Total Number of Question/s - 3005

Just Exam provide question bank for JEE MAIN standard. Currently number of question's are 3005. We provide this data in all format (word, excel, pdf, sql, latex form with images) to institutes for conducting online test/ examinations. Here we are providing some demo contents.

• 1. Sets, Relations and Functions - Quiz

SAMPLE QUESTIONS

1. The graph of the function y = f(x) is symmeterical about the line x = 2, then
a) f(x+2) = f(x-2)
b) f(2+x) = f(2-x)
c) f(x) = f(-x)
d) f(x) = -f(-x)

2. Let R = {(3,3), (6,6), (9,9), (12,12),(6.12), (3,9), (3,12), (3,6)} be a relation on the set A = {3,6,9,12}. The relation is
a) reflexive and symmetric only
b) an equivalence relation
c) reflexive only
d) reflexive and transitive only

• 2. Complex Numbers and Quadratic Equations - Quiz

SAMPLE QUESTIONS

1. If (1-p) is a root of quadratic equation x2 + px + (1-p) = 0, then its roots are
a) 0,1
b) -1,1
c) 0,-1
d) -1, 2

2. If the roots of the quadratic equation x2 + px + q = 0 are tan 300 and tan 15 respectively, then the value of 2 + q - p is
a) 3
b) 0
c) 1
d) 2

• 3. Matrices and Determinants - Quiz

SAMPLE QUESTIONS

1. Let A and b be two symmetric matrices of order 3.
Statement I A (BA) and (AB) A are symmetric matrices.
Statement II AB is symmetric matrix, if matrix multiplication of A and B is communitative.
a) Statement 1 is true, Statement II is true; Statement II is not a correct explanation for Statement I.
b) Statement I is true, Statement II is false.
c) Statement I is false, Statement II is true.
d) Statement I is true, Statement II is true; Statement II is a correct explanation for Statement I.

2. If A2 - A + I = O, then the inverse of A is
a) I-A
b) A-I
c) A
d) A+I

• 4. Permutations and Combinations - Quiz

SAMPLE QUESTIONS

1. How many ways are there to arrange the letter in the word GARDEN with the vowels in apphabetical order.
a) 120
b) 240
c) 360
d) 480

2. The set S = {1,2,3, .....,12} is to be partitioned into three sets A,B,C of equal size.
Thus, A ∪ B ∪ C = S,
A ∩ B = B ∩ C = A ∩ C = φ
The number of ways to partition S is
a) 12!/3!(4!)3
b) 12!/3!(3!)4
c) 12!/(4!)3
d) 12!/(3!)4

• 5. Mathematical Induction - Quiz

SAMPLE QUESTIONS

1. If A = $\begin{bmatrix} 1 &0 \\ 1& 1 \end{bmatrix}$ and I = $\begin{bmatrix} 1 &0 \\ 0& 1 \end{bmatrix}$, then which one of the following holds for all n ≥ 1, by the principle of mathematical induction?
a) $A^{n}$ = $2^{n-1}A + \left (n-1 \right )I$
b) $A^{n}$ = $nA + \left (n-1 \right )I$
c) An = $2^{n-1}A-\left (n-1 \right )I$
d) An = nA - (n-1)I

2. Let s(k) = 1 + 3 + 5 + ...... + (2k - 1) = 3 + k2. Then which of the following is true?
a) S(1) is correct
b) s(k) ⇒ S(k+1)
c) S(k) ⇒ S(k+1)
d) Principle of mathematical induction can be used to prove the formula.

• 6. Binomial Theorem - Quiz

SAMPLE QUESTIONS

1. The coefficient of x5 in (1 + 2x + 3x2 + ......)-3/2 is
a) 21
b) 25
c) 26
d) None of these

2. In the bionomial expansion of (a-b)n, n ≥ 5, the sum of 5th and 6th terms is zero, then $\frac{a}{b}$ equals
a) $\frac{5}{n-4}$
b) $\frac{6}{n-5}$
c) $\frac{n-5}{6}$
d) $\frac{n-4}{5}$

• 7. Sequences and Series - Quiz

SAMPLE QUESTIONS

1. Then sum of the series
1 + $\frac{1}{4.2!} + \frac{1}{16.4!} + \frac{1}{64.4!} + .... \infty$ is
a) $\frac{e + 1}{2\sqrt{2}}$
b) $\frac{e - 1}{2\sqrt{2}}$
c) $\frac{e + 1}{\sqrt{2}}$
d) $\frac{e - 1}{\sqrt{2}}$

