If the line ax + by + c = 0 is a normal to the curve y =1, then :

Subject

Mathematics

Class

JEE Class 12

Test Series

Take Zigya Full and Sectional Test Series. Time it out for real assessment and get your results instantly.

Test Yourself

Practice and master your preparation for a specific topic or chapter. Check you scores at the end of the test.
Advertisement

 Multiple Choice QuestionsMultiple Choice Questions

1.

The value of sinsin-113 + sec-13 + costan-112 + tan-12 is :

  • 1

  • 2

  • 3

  • 4


2.

If f(x) = xx - x +1, then :

  • f(x) is continuous but not differentiable at x = 0

  • f(x) is not differentiable at x = 0

  • f(x) is differentiable at x = 0

  • None of the above


3.

Let A, B and C be n x n matrices. Which one of the following is a correct statement?

  • If AB = AC, then B = C

  • If A3 + 2A2 + 3A + 51 = 0, then A is invertible

  • If A2 = 0,then A = 0

  • None of these


4.

The value of cot-19 + csc-1414 is given by :

  • 0

  • π4

  • π2

  • tan-12


Advertisement
Advertisement

5.

If the line ax + by + c = 0 is a normal to the curve y =1, then :

  • a > 0, b > 0

  • a > 0, b < 0

  • a < 0, b < 0

  • Data is insufficient


B.

a > 0, b < 0

The given equation of curve is xy = 1

On differentiating w.r.t. x, we get

Let t, 1t be any point on the curve at which normal to the curve can be drawn.

 dydxt, 1t = - 1t2  So, slope of normal = t2 Line ax + by + c = 0 will be normal to the curve, if t2 = - ba           t2 > 0 - ba > 0 if b > 0, a < 0 or b > 0, a > 0


Advertisement
6.

If f(x) = cos(log(x)), then f(x)f(y) - 12fxy + fxy has the value :

  • - 1

  • 12

  • - 2

  • zero


7.

If y = 3x - 1 + 3-x - 1 (x real), then the least value ofy is

  • 2

  • 6

  • 2/3

  • None of these


8.

0π2cotxcotx + tanxdx is equal to :

  • 1

  • - 1

  • π2

  • π4


Advertisement
9.

Area bounded by the curve y = loge(x), x = 0, y  0 and x - axis is :

  • 1 sq unit

  • 12 sq unit

  • 2 sq unit

  • None of these


10.

If a × b2 +a . b2 = 144 and a = 4, then b is equal to

  • 12

  • 3

  • 8

  • 4


Advertisement