Select Board & Class

• Question 1
In ∆PQR, the bisector of ∠P intersects $\overline{\mathrm{QR}}$ in D. If QD : RD = 4 : 7, PR = 14, Then PQ = ……………
(A) 4
(B) 8
(C) 12
(D) 15 VIEW SOLUTION
• Question 2
If cosec $\mathrm{A}=\frac{4}{3}$ and A + B = 90, then sec B = …………..
(A) $\frac{16}{9}$

(B) $\frac{4}{3}$

(C) $\frac{3}{4}$

(D) $\frac{7}{3}$ VIEW SOLUTION
• Question 3
From the top of a building h metre high, the angle of depression of an object on the ground has a measure θ. The distance of the object from the building is
(A) h cos θ metre
(B) h sin θ metre
(C) tan θ metre
(D) h cot θ metre VIEW SOLUTION
• Question 4
For A (1, 2) and B (3, −2), the coordinates of the midpoint of AB are is ……………………
(A) (2, 2)
(B) (0, 0)
(C) (2, 0)
(D) (0, 2) VIEW SOLUTION
• Question 5
On walking …………… metres on a slope at an angle of measure 30° with the ground, one can reach the height 'a' metres from the ground.

(A) $\frac{2a}{\sqrt{3}}$

(B) $\frac{\sqrt{3}}{2}a$

(C) 2a

(D) $\frac{a}{2}$ VIEW SOLUTION
• Question 6
$\frac{{\mathrm{sin}}^{4}\theta -{\mathrm{cos}}^{4}\theta }{{\mathrm{sin}}^{2}\theta -{\mathrm{cos}}^{2}\theta }=$

(A) 3
(B) 2
(C) 0
(D) 1 VIEW SOLUTION
• Question 7
From the natural number of single digit, the probability of getting an even number is ………………….

(A) $\frac{5}{9}$

(B) $\frac{5}{10}$

(C) $\frac{4}{9}$

(D) $\frac{1}{9}$ VIEW SOLUTION
• Question 8
In ∆ABC, correspondence ABC ↔ BAC is similarity. From the following …………………… is true.
(A) ∠C ≅ ∠A
(B) ∠B ≅ ∠C
(C) ∠A ≅ ∠B
(D) ∠A ≅ ∠B ≅ ∠C VIEW SOLUTION
• Question 9
If sin 7θ = cos 2θ for acute angles 7θ and 2θ, then θ = …………………….
(A) 10
(B) 90
(C) 20
(D) 30 VIEW SOLUTION
• Question 10
In a two digit number, the digit at the units place is x and the digit at tens place is y. If y = 5, then the number is …………………
(A) 50x + 5
(B) 5x
(C) 30x + 5
(D) x + 50 VIEW SOLUTION
• Question 11
The chord of a ⊙ (0, 5) touches ⊙ (0, 3). The length of the chord is ………………………..
(A) 8
(B) 6
(C) 7
(D) 2 VIEW SOLUTION
• Question 12
The perimeter of an equilateral triangle is 6. The length of an altitude drawn on any of its sides is …………..

(A) $2\sqrt{3}$

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

(C) 2

(D) $\sqrt{3}$ VIEW SOLUTION
• Question 13
As shown in the following figure, the area of square ABCD is 16 cm2 and the area of square CIPO is 9cm2. If $\overline{)\mathrm{BC}}\perp \overline{)\mathrm{CO}}$ then the length of  ………………………… cm.

