- Question 1
In ΔABC, D, E and F are midpoints of $\overline{)\mathrm{AB}},\overline{)\mathrm{BC}}\mathrm{and}\overline{)\mathrm{AC}}$ respectively. If ABC = 40 then DEF = ----- .

(A) 10

(B) $\frac{40}{3}$

(C) 20

(D) 5 VIEW SOLUTION

- Question 2
From the given figure AD = ----

(A) 2

(B) $2\sqrt{3}$

(C) $\frac{\sqrt{3}}{2}$

(D) $\sqrt{3}$ VIEW SOLUTION

- Question 3
In ΔABC, if m∠B = 90, & AC = 10 then length of median $\overline{\mathrm{BM}}$ = ---------.

(A) 6

(B) $5\sqrt{2}$

(C) 5

(D) 8 VIEW SOLUTION

- Question 4

- Question 5
From the graph OA
^{2}= --------.

(A) 0

(B) a^{2}+ b^{2}

(C) $\sqrt{{\mathrm{a}}^{2}+{\mathrm{b}}^{2}}$

(D) $\sqrt{\mathrm{a}+\mathrm{b}}$ VIEW SOLUTION

- Question 6
(1, 0), (0, 1), (1, 1) are the co-ordinates of vertices of a triangle. The triangle is ------ triangle.

(A) Isosceles

(B) Obtuse angled

(C) Acute angled

(D) Equilateral VIEW SOLUTION

- Question 7
In given figure, co-ordinates of foot of perpendicular P are -----------.

(A) (5, 0)

(B) (–5, 1)

(C) (–1, 0)

(D) (0, –1) VIEW SOLUTION

- Question 8
If O (0, 0) and P (–8, 0) then co-ordinates of its midpoint at ----------.

(A) (–4, 0)

(B) (4,0)

(C) (0, –4)

(D) (0, 0) VIEW SOLUTION

- Question 9

- Question 10

- Question 11
From given figure tan A$\xb7$tan C = ____________.

(A) $\frac{1}{\sqrt{2}}$

(B) 2

(C) $\sqrt{2}$

(D) 1 VIEW SOLUTION

- Question 12
If cos
^{2}45° – cos^{2}30° = x. cos 45°sin 45° then x = ________.

(A) –1/2

(B) 1/2

(C) 2

(D) 3/4 VIEW SOLUTION

- Question 13
In given figure, the minimum distance to reach from point “C” to point “A” will be _________.

(A) a^{2}

(B) $\sqrt{2}$

(C) 2

(D) 2a VIEW SOLUTION

- Question 14
To find the length of a ladder making an angle θ with wall ________ trigonometric ratio is used.

(A) tan θ

(B) cot θ

(C) cosec θ

(D) none VIEW SOLUTION

- Question 15
If the ratio of the height of tower and the length of its shadow is 1: $\sqrt{3}$, then the angle of elevation of the sun has measure __________.

(A) 60°

(B) 45°

(C) 30°

(D) 75° VIEW SOLUTION

- Question 16
___________ is true for a tangent of a circle.

P: line intersect circle in one & only one point

Q: line and circle must be in same plane.

R: line passes from the centre of a circle.

(A) Q and R

(B) Only Q

(C) Only P

(D) P and Q VIEW SOLUTION

- Question 17
In an isosceles right angled triangle ΔABC, r = _______.

(A) 2

(B) 1

(C) $1-\frac{1}{\sqrt{2}}$

(D) $2-\sqrt{2}$ VIEW SOLUTION

- Question 18
In the figure, from one handkerchief from four corners, sectors P, Q, R, S each of 2 cm are cut, whose sum is P + Q + R + S = A
_{1}and a circle of diameter 4 cm from the centre is cut whose area is A_{2 }, then __________ is possible.

(A) A_{1}≠ A_{2}

(B) A_{1}< A_{2}

(C) A_{1}> A_{2}

(D) A_{1}= A_{2}VIEW SOLUTION

- Question 19

- Question 20
If radius of circle is decreased by 10% then there is __________ decrease in its area.

