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

Q1. Order of a differential equation is defined as

A. the order of the highest order derivative of the dependent variable

B. the number of constant terms

C. the order of the lowest order derivative ofthe dependent variable

D. the number of derivative terms

Answer : Option A
Explaination / Solution:

Order of a differential equation is defined as the order of the highest order derivative of the dependent variable present in the differential equation.

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

Q2. If l, m, n are the direction cosines of a line, then

A. 2l2+ m2+ n2= 1.

l^{2} + m^{2} + 2 n^{2} = 1.

C. l2+ 2m2+ n2= 1.

D. l2+ m2+ n2= 1.

Answer : Option D
Explaination / Solution:

we know that direction cosines is coefficient of i,j,k of unit vector along that line ,i.e those coefficient are l,m,n .the length of the line r is such that

\vec{r} = l \hat{i} + m \hat{j} + n \hat{k}

and magnitute of unit vector r is 1 and .

\sqrt{l^{2} + m^{2} + n^{2}}

on squaring both side we get

l^{2} + m^{2} + n^{2} = 1.

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

Q3. In a triangle ABC, if A =

75^{o}

and B =

45^{o}

then b + 2 c is equal to

A. 12(a+b+c)

B. 2a

C. a+b+c

D. a

Answer : Option B
Explaination / Solution:

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

Q4. The area of the loop between the curve y = a sin x and the x – axis and x= 0 , x=π. is

A. 3a

Answer : Option D
Explaination / Solution:

Required area =

∫0πasinxdx=a[−cosx]π0=a(−cosπ+cos0)=a(1+1)=2a

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

Q5. The direction cosines of X -axis are

A. < 0 , 1 , 1 >

B. < 1 , 0 , 0 >

C. < 0 , 0 , 1 >

D. < 0 , 1 , 0 >

Answer : Option B
Explaination / Solution:

As we know that if a lines makes angles a , b and c with X-axis , Y-axis and Z-axis respectively then direction cosines are given by < cos a , cos b ,cos c >

In our case line is X-axis itself which we know makes angle of 0 $^{\circ}$ , 90 $^{\circ}$ , 90 $^{\circ}$ with X-axis , Y-axis and Z-axis respectively then direction cosine will be

= < 1 0 0 >

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

Q6. The number of all possible matrices of order 3×3 with each entry 0 or 1 is

A. 81

B. none of these

C. 512

D. 18

Answer : Option C
Explaination / Solution:

$2^{3 x 3} = 2^{9} = 512.$

The number of elements in a 3 X 3 matrix is the product 3 X 3=9.

Each element can either be a 0 or a 1.

Given this, the total possible matrices that can be selected is 29=512

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

Q7. If the graph of a differentiable function y = f (x) meets the lines y = – 1 and y = 1, then the graph

A. meets the line y = 0 at least twice

B. does not meet the line y = 0.

C. meets the line y = 0 at least once

D. meets the line y = 0 at least thrice

Answer : Option C
Explaination / Solution:

Since the graph cuts the lines y = -1 and y = 1 , therefore ,it must cut y = 0 atleast once as the graph is a continuous curve in this case.

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

Q8. Let A and B be two sets such that {tex}n(A)=35,n(B)=42\quad and\quad n(A\cap B)=17{/tex}, find {tex}n(A-B){/tex}

A. 25

B. 19

C. 18

D. 17