- Question 1
In ΔABC, D, E and F are midpoints of respectively. If ABC = 40 then DEF = ----- .
(A) 10
(B)
(C) 20
(D) 5 VIEW SOLUTION
- Question 2
- Question 3
In ΔABC, if m∠B = 90, & AC = 10 then length of median = ---------.
(A) 6
(B)
(C) 5
(D) 8 VIEW SOLUTION
- Question 4
- Question 5
- 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
- Question 12
If cos2 45° – cos2 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) a2
(B)
(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: , 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
- 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 = A1 and a circle of diameter 4 cm from the centre is cut whose area is A2 , then __________ is possible.
(A) A1 ≠ A2
(B) A1 < A2
(C) A1 > A2
(D) A1 = A2 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
- Question 22
If the circumference of base of a hemisphere is 2π then it volume is ______________ cm3.
(A)
(B)
(C)
(D) 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
- Question 27
To get the terminating decimal expansion of a rational number . If q = 2m 5n then m and n must belong to __________.
(A) Z
(B) N U {0}
(C) N
(D) R VIEW SOLUTION
- Question 28
For polynomial p(x) = x2 – 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)
(B)
(C)
(D) 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) = ax2 + bx + c, = ____________.
(A)
(B)
(C)
(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, 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)
(B)
(C)
(D) VIEW SOLUTION
- Question 36
- 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 + 3x = 12 → ① & 8x + 3y = 17 → ②, equation ② is to be multiplied by ______________.
(A) 8
(B)
(C)
(D) 3 VIEW SOLUTION
- Question 39
Equation 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) = x2 + 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 x2 + 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 kx2 – 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)
(D) 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
- 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 is irrational. VIEW SOLUTION
- Question 52
For polynomial P(x) = 6x3 + 29x2 + 44x + 21 find P (–2). VIEW SOLUTION
- 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
- 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.
- 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 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 F1 and F2.
Class 0 – 49 50 – 99 100 – 149 150 – 199 200 – 249 250 – 299 300 – 349 Frequency 10 15 F1 20 15 F2 2
- 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. VIEW SOLUTION
- Question 65
The length of a side of a square field is 20 m. A cow is tied at the corner by means of a 7 m 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
OR
Write converse of Pythagoras theorem and prove it. VIEW SOLUTION