(A) 10%

(B) 21%

(C) 19%

(D) 20% VIEW SOLUTION

- Question 21
Formula to find area of sector is ____________.

(A) $\frac{1}{2}\mathrm{rl}$

(B) $\frac{\mathrm{\pi r\theta}}{360}$

(C) $\frac{{\mathrm{\pi r}}^{2}\mathrm{\theta}}{180}$

(D) πr^{2}VIEW SOLUTION

- Question 22
If the circumference of base of a hemisphere is 2π then it volume is ______________ cm
^{3}.

(A) $\frac{2\mathrm{\pi}}{3}{\mathrm{r}}^{3}$

(B) $\frac{2\mathrm{\pi}}{3}$

(C) $\frac{8\mathrm{\pi}}{3}$

(D) $\frac{\mathrm{\pi}}{12}$ VIEW SOLUTION

- Question 23
In the given cylinder the stick of maximum length __________ can be kept inside it.

(A) 10

(B) 12

(C) 13

(D) 17 VIEW SOLUTION

- Question 24
Total area of the given closed figure will be ____________ square units.

(A) 31

(B) 45

(C) 25

(D) 40 VIEW SOLUTION

- Question 25
The ratio of the radii of two cones having equal height is 2:3 then ratio of their volume is ____________.

(A) 3:2

(B) 9:4

(C) 8:27

(D) 4:9 VIEW SOLUTION

- Question 26
The conjugate surd of $2-\sqrt{3}$ is __________.

(A) $-2+\sqrt{3}$

(B) $2-\left(-\sqrt{3}\right)$

(C) $3+\sqrt{2}$

(D) $\frac{1}{2-\sqrt{3}}$ VIEW SOLUTION

- Question 27
To get the terminating decimal expansion of a rational number $\frac{\mathrm{p}}{\mathrm{q}}$. If
*q*= 25^{m}then m and n must belong to __________.^{n}

(A) Z

(B) N U {0}

(C) N

(D) R VIEW SOLUTION

- Question 28
For polynomial p(x) = x
^{2}– 4x + 3, α + β = _______.

(A) Positive fraction

(B) Negative integer

(C) Positive integer

(D) Zero VIEW SOLUTION

- Question 29
The graph of polynomial P(x) = ax – b, where a ≠ 0; a, b ∈ R intersect

(A) $\left(\frac{\mathrm{b}}{\mathrm{a}},0\right)$

(B) $\left(0,\frac{\mathrm{b}}{\mathrm{a}}\right)$

(C) $\left(-\frac{\mathrm{b}}{\mathrm{a}},0\right)$

(D) $\left(-\frac{\mathrm{a}}{\mathrm{b}},0\right)$ VIEW SOLUTION

- Question 30
The graph of p(x) = 5x + 3, x ∈ R is __________.

(A) ray

(B) parabola

(C) line segment

(D) line VIEW SOLUTION

- Question 31
For the zeroes α & β of polynomial P(x) = ax
^{2}+ bx + c, $\frac{1}{\mathrm{\alpha}}+\frac{1}{\mathrm{\beta}}$ = ____________.

(A) $-\frac{\mathrm{b}}{\mathrm{c}}$

(B) $-\frac{\mathrm{b}}{\mathrm{a}}$

(C) $\frac{\mathrm{c}}{\mathrm{a}}$

(D) none VIEW SOLUTION

- Question 32
The probability of complement event of impossible event is ___________.

(A) 0.5

(B) 0

(C) 1

(D) 0.46 VIEW SOLUTION

- Question 33
Find the probability of having 5 Sundays in the month of February in leap year 2004.

(A) 2/7

(B) 0

(C) 1/7

(D) 1 VIEW SOLUTION

- Question 34
Class 0 – 10 10 – 20 20 – 30 30 – 40 40 – 50 Frequancy 5 15 13 17 10

For the information given above, $\left(\frac{\mathrm{n}}{2}-\mathrm{cf}\right)$ will be = ____________.

(A) 10

(B) 20

(C) 30

(D) 25 VIEW SOLUTION

- Question 35
For the measures of central tendency, __________ of the following is not true.

