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. Let f : N → Y be a function defined as f(x) = 4x + 3 where
Y = { y ∈ N : y = 4x + 3 for some x ∈ N}.
Show that f is invertible and its inverse is
a) g(y) = $\frac{y-3}{4}$
b) g(y) = $\frac{3y+4}{3}$
c) g(y) = $4 + \frac{y+3}{4}$
d) g(y) = $\frac{y+3}{4}$

2. Let f be a function defined by f(x) = (x-1)2 + 1, (x ≥ 1)
Statement I
The set { x : f(s) = f-1(x)} = {1,2}
Statement II
f = f is bijection and f-1(s) = 1 + $\sqrt{x - 1}$, x ≥ 1
a) Statement I is false, Statement II is true.
b) Statement I is true , Statement II is true; Statement II is a correct explanation for Statement I.
c) Statement I is true, Statement II is true, Statement II is not a correct explanation for explanation I.
d) Statement I is true, Statement I is true, Statement II is false.

• 2. Complex Numbers and Quadratic Equations - Quiz

SAMPLE QUESTIONS

1. Let α, β be real and z be a complex number. If z2 + az + β = 0 has two distinct roots on the line Re z = 1, then it is necessary that
a) β ∈ (-1,0)
b) |β| = 1
c) β ∈ (1,∞)
d) β ∈ (0,1)

2. If ω is an imaginary cube root of unity, then (1 + ω - ω2)7 equals
a) 128ω
b) -128ω
c) 128ω2
d) -128ω2

• 3. Matrices and Determinants - Quiz

SAMPLE QUESTIONS

1. 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

2. Let A be a 2 x 2 matrix with real entries. Let I be the 2 x identity matrix. Denote by tr(A), the sum of diagonal entries of A. Assume that A2 = I.
Statement I
If A ≠ I and A ≠ , then det(A) = -1.
Statement II
If A ≠ I and A ≠ -I, then tr(A) ≠ 0.
a) Statement I is false, Statement II is true
b) Statement I is true, Statement II is false;Statement II is a 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

• 4. Permutations and Combinations - Quiz

SAMPLE QUESTIONS

1. If the letters of the word SACHIN are arranged in all possible ways and these words are written out as in dictionary , then the word SACHIN appears at serial number
a) 602
b) 603
c) 600
d) 601

2. In a shop there are five types of ice-creams available. A child buys six ice-cream available. A child buys six ice-creams
Statement I The number of different ways the child can buy the six ice-creams is 10C5.
Statement II The number of different ways the child can buy the six ice-creams is equal to the number of different ways of arranging 6A's and 4B's in a row.
a) Statement I is false, Statement II is true
b) Statement I is true, Statement II is true; Statement II is a 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

• 5. Mathematical Induction - Quiz

SAMPLE QUESTIONS

1. 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.

2. 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

• 6. Binomial Theorem - Quiz

SAMPLE QUESTIONS

1. If the coefficient of x7 in $\left [ax^{2} + \frac{1}{bx} \right ]^{11}$ equals the coefficient of x-7 in $\left [ax^{2} - \frac{1}{bx} \right ]^{11}$, then a and b satisfy the relation
a) ab = 1
b) $\frac{a}{b}$ = 1
c) a + b = 1
d) a - b = 1

2. Let S1 = $\sum_{j=1}^{10}j\left (j-1 \right )^{10}C_{j}, S_{2}$ = $\sum_{j=1}^{10} j^{10}C_{j} \ and \ S_{3}$ = $\sum_{j=1}^{10}$ j2 10Cj
Statement I S3 = 55 × 29.
Statement II S1 = 90 x 28 and S2 = 10 x 28.
a) Statement I is false, Statement II is true.
b) Statement I is true, Statement II is true; Statement II is a correct explanations of 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.

• 7. Sequences and Series - Quiz

SAMPLE QUESTIONS

1. A person is to count 4500 currently notes. Let a11, denotes the number of notes he counts in the nth minute . If a1 = a2 = .... = a10 = 150 and a10, a11,.... are in AP with common difference -2, then the common difference -2, then the time taken by him to count to count all notes, is
a) 24 min
b) 34 min
c) 125 min
d) 135 min

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. Let f : R → [0,∞) be such that $lim_{x \rightarrow 5}f\left (x \right )$ exists and $lim_{x \rightarrow 5 }\frac{\left [f\left (x \right ) \right ]^{2} - 9}{\sqrt{\left | x - 5 \right |}}$ = 0. Then, $lim_{x \rightarrow 5}f\left (x \right )$ equals to
a) 3
b) 0
c) 1
d) 2

