The mean of five numbers is 30. If one number is excluded, their mean becomes 28. The excluded number is:
- A38
- B30
- C35
- D28
Question types
Model Paper 10 question types
45 questions across 6 question groups — pick any mix to generate a MATHS paper with step-by-step answer keys.
45
Questions
6
Question groups
5
Question types
01
M.C.Q (1 Marks)
18 Q→022 Marks Questions
7 Q→033 Marks Question
9 Q→045 Marks Questions
6 Q→05Assertion (A) & Reason (B) MCQ
2 Q→06Case study (4 Marks)
3 Q→Sample Questions
Model Paper 10 questions
One sample from each question group in this chapter. Select any group above to see the full set with answer keys.
Find the value of $\sec \left(\frac{-19 \pi}{3}\right)$.
- A$\frac{1}{2}$
- B-2
- C2
- D$\frac{-1}{2}$
In how many ways can 5 persons occupy 3 seats?
- A30
- B15
- C60
- D20
$\lim _{x \rightarrow 3} \frac{x-3}{|x-3|}$ is equal to:
- A1
- B-1
- C$0$
- DNone of these
The value of $\frac{2\left(\sin 2 x+2 \cos ^2 x-1\right)}{\cos x-\sin x-\cos 3 x+\sin 3 x}$ is
- Asin x
- Bcos x
- Ccosec x
- Dsec x
Is $B =\left\{ x : x ^2+2 x +1=0, x \in N \right\}$ a singleton set?
View full solution →If A and B are two events associated with a random experiment for which P(A) = 0.60, P(A or B) = 0.85 and P(A and B) = 0.42, find P(B).
Find a point on the y-axis which is equidistant from A (-4, 3) and B(5, 2).
Differentiate: $\left(x^2-4 x+5\right)\left(x^3-2\right)$.
View full solution →Let R be a relation from N to N defined by $R =\left\{( a , b ): a , b \in N\right.$ and $\left.a = b ^2\right\}$. Are the following true?
(i) $( a , a ) \in R$ for all $a \in N$
(ii) $( a , b ) \in R$ implies $( b , a ) \in R$
(iii) (a, b) $\in R$, (b, c) $\in R$ implies (a, c) $\in R$
Justify your answer in each case.
View full solution →(i) $( a , a ) \in R$ for all $a \in N$
(ii) $( a , b ) \in R$ implies $( b , a ) \in R$
(iii) (a, b) $\in R$, (b, c) $\in R$ implies (a, c) $\in R$
Justify your answer in each case.
Three vertices of a parallelogram ABCD are A(3, -1, 2), B(1, 2, -4) and C(-1, 1, 2). Find the coordinates of the fourth vertex.
If ${ }^{22} P_{r+1}:{ }^{20} P_{r+2}=11: 52$. find r .
View full solution →In a class, 18 students took Physics, 23 students took Chemistry and 24 students took
Mathematics of these 13 took both Chemistry and Mathematics, 12 took both Physics and Chemistry and 11 took both Physics an Mathematics. If 6 students offered all the three subjects, find:
i. The total number of students.
ii. How many took Maths but not Chemistry.
iii. How many took exactly one of the three subjects.
Mathematics of these 13 took both Chemistry and Mathematics, 12 took both Physics and Chemistry and 11 took both Physics an Mathematics. If 6 students offered all the three subjects, find:
i. The total number of students.
ii. How many took Maths but not Chemistry.
iii. How many took exactly one of the three subjects.
Evaluate: $\sum_{k=1}^{11}\left(2+3^k\right)$
View full solution →If the AM and GM of two positive numbers a and b are in the ratio $m : n$, show that $a : b =\left(m+\sqrt{m^2-n^2}\right):\left(m-\sqrt{m^2-n^2}\right)$
View full solution →Find the equation of a circle concentric with the circle $x^2+y^2+4 x+6 y+11=0$ and passing through the point $(5,4)$.
View full solution →Prove that $\cos 12^{\circ}+\cos 60^{\circ}+\cos 84^{\circ}=\cos 24^{\circ}+\cos 48^{\circ}$
View full solution →Prove that: $\sin 20^{\circ} \sin 40^{\circ} \sin 80^{\circ}=\frac{\sqrt{3}}{8}$
View full solution →Find the equation of the hyperbola, the length of whose latus rectum is 4 and the eccentricity is 3.
Assertion (A): If the numbers $\frac{-2}{7}, K, \frac{-7}{2}$ are in GP, then $k = \pm 1$.
Reason (R): If $a_1, a_2, a_3$ are in GP, then $\frac{a_2}{a_1}=\frac{a_3}{a_2}$.
Reason (R): If $a_1, a_2, a_3$ are in GP, then $\frac{a_2}{a_1}=\frac{a_3}{a_2}$.
- ABoth A and R are true and R is the correct explanation of A.
- BBoth A and R are true but R is not the correct explanation of A.
- CA is true but R is false.
- DA is false but R is true.
Assertion (A): The set A = {a, b, c, d, e, g} is finite set
Reason (R): The set B = {men living presently in different parts of the world} is finite set.
Reason (R): The set B = {men living presently in different parts of the world} is finite set.
- ABoth A and R are true and R is the correct explanation of A.
- BBoth A and R are true but R is not the correct explanation of A.
- CA is true but R is false.
- DA is false but R is true.
Generate a Model Paper 10 paper free
Pick question groups from the list above, set marks and difficulty, and export a branded PDF with step-by-step answer keys. First 3 chapters free — no signup.