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

Q1. Skew lines are lines in different planes which are

A. parallel

B. neither parallel nor intersecting

C. parallel and intersecting

D. intersecting

Answer : Option B
Explaination / Solution:

By definition : The Skew lines are lines in different planes which are neither parallel nor intersecting .

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

Q2. The perimeter of a triangle ABC is 6 times the arithmetic mean of the sines of its angles. If the side b is 2, then the angle B is

A. 120∘

B. 90∘

C. 30∘

D. 60∘

Answer : Option B
Explaination / Solution:

$G i v e n a + b + c = \frac{6 (s i n A + s i n B + s i n C)}{3} \Rightarrow a + b + c = 2 (s i n A + s i n B + s i n C) N o w u s i n g s i n e r u l e a = k \sin A, b = k \sin B, c = k \sin C \Rightarrow k (s i n A + s i n B + s i n C) = 2 (s i n A + s i n B + s i n C) \Rightarrow k = 2$

Now when

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

Q3. The area lying in the first quadrant and bounded by the curve y =

x^{3}

, the x – axis and the ordinates at x = - 2 and x = 1 is

A. 3

B. 6

C. 2

D. 15/4

Answer : Option D
Explaination / Solution:

Required area :

= \int_{- 2}^{1} x^{3} d x = {[\frac{x^{4}}{4}]}_{- 2}^{1} = \frac{15}{4}

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

Q4. the numbers 3, 4 , 5 can be

A. coordinates of a point on the line y = 4 , z = 0

B. direction cosines of a line in space

C. direction numbers of a line in space

D. coordinates of a point in the plane x + y – z = 0

Answer : Option C
Explaination / Solution:

the numbers 3, 4 , 5 can be direction ratio of any line these not satisfying any other option

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

Q5. If

[\begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 1 & 0 \end{matrix}]

then A is

A. a nilpotent matrix

B. an invertible matrix

C. an idempotent matrix

D. none of these

Answer : Option A
Explaination / Solution:

A square matrix A for which $A^{n} = 0$ , where n is a positive integer, is called a Nilpotent matrix.

The determinant and trace of the matrix is always Zero for a Nilpotent Matrix.

For the given matrix "A", determinant (A)=0 and trace(A)=0.

Under Graduate Entrance Exams IIT JEE IEEE Entrance Exam # Mathematics Application of Derivatives Prepare / Learn

Q6. The function f (x) =

x^{2}

– 2 x is increasing in the interval

A. x⩾1

B. x≠−1

C. x⩾−1

D. x≠1

Answer : Option A
Explaination / Solution:

f(x) = x2- 2x

\Rightarrow

f'(x) = 2x - 2 = 2(x - 1)
So , f( x) is increasing if 2(x-1)

\geq

0 , i.e.if x

\geq

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

Q7. Let A = { 1,2,3,4} , B = { 2,3,4,5,6 } , then (A∩B)(A∩B)is equal to :

A. { 1 }

B. { 2,3,4 }

C. { 5,6 }

D. { 1,2,3 }

Answer : Option B
Explaination / Solution:

Under Graduate Entrance Exams IIT JEE IEEE Entrance Exam # Mathematics Complex Numbers and Quadratic Equations Prepare / Learn

Q8. Let x,y∈R, then x + iy is a non real complex number if

A. y ≠ 0

B. x = 0

C. y = 0

D. x ≠ 0

Answer : Option A
Explaination / Solution:

If a complex number has to be a non real complex number then its imaginary part should not be zero ⇒iy≠0⇒y≠0

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

Q9. The value of the determinant