Class/Course  Engineering Entrance
Subject  Mathematics
Total Number of Question/s  3005
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1. Sets, Relations and Functions  Quiz
1. Let f(x) = (x + 1)^{2}  1, x ≥ 1
Statement I The set {x : f(x) = f^{1}(x)} = {0,1}
Statement II f is a bijection
a) Statement I is false, Statement II is true
b) Statement I is true, Statement II is true;
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 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) = $\frac{y3}{4}$
b) g(y) = $\frac{3y+4}{3}$
c) g(y) = $4 + \frac{y+3}{4}$
d) g(y) = $\frac{y+3}{4}$

2. Complex Numbers and Quadratic Equations  Quiz
1. If the roots of the quadratic equation x^{2} + px + q = 0 are tan 30^{0} and tan 15 respectively, then the value of 2 + q  p is
a) 3
b) 0
c) 1
d) 2
2. If the cube roots of unity are 1, ω , ω^{2}, then the roots of the equation (x1)^{3} + 8 = 0, are
a) 1, 1+2ω, 1 + 2ω^{2}
b) 1, 1  2ω, 1  2ω^{2}
c) 1, 1, 1
d) 1, 1 + 2ω , 1  2ω^{2}

3. Matrices and Determinants  Quiz
1. The system od equations
αx + y + z = α  1
x + αy + z α  1
x + y + αz = α  1
has no solution, if α is
a) 1
b) not 2
c) either 2 or 1
d) 2
2. If (ω ≠ 1) is a cube root of unity, then $\begin{vmatrix} 1 &1 + i + \omega^{2} & 1\\ 1i& 1 & \omega^{2}1\\ i & 1+\omega  i &1 \end{vmatrix}$ equals
a) 0
b) 1
c) i
d) ω

4. Permutations and Combinations  Quiz
1. 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
2. Statement I The number of ways distributing 10 identical balls in 4 distinct boxes such that no box is empty is ^{9}C_{3}.
statement II The number of ways of choosing any 3 places from 9 different places is ^{9}C_{3}.
a) Statem,ent I is true, Statement II is true; Statement II is not a correct explanation for Statement I.
b) Statement I is true,Statement I is false.
c) Statement I is false,Statement I is true.
d) Statement I is true, Statement II is true; Statement II is a correct explanation for Statement I.

5. Mathematical Induction  Quiz
1. Statement I For every natural number n ≥ 2
$\frac{1}{\sqrt{1}} + \frac{1}{\sqrt{2}} + .......... + \frac{1}{\sqrt{n}}$ > $\sqrt{n}$
statement II For every natural number $n \ge 2. \sqrt{n\left (n + 1 \right )} < + 1$
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. 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.

6. Binomial Theorem  Quiz
1. If S_{n} = $\sum_{r = 0}^{n}\frac{1}{^{n}C_{r}} \ and \ t_{n}= \sum_{r=0}^{n}\frac{r}{^{n}C_{r}} \ then \ \frac{t_{n}}{S_{n}}$ is equal to
a) $\frac{n}{2}$
b) $\frac{n}{2}$  1
c) n1
d) $\frac{2n1}{2}$
2. The coefficient of x^{5} in (1 + 2x + 3x^{2} + ......)^{3/2} is
a) 21
b) 25
c) 26
d) None of these

7. Sequences and Series  Quiz
1. 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}$\left (\frac{4}{e} \right )$
2. The value of 2^{1/4}. 4^{1/8}, 8^{1/16} .... is
a) 1
b) 2
c) $\frac{3}{2}$
d) 4

