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776 |
Suppose f (x) = (x + 1)2 for x ≥ . If g (x) is the function whose graph is the reflection of the graph of f (x) with respect to the line y = x then g (x) equals a) , 0 b)  c)  d) 
Suppose f (x) = (x + 1)2 for x ≥ . If g (x) is the function whose graph is the reflection of the graph of f (x) with respect to the line y = x then g (x) equals a) , 0 b)  c)  d) 
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IIT 2000 |
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777 |
Let a, b, c be three positive real numbers and  Then tan θ = ……….. a) 0 b) 1 c) 2 d) 3
Let a, b, c be three positive real numbers and  Then tan θ = ……….. a) 0 b) 1 c) 2 d) 3
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IIT 1981 |
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778 |
If X and Y are two sets and f : X Y If { f (c) = y, c ⊂ x, y ⊂ Y } then the true statement is a)  b)  c) , a ⊂ X d) 
If X and Y are two sets and f : X Y If { f (c) = y, c ⊂ x, y ⊂ Y } then the true statement is a)  b)  c) , a ⊂ X d) 
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IIT 2005 |
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779 |
Let O (0, 0), P (3, 4), Q (6, 0) be the vertices of the triangle OPQ. The point inside the triangle OPQ is such that OPR, PQR, OQR are of equal area. The coordinates of R are a)  b)  c)  d) 
Let O (0, 0), P (3, 4), Q (6, 0) be the vertices of the triangle OPQ. The point inside the triangle OPQ is such that OPR, PQR, OQR are of equal area. The coordinates of R are a)  b)  c)  d) 
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IIT 2006 |
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780 |
If f be a one–one function with domain { x, y, z}and range { 1, 2, 3}. It is given that exactly one of the following statements is true and the remaining statements are false. Determine (1) 1. f(x) = 1 2. f(y) ≠ 1 3. f(z) ≠ 2 a) {0} b) {1} c) {y} d) none of the above
If f be a one–one function with domain { x, y, z}and range { 1, 2, 3}. It is given that exactly one of the following statements is true and the remaining statements are false. Determine (1) 1. f(x) = 1 2. f(y) ≠ 1 3. f(z) ≠ 2 a) {0} b) {1} c) {y} d) none of the above
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IIT 1982 |
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781 |
One or more correct answers In triangle ABC the internal angle bisector of ∠A meets the side BC in D. DE is a perpendicular to AD which meets AC in E and AB in F. Then a) AE is harmonic mean of b and c b) AD  c)  d) Δ AEF is isosceles
One or more correct answers In triangle ABC the internal angle bisector of ∠A meets the side BC in D. DE is a perpendicular to AD which meets AC in E and AB in F. Then a) AE is harmonic mean of b and c b) AD  c)  d) Δ AEF is isosceles
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IIT 2006 |
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782 |
For a triangle ABC it is given that , then Δ ABC is equilateral. a) True b) False
For a triangle ABC it is given that , then Δ ABC is equilateral. a) True b) False
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IIT 1984 |
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783 |
True / False The function f (x) = is not one to one. a) True b) False
True / False The function f (x) = is not one to one. a) True b) False
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IIT 1983 |
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784 |
Find the set of all values of a such that are sides of a triangle. a) (0, 3) b) (3, ∞) c) (0, 5) d) (5, ∞)
Find the set of all values of a such that are sides of a triangle. a) (0, 3) b) (3, ∞) c) (0, 5) d) (5, ∞)
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IIT 1985 |
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785 |
Fill in the blank Let A be the set of n distinct elements then the total number of distinct functions from A to A is ……… and out of these …… are onto a) n!, 1 b) nn, n! c) nn, 1 d) none of the above
Fill in the blank Let A be the set of n distinct elements then the total number of distinct functions from A to A is ……… and out of these …… are onto a) n!, 1 b) nn, n! c) nn, 1 d) none of the above
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IIT 1985 |
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|
786 |
In a triangle of base a the ratio of the other two sides is r (< 1). Then the altitude of the triangle is less than or equal to . a) True b) False
In a triangle of base a the ratio of the other two sides is r (< 1). Then the altitude of the triangle is less than or equal to . a) True b) False
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IIT 1991 |
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787 |
The value of k such that lies in the plane is a) 7 b) – 7 c) No real value d) 4
The value of k such that lies in the plane is a) 7 b) – 7 c) No real value d) 4
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IIT 2003 |
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788 |
If ABCD are four points in a space, prove that 
If ABCD are four points in a space, prove that 
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IIT 1987 |
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789 |
