Mathematics | IIT JEE IEEE Entrance Exam | Under Graduate Entrance Exams Online Objective Test

Under Graduate Entrance Exams IIT JEE IEEE Entrance Exam # Mathematics Integrals Prepare / Learn

Q1.

\int_{0}^{2} \sqrt{\frac{2 + x}{2 - x}} d x

is equal to

A. π+32

B. π+1

C. π+2

D. π2+1

Answer : Option C
Explaination / Solution:

Under Graduate Entrance Exams IIT JEE IEEE Entrance Exam # Mathematics Vector Algebra Prepare / Learn

Q2. Negative of a Vector

\vec{a}

is a

A. A vector whose magnitude is the same as that

\vec{a}

of but direction is 120° to that of

\vec{a}

B. A scalar whose magnitude is the same as that

\vec{a}

C. A vector whose magnitude is the same as that

\vec{a}

of but direction is opposite to that of

\vec{a}

D. A vector whose magnitude is the same as that

\vec{a}

of but direction is perpendicular to that of

\vec{a}

Answer : Option C
Explaination / Solution:

egative of

\vec{a}

is equal to -

\vec{a}

, i.e. A vector whose magnitude is the same as that of

\vec{a}

,but direction is opposite to that of

\vec{a}

Under Graduate Entrance Exams IIT JEE IEEE Entrance Exam # Mathematics Probability Prepare / Learn

Q3. If P(A) =

\frac{6}{11}

, P(B) =

\frac{5}{11}

and P(A ∪ B) =

\frac{7}{11} .

find P(A∩B)

A. 4/11

B. 4/13

C. 5/11

D. 5/17

Answer : Option A
Explaination / Solution:

Under Graduate Entrance Exams IIT JEE IEEE Entrance Exam # Mathematics Inverse Trigonometric Functions Prepare / Learn

Q4. The period of the function f(x)=cos 4x + tan 3x is

A. none of these

B. π2

C. π3

D. π

Answer : Option D
Explaination / Solution:

f(π)=(cos4π+tan3π)gives the same value as f (0) .Therefore,the period of the function is π

Under Graduate Entrance Exams IIT JEE IEEE Entrance Exam # Mathematics Principle of Mathematical Induction Prepare / Learn

Q5. The inequality

n! > 2^{n - 1}

is true

A. for no n ∈ N

B. for all n > 1

C. for all n> 2 ,n∈N

D. for all n ∈ N

Answer : Option C
Explaination / Solution:

Since when n = 1 , we get the inequality as 1>1, which is not true. also for n = 2 , we get 2>2, which is false. Hence the given statement is true for n>2

Under Graduate Entrance Exams IIT JEE IEEE Entrance Exam # Mathematics Continuity and Differentiability Prepare / Learn

Q6. The function f (x) = 1 + | sin x l is

A. differentiable nowhere

B. differentiable everywhere.

C. continuous nowhere

D. continuous everywhere

Answer : Option D
Explaination / Solution:

f (x) = 1 + | s i n x |

is not derivable at those x for which

x f o r w h i c h s i n x = 0, h o w e v e r, 1 + | s i n x |

is continuous everywhere (being the sum of two continuous functions)

Under Graduate Entrance Exams IIT JEE IEEE Entrance Exam # Mathematics Conic Sections Prepare / Learn

Q7.

$x^{2} + y^{2} - 6 x + 8 y - 11 = 0$ is a circle. The points (0, 0) and ( 1, 8) lie

A. one on the circle and the other outside

B. one outside the circle and one inside

C. both inside the circle

D. both outside the circle

Answer : Option B
Explaination / Solution:

so the center is (3,-4) and radius is 6 units.

distance between center and (0,0) is

units which is less than the radius so it lies inside the circle

whereas the distance between center and (1,8) is

which is greater than the radius so it lies outside the circle

Under Graduate Entrance Exams IIT JEE IEEE Entrance Exam # Mathematics Differential Equations Prepare / Learn

Q8. What is the order of differential equation :

\frac{d^{3} y}{d x^{3}} + \frac{d^{2} y}{d x^{2}} + {(\frac{d y}{d x})}^{2} = e^{x}

A. 2

B. 1

C. 0

D. 3

Answer : Option D
Explaination / Solution:

Order = 3.Since the third derivative is the highest derivative present in the equation. i.e.

\frac{d^{3} y}{d x^{3}}

Under Graduate Entrance Exams IIT JEE IEEE Entrance Exam # Mathematics Permutations and Combinations Prepare / Learn

Q9. 4 boys and 4 girls are to be seated in a row. The number of ways in which this can be done, if the boys and girls sit alternately, is

A. 4! × 4!

B. 2 ×4! × 4!

C. None of these

D. P(8,8)

Answer : Option B
Explaination / Solution:

there are 4 boys and 4 girls and the row can start either with a boy or girl, therefore the number of ways are 4! x 4! x 2

Under Graduate Entrance Exams IIT JEE IEEE Entrance Exam # Mathematics Three Dimensional Geometry Prepare / Learn

Q10.

Cartesian equation of a line that passes through two points

(x_{1}, y_{1}, z_{1})

and

(x_{2}, y_{2}, z_{2})

A. x−x1x2−x1=y−y1y2−y1=z+z1z2−z1

B. x−x1x2−x1=y−y1y2−y1=z+z1z2−z1

\frac{x - x_{1}}{x_{2} - x_{1}} = \frac{y - y_{1}}{y_{2} - y_{1}} = \frac{z - z_{1}}{z_{2} - z_{1}}

D. x+x1x2−x1=y−y1y2+y1=z−z1z2−z1

Answer : Option C
Explaination / Solution:

Cartesian equation of a line that passes through two points

(x_{1}, y_{1}, z_{1})

and

(x_{2}, y_{2}, z_{2})

is given by :

\frac{x - x_{1}}{x_{2} - x_{1}} = \frac{y - y_{1}}{y_{2} - y_{1}} = \frac{z - z_{1}}{z_{2} - z_{1}}

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