(A) 7
(B) 25
(C) 625
(D) 5 VIEW SOLUTION
• Question 14
In a given A.P., T25 – T20 = 15. ∴ d = ………………. for the A.P.
(A) 5
(B) 3
(C) 25
(D) 120 VIEW SOLUTION
• Question 15
3 years ago, the sum of the ages of a father and his son was 40 years. After 2 years, the sum of their ages will be…………….
(A) 46 years
(B) 40 years
(C) 50 years
(D) 60 years VIEW SOLUTION
• Question 16
The ratio of the areas of two similar triangles is 25 : 16. The ratio of their perimeters is …………………….
(A) 625 : 256
(B) 5 : 6
(C) 25 : 16
(D) 5 : 4 VIEW SOLUTION
• Question 17
If $y=\frac{2}{3}$ is a root of the quadratic equation 3y2 − ky + 8 = 0, then the value of k is ……………………..
(A) 13
(B) −14
(C) 14
(D) −13 VIEW SOLUTION
• Question 18
From the equations given below, a root of one equation is 3. The equation is…………………
(A) x2 + x − 6 = 0
(B) x2 − x − 6 = 0
(C) x2 − x + 6 = 0
(D) x2 + x + 6 = 0 VIEW SOLUTION
• Question 19
If α , β, γ are the zeros of a polynomial P(x) = ax3 + bx2 + cx + d (a 0) then

$\frac{1}{\alpha }+\frac{1}{\beta }+\frac{1}{\gamma }=\dots \dots \dots \dots \dots .$

(A) $-\frac{b}{a}$

(B) $-\frac{c}{d}$

(C) $\frac{c}{d}$

(D) $-\frac{c}{a}$ VIEW SOLUTION
• Question 20
With the help of match-sticks, Zalak prepared a pattern as shown below. When 97 matchsticks are used, the serial number of the figure will be ___________ .

(A) Figure 32
(B) Figure 95
(C) Figure 49
(D) Figure 48 VIEW SOLUTION
• Question 21
The volume of a cylinder is 550 cm3. If its radius is 5 cm, then its height is ………….. cm.
(A) 12
(B) 9
(C) 7
(D) 14 VIEW SOLUTION
• Question 22
In the following figure ∆ABC is an equilateral triangle and AC = x cm. $\overline{)\mathrm{AD}}$ is median on $\overline{)\mathrm{BC}}$, D$\overline{)\mathrm{BC}}$ . If AD = y cm, then y = ……………………. cm.

(A) $\sqrt{\frac{3}{2}·x}$

(B) $\frac{\sqrt{3}}{2}·x$

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

(D) $\frac{3}{2}·x$VIEW SOLUTION
• Question 23
In any A.P., S n – 2 Sn – 1 + S n – 2 = ................(n > 2).
(A) a + d
(B) 2d
(C) d
(D) a VIEW SOLUTION
• Question 24
The foot of the perpendicular drawn from P(−3, 2) to the y-axis is M. The coordinates of M are…………….

(A) (0, 2)

(B) (3, 0)

(C) $\left(\frac{3}{2},-1\right)$

(D) (–3, 2) VIEW SOLUTION
• Question 25
If 7 cos2θ + 3 sin2θ = 4, then cot θ =

(A) $\frac{7}{3}$

(B) 7

(C) $\sqrt{3}$

(D) $\frac{1}{\sqrt{3}}$ VIEW SOLUTION
• Question 26
The formula to find the total surface area of a Rs. 5 coin is …………………..
(A) πr2h
(B) πr(r + h)
(C) πr3h
(D) 2πr(h + r) VIEW SOLUTION
• Question 27
If the area and the circumference of a circle are numerically equal, then the radius of the circle is ………………………

