Class/Course  Engineering Entrance
Subject  Mathematics
Total Number of Question/s  3005
Just Exam provide question bank for Engineering Entrance 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. Interested person may contact us at info@justexam.in

1. Sets, Relations and Functions  Quiz
1. Domain of definition of the function f(x) = $\frac{3}{4  x^{2}} + log_{10}\left (x^{3}  x\right )$ , is
a) (1,2)
b) (1,0) ∪ (1,2)
c) (1,2) ∪ (2,$\infty$)
d) (1,0) ∪ (1,2) ∪ (2,$\infty$ )
2. Let for a ≠ a1 ≠ 0, f(x) = ax^{2} = ax^{2} + bx + c,
g(x) = a_{1}x^{2} + b_{1} x + c_{1} and p(x) = f(x)  g(x) , If p(x) = 0 only for x = 1 and p(2) = 2, then the value of p(2) is
a) 18
b) 3
c) 9
d) 6

2. Complex Numbers and Quadratic Equations  Quiz
1. Let z, w be complex numbers such that $\bar{z} + i\bar{w}$ = 0 and arg (zw) = π . Then arg (z) equals
a) $\frac{\pi}{4}$
b) $\frac{\pi}{2}$
c) $\frac{3\pi}{4}$
d) $\frac{5\pi}{4}$
2. If both the roots of the quadratic equation x^{2}  2kx + k^{2} + k 5 = 0 are less than k lies in the interval
a) [4,5]
b) (∞,4)
c) (6,∞)
d) (5,6]

3. Matrices and Determinants  Quiz
1. If the trivial solution is the only soluytion of the system of equations
x  ky + z = 0
k + 3y  kz = 0
3x + y  z = 0
Then the set of lal values of k is
a) {2,3}
b) R{2,3}
c) R{2}
d) R{3}
2. If l , m , n are the pth, qth and rth terms of an GP and all positive, then $\begin{bmatrix} 1 & \omega^{n} &\omega^{2n} \\ \omega^{n} & \omega^{2n} &1 \\ \omega^{2n} &1 & \omega^{n} \end{bmatrix}$ equals
a) 3
b) 2
c) 1
d) 0

4. Permutations and Combinations  Quiz
1. The number of ways in which 6 men and 15 women can dine at a round table, if no women are to sit together, is given by
a) 6! X 5!
b) 30
c) 5! X 4!
d) 7! X 5!
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
1. Statement I For each natural number n,(n+1)^{7}  n^{7}  1 is divisible by 7.
Statement II For each natural number n, n^{7}  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. Let s(k) = 1 + 3 + 5 + ...... + (2k  1) = 3 + k^{2}. 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
1. If the expansion in powers of x of the function $\frac{1}{\left (1ax \right )\left (1bx \right )}$ is $a_{0} + a_{1}x + a_{2}x^{2} + a_{3}x^{3} + ..... $ then a_{n} is
a) $\frac{a^{n}  b^{n}}{ba}$
b) $\frac{a^{n+1}  b^{n+1}}{ba}$
c) $\frac{b^{n+1}  a^{n+1}}{ba}$
d) $\frac{b^{n}  a^{n}}{ba}$
2. For natural numbers m,n if (1  y)^{m}(1+y)^{n} = 1 + a_{1}y + a_{2}y^{2} + .... and a_{1} = a_{2} = 10, then (m,n) is
a) (35,20)
b) (45,35)
c) (35,45)
d) (20,45)

7. Sequences and Series  Quiz
1. In a geometric progressions consisting of positive terms, each term equals the sum of the next two terms. Then , the common ratio of the progression equals.
a) $\frac{1}{2}\left (1\sqrt{5} \right )$
b) $\frac{1}{2}\sqrt{5}$
c) $\sqrt{5}$
d) $\frac{1}{2}\left (\sqrt{5}  1 \right )$
2. The sum of the series $\frac{1}{1.2}  \frac{1}{2.3} + \frac{1}{3.4}  .......$ upto ∞ is equal to
a) 2log_{e}2
b) log_{e} 21
c) log_{2}e
d) log_{2}$\left (\frac{4}{e} \right )$

8. Limits, Continuity and Differentiabilty  Quiz
1. Suppose the cubic x^{3}  px + q has three distinct real roots where p > 0 and q > 0 . Then which one of the following holds?
a) The cubic has maxima at both $\sqrt{\frac{p}{3}}$ and $\sqrt{\frac{p}{3}}$
b) The cubic has minima at $\sqrt{\frac{p}{3}}$ and maxima at $\sqrt{\frac{p}{3}}$
c) The cubic has minima at $\sqrt{\frac{p}{3}}$ and maxima at $\sqrt{\frac{p}{3}}$
d) The cubic has minima at both $\sqrt{\frac{p}{3}}$ and $\sqrt{\frac{p}{3}}$
2. Let f(2) = 4 and f'(2) = 4, Then, $lim_{x \rightarrow 2}\frac{xf\left (2 \right )  2f\left (x \right )}{x  2}$ is given by
a) 2
b) 2
c) 4
d) 3

