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

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

Q1.

If 12C4 + 12C5 =nC5 ,then n is equal to

A. 11

B. 13

C. None of these

D. 12

Answer : Option B
Explaination / Solution:

We have nCr - 1 + nCr = n+1Cr

Hence 12C4 + 12C5 = 13C5 ................(i)

But given 12C4 + 12C5 =nC5 ................(ii)

Comparing (i) and (ii) we get n = 13

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

Q2. If

a_{1}, b_{1}, c_{1}

and

a_{2}, b_{2}, c_{2}

are the direction ratios of two lines and

θ

is the acute angle between the two lines; then

Answer : Option A
Explaination / Solution:

If

a_{1}, b_{1}, c_{1}

and

a_{2}, b_{2}, c_{2}

are the direction ratios of two lines and

θ

is the acute angle between the two lines; then , the cosine of the angle between these two lines is given by :

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

Q3. If the angles of a triangle be in the ratio 1 : 4 : 5, then the ratio of the greatest side to the smallest side is

A. 4:5–√−1

B. (5–√−1):1

C. 5 : 1

D. 1:(5–√−1)

Answer : Option A
Explaination / Solution:

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

Q4.

The area of the figure bounded by the curve $y = \log_{e} x$ , the x – axis and the straight line x = e is

A. 5 - e

B. 3 + e

C. None of these

D. 1

Answer : Option D
Explaination / Solution:

Required area :
$

\int_{1}^{e} \log_{e} x d x

{[x \log x - x]}_{1}^{e}

(e \log e - e)

(1 \log 1 - 1)

= 1

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

Q5. The radius of the sphere through the points ( 4 ,3 , 0 ) , ( 0 , 4 , 3 ) ,( 0 , 5 , 0 ) and ( 4 , 0 , 3 ) is

A. 5

B. 7

C. 5/7

D. 7/5

Answer : Option A
Explaination / Solution:

we know that general equation of sphere is $x^{2} + y^{2} + z^{2} + 2 g x + 2 f y + 2 h z + c = 0$

since sphere passing through the points ( 4 ,3 , 0 ) , ( 0 , 4 , 3 ) ,( 0 , 5 , 0 ) and ( 4 , 0 , 3 ) so putting these values one by one in given equation , we get

16+ 9+ 8g + 6f + c=0 =>8g +6f +c = -25 -------------1)

16 +9 +8f +6h +c=0 =>8f + 6h +c= -25 -----------2)

25 + 10f +c = 0 -----------------------3)

16+ 9+ 8g + 6h +c=0 =>8g +6h +c= -25 -------------4)

by 2) - 4 ) we have f = g

using this in 1) we have 16f +c = -25 -------5)

Now solving 3) and 5) we get f=0

using value of f we have g= 0 , h= 0 , c= -25

Now radius = $\sqrt{{(- g)}^{2} + (- f) + {(- h)}^{2} - c}$ = $\sqrt{25}$ =5

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

Q6. The order of [x y z]

[\begin{matrix} a & h & g \\ h & b & f \\ g & f & c \end{matrix}] [\begin{matrix} x \\ y \\ z \end{matrix}]

A. 1×1

B. 1×3

C. 3×1

D. 3×3

Answer : Option A
Explaination / Solution:

{[x y z]}_{1 x 3}

{[\begin{matrix} a & h & g \\ h & b & f \\ g & f & c \end{matrix}]}_{3 x 3} {[\begin{matrix} x \\ y \\ z \end{matrix}]}_{3 x 1}

{[A]}_{1 x 1}

. ( where ; matrix A denotes the product of three given matrices.)

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

Q7. The function f(x) =

\tan^{- 1} x

A. strict increasing

B. strict decreasing

C. differentiable nowhere.

D. neither increasing nor decreasing

Answer : Option A
Explaination / Solution:

f′(x)=ddx(tan−1x)

= \frac{1}{1 + x^{2}} > 0 \forall x \in R .

Therefore , f is strictly increasing on R

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

Q8. If A and B are two sets , then A∪B=A∩BA∪⁡B=A∩⁡B iff

A. A ⊆ B

B. none of these

C. A=B

D. B ⊆A

Answer : Option C
Explaination / Solution:

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

Q9. If

z_{1} a n d z_{2}

are non real complex numbers such that

z_{1} + z_{2} a n d z_{1} z_{2}

are real numbers , then

A. z1= z2¯¯¯¯¯

z_{1} = \bar{z_{1}}

and

z_{2} = \bar{z_{2}}

C. z1=−z2¯¯¯¯¯

D. none of these.

Answer : Option A
Explaination / Solution:

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

Q10. If A ,B andC be the three square matrices such that A = B + C , then Det A is equal to

A. det B

B. det C

C. none of these

D. det B + detC

Answer : Option C
Explaination / Solution:

Because , if A=B+C then |A|=|B+C|

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