2. Let an be the nth term of an AP. If $\sum_{r=1}^{100}a_{2r} = \alpha \ and \ \sum_{r=1}^{100}$a2r-1 = β , then the common difference of the AP is
a) $\frac{\alpha - \beta}{200}$
b) $\alpha - \beta$
c) $\frac{\alpha - \beta}{100}$
d) β - α

• 8. Limits, Continuity and Differentiabilty - Quiz

SAMPLE QUESTIONS

1. If f(x) = xn, then the value of
f(1) - $\frac{f'\left (1 \right )}{1!} + \frac{f''\left (1 \right )}{2!} - \frac{f'''\left (1 \right )}{3!} + ......+ \frac{\left (-1 \right )^{n}f^{n}\left (1 \right )}{n!}$ is
a) 2n
b) 2n-1
c) 0
d) 1

2. $lim_{x \rightarrow \frac{\pi}{2}}\frac{\left [1 - tan\left (\frac{x}{2} \right ) \right ]\left (1 - sinx \right )}{\left [1 + tan\left (\frac{x}{2} \right ) \right ]\left (\pi - 2x \right )^{3}}$ is
a) $\frac{1}{8}$
b) 0
c) $\frac{1}{32}$
d) ∞

• 9. Integral Calculas - Quiz

SAMPLE QUESTIONS

1. Let f:R → R be a differentiable function having f(2) = 6, f'(2) = $\left (\frac{1}{48} \right)$. Then, $\lim_{x \rightarrow 2}\int_{6}^{f\left (x \right )} \frac{4t^{3}}{x - 2}dx$ dt equals
a) 18
b) 12
c) 36
d) 24

2. The area of the region enclosed by the curves y = x , x = e, y = $\frac{1}{x}$ and the positive x - axis is
a) 1 sq unit
b) $\frac{3}{2}sq. unit$
c) $\frac{5}{2}sq. unit$
d) $\frac{1}{2}sq. unit$

• 10. Differential Equations - Quiz

SAMPLE QUESTIONS

1. Consider the differential equation y2dx + $\left (x - \frac{1}{y} \right )dy$ = 0. If y(1) = 1, then x is given by
a) $1 - \frac{1}{y} + \frac{\frac{1}{e^{y}}}{e}$
b) $4 - \frac{2}{y} + \frac{\frac{1}{e^{y}}}{e}$
c) $3 - \frac{1}{y} + \frac{\frac{1}{e^{y}}}{e}$
d) $1 + \frac{1}{y} - \frac{\frac{1}{e^{y}}}{e}$

2. The differential equation of all circles passing through the origin and having their centres on the x - axis is
a) $x^{2}$ = $y^{2} + xy\frac{dy}{dx}$
b) $x^{2}$ = $y^{2} + 3xy\frac{dy}{dx}$
c) $x^{2}$ = $y^{2} + 2xy\frac{dy}{dx}$
d) $x^{2}$ = $y^{2} - 2xy\frac{dy}{dx}$

• 11. Coordinate Geometry - Quiz

SAMPLE QUESTIONS

1. If the line 2x + 3y + 1 = 0 and 3x - y - 4 = 0 lie along diameters of a circle of circumference 10π then the equation of the circle is
a) x2 + y2 - 2x + 2y - 23 = 0
b) x2 + y2 - 2x - 2y - 23 = 0
c) x2 + y2 + 2x + 2y - 23 = 0
d) x2 + y2 + 2x-2y-23=0

2. If the circles x2 + y2 + 2ax + cy + a = 0 and x2 + y2 - 3ax + dy - 1 = 0 intersect in two distinct points P and Q, then the line 5x + by - a = 0 passes through P and Q for
a) exactly two values of a
b) infinitely many value of a
c) no value of a
d) exactly one value of a

• 12. Three Dimensional Geometry - Quiz

SAMPLE QUESTIONS

1. Statement I The point A(1,0,7) is the mirror image of the point B(1,6,3) in the line $\frac{x}{1}=\frac{y-1}{2}=\frac{z-2}{3}$
Statement II The line the line segment joining $\frac{x}{1}=\frac{y-1}{2}=\frac{z-2}{3}$ bisects the line segment joining A(1,0,7) and B(1,6,3).
a) Statement I is true, Statement II is true; Statement II is not a correct explanation for Statement I.
b) Statement I is true, Statement II is false.
c) Statement I is false, Statement II is true.
d) Statement I is true, Statement II is true; Statement II is a correct Explanation for Statement I.

