Q1
mcq
If the ordered pairs $(a12, 4)$ and $(5, 2a1b)$ are equal then $(a, b)$ is :
- A. $(2, -2)$
- B. $(5, 1)$
- C. $(2, 3)$
- D. $(3, -2)$
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Q2
mcq
If the HCF of 65 and 117 is expressible in the form of $65m-117$, then the value of $m$ is :
- A. 4
- B. 2
- C. 1
- D. 3
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Q3
mcq
If $t_n$ is the $n$th term of an A.P., then $t_{8n}-t_n$ is :
- A. $(8n-1)d$
- B. $(8n-2)d$
- C. $(7n-2)d$
- D. $(7nd)$
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Q4
mcq
If $(x-6)$ is the HCF 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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Q5
mcq
Which of the following should be added to make $x^4 164$ a perfect square ?
- A. $4x^2$
- B. $16x^2$
- C. $8x^2$
- D. $-8x^2$
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Q6
mcq
The number of points of intersection of the quadratic polynomial $x^2 14x14$ with the X-axis is :
- B. 1
- C. 0 or 1
- D. 2
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Q7
mcq
If $\Delta ABC$ is an isosceles triangle with $C=908$ and $AC=5$ cm, then $AB$ is :
- A. 2.5 cm
- B. 5 cm
- C. 10 cm
- D. $5\sqrt{2}$ cm
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Q8
mcq
In a $\Delta ABC$, $AD$ is the bisector of $\angle BAC$. If $AB=8$ cm, $BD=6$ cm and $DC=3$ cm, the length of the side $AC$ is :
- A. 6 cm
- B. 4 cm
- C. 3 cm
- D. 8 cm
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Q9
mcq
If $(5, 7)$, $(3, p)$ and $(6, 6)$ are collinear, then the value of $p$ is :
- A. 3
- B. 6
- C. 9
- D. 12
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Q10
mcq
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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Q11
mcq
A tower is 60 m high. Its shadow is $x$ metres shorter when the sun's altitude is $458$ than when it had been $308$, then $x$ is equal to :
- A. 41.92 m
- B. 43.92 m
- C. 43 m
- D. 45.6 m
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Q12
mcq
If two solid hemispheres of same base radius $r$ units are joined together along their bases, then curved surface area of this new solid is :
- A. $4\pi r^2$ sq.units
- B. $6\pi r^2$ sq.units
- C. $3\pi r^2$ sq.units
- D. $8\pi r^2$ sq.units
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Q13
mcq
If the radius of the cylinder is doubled, the new volume of the cylinder will be __________ times the original volume.
- A. same
- B. 3
- C. 4
- D. 2
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Q14
mcq
The probability of getting a job for a person is $\frac{3}{x}$. If the probability of not getting the job is $\frac{2}{3}$, then the value of $x$ is :
- A. 2
- B. 1
- C. 3
- D. 1.5
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Q15
short answer
Let $A=\{1, 2, 3\}$, $B=\{x ? x is a prime number less than 10\}$. Find $A\times B$ and $B\times A$.
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Q16
short answer
The arrow diagram shows a relationship between the sets $P$ and $Q$. Write the relation in (i) set builder form (ii) Roster form.
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Q17
short answer
If $13824=2^a\times3^b$, then find $a$ and $b$.
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Q18
short answer
Which term of an A.P. 16, 11, 6, 1, ... is $-54$ ?
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Q19
short answer
Find the excluded values of the following expression $\frac{2}{7p^2+8p+13p+5}$.
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Q20
short answer
In the figure AD is the bisector of A. If BD=4 cm, DC=3 cm and AB=6 cm, find $AC$.
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Q21
short answer
Show that the points $P(-1.5, 3)$, $Q(6, -2)$, $R(-3, 4)$ are collinear.
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Q22
short answer
The line 'p' passes through the points $(3, -2)$, $(12, 4)$ and the line 'q' passes through the points $(6, -2)$ and $(12, 2)$. Is 'p' parallel to 'q' ?
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Q23
short answer
Find the equation of a straight line which has slope $\frac{5}{4}$ and passing through the point $(-1, 2)$.
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Q24
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 $308$. Find the distance of the car from the rock.
