:41 min
|
469 |
The number of solutions of the pair of equations in the interval [ 0, 2π ] is a) 0 b) 1 c) 2 d) 4
The number of solutions of the pair of equations in the interval [ 0, 2π ] is a) 0 b) 1 c) 2 d) 4
|
IIT 2007 |
07:12 min
|
470 |
The equation has a) At least one real solution b) Exactly three real solutions c) Has exactly one irrational solution d) Complex roots
The equation has a) At least one real solution b) Exactly three real solutions c) Has exactly one irrational solution d) Complex roots
|
IIT 1989 |
03:53 min
|
471 |
Show that for for any triangle with sides a, b, c 3 (ab + bc + ac) ≤ (a + b + c)2 < 4 (ab + bc + ca)
Show that for for any triangle with sides a, b, c 3 (ab + bc + ac) ≤ (a + b + c)2 < 4 (ab + bc + ca)
|
IIT 1979 |
03:38 min
|
472 |
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}
|
IIT 1981 |
02:12 min
|
473 |
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
|
IIT 1982 |
03:09 min
|
474 |
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
|
IIT 1993 |
02:04 min
|
475 |
If a > 0, b > 0, c > 0, prove that
If a > 0, b > 0, c > 0, prove that
|
IIT 1984 |
02:45 min
|