9. Integral Calculas  Quiz
1. Let f(x) be a function satisfying f'(x) = f(x) with f(0) = 1 and g(x) be a function that satisfies f(x) g(x) = x^{2}. Then the value of the integral $\int_{0}^{1} f\left (x \right ) g\left (x \right )dx$, is
a) $e  \frac{e^{2}}{2}  \frac{5}{2}$
b) $e\frac{e^{2}}{2}  \frac{3}{2}$
c) $e  \frac{e^{2}}{2}  \frac{3}{2}$
d) $e \frac{e^{2}}{2} \frac{5}{2}$
2. 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

10. Differential Equations  Quiz
1. If $\frac{dy}{dx}$ = y + 3 > 0 and y(0) = 2, then y (log 2) is equal to
a) 5
b) 13
c) 2
d) 7
2. The differential equation of the family of circles with fixed radius 5 unit and centre on the line y = 2 is
a) (x  2)^{2y'2 = 25  (y  2)2}
b) (x  2)y'^{2} = 25  (y  2)^{2}
c) (y  2)y'^{2} = 25  (y  2)^{2}
d) (y  2)^{2}y'^{2} = 25  (y  2)^{2}

11. Coordinate Geometry  Quiz
1. The point diametricall opposite to the point P(1,0) on the circle x^{2} + y^{2} + 2x + 4y  3 = 0 is
a) (3,4)
b) (3,4)
c) (3,4)
d) (3,4)
2. In an ellipse, the distance between its foci is 6 and minor axis is 8. Then its ecentricity is
a) $\frac{1}{2}$
b) $\frac{4}{5}$
c) $\frac{1}{\sqrt{5}}$
d) $\frac{3}{5}$

12. Three Dimensional Geometry  Quiz
1. If the straight lines $\frac{x  1}{k}$ = $\frac{y  2}{k}$ = $\frac{z  3}{3}$ and $\frac{x  2}{3}$ = $\frac{y  3}{k}$ = $\frac{z  1}{2}$ intersect k is equal to
a) 2
b) 5
c) 5
d) 2
2. Statement I The point A(1,0,7) is the mirror image of the point B(1,6,3) in the line $\frac{x}{1}=\frac{y1}{2}=\frac{z2}{3}$
Statement II The line the line segment joining $\frac{x}{1}=\frac{y1}{2}=\frac{z2}{3}$ 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.

13. Vector Algebra  Quiz
1. Let $\vec{u}$ = $\hat{i} + \hat{j}, \vec{v}$ = $\vec{i}  \hat{j}$ and $\vec{w}$ = $\hat{i} + 2\hat{j} + 3\hat{k}$ . If $\vec{n}$ is a unit vector such that $\vec{n}$ = 0 and $\vec{v}.\hat{n}$= 0, then $\vec{v}.\hat{n}$ is equal to
a) 0
b) 1
c) 2
d) 3
2. If $\vec{u}, \vec{v}, \vec{w}$ are noncoplanar vectors and p,q are real numbers, then the equality
$\left [3\vec{u} p\vec{v} p\vec{w} \right ]  \left [p\vec{v}\vec{w} q\vec{u} \right ]  \left [2\vec{w} q\vec{v} q\vec{u} \right ]$ holds for
a) exactly two values of (p,q)
b) more than two but not all values of (p,q)
c) all values of (p,q)
d) exactly one value of (p,q)

14. Statistics and Probabilty  Quiz
1. If A and B are two mutually exclusive events, then
a) $P\left (A \right ) < P\left (\bar{B} \right )$
b) $P\left (A \right ) > P\left (\bar{B} \right )$
c) P(A) < (B)
d) None of the above
2. The mean of the numbers a,b,8,5 10 is 6 and the varience is 6.80. Then which one of the following gives possible values of a and b?
a) a = 3, b = 4
b) a = 0,b = 7
c) a = 5, b = 2
d) a = 1, b = 6

15. Trigonometry  Quiz
1. Let α, β be such that π < α  β < 3π . If sin α + sinβ = $\frac{21}{65}$ and cos α + cos β = $\frac{27}{65}$ then the value of $cos\left (\frac{\alpha  \beta}{2} \right )$ is
a) $\frac{3}{\sqrt{130}}$
b) $\frac{3}{\sqrt{130}}$
c) $\frac{6}{65}$
d) $\frac{6}{65}$
2. The equation a sinx + b cos x = c where c > $\sqrt{a^{2} + b^{2}}$ has
a) a unique solution
b) infinite number of solutions
c) no solution
d) None of the above

16. Mathematical Reasoning  Quiz
1. Statement I $\sim$ (p ↔ ∼ q) is equivalent to p ↔ q.
Statement II ∼ (p ↔ ∼ q) is a tautology.
a) Statement I is true, Statement II 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 true.
2. The statement p → (q → p) is equivalent to
a) p → (p ↔ q)
b) p → (p → q)
c) p → (p ∨ q)
d) p → (p ∧ q)