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** **** CBSE MATHS SAMPLE PAPER / PRACTICE PAPER 2018**** **

Image Credit : www.cbse.nic.in |

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**Practice Paper – 1**

**Time Allowed : 3 Hours Maximum Marks : 100**

**General Instructions :**

**(i) All questions are compulsory.**

**(ii) This model test paper contains 30 questions.**

**(iii) Questions 1 to 6 in section – A are very short answers type questions carrying mark each.**

**(iv)Questions 7 to 12 in section – B are short answer type questions carrying 2 marks each.**

**(v) Questions 13 to 22 in section – C are long answer – I type questions carrying 3 marks each.**

**(vi) Questions 23 to 30 in section – D are long answer – II type questions carrying 4 marks each.**

**Section A**

**1.**If P( x, y) is equidistant from Q( -2, 5) and R(6, -1) then determine a relationship between x and y.

**2.**If the n

^{th }term of an A.P. is (2n + 1). What is the sum of its first three terms.

**3.**If P(E) = 0.06, then what is the probability of “not E”.

**4.**Find the value of x: If cos( 40 + x) = sin 30

^{o}.

**5.**Find the curved surface area of a right circular cone whose radius is 5cm and vertical height is 15cm.

**6.**What will be the angle of elevation of the sun when the length of a shadow of a vertical Pole is equal to its height.

**Section – B**

**7.**Solve $\frac{4}{x}-3=\frac{5}{2x+3},x\ne 0,x\ne \frac{-3}{2}$

**8.**Prove $\frac{\mathrm{sin}\mathrm{\xce\xb8}}{1-\mathrm{cos}\mathrm{\xce\xb8}}+\frac{\mathrm{tan}\mathrm{\xce\xb8}}{1+\mathrm{cos}\mathrm{\xce\xb8}}=\mathrm{sec}\mathrm{\xce\xb8}\mathrm{cos}ec\mathrm{\xce\xb8}+\mathrm{cot}\mathrm{\xce\xb8}$

**9.**Find the radius of a circle, if the length of tangent from a point at distance of 25cm from the centre of the circle is 24cm.

**10.**If Î± and Î² are the zeros of the polynomial $2{y}^{2}+7y+5$ write the values of Î± + Î² + Î±Î².

**11.**Construct a line segment AB of length 7cm, Using ruler and compass. Find a point P on AB such that P divides AB in to 3 : 2.

**12.**Prove that the points (a, b + c), (b, c + a), and (c, a + b) are collinear.

**Section – C**

**13.**Solve the quadratic equation $2{x}^{2}+x-4=0$, by method of completing square.

**14.**If ${\mathrm{tan}}^{2}\mathrm{\xce\pm}=1+2{\mathrm{tan}}^{2}\mathrm{\xce\xb2},$ Prove that $2{\mathrm{sin}}^{2}\mathrm{\xce\pm}=1+{\mathrm{sin}}^{2}\mathrm{\xce\xb2}$

**15.**From a top of a 50m high tower, the angles of depression of the bottom of a pole are observed to be 30o and 45o, respectively. Find the height of the pole. ( √3 =1.73).

**16.**What least number of the terms of the sequence $17,15\frac{4}{5},14\frac{3}{5}\mathrm{............}$ should be taken, so that the sum is negative.

**17.**ABC is an isosceles triangle such that AB = AC. D is the mid point of AC, A circle is drawn taking BD as diameter which intersects AB at the point E. Prove that $AE=\frac{1}{4}AC$

**18.**If Î± and Î² are the zeroes of the polynomial $2{x}^{2}-5x+7,$ then find a quadratic polynomial whose zeores are $\left(3\mathrm{\xce\pm}+4\mathrm{\xce\xb2}\right)\text{\hspace{0.17em}}and\text{\hspace{0.17em}}\left(4\mathrm{\xce\pm}+3\mathrm{\xce\xb2}\right)$

**19.**Mallica and Deepica are friends what is the probability that both have

**i)**different birthdays.

**Ii)**Same birthday ( ignoring a leap year)

**20.**Determine the co-ordinates of the centre of a circle passing through the points A(8, 6), B(2, -2) and C(8,-2), Also find the radius of the circle.

**21.**A survey regarding the heights( in cm) of 50 girls of class X of a school was conducted and the following data was obtained.

Heights(in cm) | 120-130 | 130-140 | 140-150 | 150-160 | 160-170 |
---|---|---|---|---|---|

No. of girls |
2 | 8 | 12 | 20 | 8 |

**22.**Solve $ax+by=1,\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}bx+ay=\frac{{\left(a+b\right)}^{2}}{{a}^{2}+{b}^{2}}-1$

**Section – D**

**23.**The perimeters of the ends of the frustum of a cone are 207.24cm and 169.56cm. If the height of the frustum be 8cm, find the whole surface of the frustum. [ Use Ï€ = 3.14].

**24.**The sum of five consecutive odd integers is 686. What are the numbers.

**25.**If $\mathrm{tan}A+\mathrm{sin}A=m\text{\hspace{0.17em}}and\text{\hspace{0.17em}}\mathrm{tan}A-\mathrm{sin}A=n$ then show that ${m}^{2}-{n}^{2}=4\sqrt{mn}$

**26.**Solve for x, if possible, $\left({m}^{2}+{n}^{2}\right){x}^{2}+\left(m+n\right)x+\frac{1}{2}=0$

**27.**Prove Basic Proportionality Theorem.

**28.**If P and Q are two points whose, Co-ordinates are $\left(a{t}^{2},2at\right)\text{\hspace{0.17em}}and\text{\hspace{0.17em}}\left(\frac{a}{{t}^{2}},\frac{-2a}{t}\right)$ respectively. S is a point (a, 0) Show that $\frac{1}{SP}+\frac{1}{SQ}$ is independent of “t”.

**29.**In given fig. triangle ABC is an obtuse triangle, obtuse angled at B. If AD is perpendicular to CB (produced)Prove that $A{C}^{2}=A{B}^{2}+B{C}^{2}+2BC.BD$

**30.**It can take 12 hours to fill a swimming pool using two pipes. If the pipe of larger diameter is used for 4 hours and the pipe of smaller diameter for 9 hours, Only half the pool can be filled . How long would it take each pipe to fill the pool separately.

Also Read : CBSE Class10 Sample Papers with Solutions

Pair Of Linear Equations in Two Variables Practice Paper

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