(A) $\frac{5}{2}$

(B) 2

(C) 1

(D) $\frac{2}{5}$ VIEW SOLUTION
• Question 28
If the ratio of the areas of two circles is 1 : 4, then the ratio of their circumferences is ……………………….
(A) 1 : 4
(B) 2 : 3
(C) 1 : 2
(D) 3 : 2 VIEW SOLUTION
• Question 29
The product of the zeroes of polynomial x2 − 4x + 3 is …………………….
(A) 4
(B) 1
(C) −4
(D) 3 VIEW SOLUTION
• Question 30
When the length of the shadow of a pole is equal to the height of the pole, the angle of elevation of the Sun has a measure of…………...........
(A) 30°
(B) 45°
(C) 60°
(D) 75° VIEW SOLUTION
• Question 31
The area of a minor sector of ⊙ (P, 30) is 300 cm2. The length of the corresponding arc in ……………. cm.
(A) 20
(B) 10
(C) 30
(D) 40 VIEW SOLUTION
• Question 32
The volume of a sphere with radius 3 cm is ………………… cm3.
(A) 14π
(B) 18π
(C) 2π
(D) 36π VIEW SOLUTION
• Question 33
Two consecutive even numbers can be………………..
(A) x, x + 1
(B) x, x + 2
(C) x, x – 1
(D) x, 2x VIEW SOLUTION
• Question 34
The area of a sector formed by two mutually perpendicular radii in ⊙ (0, 5 cm) is………………….. cm2.

(A) 4π

(B) 25π

(C) $\frac{4}{25}\mathrm{\pi }$

(D) $\frac{25}{4}\mathrm{\pi }$ VIEW SOLUTION
• Question 35
▭ABCD is cyclic. If m ∠B = 60°, then m∠D = ……………………….
(A) 120°
(B) 100°
(C) 30°
(D) 90° VIEW SOLUTION
• Question 36
The sum of two numbers is 10 and their positive difference is 2. The bigger number is ……………
(A) 8
(B) 4
(C) 2
(D) 6 VIEW SOLUTION
• Question 37
If ………………. then the roots of the quadratic equation are equal.
(A) D = 0
(B) D ≠ 0
(C) D < 0
(D) D > 0 VIEW SOLUTION
• Question 38
In usual notations, Z − M = ………………
(A) 3
(B) 2
(C) 4
(D) 1 VIEW SOLUTION
• Question 39
If then $\mathrm{P}\left(\overline{)\mathrm{C}}\right)=$ ………………………
(A) $\frac{5}{7}$

(B) $\frac{2}{7}$

(C) 0

(D) 1 VIEW SOLUTION
• Question 40
For 2x + 3y = 7 and 3x + 2y = 3, x − y = …………………….
(A) 4
(B) −4
(C) 10
(D) 21 VIEW SOLUTION
• Question 41
Distance between the points (2, −3) and (5, a) is 5. Hence a = …………………
(A) −1
(B) 6
(C) 1
(D) 7 VIEW SOLUTION
• Question 42
The modal class of the following frequency distribution is ………………
 Class 0–10 10–20 20–30 30–40 40–50 Frequency 7 15 13 17 10
(A) 20–30
(B) 10–20
(C) 30–40
(D) 40–50 VIEW SOLUTION
• Question 43
A show-piece, as shown in the figure, is made of a cube and a hemisphere. If the measure of the total surface area of the cube is represented by A, the curved surface area of the hemisphere is represented by B and the area of the base of the hemisphere is represented by C, then …………. is true for the total surface area of the show-piece.

(A) A + B + C
(B) A + B – C
(C) B + C – A
(D) A + C – B VIEW SOLUTION
• Question 44
The distance between A(−6, 7) and B (−1, −5) is ………………
(A) 12
(B) 13
(C) 7
(D) $\sqrt{37}$ VIEW SOLUTION
• Question 45
The discriminant (D) of the equation $5x-6+\frac{1}{x}=0$ is ……………
(A) 4
(B) $\sqrt{56}$
(C) 16
(D) 56 VIEW SOLUTION
• Question 46
In the formula of mean,
(A) fi – A
(B) A – xi
(C) A – f
(D) xi – A VIEW SOLUTION
• Question 47
For $\sqrt{4+\sqrt{83}},$  the correct option is ……………….

(A) does not exist as quadratic surd

(B) does not exist as real numbers

(C)

(D) VIEW SOLUTION
• Question 48
2m . 5n (m, n ∈ N) ends with
(A) 5
(B) 0
(C) 25
(D) 125 VIEW SOLUTION
• Question 49
From the graph given below, y = P(x) has …………… zeros.

