1151 |
What normal to the curve y = x2 forms the shortest normal? a) b) c) d) y = x + 1
What normal to the curve y = x2 forms the shortest normal? a) b) c) d) y = x + 1
|
IIT 1992 |
|
1152 |
If and bn = 1 – an then find the least natural number n0 such that bn > an for all n ≥ n0
If and bn = 1 – an then find the least natural number n0 such that bn > an for all n ≥ n0
|
IIT 2006 |
|
1153 |
The circle x2 + y2 = 1 cuts the X–axis at P and Q. Another circle with centre at Q and variable radius intersects the first circle at R above the X–axis and the line segment PQ at S. Find the maximum area of ΔQRS. a) b) c) d)
The circle x2 + y2 = 1 cuts the X–axis at P and Q. Another circle with centre at Q and variable radius intersects the first circle at R above the X–axis and the line segment PQ at S. Find the maximum area of ΔQRS. a) b) c) d)
|
IIT 1994 |
|
1154 |
From a point A common tangents are drawn to the circle and the parabola . Find the area of the quadrilateral formed by the common tangents drawn from A and the chords of contact of the circle and the parabola.
From a point A common tangents are drawn to the circle and the parabola . Find the area of the quadrilateral formed by the common tangents drawn from A and the chords of contact of the circle and the parabola.
|
IIT 1996 |
|
1155 |
The sides of a triangle inscribed in a given circle subtend angles α, β and γ at the centre. The minimum value of the Arithmetic mean of
The sides of a triangle inscribed in a given circle subtend angles α, β and γ at the centre. The minimum value of the Arithmetic mean of
|
IIT 1987 |
|
1156 |
Let where a is a positive constant. Find the interval in which is increasing. a) b) c) d)
Let where a is a positive constant. Find the interval in which is increasing. a) b) c) d)
|
IIT 1996 |
|
1157 |
Let y(x) be the solution of the differential equation . Given that y = 1 when x = 1, then y(e) is equal to a) e b) 0 c) 2 d) 2e
Let y(x) be the solution of the differential equation . Given that y = 1 when x = 1, then y(e) is equal to a) e b) 0 c) 2 d) 2e
|
IIT 2015 |
|
1158 |
One or more than one correct options If y(x) satisfies the differential equation y′ − ytanx = 2xsecx and y(0) = 0, then a) b) c) d)
One or more than one correct options If y(x) satisfies the differential equation y′ − ytanx = 2xsecx and y(0) = 0, then a) b) c) d)
|
IIT 2012 |
|
1159 |
At present a firm is manufacturing 2000 items. It is estimated that the rate of change of production P with respect to additional number of workers x is given by . If the firm employs 25 more workers then the new level of production of items is a) 2500 b) 3000 c) 3500 d) 4500
At present a firm is manufacturing 2000 items. It is estimated that the rate of change of production P with respect to additional number of workers x is given by . If the firm employs 25 more workers then the new level of production of items is a) 2500 b) 3000 c) 3500 d) 4500
|
IIT 2013 |
|
1160 |
Let f(x) = (1 – x)2 sin2x + x2 and Which of the following is true? a) g is increasing on (1, ∞) b) g is decreasing on (1, ∞) c) g is increasing on (1, 2) and decreasing on (2, ∞) d) g is decreasing on (1, 2) and increasing on (2, ∞)
Let f(x) = (1 – x)2 sin2x + x2 and Which of the following is true? a) g is increasing on (1, ∞) b) g is decreasing on (1, ∞) c) g is increasing on (1, 2) and decreasing on (2, ∞) d) g is decreasing on (1, 2) and increasing on (2, ∞)
|
IIT 2013 |
|
1161 |
