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. A function f from the set of natural numbers to integers defined by
f(n) = $\left\{\begin{matrix} \frac{n-1}{2}, & where \ n \ is \ odd \\ -\frac{n}{2},& when \ n \ is \ even \end{matrix}\right.$ is
a) onle-one but not onlto
b) onlto but not one-one
c) one-one and onlto both
d) neither one-one not onto

2. The domain of the function f(x) = $\frac{1}{\sqrt{|x| - x}}$ is
a) (o,∞)
b) (-∞,0)
c) (-∞,∞)-{0}
d) (-∞,∞)

• 2. Complex Numbers and Quadratic Equations - Quiz

SAMPLE QUESTIONS

1. If $\left (\frac{1 + i}{1 - i} \right )^{x}$ = 1 , then
a) x = 4n, where n is any positive integer
b) x = 2n, where n in any positive integer
c) x = 4n + 1, where n is any positive integer
d) x = 2n + 1, where n is any positive integer

2. The number of real roots of $3^{2x^{2} - 7x + 7}$ = 9 is
a) 0
b) 2
c) 1
d) 4

• 3. Matrices and Determinants - Quiz

SAMPLE QUESTIONS

1. Let a, b, c be any real numbers. Suppose that there are real numbers x, y, z not all zero such that x = cy + bz, y = az + cx, and z = bx + ay. Then a2 + b2 + c2 + 2abc is equal to
a) 1
b) 2
c) -1
d) 0

2. If ω ≠ 1 is the complex cube root of unity and matrix H - $\begin{bmatrix} \omega & 0\\ 0& \omega \end{bmatrix}$ , then H70 is equal to
a) H
b) 0
c) -H
d) H2

• 4. Permutations and Combinations - Quiz

SAMPLE QUESTIONS

1. At an election , a voter may vote for any number of candidates not greater than the number to be elected. There are 10 candidates and 4 are to be elected. If a voter votes for at least one candidate, then the number of ways in which he can vote, is
a) 6210
b) 385
c) 600
d) 601

2. From 6 different novels and 3 different dictionaries, 4 novels and 1 dictionary are to be selected and arranged in a row on the shelf so that the dictionary is always in the middle. Then , the middle of such arrangements is
a) at least 500 but less than 750
b) at least 750 but less than 1000
c) at least 1000
d) less than 500

• 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. Statement I For each natural number n,(n+1)7 - n7 - 1 is divisible by 7.
Statement II For each natural number n, n7 - n is divisible by 7.
a) Statement I is false , Statement II is true.
b) Statement I is true, Statement II is true; Statement II is correct explanation for Statement I.
c) Statement I is true, Statement II is true; Statement II is not a correct explanation for Statement I.
d) Statement I is true, Statement II is false.

• 6. Binomial Theorem - Quiz

SAMPLE QUESTIONS

1. The value of 50C4 $\sum_{r=1}^{6}$ 56-3C3 is
a) $^{56}C_{4}$
b) $^{56}C_{3}$
c) $^{55}C_{3}$
d) $^{55}C_{4}$

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

• 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. In p and q are positive real numbers such that p2 + q2 =1, then the maximum value of (p + q) is
a) 2
b) $\frac{1}{2}$
c) $\frac{1}{\sqrt{2}}$
d) $\sqrt{2}$

• 8. Limits, Continuity and Differentiabilty - Quiz

SAMPLE QUESTIONS

1. If $lim_{x \rightarrow \infty}\left (1 + \frac{a}{x} + \frac{b}{x^{2}} \right )^{2x}$, then the values of a and b are
a) a ∈ R, b ∈ R
b) a = 1, b ∈ R
c) a ∈ R, b = 2
d) a = 1, b = 2

2. Let f be a function defined by
f(x) = $\left\{\begin{matrix} \frac{tan x}{x} ,&x \ne 0 \\ 1,& x = 0 \end{matrix}\right.$
Statement I x = 0 is point of minima of f.
Statement II f'(0) = 0
a) Statement I is false, Statement II is true
b) Statement I is true, Statement II is true; Statement II is correct explanation for Statement I.
c) Statement I is true, Statement II is true; Statement II is not a correct explanation for Statement I.
d) Statement I is true, Statement II is false.

