# Board Paper of Class 10 2017 Maths - Solutions

(1) Check the question paper for fairness of printing. If there is any lack of fairness, inform the Hall Supervisor immediately.(2) Use Blue or Black ink to write and underline and pencil to draw diagrams.Note : This question paper contains four sections.

- Question 1

- Question 2
If
*k*+ 2, 4*k*− 6, 3*k*− 2 are the three consecutive terms of an A.P., then the value of k is :

(a) 2

(b) 3

(c) 4

(d) 5 VIEW SOLUTION

- Question 3
If the product of the first four consecutive terms of a G.P. is 256 and if the common ratio is 4 and the first term is positive, then its 3
^{rd}term is:

(a) 8

(b) $\frac{1}{16}$

(c) $\frac{1}{32}$

(d) 16 VIEW SOLUTION

- Question 4
The remainder when
*x*^{2 }− 2*x*+ 7 is divided by*x*+ 4 is :

(a) 28

(b) 29

(c) 30

(d) 31 VIEW SOLUTION

- Question 5
The common root of the equations
*x*^{2 }−*bx + c*= 0 and*x*^{2}+*bx*−*a*= 0 is :

(a) $\frac{c+a}{2b}$

(b) $\frac{c-a}{2b}$

(c) $\frac{c+b}{2a}$

(d) $\frac{a+b}{2c}$ VIEW SOLUTION

- Question 6
If $\mathrm{A}=\left(\begin{array}{cc}7& 2\\ 1& 3\end{array}\right)\mathrm{and}\mathrm{A}+\mathrm{B}=\left(\begin{array}{cc}-1& 0\\ 2& -4\end{array}\right)$, then the matrix B =

(a) $\left(\begin{array}{cc}1& 0\\ 0& 1\end{array}\right)$

(b) $\left(\begin{array}{cc}6& 2\\ 3& -1\end{array}\right)$

(c) $\left(\begin{array}{cc}-8& -2\\ 1& -7\end{array}\right)$

(c) $\left(\begin{array}{cc}8& 2\\ -1& 7\end{array}\right)$ VIEW SOLUTION

- Question 7
Slope of the straight line which is perpendicular to the straight line joining the points (−2, 6) and (4, 8) is equal to :

(a) $\frac{1}{3}$

(b) 3

(c) –3

(d) $-\frac{1}{3}$ VIEW SOLUTION

- Question 8
If the points (2, 5), (4, 6) and (a, a) are collinear, then the value of ‘
*a*’ is equal to :

(a) −8

(b) 4

(c) −4

(d) 8 VIEW SOLUTION

- Question 9
The perimeters of two similar triangles are 24 cm and 18 cm respectively. If one side of the first triangle is 8 cm, then the corresponding side of the other triangle is :

(a) 4 cm

(b) 3 cm

(c) 9 cm

(d) 6 cm VIEW SOLUTION

- Question 10
ΔABC is a right angled triangle where ∠B = 90° and BD ⊥ AC. If BD = 8 cm, AD = 4 cm, then CD is :

(a) 24 cm

(b) 16 cm

(c) 32 cm

(d) 8 cm VIEW SOLUTION

- Question 11

- Question 12

- Question 13
If the surface area of a sphere is 100 π cm
^{2}, then its radius is equal to :

(a) 25 cm

(b) 100 cm

(c) 5 cm

(d) 10 cm VIEW SOLUTION

- Question 14
Standard deviation of a collection of a data is $2\sqrt{2}$. If each value is multiplied by 3, then the standard deviation of the new data is :

(a) $\sqrt{12}$

(b) $4\sqrt{2}$

(c) $6\sqrt{2}$

(d) $9\sqrt{2}$ VIEW SOLUTION

- Question 15
A card is drawn from a pack of 52 cards at random. The probability of getting neither an ace nor a king card is :

(a) $\frac{2}{13}$

(b) $\frac{11}{13}$

(c) $\frac{4}{13}$

(d) $\frac{8}{13}$ VIEW SOLUTION

- Question 16
Given, A = {1, 2, 3, 4, 5}, B = {3, 4, 5, 6} and C = {5, 6, 7, 8}, show that A⋃ (B ⋃ C) = (A ⋃ B) ⋃ C. VIEW SOLUTION

- Question 17
The following table represents a function from A = {5, 6, 8, 10} to B = {19, 15, 9, 11} where
*f*(*x*) = 2*x*− 1. Find the values of*a*and*b*.