If a, b, c are distinct positive numbers then the expression ( b + c – a ) ( c + a – b ) ( a + b – c ) –abc is a) Positive b) Negative c) Non–positive d) None of these
If a, b, c are distinct positive numbers then the expression ( b + c – a ) ( c + a – b ) ( a + b – c ) –abc is a) Positive b) Negative c) Non–positive d) None of these
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IIT 1986 |
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790 |
Let A and B be square matrices of equal degree, then which one is correct amongst the following a) A + B = B + A b) A + B = A – B c) A – B = B – A d) AB = BA
Let A and B be square matrices of equal degree, then which one is correct amongst the following a) A + B = B + A b) A + B = A – B c) A – B = B – A d) AB = BA
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IIT 1995 |
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791 |
The edges of a parallelepiped are of unit length and are parallel to non-coplanar unit vectors such that . Then the volume of the parallelepiped is a)  b)  c)  d) 
The edges of a parallelepiped are of unit length and are parallel to non-coplanar unit vectors such that . Then the volume of the parallelepiped is a)  b)  c)  d) 
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IIT 2008 |
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|
792 |
If P = , A = and Q = PAPT then PT (Q2005) P is equal to a)  b)  c)  d) 
If P = , A = and Q = PAPT then PT (Q2005) P is equal to a)  b)  c)  d) 
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IIT 2005 |
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793 |
Consider three planes P1 : x – y + z = 1 P2 : x + y – z = −1 P3 : x – 3y + 3z = 2 Let L1, L2, L3 be lines of intersection of planes P2 and P3, P3 and P1, and P1 and P2 respectively. Statement 1 – At least two of the lines L1, L2, L3 are non parallel Statement 2 – The three planes do not have a common point. a) Statement 1 is true. Statement 2 is true. Statement 2 is a correct explanation of statement 1. b) Statement 1 is true. Statement 2 is true. Statement 2 is not a correct explanation of statement 1. c) Statement 1 is true. Statement 2 is false. d) Statement 1 is false. Statement 2 is true.
Consider three planes P1 : x – y + z = 1 P2 : x + y – z = −1 P3 : x – 3y + 3z = 2 Let L1, L2, L3 be lines of intersection of planes P2 and P3, P3 and P1, and P1 and P2 respectively. Statement 1 – At least two of the lines L1, L2, L3 are non parallel Statement 2 – The three planes do not have a common point. a) Statement 1 is true. Statement 2 is true. Statement 2 is a correct explanation of statement 1. b) Statement 1 is true. Statement 2 is true. Statement 2 is not a correct explanation of statement 1. c) Statement 1 is true. Statement 2 is false. d) Statement 1 is false. Statement 2 is true.
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IIT 2008 |
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794 |
Show that the system of equations 3x – y + 4z = 3 x + 2y − 3z = −2 6x + 5y + λz = −3 has at least one solution for any real number λ ≠ −5. Find the set of solutions if λ = −5 a)  b)  c)  d) 
Show that the system of equations 3x – y + 4z = 3 x + 2y − 3z = −2 6x + 5y + λz = −3 has at least one solution for any real number λ ≠ −5. Find the set of solutions if λ = −5 a)  b)  c)  d) 
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IIT 1983 |
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|
795 |
The solution of primitive equation is . If and then is a)  b)  c)  d) 
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IIT 2005 |
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796 |
If then prove that 
If then prove that 
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IIT 1983 |
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|
797 |
A = , B = , U = , V =  If AX = U has infinitely many solutions, prove that BX = V has no unique solution. Also prove that if afd ≠ 0 then BX = V has no solution. X is a vector.
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IIT 2004 |
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798 |
If , for every real number x, then the minimum value of f a) does not exist because f is unbounded b) is not attained even though f is bounded c) is equal to 1 d) is equal to –1
If , for every real number x, then the minimum value of f a) does not exist because f is unbounded b) is not attained even though f is bounded c) is equal to 1 d) is equal to –1
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IIT 1998 |
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|
799 |
Let u (x) and v (x) satisfy the differential equations and where p (x), f (x) and g (x) are continuous functions. If u (x1) > v (x1) for some x1 and f (x) > g (x) for all x > x1, prove that at any point (x, y) where x > x1 does not satisfy the equations y = u (x) and y = v (x)
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IIT 1997 |
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800 |
The function is defined by then is a)  b)  c)  d) None of these
The function is defined by then is a)  b)  c)  d) None of these
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IIT 1999 |
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