Q. In a two digit number, the digit at the ten's place is $4$ and the product of the two two digits is $4$ times greater than the value of the digit in the ten's place. What is the two digit number?

1. $42$
2. $84$
3. $44$
4. $48$

Q. $S_n=2n^2+3n$; then $d=$..........

1. $13$
2. $4$
3. $9$
4. $-2$

Q. Given is a graph showing two lines.
Which of the following statements is true about the solution(s) of the pair of equations represented by these lines?

1. They have a unique solution.
2. They do not have any solution.
3. We cannot predict the number of solutions without knowing the algebraic form of these equations.
4. They have infinite solutions.

Q. In Euclid's division Lemma for positive integers $a$ and $b$, the unique integers $q$ and $r$ are obtained such that $a=bq+r$ is

1. $0<r\le b$
2. $0<r<b$
3. $0\le r<b$
4. $0\le r\le b$

Q. In $△ABC$, the measures of $\overline{BC},\overline{CA},\overline{AB}$ are in the ratio $3:4:5$. Correspondence $ABC\leftrightarrow PQR$ is congruence. If $PR=12$, then the perimeter of $△PQR$ is .......... .

1. $24$
2. $27$
3. $36$
4. $12$

Q. Out of the following triplets ................ is not a Pythagorean triplet.

1. $20,21,29$
2. $11,60,61$
3. $13,35,37$
4. $7,24,25$

Q. $\tan 7\theta .\tan 3\theta =1$, $\therefore$ $\theta -=$

1. $0^o$
2. $9^o$
3. ${10}^o$
4. ${18}^o$

Q. In a Math test taken by $35$ students, the average score of $15$ girls is $10$ and that of $20$ boys is also $10$. Which of the following can be calculated based on the above data?

1. The highest score in the class.
2. The lowest score among the boys in the class.
3. All of the above.
4. The sum of the scores of the $35$ students of the whole class.

Q. Rachna had an average score of $45$ from $6$ test. Her teacher dropped her lowest score, which is $30$ and calculated the average of the remaining scores to decide her grade. Which of the following gives her new average score?

1. $\frac{(45\times 5-30)}{5}$
2. $\frac{(45\times 5-30)}{6}$
3. $\frac{(45\times 6-30)}{5}$
4. $\frac{(45\times 6-30)}{6}$

Q. Which of the following pair is a correct trignometric inter-relationship?

(1) $\cos \theta$	(a) $\frac{1}{\tan \theta }$
(2) $\tan \theta$	(b) $\frac{1}{co\sec \theta }$
(3) $\cot \theta$	(c) $\frac{1}{\sec \theta }$
(4) $\sin \theta$	(d) $\frac{1}{\cot \theta }$

1. $1-d,2-e,3-b,4-a$
2. $1-b,2-a,3-e,4-d$
3. $1-c,2-d,3-a,4-b$
4. $1-e,2-b,3-c,4-d$

Q. ${\tan }^2\theta ={\sin }^2\theta +{\cos }^2\theta$, then $\theta =$.............

1. $30$
2. $45$
3. $60$
4. $90$

Q. The probability of an event $k$ is

1. $0\ge P\left(k\right)\ge 1$
2. $0\le P\left(k\right)\le 1$
3. $0>P\left(k\right)>1$
4. $0<P\left(k\right)<1$

Q. 2 years ago, the addition of ages of father-mother and their two daughters was $40$ years. After 3 years the addition of their ages will be ..............

1. $50$
2. $46$
3. $60$
4. $40$

Q. The sequence $1,1,2,3,5,8,13,21,34,........$ is said to be in ............

1. Finite Sequence
2. Arithmetic Progression
3. Fibonacci Sequence
4. None of the above

Q. In $△ABC$, the bisector of $\angle A$ intersects $\overline{BC}$ at a point $D$. Then:

1. $BD\times AC=BC\times AB$
2. $BD\times AB=DC\times AC$
3. $BD\times AC=DC\times AB$
4. $AC\times AB=DC\times BC$

Q. If ............, then the quadratic equation does not have real solution.

1. $D<0$
2. $D>0$
3. $D\ge 0$
4. $D=0$

Q. On walking $x$ meters, making an angle of ${30}^o$ with the ground, to find a ball fallen in a valley, one can reach a depth of '$y$' meters below the ground, then

1. $x=y$
2. $x=2y$
3. $2x=y$
4. $2x=\sqrt{3}y$

Q. The cubic polynomial $p\left(a\right)=a^3-a$ has ................ zeros.

1. $0$
2. $1$
3. $2$
4. $3$

Q. If the length of a minor arc $\widehat{AB}$ of a circle is $\frac{1}{4}$ of its circuference, then the angle subtended by the minor arc $\widehat{AB}$ at the center will be

1. $30$
2. $45$
3. $90$
4. $60$

Q. When observed from top of a tower, the angle of depression of two houses $A$ and $B$ in the eastern and western directions is ${30}^o$ and ${60}^o$ respectively, then

1. House $A$ is nearer to the tower than house $B$.
2. House $B$ is nearer to the tower than house $A$.
3. House $A$ and $B$ are equidistant from the tower.
4. None of the above.

Q. $x=$............... is identified as a GOLDEN RATIO

1. $\frac{1+\sqrt{5}}{2}$
2. $1$
3. $\frac{1+\sqrt{2}}{2}$
4. $0$

Q. In Mathematics Exam, the probability of Aayushi scoring $100$ out of $100$ is

1. $\frac{1}{100}$
2. $1$
3. $\frac{1}{101}$
4. $0$

Q. If $2k+1,13$ and $5k-3$ are three consecutive terms in an A.P., then, $k=$

1. $17$
2. $13$
3. $4$
4. $9$

Q. The diagram below shows two sticks- one BLACK and the other WHITE. Based on the measurements shown, what is the length of the white stick?

1. $5cm$
2. $8.5cm$
3. $13.5cm$
4. $17cm$

Q. $\overline{x}-Z=3,\overline{x}+Z=45$, then $\overline{x}=$

1. $2$
2. $23$
3. $26$
4. $24$

Q. As per the figure, the graph of $y=p\left(x\right)$ has ................ real zeros.

1. $1$
2. $0$
3. $2$
4. $3$

Q. If a dice is tossed once, then the probability of getting a prime number is

1. $\frac{1}{6}$
2. $\frac{1}{2}$
3. $1$
4. $\frac{1}{3}$

Q. The discriminant value of equation $5x^2-6x+1=0$ is ...............

1. $16$
2. $\sqrt{56}$
3. $4$
4. $56$

Q. In $△ABC,\overline{AD}$ is a median, hence according to the Apollonius theorem, ............ is true.

1. ${AB}^2+{AC}^2=2({AD}^2+{BC}^2)$
2. ${AB}^2+{AC}^2=2({BD}^2+{DC}^2)$
3. ${AB}^2+{AC}^2=2({AD}^2+{DC}^2)$
4. ${AB}^2+{AC}^2=2({BD}^2+{BC}^2)$

Q. The product of the zeroes of the cubic polynomial $p\left(x\right)$ is ...............

1. $\frac{\text{Coefficient of}-x^2}{\text{Coefficient of}{x}^3}$
2. None of these
3. $\frac{\text{-The constant Term}}{\text{Coefficient of}{x}^2}$
4. $\frac{\text{Coefficient of}x}{\text{Coefficient of}{x}^3}$