(A) $\mathrm{Z}=3\mathrm{M}\u20132\overline{)\mathrm{x}}$

(B) $2\overline{)\mathrm{x}}+\mathrm{Z}=3\mathrm{M}$

(C) $2\overline{)\mathrm{x}}-3\mathrm{M}=-\mathrm{Z}$

(D) $2\overline{)\mathrm{x}}=\mathrm{Z}-3\mathrm{M}$ VIEW SOLUTION

- Question 36
If $\overline{)\mathrm{x}}-\mathrm{Z}=3\mathrm{and}\overline{)\mathrm{x}}+\mathrm{Z}=45$, then M = ________.

(A) 26

(B) 22

(C) 24

(D) 23 VIEW SOLUTION

- Question 37
If before three years sum of ages of father and son was 59 years then before five years the sum of their ages would have been __________.

(A) 55

(B) 61

(C) 69

(D) 57 VIEW SOLUTION

- Question 38
To eliminate
*x*from equations*x + y*+ 3*x*= 12 → ① & 8*x*+ 3*y*= 17 → ②, equation ② is to be multiplied by ______________.

(A) 8

(B) $-\frac{1}{2}$

(C) $\frac{1}{2}$

(D) 3 VIEW SOLUTION

- Question 39
Equation $\frac{\mathrm{x}}{3}-\frac{\mathrm{y}}{2}=1$ can be written in standard form as _______.

(A) 3x – 2y – 6 = 0

(B) 2x – 3y – 6 = 0

(C) 2x – 3y = 6

(D) 2x – 3y = 1 VIEW SOLUTION

- Question 40
In a two digit number, if number in unit place is 8 and number in tens place is y then that number is ____________.

(A) y + 8

(B) y + 80

(C) 10y + 8

(D) 80 y VIEW SOLUTION

- Question 41
The factors of quadratic polynomial P(x) = x
^{2}+ 4x – 5 are ____________.

(A) (x + 5) (x – 1)

(B) (x + 5) (x + 1)

(C) (x + 1) (x – 5)

(D) (x – 1) (x – 5) VIEW SOLUTION

- Question 42
______________ is true for discriminate of quadratic equation x
^{2}+ x + 1= 0.

(A) D = 0

(B) D < 0

(C) D > 0

(D) D is a perfect square VIEW SOLUTION

- Question 43
If one of the roots of the equation kx
^{2}– 7x + 3 = 0 is 3, then k = ___________.

(A) –3

(B) 3

(C) –2

(D) 2 VIEW SOLUTION

- Question 44
______________ cannot be the sum of a non zero number and its reciprocal.

(A) 0

(B) 2

(C) $\mathrm{x}+\frac{1}{\mathrm{x}}$

(D) $\frac{5}{2}$ VIEW SOLUTION

- Question 45
For a quadratic equation, if discriminate D = 0, then _____________ is not possible for its roots α + β.

(A) α = β

(B) α – β = 0

(C) α + β = 2α

(D) α + β = 0 VIEW SOLUTION

- Question 46
_____________ can be one of the term in Arithmetic progression 4, 7, 10, ------.

(A) 103

(B) 123

(C) 171

(D) 99 VIEW SOLUTION

- Question 47
(
*n*– 2)th term of an arithmetic progression will be ___________.

(A) a + (n – 1)d

(B) a + (n – 3)d

(C) a + (n – 2)d

(D) none VIEW SOLUTION

- Question 48
In the AP, 5, 7, 9, 11, 13, ------ the sixth term which is prime is __________.

(A) 15

(B) 19

(C) 17

(D) 23 VIEW SOLUTION

- Question 49
From the given BD = __________.

(A) x + y

(B) $\sqrt{\mathrm{xy}}$

(C) xy

(D) $\sqrt{\mathrm{x}+\mathrm{y}}$ VIEW SOLUTION

- Question 50
For ΔABC & ΔPQR, if m∠A = m∠R and m∠C = m∠Q, then ABC ↔ ___________ is a similarity.