Let PS is the median of the triangle with vertices P(2, 2), Q(6, −1) and R(7, 3), then the equation of the line passing through (1, −1) and parallel to PS is a) 4x – 7y – 11 = 0 b) 2x + 9y + 7 = 0 c) 4x + 7y + 3 = 0 d) 2x – 9y – 11 = 0
Let PS is the median of the triangle with vertices P(2, 2), Q(6, −1) and R(7, 3), then the equation of the line passing through (1, −1) and parallel to PS is a) 4x – 7y – 11 = 0 b) 2x + 9y + 7 = 0 c) 4x + 7y + 3 = 0 d) 2x – 9y – 11 = 0
|
IIT 2014 |
|
1162 |
One or more than one correct option For a > b > c > 0, the distance between (1, 1) and the point of intersection of the lines ax + by + c = 0 and bx + ay + c = 0 is less than , then a) a + b – c > 0 b) a − b + c < 0 c) a − b + c > 0 d) a + b – c < 0
One or more than one correct option For a > b > c > 0, the distance between (1, 1) and the point of intersection of the lines ax + by + c = 0 and bx + ay + c = 0 is less than , then a) a + b – c > 0 b) a − b + c < 0 c) a − b + c > 0 d) a + b – c < 0
|
IIT 2014 |
|
1163 |
If one of the diameters of the circle, given by the equation x2 + y2 – 4x + 6y – 12 = 0 is a chord of a circle S whose centre is at (−3, 2), then the radius of S is a) b) c) d)
If one of the diameters of the circle, given by the equation x2 + y2 – 4x + 6y – 12 = 0 is a chord of a circle S whose centre is at (−3, 2), then the radius of S is a) b) c) d)
|
IIT 2016 |
|
1164 |
For how many values of p, the circlex2 + y2 + 2x + 4y – p = 0 and the coordinate axis have exactly three common points a) 0 b) 1 c) 2 d) 3
For how many values of p, the circlex2 + y2 + 2x + 4y – p = 0 and the coordinate axis have exactly three common points a) 0 b) 1 c) 2 d) 3
|
IIT 2014 |
|
1165 |
A tangent PT is drawn to the circle x2 + y2 = 4 at the point . A straight line L, perpendicular to PT is tangent to the circle (x – 3)2 + y2 = 1A common tangent to the circles is a) x = 4 b) y = 2 c) d)
A tangent PT is drawn to the circle x2 + y2 = 4 at the point . A straight line L, perpendicular to PT is tangent to the circle (x – 3)2 + y2 = 1A common tangent to the circles is a) x = 4 b) y = 2 c) d)
|
IIT 2012 |
|
1166 |
The locus of the middle points of the chord of tangents drawn from points lying on the straight line 4x – 5y = 20 to the circle x2 + y2 = 9 is a) 20(x2 + y2) – 36x + 45y = 0 b) 20(x2 + y2) + 36x − 45y = 0 c) 36(x2 + y2) – 20x + 45y = 0 d) 36(x2 + y2) + 20x − 45y = 0
The locus of the middle points of the chord of tangents drawn from points lying on the straight line 4x – 5y = 20 to the circle x2 + y2 = 9 is a) 20(x2 + y2) – 36x + 45y = 0 b) 20(x2 + y2) + 36x − 45y = 0 c) 36(x2 + y2) – 20x + 45y = 0 d) 36(x2 + y2) + 20x − 45y = 0
|
IIT 2012 |
|
1167 |
The radius of a circle having minimum area which touches the curve y = 4 – x2 and the line y = |x| is a) b) c) d)
The radius of a circle having minimum area which touches the curve y = 4 – x2 and the line y = |x| is a) b) c) d)
|
IIT 2017 |
|
1168 |
Given a circle 2x2 + 2y2 = 5 and a parabola Statement 1: An equation of a common tangent to the curves is Statement 2: If the line is the common tangent then m satisfies m4 – 3m2 + 2 = 0 a) Statement 1 is correct. Statement 2 is correct. Statement 2 is a correct explanation for statement 1 b) Statement 1 is correct. Statement 2 is correct. Statement 2 is not a correct explanation for statement 1 c) Statement 1 is correct. Statement 2 is incorrect. d) Statement 1 is incorrect. Statement 2 is correct.