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Q25
short answer
The radius of a spherical balloon increases from 12 cm to 16 cm as air being pumped into it. Find the ratio of the surface area of the balloons in the two cases.
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Q26
short answer
The volumes of two cones of same base radius are 3600 cm$^3$ and 5040 cm$^3$. Find the ratio of heights.
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Q27
short answer
Two coins are tossed together. What is the probability of getting different faces on the coins ?
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Q28
short answer
If $P=\frac{x}{x+y}$, $Q=\frac{y}{x+y}$, then find $P^2Q^2$.
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Q29
short answer
Let $A=$ The set of all natural numbers less than 8, $B =$ The set of all prime numbers less than 8, $C =$ The set of even prime numbers. Verify $A\times(B-C)=(A\times B)-(A\times C)$.
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Q30
long answer
If $l$th, $m$th and $n$th terms of an A.P. are $x$, $y$, $z$ resp., then show that:
(i) $x(m-n)+y(n-l)+z(l-m)=0$
(ii) $(x-y)n+(y-z)l+(z-x)m=0$
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Q31
short answer
The ratio of 6th and 8th term of an A.P. is $7:9$. Find the ratio of 9th term to 13th term.
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Q32
short answer
If $36x^4-60x^3 161x^2-mx1n$ is a perfect square, find the values of $m$ and $n$.
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Q34
short answer
If $\alpha, \beta$ are the roots of $7x^21ax12=0$ and if $13.\,7-\beta-\alpha= $ Find the values of $a$.
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Q36
long answer
An aeroplane after take off from an airport, flies due north at a speed of 1000 km/hr. At the same time, another aeroplane takes off from the same airport and flies due west at a speed of 1200 km/hr. How far apart
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Q37
short answer
Two cones of same base radius are $3600\ \text{cm}^3$ and $5040\ \text{cm}^3$. Find the ratio of heights.
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Q38
long answer
If the $l^{\text{th}}$, $m^{\text{th}}$ and $n^{\text{th}}$ terms of an A.P. are $x$, $y$, $z$ respectively, then show that:
(i) $x(m-n)+y(n-l)+z(l-m)=0$
(ii) $(x-y)n+(y-z)l+(z-x)m=0$
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Q39
short answer
The ratio of 6$^{\text{th}}$ and 8$^{\text{th}}$ term of an A.P. is $7:9$. Find the ratio of 9$^{\text{th}}$ term to 13$^{\text{th}}$ term.
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Q40
short answer
A quadrilateral has vertices at $A(-4,-2)$, $B(5,-1)$, $C(6,5)$ and $D(-7,6)$. Show that the mid-points of its sides form a parallelogram.
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Q41
short answer
From a point on the ground, the angles of elevation of the bottom and top of a tower fixed at the top of a 30 m high building are $45^\circ$ and $60^\circ$ respectively. Find the height of the tower. $(\sqrt{3}=1.732)$
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Q42
short answer
A container open at the top is in the form of frustum of a cone of height 16 cm with radii of its lower and upper ends are 8 cm and 20 cm respectively. Find the cost of milk which can completely fill the container at the rate of `40 per litre.
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Q43
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 length of the model is 12 cm and its diameter is 3 cm. If each cone has a height of 2 cm, find the volume of the model that Nathan made.
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Q44
short answer
In a class of 50 students, 28 opted for NCC, 30 opted for NSS and 18 opted both NCC and NSS. One of the students is selected at random. Find the probability that:
(i) the student opted for NCC but not NSS.
(ii) the student opted for NSS but not NCC.
(iii) the student opted for exactly one of them.
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Q45
short answer
Find the equation of the line passing through $(2,2)$ and $(-6)$ and having intercept on x-axis exceeds the intercept on y-axis by 5 units.
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Q46
long answer
(a) Construct a $\triangle ABC$ such that $AB=5.5$ cm, $\angle C=25^\circ$ and the altitude from $C$ to $AB$ is 4 cm.
OR
(b) Draw the two tangents from a point which is 5 cm away from the centre of a circle of diameter 6 cm. Also, measure the lengths of the tangents.
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Q47
long answer
(a) Draw the graph of $y=x^2-4x+3$ and use it to solve $x^2-6x+9=0$.
OR
(b) Draw the graph of $x^2-4x+4=0$ and state the nature of their solution.
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