Statement I An equation of a common tangent to the parabola  a

Subject

Mathematics

Class

JEE Class 12

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 Multiple Choice QuestionsMultiple Choice Questions

1.

The equation esinx-e-sinx -4 = 0 has

  • infinite number of real roots

  • No real root

  • exactly one real root

  • exactly one real root

312 Views

2.

Statement 1: The sum of the series 1 + (1 + 2 + 4) + (4 + 6 + 9) + (9 + 12 + 16) + ...... + (361 + 380 +400) is 8000.
Statement 2: sum from straight k space equals 1 to straight n equals space 1 of left square bracket straight k cubed minus left parenthesis straight k minus 1 cubed right parenthesis right square bracket space equals space straight n cubed, for any natural number n.

  • Statement 1 is false, statement 2 is true

  • Statement 1 is true, statement 2 is true; statement 2 is a correct explanation for statement 1

  • Statement 1 is true, statement 2 is true; statement 2 is not a correct explanation for statement 1

  • Statement 1 is true, statement 2 is true; statement 2 is not a correct explanation for statement 1

178 Views

3.

The negation of the statement “If I become a teacher, then I will open a school” is

  • I will become a teacher and I will not open a school

  • Either I will not become a teacher or I will not open a school

  • Neither I will become a teacher nor I will open a school

  • Neither I will become a teacher nor I will open a school

208 Views

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4.

Statement I An equation of a common tangent to the parabola straight y squared space equals space 16 space square root of 3 straight x end root and the ellipse 2x2 +y2 =4 is space straight y space equals 2 straight x space plus 2 square root of 3.
Statement II If the line straight Y space equals space mx space plus fraction numerator 4 square root of 3 over denominator straight m end fraction comma space left parenthesis straight m space not equal to 0 right parenthesis is a common tangent to the parabola straight y squared space equals space 16 space square root of 3 straight x and the ellipse 2x2 +y2 =4, then m satisfies m4 +2m2 =24

  • Statement 1 is false, statement 2 is true

  • Statement 1 is true, statement 2 is true; statement 2 is a correct explanation for statement 1

  • Statement 1 is true, statement 2 is true; statement 2 is not a correct explanation for statement 1

  • Statement 1 is true, statement 2 is true; statement 2 is not a correct explanation for statement 1


C.

Statement 1 is true, statement 2 is true; statement 2 is not a correct explanation for statement 1

straight y squared space equals space 16 space square root of 3 straight x
straight x squared over 2 plus straight y squared over 4 space equals 1
straight y space equals space mx space plus fraction numerator 4 square root of 3 over denominator straight m end fraction space is space tangent space to space parabola
which space is space tangent space to space ellipse
rightwards double arrow space straight c squared space equals space straight a squared straight m squared space plus straight b squared
rightwards double arrow space 48 over straight m squared space equals space 2 straight m squared space plus 4
rightwards double arrow straight m to the power of 4 space plus 2 straight m squared space equals space 24
rightwards double arrow space straight m squared space equals space 4
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5.

If n is a positive integer, then open parentheses square root of 3 plus 1 close parentheses to the power of 2 straight n end exponent minus space left parenthesis square root of 3 minus 1 right parenthesis to the power of 2 straight n end exponent space is

  • an irrational number

  • an odd positive integer

  • an even positive integer

  • an even positive integer

170 Views

6.

If 100 times the 100th term of an AP with non zero common difference equals the 50 times its 50th term, then the 150th term of this AP is

  •  –150

  • 150

  • times its 50th term

  • times its 50th term

263 Views

7.

In a ∆PQR, if 3 sin P + 4 cos Q = 6 and 4 sin Q + 3 cos P = 1, then the angle R is equal to

  • 5π/6

  • π/6

  • π/4

  • π/4

163 Views

8.

An equation of a plane parallel to the plane x – 2y + 2z – 5 = 0 and at a unit distance from the origin is

  • x – 2y + 2z – 3 = 0

  • x – 2y + 2z + 1 = 0

  • x – 2y + 2z – 1 = 0

  • x – 2y + 2z – 1 = 0

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9.

If the line 2x + y = k passes through the point which divides the line segment joining the points (1, 1) and (2, 4) in the ratio 3 : 2, then k equals

  • 29/5

  • 5

  • 6

  • 6

224 Views

10.

Let x1, x2, ......, xn be n observations, and let top enclose straight x be their arithmetic mean and σ2 be their variance.
Statement 1: Variance of 2x1, 2x2, ......, 2xn is 4 σ2.
Statement 2: Arithmetic mean of 2x1, 2x2, ......, 2xn is 4top enclose straight x.

  • Statement 1 is false, statement 2 is true

  • Statement 1 is true, statement 2 is true; statement 2 is a correct explanation for statement 1

  • Statement 1 is true, statement 2 is true; statement 2 is not a correct explanation for statement 1

  • Statement 1 is true, statement 2 is true; statement 2 is not a correct explanation for statement 1

213 Views

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