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If y = (tan^–1 x)², then (x² +1)² y₂ + 2x(x² + 1)y₁is equal to

1) 4 2) 0 3) 2 4) 1 Solution: y = (tan–1 x)2 Differentiate w.r.t.x dy/dx = 2 tan-1x (1/1+x2)... View Article

If x √(1+y) + y√(1+x) = 0, then dy/dx is equal to

(1) 1/(1+x)2 (2) -1/(1+x)2 (3) 1/(1+x2) (4) 1/(1-x2) Solution: Given x √(1+x) + y√(1+x) = 0 x √(1+x) = –... View Article

If (1 / x) + (1 / y) = 1, the function a³x² + b³y² is minimum, then x and y are

1) a + b, a – b 2) a, b 3) (a / (a + b)), b / (a +... View Article

If two sides of a triangle are given, then the area of the triangle will be maximum if the angle between the given sides be

1) π / 3 2) π / 4 3) π / 6 4) π / 2 Solution: (4) π /... View Article

The function x√1 – x², (x > 0) has

1) A local maxima 2) A local minima 3) Neither local maxima nor a local minima 4) None of the... View Article

For x ∈ (0, 5π / 2), defined f (x) = integral from 0 to x √t sint dt. Then f has

1) Local maximum at π and 2 π 2) Local minimum at π and 2 π 3) Local minimum at... View Article

Local maximum value of the function log x / x is

1) e 2) 1 3) 1 / e 4) 2e Solution: (3) 1 / e f (x) = log x... View Article

The minimum value of |x| + |x + (1 / 2)| + |x – 3| + |x – (5 / 2)| is

1) 0 2) 2 3) 4 4) 6 Solution: (4) 6 f (x) = |x| + |x + (1 /... View Article

The function x² log x in the interval (1,e) has

1) A point of maximum 2) A point of minimum 3) Point of maximum as well as of a minimum... View Article

The maximum value of the function x³ + x² + x – 4 is

1) 127 2) 4 3) Does not have a maximum value 4) None of the above Solution: (3) Does not... View Article

The minimum value 4e^2x + 9e^–2x is

1) 11 2) 12 3) 10 4) 14 Solution: (2) 12 f (x) = 4e2x + 9e-2x f’ (x) =... View Article

The function x⁵ – 5x⁴ + 5x³ – 10 has a maximum where x =

1) 3 2) 2 3) 1 4) 0 Solution: (3) 1 f (x) = x5 – 5x4 + 5x3 –... View Article

Local maximum and local minimum values of the function (x – 1)(x + 2)² are

1) –4, 0 2) 0, –4 3) 4, 0 4) None of these Solution: (2) 0, –4 f (x) =... View Article

The maximum and minimum values of the function |sin 4x + 3| are

1) 1, 2 2) 4, 2 3) 2, 4 4) –1, 1 Solution: (2) 4, 2 f (x) = |sin... View Article

The value of the function (x – 1)(x – 2)² at its maxima is

1) 1 2) 2 3) 0 4) 4/27 Solution: (4) 4/27 f (x) = (x – 1)(x – 2)2 f... View Article

In the section each question has some statements (A, B,C,D,…) given in Column – I and some statements (p,q,r,s,t,…) in column – II. Any given statement is column – I can have correct matching with ONE OR MORE statement(s) in column – II for example, if for a given question, statement B matches with the statements given in q and r, then for that particular question against statement B, darken the bubbles corresponding to q and r in the ORS. i.e., answer r will be q and r

1) A → p; B → r 2) A → r; B → q 3) A → p; B →... View Article

In the section, each question has some statements (A, B, C, D,…) given in Column – I and some statements (p,q,r,s,t,…) in column – II. Any given statement is column – I can have correct matching with ONE OR MORE statement(s) in the column – II for example, if for a given questions, statement B matches with the statements given in q and r, then for that particular question against statement B, darken the bubbles corresponding to q and r in the ORS. i.e., answer r will be q and r. In the following [x] denotes the greatest integer less than or equal to x. Match the functions in Column – I with the properties in the column – II

In the following [x] denotes the greatest integer less than or equal to x. Match the functions in Column –... View Article

In the section, each question has some statements (A, B, C, D,…) given in Column– I and some statements (p,q,r,s,t,…) in the column – II. Any given statement is column – I can have correct matching with ONE OR MORE statement(s) in the column – II for example, if for a given questions, statement B matches with the statements given in q and r, then for that particular question against statement B, darken the bubbles corresponding to q and r in the ORS. i.e., answer r will be q and r. Match that statements are given in Column – I with the intervals/union of intervals given in Column – II

Match that statements are given in Column – I with the intervals/union of intervals given in Column – II 1)... View Article

This section contains some integer type questions. The answers to each of the questions is a single – digit integer, ranging from 0 to 9. Let p(x) be a real polynomial of least degree which has a local maximum at x = 1 and a local minimum at x = 3. If p(1) = 6 and p(3) = 2, then p’(0) is

Let p(x) be a real polynomial of least degree which has a local maximum at x = 1 and a... View Article

This section contains some integer type questions. The answers to each of the questions is a single – digit integer, ranging from 0 to 9. Let p(x) be a real polynomial of least degree which has a local maximum at x = 1 and a local minimum at x = 3. If p(1) = 6 and p(3) = 2, then p’(0) is

Let p(x) be a real polynomial of least degree which has a local maximum at x = 1 and a... View Article

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