Q1
mcq
1 mark
The range of the relation $R=\{(x, x^2) \mid x$ is a prime number less than $13\}$ is :
- A. $\{2, 3, 5, 7\}$
- B. $\{2, 3, 5, 7, 11\}$
- C. $\{4, 9, 25, 49, 121\}$
- D. $\{1, 4, 9, 25, 49, 121\}$
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Q2
mcq
1 mark
Let $n(A)=m$ and $n(B)=n$, then the total number of functions that exist from $B$ to $A$ is :
- A. $m^n$
- B. $n^m$
- C. $2^{mn-1}$
- D. $2^{mn}$
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Q3
mcq
1 mark
Euclid's division lemma states that for positive integers $a$ and $b$, there exist unique positive integers $q$ and $r$ such that $a=bq+r$, where $r$ must satisfy.
- A. $1<r<b$
- B. $0<r<b$
- C. $0\le r<b$
- D. $0<r\le b$
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Q4
mcq
1 mark
If 6 times of $6^{\text{th}}$ term of an A.P. is equal to 7 times the $7^{\text{th}}$ term, then the $13^{\text{th}}$ term of the A.P. is :
- B. 6
- C. 7
- D. 13
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Q5
mcq
1 mark
If $(x-6)$ is the H.C.F. of $x^2-2x-24$ and $x^2-kx-6$, then the value of $k$ is :
- A. 3
- B. 5
- C. 6
- D. 8
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Q6
mcq
1 mark
Transpose of a column matrix is :
- A. unit matrix
- B. diagonal matrix
- C. column matrix
- D. row matrix
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Q7
mcq
1 mark
A tangent is perpendicular to the radius of a circle at the :
- A. Centre
- B. Point of Contact
- C. Infinity
- D. Chord
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Q8
mcq
1 mark
The equation of a line passing through the origin and parallel to the line $7x-3y+14=0$ is :
- A. $7x-3y+14=0$
- B. $3x-7y+14=0$
- C. $3x+17y=0$
- D. $7x-3y=0$
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Q9
mcq
1 mark
The slope of the line which is perpendicular to a line joining the points $(0, 0)$ and $(-8, 8)$ is :
- A. -1
- B. 1
- C. $\frac{1}{3}$
- D. -8
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Q10
mcq
1 mark
If the ratio of the height of a tower and the length of its shadow is $3:1$, then the angle of elevation of the sun has measure :
- A. 45$^{\circ}$
- B. 30$^{\circ}$
- C. 90$^{\circ}$
- D. 60$^{\circ}$
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Q11
mcq
1 mark
The curved surface area of a right circular cone of height 15 cm and base diameter 16 cm is :
- A. $60\pi\ \text{cm}^2$
- B. $68\pi\ \text{cm}^2$
- C. $120\pi\ \text{cm}^2$
- D. $136\pi\ \text{cm}^2$
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Q12
mcq
1 mark
The volume (in cm$^3$) of the greatest sphere that can be cut off from a cylindrical log of wood of base radius 1 cm and height 5 cm is :
- A. $\frac{4}{3}\pi$
- B. $\frac{10}{3}\pi$
- C. $5\pi$
- D. $\frac{20}{3}\pi$
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Q13
mcq
1 mark
Which of the following is incorrect ?
- A. $P(A)>1$
- B. $0\le P(A)\le 1$
- C. $P(\phi)=0$
- D. $P(A)+P(A)=1$
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Q14
mcq
1 mark
A purse contains 10 notes of $2000, 15 notes of $500 and 25 notes of $200. One note is drawn at random. What is the probability that the note is either a $500 note or $200 note ?
- A. $\frac{1}{5}$
- B. $\frac{3}{10}$
- C. $\frac{2}{3}$
- D. $\frac{4}{5}$
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Q16
short answer
Find $f\circ g$ and $g\circ f$ when $f(x)=2x+11$ and $g(x)=x^2-2$.
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Q21
short answer
The line through the points $(-2,a)$ and $(9,3)$ has slope $-\frac{1}{2}$. Find the value of $a$.
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Q22
short answer
Show that the straight lines $x-2y+13=0$ and $6x+13y-18=0$ are perpendicular.
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Q23
short answer
From the top of a rock $50\sqrt{3}$ m high, the angle of depression of a car on the ground is observed to be $30^\circ$. Find the distance of the car from the rock.