Given a circle 2x2 + 2y2 = 5 and a parabola Statement 1: An equation of a common tangent to the curves is Statement 2: If the line is the common tangent then m satisfies m4 – 3m2 + 2 = 0 a) Statement 1 is correct. Statement 2 is correct. Statement 2 is a correct explanation for statement 1 b) Statement 1 is correct. Statement 2 is correct. Statement 2 is not a correct explanation for statement 1 c) Statement 1 is correct. Statement 2 is incorrect. d) Statement 1 is incorrect. Statement 2 is correct.
|
IIT 2013 |
|
1169 |
One or more than one correct option Let L be a normal to the parabola y2 = 4x. If L passes through the point (9, 6) then L is given by a) y – x + 3 = 0 b) y + 3x – 33 = 0 c) y + x – 15 = 0 d) y – 2x + 12 = 0
One or more than one correct option Let L be a normal to the parabola y2 = 4x. If L passes through the point (9, 6) then L is given by a) y – x + 3 = 0 b) y + 3x – 33 = 0 c) y + x – 15 = 0 d) y – 2x + 12 = 0
|
IIT 2011 |
|
1170 |
Consider the lines given by L1 : x + 3y – 5 = 0; L2 = 3x – ky – 1 = 0; L3 = 5x + 2y −12 = 0. Match the statement/expressions in column 1 with column 2. Column 1 | Column 2 | A. L1, L2, L3 are concurrent, if | p. k = −9 | B. One of L1, L2, L3 is parallel to at least one of the other two, if | q. | C. L1, L2, L3 form a triangle, if | r. | D.L1, L2, L3 do not form a triangle, if | s. k = 5 |
Consider the lines given by L1 : x + 3y – 5 = 0; L2 = 3x – ky – 1 = 0; L3 = 5x + 2y −12 = 0. Match the statement/expressions in column 1 with column 2. Column 1 | Column 2 | A. L1, L2, L3 are concurrent, if | p. k = −9 | B. One of L1, L2, L3 is parallel to at least one of the other two, if | q. | C. L1, L2, L3 form a triangle, if | r. | D.L1, L2, L3 do not form a triangle, if | s. k = 5 |
|
IIT 2008 |
|
1171 |
Match the following Column 1 | Column 2 | i) Re z = 0 | A) Re = 0 | ii) Arg z = π/4 | B) Im = 0 | | C) Re = Im |
Match the following Column 1 | Column 2 | i) Re z = 0 | A) Re = 0 | ii) Arg z = π/4 | B) Im = 0 | | C) Re = Im |
|
IIT 1992 |
|
1172 |
Find the equation of the normal to the curve
Find the equation of the normal to the curve
|
IIT 1993 |
|
1173 |
The integral is equal to a) b) c) d)
The integral is equal to a) b) c) d)
|
IIT 2014 |
|
1174 |
Statement 1: The value of the integral is equal toStatement 2: a) Statement 1 is correct, statement 2 is correct. Statement 2 is correct explanation of statement 1 b) Statement 1 is correct, statement 2 is correct. Statement 2 is not a correct explanation of statement 1 c) Statement 1 is correct, statement 2 is false d) Statement 1 is incorrect, statement 2 is correct
Statement 1: The value of the integral is equal toStatement 2: a) Statement 1 is correct, statement 2 is correct. Statement 2 is correct explanation of statement 1 b) Statement 1 is correct, statement 2 is correct. Statement 2 is not a correct explanation of statement 1 c) Statement 1 is correct, statement 2 is false d) Statement 1 is incorrect, statement 2 is correct
|
IIT 2013 |
|
1175 |
One or more than one correct options If then a) b) c) d)
One or more than one correct options If then a) b) c) d)
|
IIT 2017 |
|