2. If xmyn = (x + y)m+n, then $\frac{dy}{dx}$ is
a) $\frac{x + y}{xy}$
b) xy
c) $\frac{x}{y}$
d) $\frac{y}{x}$

• 9. Integral Calculas - Quiz

SAMPLE QUESTIONS

1. The value of the integral I = $\int_{0}^{1}x\left (1 - x \right )^{n}dx$ is
a) $\frac{1}{n + 1}$
b) $\frac{1}{n + 2}$
c) $\frac{1}{n + 1}$ - $\frac{1}{n + 21}$
d) $\frac{1}{n + 1}$ + $\frac{1}{n + 2}$

2. The value of $\int_{1}^{a}$[x]f'(x) dx , a > 1 where [x] denotes the greatest integer not exceeding x, is
a) [a]f(a) - {f(1) + f(2) + ....... + f([a])}
b) [a]f([a]) - {f(1) + f(2) + ...... + f(a)}
c) af([a]) - {f(1) + f(2) + ..... + f(a)}
d) af(a) - {f(1) + f(2) + ...... + f([a])}

• 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 differential equaltion which represents the family of curve y = c1ec2x, where c1 and c2 are arbitrary constants is
a) y' = y2
b) y" = y'y
c) yy" = y'
d) yy" = (y')2

• 11. Coordinate Geometry - Quiz

SAMPLE QUESTIONS

1. 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

2. A parabola has the origin as its focus and the line x = 2 as the directrix. Then , the vertex of the parabola is at
a) (2,0)
b) (0,2)
c) (1,0)
d) (0,1)

• 12. Three Dimensional Geometry - Quiz

SAMPLE QUESTIONS

1. Statement I The point A(3,1,6) is the mirror image of the point B(1,3,4) in the plane x - y + z = 5
Statement II The plane x - y + z = 5 bisects the line segments joining A(3,1,6) and B(1,3,4)
a) Statement I is true, Statement II is a correct explanation for Statement I.
b) Statement I is true, Statement II is true, Statement II is not a correct explanation for Statement I.
c) Statement I is true, Statement II is false.
d) Statement I is false, Statement II is true.

2. The two lines x = ay + b, z = cy + d and x = a'y + b', z = c'y + d' are perpendicular to each other, if
a) aa' + cc' = 1
b) $\frac{a}{a'} + \frac{c}{c'}$ = -1
c) $\frac{a}{a'} + \frac{c}{c'}$ = 1
d) aa' + cc' = -1

• 13. Vector Algebra - Quiz

SAMPLE QUESTIONS

1. If the vectors $\vec{a}, \vec{b}$, and $\vec{c}$ from the sides BC, CA and AB respectively of a triangle ABC, then
a) $\vec{a}.\vec{b}$ = $\vec{b}.\vec{c}$ = $\vec{c}, \vec{b}$ = 0
b) $\vec{a}\times \vec{b}$ = $\vec{b}\times \vec{c}$ = $\vec{c} \times \vec{a}$ = 0
c) $\vec{a}.\vec{b}$ = $\vec{b}.\vec{c}$ = $\vec{c}, \vec{a}$ = 0
d) $\vec{a}\times \vec{a}$ = $\vec{a}\times \vec{c}$ = $\vec{c} \times \vec{a}$ = 0

2. The distance between the line $\vec{r}$ = $2\vec{i} + 2\vec{j} + 3\vec{k} + \lambda \left ( \vec{i} - \vec{j} + 4 \vec{k} \right )$ and the plane $\vec{r}. \left (\hat{i} + 5\hat{j} + \hat{k} \right )$= 5 is
a) $\frac{10}{3}$
b) $\frac{3}{10}$
c) $\frac{10}{3\sqrt{3}}$
d) $\frac{10}{9}$

• 14. Statistics and Probabilty - Quiz

SAMPLE QUESTIONS

1. 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)

2. Statement I The varience of first n even natural numbers is $\frac{n^{2} - 1}{4}$.
Statement II The sum first n natural numbers is $\frac{n\left (n + 1 \right )}{2}$ and the sum of squares of first n natiural numbers is $\frac{n\left (n + 1 \right )\left (2n + 1 \right )}{6}$
a) Statement I is true, Statement II is true; Statement II is a correct explanation for Statement I.
b) Statement I is true, Statement II is true; Statement II is not a correct explanation for Statement I.
c) Statement I is true, Statement II is false.
d) Statement I is false, Statement II is false.

• 15. Trigonometry - Quiz

SAMPLE QUESTIONS

1. The upper $\left (\frac{3}{4} \right )th$ portion of a vertical pole substends an angle $tan^{-1}\left (\frac{3}{5} \right )$ at a point in the horizontal plane through its foot and at a distance 40m from the foot. A possible height of the vertical pole is
a) 20 m
b) 40m
c) 60 m
d) 80 m

2. The value of $\frac{1 - tan^{2}15^{0}}{1 + tan^{2}15^{0}}$ is
a) 1
b) $\sqrt{3}$
c) $\frac{\sqrt{3}}{2}$
d) 2

• 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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