(A) RQP

(B) PQR

(C) RPQ

(D) QP VIEW SOLUTION

- Question 51
If 7 is prime, then prove that $\sqrt{7}$ is irrational. VIEW SOLUTION

- Question 52

- Question 53
Find the solution of given pair of linear equation by elimination method.

3x + 4y = – 17 → ①

5x + 2y = – 19 → ② VIEW SOLUTION

- Question 54
For an AP, $\frac{1}{3},\frac{4}{3},\frac{7}{3},\frac{{\displaystyle 10}}{3}.......,\mathrm{Find}{\mathrm{T}}_{18}$

ORFor an AP, 3, 9, 15, 21......., Find S

_{10}VIEW SOLUTION

- Question 55
Write statement of Pythagoras theorem and show that 6, 8, and 10 are Pythagorean triplets. VIEW SOLUTION

- Question 56
If X(3, 1), Y(4, 5) and Z(–2, –1) are co-ordinates of vertices of ΔXYZ then find area of ΔXYZ. VIEW SOLUTION

- Question 57
If sin θ = a then find the value of cot θ + sec θ.

**OR**

For ΔABC, prove that tan $\left(\frac{\mathrm{A}+\mathrm{C}}{2}\right)=\mathrm{cot}\frac{\mathrm{B}}{2}$. VIEW SOLUTION

- Question 58
Find mode given data:

Class 20 – 29 30 – 39 40 – 49 50 – 59 60 – 69 Frequency 15 20 50 30 10

- Question 59
Write standard form of quadratic equation and find the roots of the equation $3{\mathrm{x}}^{2}+5\sqrt{2}\mathrm{x}+2=0$ using general formula. VIEW SOLUTION

- Question 60
From top of a tower the angle of depression of top and bottom of a multistoreyed building are 30° and 60° respectively. If the height of the building is 100 m. find the height of a tower. VIEW SOLUTION

- Question 61
The mean of the following frequency distribution of 100 observations is 148. Find missing frequencies F
_{1}and F_{2}.

Class 0 – 49 50 – 99 100 – 149 150 – 199 200 – 249 250 – 299 300 – 349 Frequency 10 15 F _{1}20 15 F _{2}2 **OR**

The median of 230 observations is 46. Find a and b.Class 10 – 20 20 – 30 30 – 40 40 – 50 50 – 60 60 – 70 Frequency 12 30 a 65 b 25

- Question 62
A box contains 100 cards marked with numbers 1 to 100. If one card is drawn randomly from the box. Find the probability that it bears.

(1) Even prime number.

(2) A number divisible by 7.

(3) The number at unit place is 9. VIEW SOLUTION

- Question 63
Prove that, tangents drawn to the end points of diameter of the circle are parallel to each other. VIEW SOLUTION

- Question 64
A cylindrical container having diameter 16 cm and height 40 cm is full of ice cream. The ice-cream is to be filled into cones of height 12 cm and diameter 4 cm, having a hemispherical shape on the top. Find the number of such cones which can be filled with ice-cream.
**OR**

A cylinder has hemispherical ends having radius 7 cm and total height of solid is104 cm. If its outer surface is to be polished & cost of polish is Rs 100 per sq. mtr. find the total cost of polish. VIEW SOLUTION

- Question 65
The length of a side of a square field is 20 mtr. A cow is tied at the corner by means of a 7 mtr long rope. Find the area of the field which cow can graze. If the length of rope is doubled then find the increase in the grazing area. VIEW SOLUTION

- Question 66
Divide a given line segment in ratio of 3:5 and write steps of construction. VIEW SOLUTION

- Question 67
If for acuted angled ΔABC and ΔPQR ABC ↔ PQR is similarity then prove that $\frac{\mathrm{A}\left(\u25b3\mathrm{ABC}\right)}{\mathrm{A}\left(\u25b3\mathrm{PQR}\right)}=\frac{{\mathrm{AB}}^{2}}{{\mathrm{PQ}}^{2}}=\frac{{\mathrm{BC}}^{2}}{{\mathrm{QR}}^{2}}=\frac{{\mathrm{AC}}^{2}}{{\mathrm{PR}}^{2}}$

OR

Write converse of Pythagoras theorem and prove it. VIEW SOLUTION