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1 |
A cubic f (x) vanishes at x = −2 and has a relative minimum/maximum at x = −1 and  . If  , find the cube f (x). a) x3 + x2 + x + 1 b) x3 + x2 − x + 1 c) x3 − x2 + x + 2 d) x3 + x2 − x + 2
A cubic f (x) vanishes at x = −2 and has a relative minimum/maximum at x = −1 and . If , find the cube f (x). a) x3 + x2 + x + 1 b) x3 + x2 − x + 1 c) x3 − x2 + x + 2 d) x3 + x2 − x + 2
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IIT 1992 |
05:24 min
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2 |
If a circle passes through the points (a, b) and cuts the circle  orthogonally, then the equation of the locus of its centre is a)  b)  c)  d) 
If a circle passes through the points (a, b) and cuts the circle orthogonally, then the equation of the locus of its centre is a) b) c) d)
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IIT 1988 |
04:03 min
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3 |
In ΔPQR, angle R . If tan  and tan  are roots of the equation  a)  b)  c)  d) 
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IIT 1999 |
02:23 min
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4 |
Prove that 
where  and n is an even integer.
Prove that
where and n is an even integer.
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IIT 1993 |
09:38 min
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5 |
 equals
a) – π b) π c)  d) 1
equals a) – π b) π c) d) 1
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IIT 2001 |
03:01 min
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6 |
Evaluate 
Evaluate
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IIT 1995 |
09:27 min
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7 |
The locus of the centre of circles which touches externally  and which touches the Y-axis is given by the equation a)  b)  c)  d) 
The locus of the centre of circles which touches externally and which touches the Y-axis is given by the equation a) b) c) d)
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IIT 1993 |
04:38 min
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8 |
The values of θ ε (0, 2π) for which  are a)  b)  c)  d) 
The values of θ ε (0, 2π) for which are a) b) c) d)
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IIT 2006 |
03:08 min
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9 |
Prove that
Prove that
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IIT 1997 |
09:29 min
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10 |
Evaluate  a)  b)  c)  d) 
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IIT 1999 |
01:51 min
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11 |
A, B, C , D are four points in a plane with position vectors a, b, c, d respectively, such that  . The point D then is the . . . . . . . of the triangle ABC.
A, B, C , D are four points in a plane with position vectors a, b, c, d respectively, such that . The point D then is the . . . . . . . of the triangle ABC.
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IIT 1984 |
02:30 min
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12 |
If  are altitudes of a triangle from the vertices A, B, C and Δ the area of the triangle then  a) True b) False
If are altitudes of a triangle from the vertices A, B, C and Δ the area of the triangle then a) True b) False
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IIT 1978 |
03:23 min
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13 |
The sum of the coefficients of the polynomial (1 + x – 3x2)2163 is
The sum of the coefficients of the polynomial (1 + x – 3x2)2163 is
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IIT 1982 |
01:22 min
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14 |
If  at x = π a)  b) π c) 2π d) 4π
If at x = π a) b) π c) 2π d) 4π
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IIT 2004 |
01:14 min
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15 |
If the vectors
 are coplanar then the value of  . . . . . .
If the vectors
are coplanar then the value of . . . . . .
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IIT 1987 |
04:15 min
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16 |
Let n be a positive integer. If the coefficient of the 2nd, 3rd and 4th terms in the expansion of (1 + x)n are in arithmetic progression then n = …..
Let n be a positive integer. If the coefficient of the 2nd, 3rd and 4th terms in the expansion of (1 + x)n are in arithmetic progression then n = …..
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IIT 1994 |
03:54 min
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17 |
Multiple choices If x + |y| = 2y, then y as a function of x is a) Defined for all real x b) Continuous at x = 0 c) Differentiable for all x d) Such that  for x < 0
Multiple choices If x + |y| = 2y, then y as a function of x is a) Defined for all real x b) Continuous at x = 0 c) Differentiable for all x d) Such that for x < 0
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IIT 1984 |
03:53 min
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18 |
The value of the integral  is equal to a a) True b) False
The value of the integral is equal to a a) True b) False
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IIT 1988 |
01:46 min
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19 |
A unit vector coplanar with  and  and perpendicular to  is . . . . .
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IIT 1992 |
04:49 min
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20 |
The centre of the circle inscribed in the square formed by the lines  and  a) (4, 7) b) (7, 4) c) (9, 4) d) (4, 9)
The centre of the circle inscribed in the square formed by the lines and a) (4, 7) b) (7, 4) c) (9, 4) d) (4, 9)
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IIT 2003 |
02:21 min
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21 |
Find the number of solutions of  a) 0 b) 1 c) 2 d) Infinitely many
Find the number of solutions of a) 0 b) 1 c) 2 d) Infinitely many
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IIT 1982 |
02:37 min
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22 |
The domain of definition of the function
y =  +  a) (−3, −2) excluding −2.5 b) [0, 1] excluding 0.5 c) [−2, 1) excluding 0 d) None of these
The domain of definition of the function
y = + a) (−3, −2) excluding −2.5 b) [0, 1] excluding 0.5 c) [−2, 1) excluding 0 d) None of these
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IIT 1983 |
01:30 min
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23 |
Multiple choices Let g(x) be a function defined on  If the area of the equilateral triangle with two of its vertices at (0, 0) and (x, g (x)) is  then the function g (x) is a)  b)  c)  d) 
Multiple choices Let g(x) be a function defined on If the area of the equilateral triangle with two of its vertices at (0, 0) and (x, g (x)) is then the function g (x) is a) b) c) d)
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IIT 1989 |
02:18 min
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24 |
The value of  is
The value of is
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IIT 1993 |
08:21 min
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25 |
Ten different letters of an alphabet are given. Words with five letters are formed from the given letters. Then the number of words which have at least one letter repeated is a) 69760 b) 30240 c) 99748 d) None of these
Ten different letters of an alphabet are given. Words with five letters are formed from the given letters. Then the number of words which have at least one letter repeated is a) 69760 b) 30240 c) 99748 d) None of these
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IIT 1980 |
04:41 min
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