8. Limits, Continuity and Differentiabilty  Quiz
1. The values of p and q for which the function
f(x) = $\left\{\begin{matrix} \frac{sin\left (p + 1 \right )x + sinx}{x}, &x < 0 \\ q, &x = 0 \\ \frac{\sqrt{x + x^{2}}  \sqrt{x}}{x^{3/2}}, x > 0& \end{matrix}\right.$
is continuous for all x in R, are
a) p = $\frac{5}{2}$, q = $\frac{1}{2}$
b) p = $\frac{3}{2}$, q = $\frac{1}{2}$
c) p = $\frac{1}{2}$, q = $\frac{3}{2}$
d) p = $\frac{1}{2}$, q = $frac{3}{2}$
2. If x^{m}y^{n} = (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
1. $lim _{n \rightarrow \infty} \sum_{r = 1}^{n}\frac{1}{n}e^{r/n}$ is
a) e
b) e  1
c) 1  e
d) e + 1
2. If $\int_{0}^{\pi}x f\left (sin x \right )dx$ = $A\int_{0}^{\pi/2}$ , then A is equal to
a) 0
b) π
c) $\frac{\pi}{4}$
d) 2π

10. Differential Equations  Quiz
1. The solution of the differential equation
$\left (1 + y^{2} \right ) + \left (x  e^{tan^{1}y} \right )\frac{dy}{dx}$ = 0 is
a) $\left (x  2 \right )$= $ce^{2tan^{1}y}$
b) $2xe^{tan^{1}y}$ = $2^{tan^{1}y} + c$
c) $xe^{tan^{1}y}$ = $tan^{1}y + c$
d) $xe^{2tan^{1}y}$ = $e^{tan^{1}y} + c$
2. The differential equation for the family of curves x^{2} + y^{2}  2ay = 0, where a is an arbitrary constant, is
a) 2(x^{2}  y^{2})y' = xy
b) 2(x^{2} + y^{2})y' = xy
c) (x^{2}  y^{2})y' = 2xy
d) (x^{2} + y^{2})y' = 2xy

11. Coordinate Geometry  Quiz
1. 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)
2. A triangle with vertices (4,0), (1,1), (3,5) is
a) isosceles and right angled
b) isosceles but not right angled
c) right angled but not isosceles
d) neither right angled nor isosceles

12. Three Dimensional Geometry  Quiz
1. The line passing through the points (5,1,a) and (3,b,1) crosses the yzplane at the point $\left (0, \frac{17}{2}, \frac{13}{2} \right )$. Then,
a) a = 8, b = 2
b) a = 2, b = 8
c) a = 4, b = 6
d) a = 6, b = 4
2. If a line makes an angle of $\frac{\pi}{4}$ with the positive fdirections of each of xaxis and yaxis, then the angle that the line makes with the positive direction of the zaxis is
a) $\frac{\pi}{6}$
b) $\frac{\pi}{3}$
c) $\frac{\pi}{4}$
d) $\frac{\pi}{2}$

13. Vector Algebra  Quiz
1. If C is the mid point of AB and P is any point outside AB, then
a) $\vec{PA} + \vec{PB} + \vec{PC}$ = $\vec{0}$
b) $\vec{PA} + \vec{PB} + 2\vec{PC}$ = $\vec{0}$
c) $\vec{PA} + \vec{PB}$ = $\vec{PC}$
d) $\vec{PA} + \vec{PB}$ = $2\overrightarrow{PC}$
2. 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

14. Statistics and Probabilty  Quiz
1. Consider he following statements
(1) Mode can be compound from histogram
(2) Median is not independent of change of scale
(3) Varience is independent of change of origin and scale
Which of these is/are correct?
a) Only (1)
b) Only (2)
c) Only (1) and (2)
d) (1), (2) and (3)
2. The mean and the variance of a bionomial distribution are 4 and 2 respectively. Then the probability of 2 sucesses is
a) $\frac{37}{256}$
b) $\frac{219}{256}$
c) $\frac{128}{256}$
d) $\frac{28}{256}$

15. Trigonometry  Quiz
1. 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
2. In a triangle ABC, medians AD and BE are drawn, IF AD = 4, ∠DAB = $\frac{\pi}{6}$ and ∠ABE = $\frac{\pi}{3}$>, then the area of the δABC is
a) $\frac{8}{3}$ sq unit
b) $\frac{16}{3}$ sq unit
c) $\frac{32}{\sqrt{3}}$ sq unit
d) $\frac{64}{3}$ sq unit

16. Mathematical Reasoning  Quiz
1. 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
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)