(A) 1
(B) 5
(C) 3
(D) 4 VIEW SOLUTION
• Question 50
The zero of the polynomial

(A) $\sqrt{5}$

(B)  $-\sqrt{5}$

(C) $\frac{\sqrt{5}}{5}$

(D) −5 VIEW SOLUTION
• Question 51
Find the square root of $6+4\sqrt{2}.$ VIEW SOLUTION
• Question 52
Find the sum of the zeroes and the product of the zeroes of the quadratic polynomial p(x) = 3x2 + 7x + 4, without finding the zeroes. VIEW SOLUTION
• Question 53
Solve the following pair of equations by cross-multiplication method:
2x – 5y = 4, 3x – 8y = 5 VIEW SOLUTION
• Question 54
(−100) + (−92) + (−84) + . . . + 92

OR

In a given A.P. a = 8, Tn = 33, Sn = 123. Find d and n. VIEW SOLUTION
• Question 55
In ΔABC, m∠B = 90°, $\overline{)\mathrm{BM}}\perp \overline{)\mathrm{AC}},$ M ∈ AC. If AM – MC = 7 and AB2 – BC2 = 175, then find AC. VIEW SOLUTION
• Question 56
Find the distance between A(a + b, b – a) and B(a – b, a + b). VIEW SOLUTION
• Question 57
If A + B = 90°, then prove that

OR

Prove that: $\sqrt{\frac{1-\mathrm{sin\theta }}{1+\mathrm{sin\theta }}}=\mathrm{sec\theta }-\mathrm{tan\theta }$ VIEW SOLUTION
• Question 58
The mean of a data is $\overline{)\mathrm{x}}=35.8.$ If and c = 10, then find the assumed mean (A). VIEW SOLUTION
• Question 59
Solve the given pair of linear equations:

VIEW SOLUTION
• Question 60
The angles of elevation of the top of a tower from two points at a distance a and b from the base, and in the same straight line with it, are complementary. Prove that the height of the tower is $\sqrt{\mathrm{ab}}$. VIEW SOLUTION
• Question 61
There are 5 red, 2 yellow and 3 white roses in a flowerpot. One rose is selected from it at random. What is the probability that the selected rose is (1) red (2) yellow (3) not white colour? VIEW SOLUTION
• Question 62
Find the mean of the following frequency distribution:
 Class 0-50 50-100 100-150 150-200 200-250 250-300 300-350 Frequency 10 15 30 20 15 8 2

OR

Find the median of the following frequency distribution:
​  Class 0-100 100-200 200-300 300-400 400-500 500-600 Frequency 64 62 84 72 66 52
VIEW SOLUTION
• Question 63
Prove that a tangent to a circle is perpendicular to the radius drawn from the point of contact. VIEW SOLUTION
• Question 64
OA and OB are two mutually perpendicular radii of a circle with radius 10.5 cm.
D ∈ OB and OD = 6 cm. Find the area of the shaded region in the figure given below:

VIEW SOLUTION
• Question 65
The cost of painting the surface of a sphere is Rs. 1526 at the rate of Rs. 6 per m2. Find the radius of the sphere. (π = 3.14)

OR

A well of diameter 7 m and 30 m deep is dug and the soil obtained by digging the well is evenly spread out to form a platform of size 30 m × 10 m. Find the height of the platform. VIEW SOLUTION
• Question 66
⊙ (P, 4 cm) is given. Draw a pair of tangents through A, which is in the exterior of the ⊙ (P, 4 cm) such that the measure of the angle between the tangents is 60°. Write the construction steps. VIEW SOLUTION
• Question 67
Prove that the areas of two similar acute triangles are proportional to the squares of the corresponding sides.

OR

In ΔABC, m∠B = 90°. Prove that AC2 = AB2 + BC2. VIEW SOLUTION
What are you looking for?

Syllabus