• 9. Integral Calculas - Quiz

SAMPLE QUESTIONS

1. $\int\frac{dx}{x\left (x^{n} + 1 \right )}$ is equal to
a) $\frac{1}{n}log\left (\frac{x^{n}}{x^{n} + 1} \right ) + c$
b) $\frac{1}{n}log\left (\frac{x^{n} + 1}{x^{n}} \right ) + c$
c) $log\left (\frac{x^{n}}{x^{n} + 1} \right ) + c$
d) None of the above

2. The area of the region bounded by the curves y = | x - 1| and y = 3 - |x| is
a) 2 sq unit
b) 3 sq unit
c) 4 sq unit
d) 6 sq unit

• 10. Differential Equations - Quiz

SAMPLE QUESTIONS

1. The differential equation for the family of curves x2 + y2 - 2ay = 0, where a is an arbitrary constant, is
a) 2(x2 - y2)y' = xy
b) 2(x2 + y2)y' = xy
c) (x2 - y2)y' = 2xy
d) (x2 + y2)y' = 2xy

2. The solution of the differential equation
$\frac{dy}{dx}$ = $\frac{x + y}{x}$
satisfying the condition y(1) = 1 is
a) y = x log x + x
b) y = log x + x
c) y = x log x + x2
d) y = xe(x-1)

• 11. Coordinate Geometry - Quiz

SAMPLE QUESTIONS

1. If the sum of the slopes of the lines given by x2 - 2cxy - 7y2 = 0 is four times their product, then c has the value
a) 1
b) -1
c) 2
d) -2

2. The greater distance of the point P(10,7) from the circle x2 + y2 - 4x - 2y - 20 = 0 is
a) 10 unit
b) 15 unit
c) 5 unit
d) None of these

• 12. Three Dimensional Geometry - Quiz

SAMPLE QUESTIONS

1. The radius of the circle in which the sphere x2 + y2 + z2 + 2x - 2y - 4z - 19 = 0 is cut by the plane x + 2y + 2z + 7 = 0 is
a) 1
b) 2
c) 3
d) 4

2. If the angle θ between the line $\frac{x + 1}{1}$ = $\frac{y - 1}{2}$ = $\frac{z - 2}{2}$ and the plane 2x - y + $\sqrt{\lambda }z$ + 4 = 0 is such that sinθ = $\frac{1}{3}$. The value of λ is
a) $-\frac{4}{3}$
b) $\frac{3}{4}$
c) $-\frac{3}{5}$
d) $\frac{5}{3}$

• 13. Vector Algebra - Quiz

SAMPLE QUESTIONS

1. Let $\vec{a}$ = $\hat{i} + \hat{j} + \hat{k} , \vec{b}$ = $\hat{i} - \hat{j} + 2\hat{k}$ and $\vec{c}$ and $x\hat{i} + \left (x - 2 \right )\hat{j} - \hat{k}$ . If the vector $\vec{c}$ lies in the plane of $\vec{a} and \vec{b}$ , then x equals
a) 0
b) 1
c) -4
d) -2

2. Let $\vec{a}$ = $\hat{j} - \hat{k} and \vec{c}$ = $\hat{i} - \hat{j} - \hat{k}$ . Then the vector $\vec{b}$ satisfying $\vec{a} \times \vec{b} + \vec{c}$ = 0 and \vec{a}.\vec{b}$= 3, is a)$-\hat{i} + \hat{j} - 2\hat{k}$b)$2\hat{i} - \hat{j} + 2\hat{k}$c)$\hat{i} - \hat{j} - 2\hat{k}$d)$\hat{i} + \hat{j} - 2\hat{k}$• 14. Statistics and Probabilty - Quiz SAMPLE QUESTIONS 1. The median of a set of 9 distinct observations is 20.5. If each of the largest 4 observations of the set is increased by 2, then the median of the new set a) is increased by 2 b) is decreased by 2 c) is two times the original median d) remains the same as that of the original set 2. If C and D are two events such that the C ⊂ D and P(D) ≠ 0, then the correct statement among the following is a) P(C|D) ≥ P(C) b) P(C|D) < P(C) c) P(C|D) =$\frac{P\left (D \right )}{P\left (C \right )}$d) P(C|D) = P(C) • 15. Trigonometry - Quiz SAMPLE QUESTIONS 1. 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}$2. If$sin^{-1}\left (\frac{x}{5} \right ) + cosec^{-1}\left (\frac{5}{4} \right )$=$\frac{\pi}{2}\$ , then a value of x is
a) 1
b) 3
c) 4
d) 5

• 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. The only statement among the following that is a tautology is
a) B → ∧ ( A → B)]
b) A ∧ (A ∨ B)
c) A ∨ (A ∧ B)
d) [A ∧ (A → B)] → B

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