2. A line with direction cosines proportional to 2, 1, 2 meets each of the lines x = y + a = z and x + a = 2y = 2z. The coordinates of each of the points of intersection are given by
a) (3a, 3a, 3a), (a, a, a)
b) (3a, 2a, 3a), (a, a, a)
c) (3a, 2a, 3a), (a, a, 2a)
d) (2a, 3a, 3a),(2a, a, a)

• 13. Vector Algebra - Quiz

SAMPLE QUESTIONS

1. If $\begin{vmatrix} a & a^{2} &1 + a^{3} \\ b &b^{2} &a + b^{3} \\ c& c^{2} & 1 + c^{3} \end{vmatrix}$ = 0 and vectors (1,a,a2), (1,b,b2) and (1,c,c2) are non coplanar, then the product abc equals
a) 2
b) -1
c) 1
d) 0

2. The vactor $\vec{a}$ and $\vec{b}$ are not perpendicular and $\vec{c}$ and $\vec{d}$ are two vectors satisfying $\vec{b} \times \vec{c}$ = $\vec{b} \times \vec{d}$ and $\vec{a} \times \vec{d}$ = 0. Then the vectors $\vec{d}$ is equal to
a) $\vec{c}+ \left ( \frac{\vec{a}\cdot \vec{c}}{\vec{a}\cdot \vec{b}} \right )\vec{b}$
b) $\vec{b}+ \left ( \frac{\vec{b}\cdot \vec{c}}{\vec{a}\cdot \vec{b}} \right )\vec{c}$
c) $\vec{c}- \left ( \frac{\vec{a}\cdot \vec{c}}{\vec{a}\cdot \vec{b}} \right )\vec{b}$
d) $\vec{b}- \left ( \frac{\vec{b}\cdot \vec{c}}{\vec{a}\cdot \vec{b}} \right )\vec{c}$

• 14. Statistics and Probabilty - Quiz

SAMPLE QUESTIONS

1. In a class of 100 students there are 70 boys whose average marks in a subject are 75. If the average marks of the complete class is 72, then what is the average of the girls?
a) 73
b) 65
c) 68
d) 74

2. Let A and B be two real events such that $P\left (\overline{A \cup B} \right )$ , $\frac{1}{6}$, $P \left (A \cap B \right )$ = $\frac{1}{4}$ and P(A) = $P\left (\bar{A} \right )$ = $\frac{1}{4}$ , where A stands for complement of event A. Then, events A and B are
a) mutually exclusive and independent
b) independent but not equally likely
c) equally likely but not independent
d) equally likely and mutually exclusive

• 15. Trigonometry - Quiz

SAMPLE QUESTIONS

1. Let cos(α + β) = $\frac{4}{5}$ and let sin(aα - β) = $\frac{5}{13}$ where 0 ≤ α , β ≤ $\frac{\pi}{4}$ . Then tan 2α is equal to
a) $\frac{25}{16}$
b) $\frac{56}{33}$
c) $\frac{19}{12}$
d) $\frac{20}{7}$

2. A tower stands at the centre of a circular park. A and B are two points on the boundary of the park such that AB = ( = a) subtends an angle of 600 at the foot of the tower and the angles of elevation of the top of the tower A or B is 300. The height of the tower is
a) $\frac{2a}{\sqrt{3}}$
b) $2a\sqrt{3}$
c) $\frac{a}{\sqrt{3}}$
d) $\sqrt{3}$

• 16. Mathematical Reasoning - Quiz

SAMPLE QUESTIONS

1. Consider the following statements
P : Suman is brilliant.
Q : Suman is rich.
R : Suman is honest.
The negative of the statement. Suman is brilliant and dishonest if and only if Suman is rich can be expressed as
a) ∼ (Q ↔ (O P ∼ R)
b) ∼ Q ↔ P ^ R
c) ∼ (P ^ ∼ R) ↔ Q
d) ∼ P ^ (Q ↔ ∼ R)

2. Let S be a non-empty subset of R. Consider the following statement.
P : There is a rational number x ∈ S such that x > 0.
Which of the following statements is the negation of the statement P ?
a) There is a rational number x ∈ S such that x ≤ 0
b) There is no rational number x ∈ S such that x ≤ 0
c) Every rational number x ≤ S satisfies x ≤ 0
d) x ∈ S and x ≤ 0 ⇒ x is not rational

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