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Q26
short answer
Find the range of the following distribution:
Age (in years): 16 - 18, 18 - 20, 20 - 22, 22 - 24, 24 - 26, 26 - 28
Number of Students: 0, 4, 6, 8, 2, 2
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Q27
short answer
A flower is selected at random from a basket containing 80 yellow, 70 red and 50 white flowers. Find the probability of selecting a yellow coloured flower.
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Q28
short answer
Check whether the sequence 2, 8, 18, 32, 50, ... is an A.P. or not. If it is an A.P., then find the common difference.
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Q29
long answer
Let $A$ be the set of all natural numbers less than 8, $B$ the set of all prime numbers less than 8 and $C$ the set of even prime numbers. Verify that $(A\cap B)\times C=(A\times C)\cap(B\times C)$.
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Q30
short answer
Let $f : A \to B$ be a function defined by $f(x)=\frac{1}{2}x-1$. Here, $A=\{2,4,6,10,12\}$, $B=\{0,1,2,4,5,9\}$. Represent $f$ by (i) set of ordered pairs (ii) a table (iii) an arrow diagram (iv) a graph.
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Q31
short answer
If $p_1^{31} \times p_2^2 \times p_3^4 \times p_4^{113400} = x_1 \times x_2 \times x_3 \times x_4$, where $p_1, p_2, p_3, p_4$ are primes in ascending order and $x_1, x_2, x_3, x_4$ are integers, find the value of $p_1, p_2, p_3, p_4$ and $x_1, x_2, x_3, x_4$.
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Q32
short answer
Find the sum of the series $6, 17, 18, \ldots, 121$.
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Q33
short answer
If $A=\begin{pmatrix}1 & 2 & 1\\ 2 & 1 & 1\end{pmatrix}$ and $B=\begin{pmatrix}2 & 1\\ 1 & 4\\ 0 & 2\end{pmatrix}$, show that $(AB)^T=B^T A^T$.
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Q35
short answer
Find the value of $k$, if the area of a quadrilateral is 28 sq. units, whose vertices are taken in the order $(-4,-2)$, $(-3,k)$, $(3,-2)$ and $(2,3)$.
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Q36
short answer
A line makes positive intercepts on coordinate axes whose sum is 7 and it passes through $(-3,8)$. Find its equation.
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Q37
short answer
Prove that $\dfrac{\sin^3 A+\cos^3 A}{\sin A+\cos A} = 2-\sin A\cos A$.
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Q38
short answer
Nathan, an engineering student was asked to make a model shaped like a cylinder with two cones attached at its two ends. The diameter of the model is 3 cm and its length is 12 cm. If each cone has a height of 2 cm, find the volume of the model that Nathan made.
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Q39
short answer
A metallic sphere of radius 16 cm is melted and recast into small spheres each of radius 2 cm. How many small spheres can be obtained?
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Q40
short answer
The total marks scored by two students, Sathya and Vidhya in 5 subjects are 460 and 480 with standard deviation 4.6 and 2.4 respectively. Who is more consistent in performance?
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Q41
mcq
A bag contains 5 red balls, 6 white balls, 7 green balls, 8 black balls. One ball is drawn at random from the bag. Find the probability that the ball drawn is
- A. (i) white
- B. (ii) black or red
- C. (iii) not white
- D. (iv) neither white nor black
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Q42
short answer
Determine the nature of the roots of the equation: $(x-1)^2+1(x-2)^2+1(x-3)^2=0$.
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Q43
long answer
(A) If $BC=8$ cm, $\angle A=60^\circ$ and the perpendicular bisector of $\angle A$ meets $BC$ at $D$ such that $BD=6$ cm, construct triangle $ABC$. Or (B) Draw a circle of radius 4 cm and mark a point at a distance of 11 cm from its center. Draw the two tangents from that point to the circle.
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Q43
long answer
16 marks
(a)Draw a triangle ABC of base BC=8 cm, ∠A=608 and the bisector of ∠A meets BC at D such that BD=6 cm. OR (b)Take a point which is 11 cm away from the centre of a circle of radius 4 cm and draw the two tangents to the circle from that point.
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Q44
long answer
16 marks
(a)Graph the quadratic equation $x^2-9x120=0$ and state the nature of solution. OR (b)A bus is travelling at a uniform speed of 50 km/hr. Draw the distance - time graph and hence find. (i)the constant of variation. (ii)how far will it travel in 90 minutes ? (iii)the time required to cover a distance of 300 km.
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