*x*5 6 8 10 *f*(*x*)*a*11 *b*19

- Question 18

- Question 19

- Question 20
Simplify : $\frac{6{x}^{2}+9x}{3{x}^{2}-12x}$ VIEW SOLUTION

- Question 21

- Question 22
Let $\mathrm{A}=\left(\begin{array}{cc}3& 2\\ 5& 1\end{array}\right)\mathrm{and}\mathrm{B}=\left(\begin{array}{cc}8& -1\\ 4& 3\end{array}\right)$ . Find the matrix C, if C = 2A + B. VIEW SOLUTION

- Question 23
Find the coordinates of the point which divides the line segment joining (−3, 5) and (4, −9) in the ratio 1 : 6 internally. VIEW SOLUTION

- Question 24
“The points (0,
*a*),*a*> 0 lie on*x*-axis for all*a*”. Justify the truthness of the statement. VIEW SOLUTION

- Question 25
In ΔPQR, AB||QR. If AB is 3 cm, PB is 2 cm and PR is 6 cm, then find the length of QR. VIEW SOLUTION

- Question 26
The angle of elevation of the top of a tower as seen by an observer is 30°. The observer is at a distance of 30$\sqrt{3}$ m from the tower. If the eye level of the observer is 1.5 m above the ground level, then find the height of the tower. VIEW SOLUTION

- Question 27
The total surface area of a solid right circular cylinder is 1540 cm
^{2}. If the height is four times the radius of the base, then find the height of the cylinder. VIEW SOLUTION

- Question 28
The smallest value of a collection of data is 12 and the range is 59. Find the largest value of the collection of data. VIEW SOLUTION

- Question 29
In tossing a fair coin twice, find the probability of getting :

(i) Two heads

(ii) Exactly one tail VIEW SOLUTION

- Question 30
(a) If the volume of a solid sphere is $7241\frac{1}{7}$ cu. cm, then find its radius. $\left(\mathrm{Take}\mathrm{\pi}=\frac{22}{7}\right)$(b) If

OR

*x*=*a*sec θ +*b*tan θ and*y*=*a*tan θ +*b*sec θ, then prove that*x*^{2 }−*y*^{2 }=*a*^{2 }−*b*^{2}. VIEW SOLUTION

- Question 31
Let A = {
*a*,*b*,*c*,*d*,*e*,*f*,*g*,*x*,*y*,*z*}, B = {1, 2,*c*,*d*,*e*} and C = {*d*,*e*,*f*,*g*, 2,*y*}. Verify A\(B ⋃ C) = (A\B) ⋂ (A\C). VIEW SOLUTION

- Question 32
Let A={6, 9, 15, 18, 21}; B = {1, 2, 4, 5, 6} and
*f*: A → B be defined by $f\left(x\right)=\frac{x-3}{3}$. Represent*f*by :

(i) an arrow diagram

(ii) a set of ordered pairs

(iii) a table

(iv) a graph VIEW SOLUTION

- Question 33

- Question 34
Find the sum of first
*n*terms of the series 7 + 77 + 777 +... VIEW SOLUTION

- Question 35
The speed of a boat in still water is 15 km/hr. It goes 30 km upstream and return downstream to the original point in 4 hrs 30 minutes. Find the speed of the stream. VIEW SOLUTION

- Question 36
Find the values of
*a*and*b*if 16*x*^{4}− 24*x*^{3 }+ (*a*− 1)*x*^{2 }+ (*b*+ 1)*x*+ 49 is a perfect square. VIEW SOLUTION

- Question 37
If $\mathrm{A}=\left(\begin{array}{cc}5& 2\\ 7& 3\end{array}\right)\mathrm{and}\mathrm{B}=\left(\begin{array}{cc}2& -1\\ -1& 1\end{array}\right)$ verify that (AB)
^{T }= B^{T}A^{T}. VIEW SOLUTION

- Question 38
Find the area of the quadrilateral formed by the points (−4, −2), (−3, −5), (3, −2) and (2, 3). VIEW SOLUTION

- Question 39
State and prove Pythagoras theorem.

VIEW SOLUTION

- Question 40
A flag post stands on the top of a building. From a point on the ground, the angles of elevation of the top and bottom of the flag post are 60° and 45° respectively. If the height of the flag post is 10 m, find the height of the building. $\left(\sqrt{3}=1.732\right)$ VIEW SOLUTION

- Question 41
The perimeter of the ends of a frustum of a cone are 44 cm and 8.4 π cm. If the depth is 14 cm, then find its volume. VIEW SOLUTION

- Question 42
The length, breadth and height of a solid metallic cuboid are 44 cm, 21 cm and 12 cm respectively. It is melted and a solid cone is made out of it. If the height of the cone is 24 cm, then find the diameter of its base. VIEW SOLUTION

- Question 43

- Question 44
If a die is rolled twice, find the probability of getting an even number in the first time or a total of 8. VIEW SOLUTION

- Question 45
(a) Find the GCD of the following polynomials 3
*x*^{4 }+ 6*x*^{3}− 12*x*^{2}− 24*x*and 4*x*^{4 }+ 14*x*^{3}+ 8*x*^{2 }− 8*x*.(b) A straight line cuts the coordinate axes at A and B. If the mid point of AB is (3, 2), then find the equation of AB. VIEW SOLUTION

OR

- Question 46
(a) Draw the two tangents from a point which is 10 cm away from the centre of a circle of radius 6 cm. Also, measure the lengths of the tangents.OR

- Question 47
(a) Solve graphically 2
*x*^{2}+*x*− 6 = 0.

OR(b) Draw the graph of

*xy*= 20,*x, y*> 0. Use the graph to find*y*when*x*= 5, and to find*x*when*y*= 10. VIEW SOLUTION